PHILOSOPHY OF BIOLOGICAL SYSTEMATICS Kirk Fitzhugh, [email protected]
Table of Contents Introduction ......................................................................................................................... 2 The Goal of Science. The goal of Biological Systematics ....................................................... 10 Causal Relationships in Systematics .................................................................................... 52 The Nature of Why-Questions ............................................................................................. 63 The Three Forms of Inference: Deduction, Induction, Abduction ......................................... 83 The Uses of Deduction, Induction, and Abduction in Science ..............................................110 Systematics Involves Abductive Inference ..........................................................................155 Inferences of Systematics Hypotheses, i.e. Taxa ..................................................................176 Some Implications for “Phylogenetic” Methods .................................................................228 The Requirement of Total Evidence ....................................................................................336 Homology & Homogeny & Homoplasy ...............................................................................403 Character Coding ...............................................................................................................466 The Mechanics of Hypothesis Testing in Biological Systematics ..........................................500 Implications for Nomenclature ...........................................................................................627 Defining Biodiversity and Conservation ..............................................................................683
THE PHILOSOPHY OF BIOLOGICAL SYSTEMATICS
Kirk Fitzhugh [email protected] Natural History Museum of Los Angeles County
This course differs from most courses on biological systematics in that the emphasis will not be on instructing you on how to use the variety of methods available to researchers. Instead, the emphasis will be on examining what is required to ensure that systematics, as a field of science, has an overarching framework that is consistent with all fields of scientific inquiry. It is from this framework that one can readily decide which methods are scientifically acceptable.
The Philosophy of Biological Systematics The contrast with a systematics course A TYPICAL ‘PHYLOGENETICS’ COURSE: • Phylogenetic theory • Characters and character coding • Tree building techniques • Tree statistics and tree support • Bayesian inference • Maximum Likelihood • Alignment
P Systematics courses usually focus on how to use methods. P The present course will focus on what is required to treat systematics as a science. P The goal is to give you the ability to determine which methods are scientifically acceptable.
• Molecular Dating • Various tree building programs (e.g., MrBayes, POY, and TNT)
The outline of topics shown here formed the basis for a recent 'phylogenetics' course in Denmark. The topics exemplify how the present course differs from what is typically covered in systematics courses.
“If science is not to degenerate into a medley of ad hoc hypotheses, it must become philosophical and must enter into a thorough criticism of its own foundations.” Alfred North Whitehead (1925: 25), Science and the Modern World.
One of the interesting phenomena surrounding the practice of systematics for the past 40 years is that distinct schools of thought have arisen regarding what it means to infer systematics hypotheses and to evaluate them. For instance, with regard to phylogenetic [sic] inference, the two most recognized schools of thought are what are said to be 'parsimony' and 'maximum likelihood.' Or, this dichotomy is sometimes seen as a distinction between hypothetico-deductive and statistical points of view. One of the hallmarks of these different opinions is that no critical assessment of the formal inferential structure of systematics is ever considered, such that neither the concept of parsimony nor likelihood are correctly justified. This lack of critical examination then extends to the matter of how one tests, evaluates, determines support, etc., for systematics hypotheses. As indicated in the quote shown here, in order to address the matter of how we are to assess whether or not one systematics hypothesis is better or worse than another requires that we carefully examine the philosophical foundations of hypothesis inference and testing.
The Philosophy of Biological Systematics Course Outline – Part 1 1.
The goal of Science. The goal of biological systematics.
2.
Causal relationships in systematics.
3.
The nature of why-questions.
4.
The three forms of inference: deduction, induction, abduction.
5.
The uses of deduction, induction, and abduction in science.
This course is arranged in four parts. Part 1 has as its focus identifying the goals of scientific inquiry and biological systematics, followed by some of the consequences of those goals. The three recognized forms of reasoning used throughout the sciences are then described in detail.
The Philosophy of Biological Systematics Course Outline – Part 2
1.
Systematics involves abductive inference.
2.
Inferences of systematics hypotheses, i.e. taxa.
3.
Some implications for “phylogenetic” methods.
In Part 2, we will identify the type of reasoning used in biological systematics to infer hypotheses. We will see that all taxa have the form of explanatory hypotheses, directed at giving us at least initial causal understanding of some of the characters we observe among organisms. Significant implications are then identified for some of the methods commonly used in phylogenetic [sic] systematics.
The Philosophy of Biological Systematics Course Outline – Part 3
1.
The requirement of total evidence.
2.
Homology & homogeny & homoplasy.
3.
Character coding.
4.
The mechanics of hypothesis testing in biological systematics.
Part 3 will address four different issues, all of which have received considerable attention in biological systmeatics, but also have been misrepresented. We will examine the correct interpretation of the requirement of total evidence, which has significant implications for the common approach of inferring systematics hypotheses from partitioned data, as well as attempts to compare cladograms inferred from different data sets. Next we will examine the definition of the term homology (sensu Owen) in relation to E. Ray Lankester's (1870) suggested replacement of that term with the two terms, homogeny and homoplasy. A general overview of character coding will then be presented as it relates to the nature of our observation statements, why-questions, and the goal of biological systematics reasoning. Finally, the nature of hypothesis testing will be carefully examined, showing that traditional attempts to characterize testing in systematics have been incorrect. The proper approach to testing systematics hypotheses will be examined.
The Philosophy of Biological Systematics Course Outline – Part 4
1.
Implications for nomenclature.
2.
Defining biodiversity and conservation.
In the final part of the course, we first will examine the implications of the inferential framework for biological systematics on our nomenclatural practices. The main focus here will be on the 'Linnean' system and the PhyloCode, to show that neither approach correctly takes into consideration the nature of our inferences. For any nomenclatural system to be successful, it must be consistent with the fact that biological systematics is about inferring explanatory hypotheses, referred to as taxa, and formal names must refer to those hypotheses, not just organisms. The last talk will be an opportunity to tie our systematics practices, as presented in this course, to new formal definitions of biodiversity and conservation. Interestingly, the outcome will be to show that the term biodiversity is largely useless and potentially deceptive.
“Science depends on judgments of the bearing of evidence on theory.... One of the central aims of the philosophy of science is to give a principled account of those judgments and inferences connecting evidence to theory.” Peter Lipton (2001: 184, Inference to the best explanation). In: A Companion to the Philosophy of Science.
The quote shown here epitomizes what will be most fundamental throughout this course. Our emphasis will be on recognizing the relations between evidence and biological systematics hypotheses. As we will see, these relations occur in different ways, depending on what we mean by 'evidence,' as well as our objectives in maintaining particular relations. It is by applying the principles of philosophy of science to biological systematics that we can clearly understand why these relations exist between evidence and hypotheses, and recognize the forms evidence takes with respect to hypotheses.
The Philosophy of Biological Systematics Course Outline – Part 1 1.
The goal of Science. The goal of biological systematics.
2.
Causal relationships in systematics.
3.
The nature of why-questions.
4.
The three forms of inference: deduction, induction, abduction.
5.
The uses of deduction, induction, and abduction in science.
Let's start by looking at the goals of science and biological systematics.
The Confusing Variety of Systematics Methods
‘What are species?’
‘What are taxa?’ total evidence?
character weighting?
hypothesis testing?
measures of support?
What is the philosophical basis for choosing a method? One of the greatest difficulties in biological systematics is that we have available a variety of methods. But, there is no clear consensus among systematists as to which methods to use. Similarly, there are fundamental questions regarding what we mean by terms like 'species' or 'taxon.' The only real way to resolve these problems is to have a philosophical basis for choosing among methods. That basis can only come from first ackowledging the goal of doing science, and then applying that goal to systematics.
Basic Criteria for Judging Methods in Biological Systematics • Recognize the goal of Science. • The goal of biological systematics should be consistent with this goal. • Does a particular systematics method satisfy the goal of Science? • Does a particular systematics method accurately represent our perceptions and why-questions?
To determine whether or not an approach to biological systematics is scientifically appropriate, we must first acknowledge the goal of doing science, as well as understand that the goal of systematics must be consistent with that more general goal. We can then determine whether or not specific methods actually serve to fulfill both the goal of science as well as systematics. In related fashion, we have to ensure that the methods we use do accurately represent our observation statements and why-questions, since these are the issues to which the goal of science inquiry is directed.
The Goal of Science: To Causally Understand What We Observe “Broadly speaking, the vocabulary of science has two basic functions: first, to permit an adequate description of the things and events that are the objects of scientific investigation; second, to permit the establishment of general laws or theories by means of which particular events may be explained and predicted and thus scientifically understood; for to understand a phenomenon scientifically is to show that it occurs in accordance with general laws or theoretical principles.” Hempel (1965: 139, emphasis original), Aspects of Scientific Explanation
An answer to the question of what is the goal of science was nicely described by the philosopher of science, Carl G. Hempel. The goal can be identified as having two parts: (1) describing the objects and events we encounter, and (2) presenting explanations of those objects and events, for the purpose of ever-increasing our understanding as well as having the ability to make predictions into the future. Overall, the goal of science is to enable us to *causally understand* phenomena. As we will see throughout this course, this goal will be the highest priority for biological systematics.
The Goal of Science: To Causally Understand What We Observe Scientific inquiry has two fundamental components: Descriptive:
Theoretical:
observations
inferences of hypotheses and theories
Based on Hempel's characterization of science, we recognize science as having two basic parts: 'descriptive' and 'theoretical.' The descriptive component refers to our communicating observations, as observation statements. The theoretical refers to our applications of theories and hypotheses to those observation statements.
The Goal of Science: To Causally Understand What We Observe Scientific inquiry has two fundamental components:
Descriptive:
Theoretical:
observations
inferences of hypotheses and theories
The descriptive and theoretical aspects of inquiry are interdependent – objects and events cannot be described in the absence of theory, and the basis for theories and hypotheses are the objects and events which are in need of understanding.
But, it is well known that observation statements cannot be made in the absence of theories, and theories and hypotheses have their origins in observations. So, the descriptive and theoretical realms are clearly interdependent.
The Goal of Science: To Causally Understand What We Observe Scientific inquiry has two fundamental components:
Descriptive:
Theoretical:
observations
inferences of hypotheses and theories
Understanding explanation / prediction
It is the interplay between the descriptive and theoretical that leads to scientific understanding.
As the principle goal of scientific inquiry is to acquire causal understanding, and from that understanding we have the ability to explain phenomena as well as make predictions of future phenomena, it is the interplay between the descriptive and theoretical that leads to the acquisition of understanding.
Scientific Understanding, Defined
“A phenomenon P can be understood if a theory T of P exists that is intelligible (and meets the usual logical, methodological and empirical requirements).” de Regt & Dieks (Synthese 2005: 150)
We have been referring to 'understanding' in the previous diagrams, so it will be useful to have a formal definition of the term. The definition shown here offers the view that to understand a phenomenon is to associate that phenomenon with some theory.
Scientific Understanding, Defined
“...the cognitive achievement realizable by scientists through their ability to coordinate theoretical and embodied knowledge that apply to a specific phenomenon.” Leonelli (2009: 197)
Leonelli (2009) offers a similar perspective with regard to biological understanding. We apply not only our theories but also our previous established knowledge to a phenomenon to provide us understanding of the latter.
“...biology can be divided into the study of proximate causes, the subject of the physiological sciences (broadly conceived), and into the study of ultimate (evolutionary) causes, the subject matter of natural history....” Mayr (1982: 67)
1904-2005
Even within biology, there have been attempts to characterize the nature of the understanding we seek regarding organisms. An excellent and very useful characterization of biological understanding was developed by evolutionary biologist, Ernst Mayr. Mayr suggested that biological inquiry seeks to acquire understanding that is causal, and that such causal understanding can be separated into 'proximate' and 'ultimate' causes. While Mayr distinguishes proximate and ultimate causes as related to 'physiological sciences' and 'natural history,' we will need to be more precise.
“...proximate causes govern the responses of the individual (and his organs) to immediate factors of the environment while ultimate causes are responsible for the evolution of the particular DNA code of information with which every individual of every species is endowed.” Mayr (1961: 1503)
1904-2005
Mayr originally published his idea of proximate and ultimate causes in biology in 1962. What might be noticed is that proximate causes refer to those causes that only occur within an organism during its lifetime. Ultimate causes, on the other hand, transcend lifetimes.
“The proximate causes of an organism’s traits occur within the lifetime of the organism.... The ultimate causes occur prior to the lifetime of the organism, within the evolutionary history of the organism’s species.” Beatty (1994: 334)
In his analysis of Mayr's proximate/ultimate distinction, Beatty (1994) offers a very good characterization, shown here.
Biological Understanding sensu Mayr proximate
ultimate
ontogenetic / functional
evolutionary
We can now begin to summarize Mayr's view of causal understanding in biology with the more general goal of science we examined earlier. We can see that proximate understanding refers to ontogenetic and functional aspects during the lifetime of an individual organism. Ultimate understanding refers to evolutionary causes that can apply to groups of organisms over time.
Biological Understanding sensu Mayr descriptive biology
ultimate
proximate
(observation statements) “It is sometimes overlooked how essential a component in the methodology of evolutionary biology the underlying descriptive work is. ”
But in addition to proximate and ultimate understanding, Mayr was very clear in his writings on the subject that there is a third dimension to understanding, what he referred to as 'descriptive biology.' Mayr was correct that in order to pursue either proximate or ultimate understanding, one must already have observations of effects that are in need of explanation. These effects are in the form of the properties, features, characters, etc., of organisms, that we communicate by way of our observation statements. Notice that Mayr's descriptive, proximate, and ultimate understanding are consistent with the goal of science presented earlier. To acquire ever-increasing understanding we see that it must be descriptive as well as causal, and also predictive. We seek descriptive understanding of what we perceive, as well as offering possible past causes that explain what we observe in the present. And we attempt to apply our understanding into the future with predictions of effects due to causal conditions that exist in the present.
Biological Understanding sensu Mayr descriptive biology
proximate
ultimate
(observation statements) “It is sometimes overlooked how essential a component in the methodology of evolutionary biology the underlying descriptive work is. ”
Mayr (1982: 70)
ontogenetic / functional
evolutionary
To what extent is biological systematics successful at acquiring ever-increasing understanding that is descriptive, proximate, and especially ultimate? An important part of this course will be to examine the extent to which descriptive, proximate, and ultimate understanding is acquired in biological systematics. These will be issues that need to be addressed both in terms of knowing the nature of our reasoning from observations to the variety of hypotheses used in systematics, as well as the correct approach to testing any of those hypotheses. It is especially the act of testing that accomplishes the task of increasing our causal understanding, which is the most fundamental goal of scientific inquiry.
SCIENCE: General Principles and Specialized Techniques Specialized Techniques
Specialized Techniques
Specialized Techniques
Astronomy
Psychology
Chemistry
Principles of Scientific Method
Biology
Specialized Techniques
Physics
Geology
Specialized Techniques
Specialized Techniques
While the goal in all fields of science is the acquisition of causal understanding, and that must be regulated by our general rules and methods in science, and more generally by philosophy of science, each field of science must adopt its own specialized techniques for the purpose of acquiring that understanding. The problem we will identify in biological systematics, however, is that the specialized techniques are too often divorced from the more general principles of scientific inquiry and philosophy. We will attempt in this course to correct that problem.
Four Fundamental Criteria Applied in Science
1. Rationality Beliefs and actions should be rational, i.e. they should make sense. A rational belief or action is one based on all evidence that is relevant to the formation of that belief or action.
In order to correctly characterize the nature of biological systematics as a field within the broader realm of science, we need to recognize four fundamental criteria that are applied throughout the sciences. The first criterion is rationality.
Four Fundamental Criteria Applied in Science
2. Truth Truth is a property of statements. The correspondence theory of truth is the most common concept of truth applied in Science: true statements correspond with reality. Facts about the world determine the truth of statements. correspondence External physical world of objects and events
Internal mental world of perceptions and beliefs
The second criterion is truth. As noted in this slide, the 'correspondence theory' is typically used in the sciences, although there are about six theories of truth available. With regard to systematics, in which there has developed a popular culture of thinking in terms of 'true phylogenetic trees' as a basis for judging methods of cladogram inference, it should be apparent that truth cannot be asserted separate from some empirical basis for the truth of statements.
Four Fundamental Criteria Applied in Science
3. Objectivity The existence of objects and events apart from human minds. Objective knowlege is concerned with physical objects and events.
The third criterion is objectivity, which should be apparent.
Four Fundamental Criteria Applied in Science
4. Realism The correspondence of human perceptions with the external and independent (and possibly unobservalbe) realities of physical objects and events.
And finally there is the criterion of realism.
The Foundations of Science Common Sense
Common Sense:
The assumption that physical reality exists.
As we have already noted, the ultimate goal of science is to acquire ever-increasing causal understanding of the phenomena (objects and events) we encounter. To successfully achieve that goal, we have to recognize the hierarchical structure within which science resides as part of human reasoning. The most general rule we have is that of common sense. In other words, we operate under the assumption that physical reality does exist - that all that we perceive around us are not just hallucinations. Without this assumption, empirical inquiry of any kind would not be possible.
The Foundations of Science Common Sense Philosophy
Philosophy:
The study of the way humans think and reason. Composed of four main branches: • logic, the study of reasoning • epistemology, the study of knowledge • metaphysics, the study of concepts and their relations • ethics, the study of moral evaluation
Within the realm of common sense, we have the field known as philosophy - the study of the way humans think and reason. And within philosophy there are four branches.
The Foundations of Science Common Sense Philosophy Philosophy of Science
Philosophy of Science:
The study of the principles and methods applied in all fields of science.
The four branches of philosophy presented in the previous slide are often applied to the subfield of philosophy, known as philosophy of science, which studies the principles and methods used throughout the sciences.
The Foundations of Science Common Sense Philosophy Philosophy of Science Scientific Methods
Scientific Methods: The processes of hypothesis and theory formation, testing, and revision, for the purpose of acquiring understanding of physical reality.
It is by way of philosophy of science that scientific methods are developed. It is those methods that are intended to enable us to achieve the goal of scientific inquiry, i.e. causal understanding.
The Foundations of Science Common Sense Philosophy Philosophy of Science Scientific Methods Scientific Specialties
Scientific Specialties: The fields of study that address specific aspects of physical reality, e.g., physics, chemistry, paleontology, systematics.
By way of particular scientific methods there are the applications of scientific specialities.
The Foundations of Science Common Sense Philosophy Philosophy of Science Scientific Methods Scientific Specialties Technology
Technology:
The specialized techniques applied in a specific field of study.
The applications of scientific methods within scientific specialities are often only possible because of technology, e.g. computers, microscopes, etc.
The Foundations of Science Common Sense Philosophy Philosophy of Science Scientific Methods Scientific Specialties Technology
Scientific methods are constrained by the principles of philosophy, as well as the philosophy of science. The problem in systematics is that methods are too often developed and considered in isolation of philosophy.
Finally, it is important to notice that if we are going to critically evaluate our scientific methods, then this must be done in the context of philosophy of science as well as philosophy in general. Scientific methods cannot operate independent of philosophical principles. Unfortunately, this is exactly what has too often occurred in biological systematics. This course is intended to help correct that error.
What is the Goal of Biological Systematics? Some common answers C “To explain shared similarities among a group of organisms.”
We have seen that the goal of scientific inquiry is to not only describe the objects and events we encounter (observation statements), but more importantly to causally understand those phenomena. We now need to determine if the goal of biological systematics is consistent with the goal of science. When we ask the question, 'What is the goal of systematics?', there are at least three general answers given. What you will notice is that most of these answers are not consistent with the goal of science. And this is a serious problem. One answer to the question we sometimes encounter is that systematics is intended to explain shared similarities.
Parsimony [sic] “A genealogy is able to explain observed points of similarity among organisms just when it can account for them as identical by virtue of inheritance from a common ancestor.” Farris (1983: 18), The logical basis of phylogenetic analysis
The idea of explaining shared similarities has been especially common in the context of cladograms. Unfortunately, this notion is not usually extended to other aspects of systematics, as we will see later in this course. The idea of explanation in systematics has been common in the cladistics literature, especially in connection with the principle of parsimony.
Likelihood [sic] “The concept of likelihood refers to situations that typically arise in natural sciences in which given some data D, a decision must be made about an adequate explanation of the data.” Schmidt & von Haeseler (2010: 181), Phylogenetic inference using maximum likelihood methods.
But we also find claims that explanation is important when 'likelihood' methods are used. But as we will see later in this course, these claims of importance of explanation are too often poorly formulated and usually insufficient.
What is the Goal of Biological Systematics? Some common answers C “To explain shared similarities among a group of organisms.” C “To show the phylogeny / evolutionary history of a group of organisms.”
A much more vague reference to explanation being the goal of systematics comes from the popular view that we want to present 'phylogeny' or 'evolutionary history.'
“Systematics is the study of organic diversity as that diversity is relevant to some specified pattern of evolutionary relationship thought to exist among the entities [sic] studied.” Wiley & Lieberman (2011: 8), Phylogenetics: Theory and Practice of Phylogenetic Systematics
And as we see in this quote, even the explain-as-phylogeny point of view can be taken to a point of being uninformative.
“A phylogenetic tree [cladogram]... is a graphic representation of the historical course of speciation.” Wiley & Lieberman (2011: 4), Phylogenetics: Theory and Practice of Phylogenetic Systematics
And the explanatory nature of cladograms is often inconsistent.
What is the Goal of Biological Systematics? Some common answers C “To explain shared similarities among a group of organisms.” C “To show the phylogeny / evolutionary history of a group of organisms.” C “To discover natural, hierarchical order, then reflect that order in classifications.”
Rather than having a direct or indirect goal of explanation of systematics, there is the still-popular school of thought that causality should be removed from systematics. In this instance, diagrams such as cladograms have no explanatory interpretation, but instead either summarize character distributions, or convey nebulous ideas such as 'natural order' or 'natural hierarchies.' The general phrase commonly used to identify this less-than-scientific perspective is 'pattern cladistics.'
“Systematics is primarily concerned with problem solving. This might seem an obvious statement, yet the majority of those interested in systematics and phylogeny approach the subject as being concerned with ‘inferences’, ‘reconstructions’, or ‘estimations’.... The general problem may be phrased as follows: ‘What are the interrelationships among organisms?’” Williams & Ebach (2008: 21)
The pattern cladistic approach has serious problems in that it is inconsistent with the goal of scientific inquiry.
What is the Goal of Biological Systematics? Some common answers C “To explain shared similarities among a group of organisms.” C “To show the phylogeny / evolutionary history of a group of organisms.” C “To discover natural, hierarchical order, then reflect that order in classifications.”
ARE ANY OF THESE GOALS CONSISTENT WITH THE OVERALL GOAL OF SCIENCE?
Based on what we have already seen regarding the goal of scientific inquiry, the commonly identified goals of biological systematics are not sufficiently consistent with the goal required of all sciences.
What is the Goal of Biological Systematics? A Formal Definition of Biological Systematics
The actions of biological systematization. The goal of which is to obtain causal understanding of the properties or characters of organisms exhibited at different stages of their life history or shared among some set of individuals. The term taxonomy is unnecessary because it is a synonym of systematics.
To correctly and effectively identify the goal of biological systematics requires that this goal be fully consistent with the more general goal of scientific inquiry. Shown here is a formal definition of biological systematics that not only places it squarely in the realm of science, but also establishes the field as having the same goal as all fields of science: to acquire causal understanding of the features we observe of organisms. Notice that with this formal definition, we no longer need to make a distinction between the terms 'systematics' and 'taxonomy.' While some might think that taxonomy refers only to 'species descriptions,' as we will see during this course, all facets of systematics have the same inferential framework, wherein all actions in systematics are directed at achieving the goal of causal understanding. Taxonomy is a term that should be regarded as a synonym of systematics. Systematics is the more accurate term to use.
What is the Goal of Biological Systematics? A Formal Definition of Taxon
Any of a set of classes of hypotheses used in biological systematics for the purpose of explaining particular characters of observed organisms.
With the formal definition of biological systematics accurately manifesting the goal of scientific inquiry, it is crucial that our reference to a taxon also be consistent with that goal. Clearly, as the goal of systematics is to present explanatory hypotheses that give us an opportunity to understand the occurrences of features among organisms, then taxa can only be regarded as synonymous with those hypotheses. Of course, this will have profound consequences, because too often taxa are thought of as being either individuals or things that exist in time and space, much like organisms. As we will see throughout this course, taxa can only be regarded as explanatory hypotheses, not as things or individuals. Indeed, our use of the term taxon or taxa is entirely unnecessary. It would be more appropriate to simply refer to hypotheses.
“...the semaphoront [‘character bearer’] corresponds to the individual in a certain, theoretically infinitely small, time span of its life, during which it can be considered unchangeable.” W. Hennig (1966: 65)
The definition of taxon presented in the previous slide refers to individual organisms and the characters we observe. In his book, "Phylogenetic Systematics" (1966), Willi Hennig correctly stressed that we make observations of individuals at particular moments in time during their entire ontogeny or life history. Hennig suggested that the appropriate term for the individuals we observe should be 'semaphoront.'
“...it follows that we should not regard the organism or the individual (not to speak of the species) as the ultimate element of the biological system. Rather it should be the organism or the individual at a particular point of time, or even better, during a certain, theoretically infinitely small, period of its life. We will call this element of all biological systematics... the character-bearing semaphoront.” W. Hennig (1966: 6, emphasis original)
Hennig's use of the term semaphoront to indicate our observations of organisms at specific times during their life history is especially significant because it better emphasizes that the fundamental units in biological systematics are individual organisms. Indeed, notice that Hennig understands that species are not the fundamental units in systematics.
What is the Goal of Biological Systematics? Obtain causal understanding of the properties or characters of organisms exhibited at different stages of their life history or shared among some set of individuals. Some Consequences: • Biological systematics involves the non-deductive inference of explanatory hypotheses and, where possible, their subsequent testing. • The goal of biological systematics is to move toward causal understanding of what we observe, not merely to obtain “cladograms,” “trees,” or to “reconstruct phylogeny.” • “Cladograms” are not things in themselves, but are very limited explanatory hypotheses of observed properties of individuals among different taxa.
With a formal definition of biological systematics that is consistent with the goal of scientific inquiry, there are several significant implications. The first is that as systematics is about the inferences of explanatory hypotheses, we will be clearly identifying the type of inference involved, as well as acknowledging that the testing of those hypotheses is very different from what has traditionally been presented by systematists. Second, since the goal of systematics is consistent with the goal of science, i.e. to acquire causal understanding, our goal is *never* to just get trees, cladograms, or reconstruct phylogeny [sic]. And finally, we will see in this course that cladograms are *very vague* explanatory accounts. Indeed, they are so poor as explanations that they offer us very little to serve as vehicles for the goal of doing systematics, much less science.
The Two Realms of Science Present (the realm of Observation)
Past
Future Cause Causal Hypothesis
abduction
‘Historical’ Sciences
prediction
Effect
Effect
‘Experimental’ Sciences
Biological systematics is part of the “historical sciences,” where observations in the present are used to infer explanatory hypotheses about past events to account for those observations. For our purposes in biological systematics, we can think of science as having two broad, operational realms: historical and experimental. The historical sciences include such fields as systematics, evolutionary biology (in part), paleontology, archaeology. The experimental sciences include physics, chemistry, geology (in part). There is, of course, a lot of overlap between these. The main distinction between the historical and experimental sciences is that the historical sciences focus on effects that exist in the present, and our goal is to develop explanatory hypotheses of possible past causal events that can account for those oberved effects. The experimental sciences, on the other hand, begin with known causal, or experimental, conditions in the present, to see if predicted effects occur in the future. Another way to think about this distinction is that the historical sciences are mainly concerned with the inferences and testing of explanatory hypotheses, whereas the experimental sciences are mainly concerned with the testing of theories. But, be cautious about this distinction, since there always are exceptions.
The Philosophy of Biological Systematics Course Outline – Part 1 1.
The goal of Science. The goal of biological systematics.
2.
Causal relationships in systematics.
3.
The nature of why-questions.
4.
The three forms of inference: deduction, induction, abduction.
5.
The uses of deduction, induction, and abduction in science.
We can now take an initial look at the nature of the relationships that are referred to in biological systematics. Since the goal of systematics is to present us with causal understanding of the features of organisms, then the nature of the relationships throughout systematics must be causal in form.
RELATIONSHIPS & BIOLOGICAL SYSTEMATICS
When we speak of ‘relationships’ in systematics, we mean causal relationships. The basic unit to which these causal relationships refer is individual organisms. Taxa – as explanatory hypotheses – indicate particular causal relationships among groups of organisms.
To start with our examination of these issues, we need to understand what we mean when we speak of 'relationships' in biological systematics. We use the term relationship on a regular basis, but, the word is often not clearly understood when it is used in systematics. We need to first recognize that when we speak of relationships, we are speaking of causal relations. For example, we say we are related to our parents, we are related to our sisters or brothers, we are related to our grand parents. In every instance, the relations we are talking about are causal relations, because it is that type of relationship that gives one understanding. And, as we will see in the remainder of this course, the units to which those causal relationships refer are individual organisms. Then, we can specifically look at the way in which we infer each of the types of causal relationships, as explanatory hypotheses, that are used in biological systematics. And again, it is causal relationships that we are interested in, because it is those types of relations that best serve the overall goal of scientific inquiry.
(1913-1976)
Hennig, W. 1966. Phylogenetic Systematics
One of the best examinations of the nature of causal relationships in biological systematics can be found in Willi Hennig's (1966) book, "Phylogenetic Systematics."
Classes of Relationships 1. ontogenetic
6
2. cyclomorphic 3. sexual dimorphic
7 4
2
4. tokogenetic 5. polymorphic 6. specific
1
3 5
Hennig, W. 1966. Phylogenetic Systematics
7. phylogenetic
Each of these classes of relationships refer to the different classes of explanatory hypotheses we call taxa.
Shown here is Hennig's (1966) well known figure 6, which we often see reproduced in other works on the principles of biological systematics. It is in this figure that Hennig identifies the fundamental classes of relationships used in systematics. But too often, what is not recognized is that Hennig pointed out that all of these relationships deal with individual organisms. He discussed in great detail seven classes of relationships involving organisms, all of which are shown in his diagram. Ontogenetic relationships. Where we speak of an individual at a particular point in it's life history. Cyclomorphic relationships. Where there are seasonal phenotypic differences among individuals of different generations. Sexual dimorphic relationships. The phenotypic differences between males and females. Tokogenetic relationships. Parents producing offsrping as a result of reproductive events (tokogeny). Polymorphic relationships. Different phenotypes expressed among individuals in a population. Specific relationships. Refers to species hypotheses, accounting for features among a group of organisms that are reproductively isolated from other groups. Phylogenetic relationships. The most general type of relationship in systematics, accounting for shared features among organisms to which different species hypotheses refer, as well as strictly asexual or strictly self-fertilizing hermphroditic organisms. But as will be noted later in the course, because of what classes of causal events are entailed by phylogenetic hypotheses, such hypotheses are actually not applicable to obligate asexual or self-fertilizing hermaphroditic organisms.
7 Classes of Causal Relationships
Proximate
1. ontogenetic
6
2. cyclomorphic 3. sexual dimorphic
7 4
2
4. tokogenetic Ultimate 5. polymorphic 6. specific (species)
Using Hennig's (1966) figure 6, we can clearly identify the three broad classes of causal understanding recognized by Ersnt Mayr, that were referred to earlier.
Kingdom Phylum Class phylogenetic hypotheses Order Family
Ultimate explanations
Genus Species Subspecies Families, demes, populations
Individuals
Semaphoronts (e.g., ‘larva,’ ‘juvenile,’ ‘adult’)
specific hypotheses intraspecific hypotheses tokogenetic hypotheses
the objects we perceive
ontogenetic hypotheses
Descriptive explanations (observation statements)
Proximate explanations
And here are the distributions of classes of hypotheses shown in the previous slide, in a different arrangement.
All taxa/hypotheses in biological systematics are inferred by way of abduction Kingdom Phylum Class phylogenetic hypotheses Order Family Genus Species Subspecies Families, demes, populations
Individuals
Semaphoronts
specific hypotheses intraspecific hypotheses tokogenetic hypotheses
the objects we perceive
(observation statements)
ontogenetic hypotheses
(e.g., ‘larva,’ ‘juvenile,’ ‘adult’)
As we saw earlier with the definition of the term 'taxon,' all taxa are explanatory hypotheses. All of the different classes of hypotheses-as-taxa shown here, indicated by the red arrows, are the products of a type of reasoning known as 'abduction,' which we will examine in depth later in the course. And abduction, or abductive inference will form the foundation for the remainder of our examination of systematics in this course.
Examples of Causal Relationships in Systematics Ontogenetic, Specific, Phylogenetic
Semaphoront: an explanatory hypothesis of ontogenetic relationships, derived from ontogenetic theories applied to a particular organism. The hypothesis accounts for features of an organism at a particular age relative to features at another age, by way of ontogeny.
individual ‘larva,’ ‘juvenile,’ ‘adult’
We can briefly look at three of the most common classes of relationships referred to in biological systematics, and discussed by Hennig (1966): semaphoront, specific (species) relationships, and phylogenetic relationships. A semaphoront is an individual at a specific point in time during its life history. In other words, it is a hypothesis that gives us an explanatory account relative to the ontogenetic history of the individual.
Examples of Causal Relationships in Systematics Ontogenetic, Specific, Phylogenetic
Species: an explanatory hypothesis of specific relationships derived from theories of character origin/fixation during tokogeny, applied to a set of semaphorants. A ‘lineage,’ accounting for features of a group of semaphoronts relative to different features in other semaphoronts (in other species).
species a-us
individual
A species is an explanatory hypothesis that refers to specific relationships.
Examples of Causal Relationships in Systematics Ontogenetic, Specific, Phylogenetic
species b-us
species c-us
‘Supraspecific’ Taxon: an explanatory hypothesis of phylogentic relationships, derived from tokogenetic, evolutionary, and population splitting theories, applied to particular semaphoronts. Accounting, by way of phylogeny, for the same features shared by semaphoronts among two or more species relative to different features in semaphoronts of other species.
b-us c-us
a-us phylogenetic relationships
species a-us
individual
And a phylogenetic hypothesis refers to phylogenetic relationships. Notice that it is more accurate to refer to such relationships as hypotheses as opposed to 'taxa.'
Not All of Systematics is ‘Phylogenetic’
‘Phylogenetic systematics’ sensu Hennig (1966) only provides causal understanding of the properties of groups of organisms to which two or more species hypotheses also refer. Explanatory hypotheses of ontogeny, tokogeny, species, etc., represent other levels at which causal understanding can also be achieved, but by using theories different from those applied in phylogeny.
As we will see, distinguishing the different classes of explanatory hypotheses used in systematics is fundamental to identifying the appropriate levels at which our why-questions should be asked and answered.
Historically, there has been confusion regarding what is meant by the phrase 'phylogenetic systematics.' Yet, when one carefully reads Hennig's (1966) book, it is clear that he understood biological ('hologenetic') systematics to refer to the variety of explanatory hypotheses, with phylogenetic systematics only referring to one of those classes of relationships. As we will see in this course, as the goal of systematics is the same as the goal in all fields of science, to acquire causal understanding, to achieve such understanding comes from different classes of hypotheses used to answer our different whyquestions.
The Philosophy of Biological Systematics Course Outline – Part 1 1.
The goal of Science. The goal of biological systematics.
2.
Causal relationships in systematics.
3.
The nature of why-questions.
4.
The three forms of inference: deduction, induction, abduction.
5.
The uses of deduction, induction, and abduction in science.
All of understanding in science begins with observations and our questions associated with those observations in need of being explained. The type of questions most commonly asked in systematics are known as why-questions. It is our why-questions that form the basis for all aspects of biological systematics.
“The scientist is not a person who gives the right answers, he's the one who asks the right questions.” Claude Levi-Strauss (1964) Le Cru et le Cuit
Unfortunately, when we speak of science, we almost always neglect to consider the questions we are actually asking, for which we seek hypotheses and theories to give us answers.
“...a logic in which the answers are attended to and the questions neglected is a false logic.” R.G. Collingwood (1938: 31), An Autobiography
Like any endeavor, science is one we perform to achieve particular goals. And as with any action carried out among a group of people, science has its social component, such that scientific procedures tend to become standardized to the point where we stop examining the bases for what we do, and we just go through the motions. Biological systematics suffers from a perspective where practitioners are seeking answers, yet they either don't know the questions they are asking, or they are asking inappropriate questions. This neglect is what has allowed for the rapid development of systematics methods and computer algorithms that offer contradictory approaches, and with no jusification based on the goal of using those methods according to the why-questions we should be asking.
Why Ask Why!Questions? Look to the goal of scientific inquiry
“To explain the phenomena in the world of our experience, to answer the question ‘why?’ rather than only the question ‘what?’, is one of the foremost objectives of all rational inquiry; and especially [for science]... to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates.” From: Hempel & Oppenheim (1948: 135), The logic of explanation. Philosophy of Science 15: 135-175.
By this time it is probably obvious why we ask why-questions -- because we seek causal understanding of the phenomena we encounter. The quote shown here, by Carl Hempel, exemplifies the reason we ask why-questions, and the fact that such questions are a fundamental part of the goal of scientific inquiry.
The Foundation for All of Systematics The Nature of Our Why-Questions
If the goal of biological systematics is to provide causal understanding of the properties of organisms, then we must first recognize the nature of our whyquestions, to which evolutionary theories and systematics hypotheses provide answers.
We now need to examine the specific properties of why-questions, without which any treatment of biological systematics would be incomplete. As we will see throughout much of this course, our why-questions are fundamental components.
Why-Questions How we usually ask them
“Why P?” Example: “Why do these specimens have lateral body wall extensions called ‘appendages’?”
It is essential to know the formal structure of the why-questions we ask. We usually think of why-questions as simply having the form, "Why P?", or "Why is it the case that x is P?" This form is, however, incomplete and thus does not fully represent the basis for such questions.
Why-Questions The proper form: Contrastive questions
“Why P in contrast to X?” Example: “Why do these specimens have lateral body wall extensions (= appendages) in contrast to other specimens with convex body walls?”
P
X
The correct form of why-questions is that they are 'contrastive.' In other words, we ask questions that contrast the surprising or unexpected condition in need of being explained with the expected condition(s) that has already been explained. In the case of systematics-based observations, our contrastive why-questions are of the form shown here.
Why-Questions Three parts: ‘why’
“Why P in contrast to X?” Example: “Why do these specimens have lateral body wall extensions (= appendages) in contrast to other specimens with convex body walls?”
P
X
There are three components to why-questions. First is that such questions are prefaced with 'why.'
Why-Questions Three parts: ‘why’ + fact(s) + foil
‘fact’
‘foil’
“Why P in contrast to X?” Example: “Why do these specimens have lateral body wall extensions (= appendages) in contrast to other specimens with convex body walls?”
P
X
The other two components of why-questions are known as 'fact' and 'foil.' The 'fact' is what is in need of being explained, in contrast to the 'foil.'
Why-Questions Three parts: ‘why’ + fact(s) + foil
‘fact’
‘foil’
“Why P in contrast to X?” contrast class
Example: “Why do these specimens have lateral body wall extensions (= appendages) in contrast to other specimens with convex body walls?”
Three parts: ‘why’ + fact(s) + foil
P
X
The 'fact' and 'foil' together comprise the 'contrast class' of a contrastive whyquestion.
Why-Questions Three parts: ‘why’ + facts-as-presuppositions + foil
Question: “Why P in contrast to X?” Presupposition: it is true that P is the case. Example: “Why do these specimens have lateral body wall extensions (= appendages) in contrast to other specimens with convex body walls?”
Another important condition is that we assume the truth of the observation statement(s) that comprise the 'fact.' These facts are then said to be presuppositions.
Why-Questions Criterion for sensibility
‘fact’
‘foil’
Question: “Why P in contrast to X?”
“...we evaluate the sensibility of a why question by considering whether the fact and foil can be viewed as [alternative] culminating outcomes of some single type of natural causal process.” Barnes, E. 1994. Why P rather than Q? The curiosities of fact and foil. Philosophical Studies 73: 35–53.
The choice of foil for why-questions is not arbitrary. Instead, correctly choosing a foil requires that fact and foil are alternative effects from a single type of causal process. The following examples exemplify this requirement.
Why-Questions Criterion for sensibility
Question: “Why did the match not ignite in contrast to igniting?”
fact
foil
Common causal process: frictional surface
In this example we have the why-question, "Why did the match not ignite in contrast to igniting?" Notice that fact and foil trace back to the common causal process of rubbing a match along a frictional or rough surface. The why-question seeks an explanation for why the match did not ignite given that under the conditions we would have expected it to ignite. The question has proper form regarding an appropriate foil for the fact.
Why-Questions Criterion for sensibility
Incorrect Question: “Why did the match not ignite in contrast to breaking?”
fact
foil
frictional surface
thumb pressure
Separate causal processes
Here is a why-question of incorrect form. Notice that the fact and foil would trace back to separate and different causal processes. Explaining why the match did not ignite cannot be contrasted with why the match broke. The two conditions refer to entirely different causal processes.
Complete Why-Questions Common cause versus separate causes
Question: “Why are these matches burned, in contrast to unburned?”
fact
foil
There is an additional issue that we need to consider with regard to why-questions. This is an issue that is of importance in systematics because we observe shared features or characters among groups of organisms. When we observe multiple effects that have the appearance of being correlated, we have to decide how to explain such correlations.
Complete Why-Questions Common cause versus separate causes
Question: “Why are these matches burned, in contrast to unburned?”
Common cause explanation
Separate cause explanation
In the example shown here, the correlation of finding a group of burned matches requires that we decide whether to answer the why-question, "Why are these matches burned, in contrast to unburned?", by either a common cause explanation or by way of separate cause explanations.
Complete Why-Questions Common cause versus separate causes
Question: “Why are these matches burned, in contrast to unburned?”
How to decide? – background knowledge
Making a decision to provide a common cause explanation or separate cause explanations requires that one take into consideration their background knowledge regarding such effects. What is important to recognize is that offereng separate cause answers will be based on a set of questions that will be different from what will be required for a common cause answer.
Complete Why-Questions Separate causes
Q1
Q2
Q3
A1
A2
A3
In the case of treating the observation of the burned matches as explainable by way of separate causes, we would treat each effect (i.e. burned match) as leading to separate why-questions and separate respective answers.
Complete Why-Questions Common cause
Q A For a common cause explanation, we regard the correlation would be far less surprising if explained by a single, commmon cause. Hence the single question shown earlier, "Why are these matches burned, in contrast to unburned?"
Complete Why-Questions All Questions Have a Contrastive Form
The contrastive nature of why-questions, plus the reasoning used to answer to those questions, provide the strongest criteria for critically evaluating the methods and procedures used in systematics.
Any critical appraisal of biological systematics must stand on two issues. The first being the form of contrastive why-questions, as we have just seen. The second is that the proper form of our why-questions then lead to inferences of answers to those questions.
The Philosophy of Biological Systematics Course Outline – Part 1
1.
The goal of Science. The goal of biological systematics.
2.
Causal relationships in systematics.
3.
The nature of why-questions.
4.
The three forms of inference: deduction, induction, abduction.
5.
The uses of deduction, induction, and abduction in science.
Now that we have identified that the goals of science and biological systematics are both to acquire causal understanding of the phenomena we encounter, we next need to carefully examine the types of reasoning used in the sciences to achieve our goal. As we will see later in the course, these types of reasoning will play critical roles in attempting to correctly characterize the tasks of systematics.
The Fundamentals of Inference Inference: The act of reasoning from a statement (premise) or statements (premises), to a conclusion or set of conclusions.
This section of the course will focus on identifying the types of reasoning, known as inference, we use every day as well as in the sciences.
Two Types of Inference Have Traditionally Been Recognized Deduction: Inferences in which a conclusion drawn from a set of (true) premises cannot contradict those premises, and therefore must also be true. • All humans are mortal • Kirk is human • Kirk is mortal
Traditionally, when people speak of logic as the study of reasoning, they only make a distinction between two types of reasoning: deductive and inductive. Let's first look at this distinction, before more accurately segregating reasoning. In this example of deduction, notice that the premises, 'All humans are mortal' and 'Kirk is human,' is separated from the conclusion, 'Kirk is mortal,' by a single line.
Two Types of Inference Have Traditionally Been Recognized Induction: Inferences in which similarities are identified between observed objects or events of a given class, and hypothetically extended to unobserved objects or future events of that class. • Kirk is human • Kirk is mortal • All humans are mortal
In the case of an induction (or any non-deductive inference), the premises are separated from the conclusion, or conclusions, by a double line.
Two Types of Inference Have Traditionally Been Recognized Deduction: Inferences in which a conclusion drawn from a set of (true) premises cannot contradict those premises, and therefore must also be true.
Induction: Inferences in which similarities are identified between observed objects or events of a given class, and hypothetically extended to unobserved objects or future events of that class.
Deduction & Induction The Popular View of Their Relations
data
d
deduction
h
induction
deduction
h hypothesis
d
þ
induction
h
(1) Deduction: predictions of potential test consequences derived from the hypothesis to be tested. (2) Induction:
performing the test; observations of test consequences, providing either confirming/ corroborating or disconfirming/falsifying evidence.
This diagram illustrates how people often speak of the relations between deduction and induction in science. Starting with a hypothesis or theory, inferred by way of induction, one uses deduction to predict potential test evidence, then induction is used in the process of testing. The view is that there are cycles of deduction and induction in a continual process of evaluating theories and hypotheses.
Deduction & Induction The Popular View of Their Relations
deduction
Given Hypothesis
Expected Data
induction
Inferred Hypothesis
Actual Data
“Deduction is reasoning from what is in the mind to what is in the world.” “Induction is reasoning from what is in the world to what is in the mind.” H.G. Gauch, Jr. (2003: 160), Scientific Method in Practice
This is another, common view of the relation between deduction and induction in science.
The Structure of Inferences The Basic Components The premises and conclusion(s) of an inference contain statements that can be categorized as three possible forms:
Rule:
a law, empirical generalization, or theory, often stating a relation between cause and effect;
Case:
a statement about a thing(s), or event(s), in the form of causal or initial conditions;
Result:
a statement of a consequence or effect that is related to the ‘Case.’
For our purposes of examining the nature of reasoning that exists throughout biological systematics, we need to make more precise distinctions between the types of reasoning used in science. To compare and contrast the different types of reasoning, we will use a set of statements that can be used as either premises or conclusions. These statements are referred to as Rule, Case, and Result. By identifying premises or conclusions as Rule, Case, and Reult, we will find that in addition to deduction and induction (sensu stricto), we will also have to recognize a third type of non-deductive reasoning, called abduction.
Deduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
S = subject P = predicate ‘end terms’ M = ‘middle term’
In this example of deduction, as well as in following examples, the components in each of the statements comprising the premises and conclusions are identified as subject, predicate, or 'middle term.' The subject and predicate are sometimes referred to as 'end terms' since in a deductive arrangement they are present in the premises and conclusion. The 'middle term,' which functions as a predicate, then joins together the end terms in the conclusion.
Deduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
Case:
This marble [S] is from this bag [M & P].
S = subject P = predicate ‘end terms’ M = ‘middle term’
Notice that 'this bag' functions as both the middle term and predicate for the Case.
Deduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
Case:
This marble [S] is from this bag [M & P].
Result: This marble [S] is red [P].
S = subject P = predicate ‘end terms’ M = ‘middle term’
The predicate 'red' in the Rule, and the subject 'marble' in th Case are brought together in the Result. The middle term, 'this bag,' is only referred to in the premises. In deduction, the middle term serves to bring together the end terms in the conclusion.
Deduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
TRUE
Case:
This marble [S] is from this bag [M & P].
TRUE
Result: This marble [S] is red [P].
TRUE
S = subject P = predicate ‘end terms’ M = ‘middle term’
Because of the form required of the premises in deduction, if the premises are true, then the conclusion must also be true. In other words, the conclusion is certain.
Deduction
Rule:
The marbles in this bag [M] are red [P].
Case:
This marble [S] is from this bag [M & P].
Result: This marble [S] is red [P].
P S M P
M
S complete inclusion
(a)
(b)
Deduction has a structure wherein the 'middle term' [M] serves to bring together the subject [S] and predicate [P] in the conclusion. This relationship is illustrated here in (a), where the solid lines indicate relations stated in the premises, and the dashed line denotes the relation provided by the conclusion. The Euler diagram in (b) provides another representation of these relations, where deduction is characterized by 'complete inclusion:' the subject [S] is a subset of the middle term [M], and the latter is a subset of the predicate [P].
Induction A Simple Example
Case:
These marbles [S] are from this bag [M & P].
Result: These marbles [S] are red [P].
With induction, the premises are comprised of the Case and Result. Notice that the subject [S] is present in both premises.
Induction A Simple Example
Case:
These marbles [S] are from this bag [M & P].
Result: These marbles [S] are red [P].
Rule:
All marbles in this bag [M] are red [P].
From the premises is concluded the Rule. You might notice that the premises state a limted set of observations, from which a general statement is inferred. In fact, the example looks very similar to a statistical inference, proceeding from observations of a sample to a conclusion about the population from which the sample was taken. As we will see later in the course, induction is the principle mode of reasoning used in statistics. And, since statistics is about testing statistical hypotheses, we will find that induction is the approach taken for testing in general.
Induction A Simple Example
Case:
These marbles [S] are from this bag [M & P].
Result: These marbles [S] are red [P]. Rule:
All marbles in this bag [M] are red [P].
TRUE TRUE TRUE / FALSE
In contrast to deduction, where true premises always guarantee a true conclusion, an inductive conclusion from true premises cannot guarantee a true conclusion. The conclusion is not certain; it is only probable, as determined by the premises. Notice that the conclusion thus makes a claim that goes beyond what is offered by the premises.
Induction
Case:
P
This marble [S] is from this bag [M & P].
M S P
Result: This marble [S] is red [P]. Rule:
The marbles in this bag [M] are red [P].
M
S partial inclusion
(a)
(b)
As shown in (a), induction differs from deduction in bringing together the predicate [P] and middle term [M] in the conclusion by the presence of the subject [S] in both premises. The Euler diagram (b) shows induction to be a matter of 'partial inclusion.'
A Third Type of Inference is Often Recognized
Abduction: Reasoning from observed effects in the present (consequents) to a conclusion(s) of possible cause (or causes) in the past (antecedent). Abduction is also the form of inference used to develop our observation statements. As a result, abductive inference is the most common type of reasoning we use on a daily basis.
In addition to deduction and induction, there is a third type of non-deductive inference that is often recognized, called abduction. Abduction is a form of reasoning we use on a daily basis to infer from observed effects to a possible cause or causes.
A Third Type of Inference is Often Recognized Abduction “[A] hypothesis cannot be admitted, even as a hypothesis, unless it be supposed that it would account for the facts or some of them. The form of inference, therefore, is this:
The surprising fact, C, is observed; But if A were true, C would be a matter of course, Hence, there is reason to suspect that A is true. ”
Charles Sanders Peirce (1839-1914)
While abduction was recognized by Aristotle, it was not until the 19th century that the importance of this type of reasoning was recognized. The most prominent proponent to study the relations of abduction to deduction and induction was Charles Sanders Peirce (pronounced 'Purse'). But, it was not until the second half of the 20th century that philosophers and scientists started to take seriously the importance of abduction.
Abduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
In abduction, the major premise is the Rule.
Abduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
Result: This marble [S] is red [P].
The minor premise is the Result. Notice that the predicate, 'red,' appears in both premises.
Abduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
Result: This marble [S] is red [P].
Case:
This marble [S] is from this bag [M & P].
What you should notice is that the Rule, as a theory, is applied to the Result, where the Result can be regarded as an effect. The conclusion, Case, then has the quality of an explanatory account. In this example, we explain why 'this marble' is red because it came from 'this bag' of red marbles.
Abduction A Simple Example
Rule:
All marbles in this bag [M] are red [P].
Result: This marble [S] is red [P]. Case:
This marble [S] is from this bag [M].
TRUE TRUE TRUE / FALSE
As with any non-deductive inference, the true premises of an abduction do not guarantee the truth of the conclusion.
Abduction
Rule:
P
The marbles in this bag [M] are red [P].
Case:
This marble [S] is from this bag [M].
S
M
Result: This marble [S] is red [P].
M
S
P exclusion
(a)
(b)
The structure of abductive inference is the conjunction of some theory or law-like statement (Rule) and observed effects (Result) to conclude a possible cause (Case). Abduction is sometimes referred to as 'reverse deduction' in that the Case (cause) is concluded from the Rule (theory) and Result (effect), rather than the Result being concluded from the Rule and Case as in deduction. As a result (a), it is the presence of the predicate (P) in both premises which suggests the relation between the subject (S) and middle term (M) in the conclusion. Unlike deduction, which shows 'inclusion,' and induction, which shows 'partial inclusion,' abduction is characterized by 'exclusion' (b).
Relations Between Non-Deductive and Deductive Inference Induction & Abduction
Deduction
• Ampliative: conclusion can imply things not stated in premises.
• Not ampliative: conclusion cannot go beyond what is stated in premises.
• Not necessarily truth preserving: truth of conclusion not guaranteed.
• Truth preserving: conclusion is true if premises are true.
• Support for conclusion by premises can vary in strength.
• Degree of support for conclusion irrelevant - conclusion is either true or false.
• Requirement of total evidence must be considered.
• Requirement of total evidence is satisfied automatically.
There are some fundamental distinctions we need to be aware of between deductive and non-deductive (induction & abduction) reasoning. As we will see, these characteristics are significantly important when examining the types of reasoning used in biological systematics.
AMPLIATIVE REASONING Requirements C Non-monotonic:
allow a certain conclusion to be defeated by inclusion of additional information in premises.
C Cut-off Point Problem:
show that generalizations from observations are justified.
C Vertical Extrapolation:
support conclusions that make reference to entities not referred to in premises.
C Eliminative Dimension:
allow multiple conclusions consistent with premises.
Since non-deductive reasoning is ampliative (see previous slide), there are four characteristics that need to be recognized.
AMPLIATIVE REASONING Requirements
C Non-monotonic:
allow a certain conclusion to be defeated by inclusion of additional information in premises.
Induction
C Cut-off Point Problem: show that generalizations from observations are justified.
Induction / Abduction
C Vertical Extrapolation: support conclusions that make reference to entities not referred to in premises.
Induction / Abduction
C Eliminative Dimension: allow multiple conclusions consistent with premises.
Induction / Abduction
Most of these characteristics apply to both induction and abduction.
The Philosophy of Biological Systematics Course Outline – Part 1 1.
The goal of Science. The goal of biological systematics.
2.
Causal relationships in systematics.
3.
The nature of why-questions.
4.
The three forms of inference: deduction, induction, abduction.
5.
The uses of deduction, induction, and abduction in science.
We are now in a position to examine the specific ways in which deduction, induction, and abduction are used in our processes of scientific inquiry.
Inferences in Science
Deduction & Induction The Popular View of Their Relations
data
d
deduction
h
induction
deduction
h hypothesis
d
þ
induction
h
(1) Deduction: predictions of potential test consequences derived from the hypothesis to be tested. (2) Induction:
performing the test; observations of test consequences, providing either confirming/ corroborating or disconfirming/falsifying evidence.
Recall that earlier we noted that people often speak of the relations of deduction and induction in science, where science is only seen as cycles of deduction and induction in a continual process of inferring and evaluating theories/hypotheses. But in fact, abduction is a fundamental component that we need to take into consideration as completely separate from induction (sensu stricto).
Operational Relations Between Types of Inference in Science
abduction
Inferences of Hypotheses & Theories
deduction
Inferences of Tests
induction
Conducting Tests: Hypothesis Acceptance or Rejection
The actual relations between abduction, deduction, and induction are summarized here. Abduction involves our reasoning process for inferring hypotheses and theories. Deduction is used to derive potential consequences from our hypotheses and theories that might serve as test evidence when the act of testing occurs. Induction is the process of testing that leads to our concluding that a theory or hypothesis is confirmed or disconfirmed.
Fact Hypothesis Theory
What do these terms mean? In order to clearly understand the different types of reasoning we use in science, including biological systematics, we need to first understand the meanings of three words that are commonly used, but too often misunderstood.
Fact
The facts Facts are objects and events. The conditions of truth or falsity do not apply to facts.
A 'fact' is nothing more than an object or event that exists, whether we perceive it or not. It is important not to confuse the observation statement, 'This is a glass of ice water,' with the facts you perceive. The facts exist independent of you. Your observation statement is a conclusion from your inference (abduction!) used to explain the facts. Also, keep in mind that the conditions of truth or falsity cannot be applied to facts. Facts simply are! What can be true or false are your statements regarding those facts.
Fact “...a fact is either the being of a thing in a given state, or an event occurring in a thing. Constructs do not qualify as facts since they are not objects that can be in a certain state, let alone undergo changes of state.... Similarly, there are no 'scientific facts': only a procedure to attain knowledge can be scientific (or not), not the object of our investigation. Accordingly, scientists neither 'collect' facts nor do they come up with or, worse, 'construct' facts, but advance hypotheses and theories referring to or representing facts.” Mahner & Bunge (1997: 34), Foundations of Biophilosophy
The quote shown here is an excellent definition of 'fact,' and corrects a longstanding misconception that we have 'scientific' facts as opposed to 'non-scientific' facts.
Inference of a Theory
Now that we know what facts are, we need to understand the meaning of the term 'theory' and how they are inferred.
Theory An explanatory concept(s), stating cause-effect relations, that we can apply to our sense perceptions, to give us understanding. • theories are spatio-temporally unrestricted. • theories are not limited to the realm of Science.
What is important to notice in this definition is that a theory is a spatio-temporally unrestricted concept. In other words, a theory can be applied to the past, present, and future. It does not refer to a specific instance. And, as you will recall that the goal of science is to increase our causal understanding, theories are the fundamentally important conceptual tools that allow us to pursue that understanding, because theories enable us to infer explanatory hypotheses.
Abductive Inference as the Mechanism for Theory Formation • background knowledge (theories, laws, etc.) • tentative theory of cause-effect relations (adapted from an analogous theory) • observed effects in need of being explained • explanatory hypothesis
The inference of a theory is by way of abduction, and often as a matter of analogy. One takes a previously established theory, and uses it as an analogy for a new theory, where that analogous application serves to explain some set of surprising or unexpected phenomena.
Abductive Inference as the Mechanism for Theory Formation • Background knowledge: variation / inheritance / differential survival and reproduction
• Tentative theory: Based on what is known of the actions of artificial selection, in conjunction with the above background knowledge, maybe an analogous system of cause and effect relations exists in nature: Natural selection - organisms with traits that enhance survival and reproduction will leave offspring with those traits .
• Observations: There are differentially shared traits among these observed organisms.
• Hypothesis: Variation arose in an ancestral population, subsequent to which the traits in question allowed for enhanced survival and reproduction.
A classic example of the combined use of analogy and abductive inference can be found in the development of Charles Darwin's (1859) theory of natural selection.
Inference of a Hypothesis
Hypothesis An explanation of some set of facts, giving us at least initial understanding of what we perceive. • hypotheses are spatio-temporally restricted. • hypotheses are not limited to the realm of Science.
Notice that unlike a theory, which does not refer to specific instances, a hypothesis does present a narrow set of conditions for a particular time and location. In the context of science, the most useful way to characterize hypotheses is as explanatory accounts, the purpose of which is to provide us with causal understanding of an observed effect or set of effects.
Abductive Inference of a Hypothesis • background knowledge • theory (cause-effect relations) • observed effects in need of being explained
• explanatory hypothesis
The schematic example shown here illustrates the most basic components of the abductive inference of a hypothesis. The premises comprise at least one theory that is applied to the effect(s) we wish to explain, from which we conclude an explanatory hypothesis that suggests that the effect(s) is/are the product of particular past causal events that are consistent with the theory.
TESTING: a definition
The inferential process of critically and empirically assessing the ability of theories and hypotheses to give us understanding.
Now that we have examined the basics of inference, including the inferences of hypotheses and theories by way of abduction, we can briefly look at the process of testing. We will address testing in greater detail later in the course, as it applies to the testing of biological systematics hypotheses.
The Two Realms of Science Present (the realm of Observation)
Past
Future Cause
Explanatory Hypothesis
abduction
prediction
Effect
Effect
‘Historical’ Sciences
‘Experimental’ Sciences
Hypothesis testing
Theory testing
Recall the distinction we made earlier between 'historical' and 'experimental' sciences. This will serve to illustrate the difference between the testing of hypotheses and theories.
Testing: Experimental vs. Historical Sciences Present (the realm of Observation)
Past
Future Known Cause (experiment)
Unknown Cause (not observable)
explanation
prediction (deduction via theory)
Effect (potentially observable)
Known Effect
‘HISTORICAL’
‘EXPERIMENTAL’
Hypothesis testing
Theory testing
While the focus of this course will be on explanatory hypotheses in the historical sciences, most discussions about testing use examples from the experimental sciences. There are some important differences between these fields regarding the nature of testing, that need to be mentioned. What is of principle interest in the experimental sciences is testing by way of controlled experiments. A theory is tested by providing controlled (e.g. experimental) causal conditions in the present. In other words, the causal conditions are known to us. It is then a matter of observing whether or not a predicted effect occurs. What you will notice is that both cause and effect can be observed. We have the opportunity to know both. But, in the case of the historical sciences, what we know in the present are effects that are in need of being explained. The difficulty is that the cause that explains observed effects occurred in the past so no longer exists in the present. As a result, the cause is often unknown and unobservable.
Testing: Experimental vs. Historical Sciences Present (the realm of Observation)
Past
Future Known Cause (experiment)
Explanatory Hypothesis
explanation
prediction (deduction via theory)
Effect (potentially observable)
Known Effect
‘HISTORICAL’
‘EXPERIMENTAL’
Hypothesis testing
Theory testing
Thus, we infer an explanatory hypothesis to account for the observed effects. It is this hypothesis that we then want to test. But, in comparison to the experimental sciences, where the relations between cause and effect can both be known, the fact that a past causal event is usually not known can make it very difficult to test explanatory hypotheses since the relevant effects needed for a test might not be available. We will see in this course that this limitation certainly applies to the testing of many biological systematics hypotheses.
Testing Explanatory Hypotheses
Present (the realm of Observation)
Past Explanatory Hypothesis
Specific Causal Condition(s)
Future abduction
deduction
Known Effect
test that should be performed
induction
testing of hypothesis by observations of effects
We can now summarize the relations between the abductive inference of an explanatory hypothesis and the subsequent testing of that hypothesis. It is from effects observed in the present that we infer by way of abduction an explanatory hypothesis. From the specific causal conditions stated in that hypothesis we deduce effects that should be observed that are only possible because the specified causal conditions that occurred in the past would allow for those effects. The deduction of such effects provides the basis for the tests that need to be performed. The act of testing the hypothesis is, however, a matter of induction, where the hypothesis is either accepted or rejected on the basis of searching for the specified test evidence. Since no test can guarantee the truth of a hypothesis, and a disconfirmed hypothesis simply leaves us with alternative hypotheses to consider, testing is always inductive.
I. ABDUCTION The Inference of Hypotheses
Hypotheses
Abduction: causal theory + observed effects
background knowledge + causal theory
‘Why...?’
Observed Effects
Let's now look a very simple summary of the relations between abduction, deduction, and induction. In this slide, the abductive inference of hypotheses is presented.
II. ABDUCTION The Inference of New Hypotheses: additional abductive inferences are required when new effects are observed
Hypotheses
Additional Effects
Very often, subsequent to inferring a hypothesis (or hypotheses), we encounter additional effects or observations that also need to be explained in the same manner as the previous effects.
II. ABDUCTION The Inference of New Hypotheses: additional abductive inferences are required when new effects are observed
Hypotheses
Additional Effects
‘Why...?’
New Set of Observed Effects (old + new)
The result is that these additional effects/observations need to be included with previous observations.
II. ABDUCTION The Inference of New Hypotheses: additional abductive inferences are required when new effects are observed
New Hypotheses Additional Effects
Abduction: causal theory + observed effects
background knowledge + causal theory
‘Why...?’
New Set of Observed Effects (old + new)
Then, a new abductive inference is performed that leads to new hypotheses, that replace the previous hypotheses, and provide us with updated explanations of our observations.
III. Ranking Hypotheses
Determine Which Hypotheses are to be Tested
ranking
Hypotheses
In some fields of science, these hypotheses might be ranked by way of some criterion, in order to determine which hypotheses will be tested first. For example, the time and/or expense involved with testing might make it more feasible to test some hypothesese as opposed to others.
IV. DEDUCTION: Predicte Possible Test Consequences
If a hypothesis provides a sufficiently detailed account of past causal conditions, then it should be possible to predicte consequences, as effects, that are related as specifically as possible to those causal conditions stated in the hypothesis.
ranking
Hypotheses
Deduction: predicted test consequences
Depending on which hypothesis or hypotheses are to be tested, the next step is to deduce from each hypothesis potential test consequences. Recall that an explanatory hypothesis presents claims that specific causal conditions existed in the past that account for the effects in the present that are in need of being explained. Thus, the potential test consequences that we might deduce from the stated causal conditions would have to be evidence as closely associated as possible with those conditions. In other words, we would want to seek effects with the lowest probability of occurrence if the stated causal conditions did not occur. We will return to this issue several times during this course.
V. INDUCTION: Hypothesis Testing Determine whether or not predicted consequences are the case.
ranking
Hypotheses
Abduction:
Deduction:
causal theory + observed effects
predicted test consequences
background knowledge + causal theory
Induction: observed test consequences, leading to one of the following conclusions –
‘Why...?’
Observed Effects
(a) hypothesis confirmation, (b) hypothesis revision, or (c) hypothesis rejection.
Finally, there is the actual act of testing. This entails putting oneself in a position to witness the necessary conditions for determining whether or not the predicted test consequences are the case. If the predicted test consequences are observed, then the hypothesis is said to be confirmed. If consequences other than what were predicted are observed, or only some test evidence is observed, then the hypothesis might be disconfirmed or in need of revision, respectively. In these cases, these observations might need to be integrated into the set of previous observed effects and a new abductive inference to a new or revised hypothesis is accomplished. Then, the process of testing can be performed again.
An Example – Hypothesis Confirmation Hypothesis: John was in my yard, throwing the ball, and it broke the window.
Abduction:
Deduction:
(a) John sometimes practices pitching in my yard, and he was there earlier today, (b) broken window + ball on the floor.
background knowledge + causal theory
John’s finger prints should be on the ball.
Induction: Observed Consequences – Finger prints are on the ball, that match John.
‘Why...?’
Therefore, the hypothesis has been confirmed.
Observed Effects: (a) my window is broken, (b) there is a ball on the floor.
Here is a simple, everyday example that illustrates how we use abductive inference to develop an explanatory hypothesis, deduce potential test evidence to evaluate that hypothesis, and then carry out testing the hypothesis. In this instance, the observed test evidence confirms the hypothesis.
An Example – Hypothesis Confirmation Hypothesis: John was in my yard, throwing the ball, and it broke the window.
Deduction: John’s finger prints should be on the ball.
* Notice that the evidence (observed consequences) confirming/ supporting the hypothesis suggests, but does not guarantee, the hypothesis is true. Acceptance of the hypothesis as confirmed is inductive.
Induction: Observed Consequences – Finger prints are on the ball, that match John.
Therefore, the hypothesis has been confirmed.
An Example – Hypothesis Revision, Part I Hypothesis: John was in my yard, throwing the ball, when it broke the window.
Abduction: (a) John sometimes practices pitching in my yard, and he was there earlier today, (b) broken window + ball on the floor.
background knowledge + causal theory
‘Why...?’
Deduction: John’s finger prints should be on the ball.
Induction: Observed Consequences – Finger prints are on the ball, that match John, but there is also red dirt on the ball. Therefore, the hypothesis has been partially confirmed, but needs to be revised.
Observed Effects: (a) my window is broken, (b) there is a ball on the floor.
In this case, however, the observed test evidence is not entirely what was predicted. There are additional observations made during the test that suggest that the hypothesis needs to be revised.
An Example – Hypothesis Revision, Part I Hypothesis: John was in my yard, throwing the ball, when it broke the window.
* Notice that while the evidence (i.e. observed consequences that John’s finger prints are on the ball) does confirm/ support the hypothesis, observing red dirt on the ball during the test suggests that the hypothesis must be revised. Red dirt only occurs at the baseball field near my house, suggesting that John was not throwing the ball in my yard, but rather was at the baseball field, which slightly alters the causal conditions stated in the hypothesis. A revision of the hypothesis then occurs through the subsequent inference of a new abduction based on a new set of observed effects, as is shown in the next diagram (Hypothesis Revision, part II).
Deduction: John’s finger prints should be on the ball.
Induction: Observed Consequences – Finger prints are on the ball, that match John, but there is also red dirt on the ball. Therefore, the hypothesis has been partially confirmed, but needs to be revised.
An Example – Hypothesis Revision, Part II Revised Hypothesis: John was at the baseball field next door, when he threw a wild pitch, and it broke the window.
New Abduction: (a) John sometimes practices pitching at the baseball field next door, (b) broken window + ball on the floor + John’s finger prints + red dirt on ball.
additional background knowledge + causal theory
‘Why...?’
New Observed Effects: (a) my window is broken, (b) there is a ball on the floor, (c) John’s fingerprints are on the ball, (d) there is red dirt on the ball.
Induction: Observed Consequences – Finger prints are on the ball, that match John, but there is also red dirt on the ball. Therefore, the hypothesis has been partially confirmed, but needs to be revised.
Thus, we need to integrate the new observations obtained during the previous test with our previous observations, and then infer a revised hypothesis.
An Example – Hypothesis Revision, Part II Revised Hypothesis: John was at the baseball field next door, when he threw a wild pitch, and it broke the window.
New Abduction: (a) John sometimes practices pitching at the baseball field next door, (b) broken window + ball on the floor + John’s finger prints + red dirt on ball.
additional background knowledge + causal theory
‘Why...?’
New Observed Effects: (a) my window is broken, (b) there is a ball on the floor, (c) John’s fingerprints are on the ball, (d) there is red dirt on the ball.
* The test of the hypothesis, presented in part I, resulted in the observation of effects that confirm/support the claim that John was a causal factor in the breaking of my window. But, there was also the additional observed effect that red dirt is on the ball, suggesting that, contrary to my initial hypothesis that John was not in my yard, he was at the nearby baseball field. This new observed effect needs to be considered in a new abductive inference to a revised explanatory hypothesis. What is important to notice is that the test that lead to the confirmation that John was responsible for the window being broken, is still inductive for it continues to suggest, but not guarantee, the truth of past events. Induction: Observed Consequences – Finger prints are on the ball, that match John, but there is also red dirt on the ball. Therefore, the hypothesis has been partially confirmed, but needs to be revised.
An Example – Hypothesis Rejection, Part I Hypothesis: John was in my yard, throwing the ball, when it broke the window.
Abduction: (a) John sometimes practices pitching in my yard, and he was there earlier today, (b) broken window + ball on the floor.
background knowledge + causal theory
‘Why...?’
Deduction: John’s finger prints should be on the ball.
Induction : Observed Consequences – Finger prints are on the ball are from Bob, not John.
Therefore, the hypothesis has been disconfirmed.
Observed Effects: (a) my window is broken, (b) there is a ball on the floor.
Here is an alternative outcome to the test, showing an instance of disconfirmation of a hypothesis. While it was predicted that John's finger prings would be found on the ball, the actual examination of finger prints reveals that they are from Bob. The evidence observed is different from what was predicted, thus the hypothesis has been disconfirmed.
An Example – Hypothesis Rejection, Part I Hypothesis: John was in my yard, throwing the ball, when it broke the window.
* Notice that the observation of consequences that were not predicted has the form of modus tollens: ‘If p, then q; not-q; therefore not-p.’ While this deductive form allows for disconfirming the hypothesis, the observed effects during the test provide the basis for the next abductive inference. The act of testing suggests that different causal events occurred. But while the original hypothesis has been rejected, a significant part of the test is that an alternative hypothesis needs to be considered. And again, this indicates that the test is inductive.
Deduction: John’s finger prints should be on the ball.
Induction : Observed Consequences – Finger prints are on the ball are from Bob, not John.
Therefore, the hypothesis has been disconfirmed.
An Example – Hypothesis Rejection, Part II New Hypothesis: Bob was in my back yard, throwing the ball, when it broke the window.
New Abduction: (a) Bob sometimes practices pitching in my yard, (b) broken window + ball on the floor + Bob’s finger prints.
additional background knowledge + causal theory
‘Why...?’
New Observed Effects: (a) my window is broken, (b) there is a ball on the floor, (c) Bob’s fingerprints are on the ball.
Induction: Observed Consequences – Finger prints are on the ball are from Bob, not John. Therefore, the hypothesis has been disconfirmed.
The test observations provide the basis for another abductive inference.
The new evidence obtained during the test of the old hypothesis must now be considered as part of the total evidence, and it is from this revised set of observations that we would then engage in a new abductive inference to an entirely new hypothesis. This new hypothesis would then be available for a new process of testing.
An Example – Hypothesis Rejection, Part II New Hypothesis: Bob was in my back yard, throwing the ball, when it broke the window.
New Abduction: (a) Bob sometimes practices pitching in my yard, (b) broken window + ball on the floor + Bob’s finger prints.
additional background knowledge + causal theory
‘Why...?’
New Observed Effects: (a) my window is broken, (b) there is a ball on the floor, (c) Bob’s fingerprints are on the ball.
* Subsequent to the rejection of the hypothesis (see previous diagram) as an explanation of the broken window, we need to consider the new observations that were made during testing, i.e. the presence of Bob’s finger prints on the ball. These new observations are combined with previous observations to give us a new set of effects in need of explanation. These effects are then conjoined with a causal theory regarding Bob, and pitching, to abductively infer a new explanatory hypothesis.
Induction: Observed Consequences – Finger prints are on the ball are from Bob, not John. Therefore, the hypothesis has been disconfirmed.
The test observations provide the basis for another abductive inference.
Deduction & Induction Traditional Relations data
d
deduction
h
induction
d
deduction
h
induction
h
hypothesis
(1) Deduction: predictions of potential test consequences derived from the hypothesis to be tested. (2) Induction:
performing the test; observations of test consequences, providing either confirming/corroborating or disconfirming/ falsifying evidence.
So, the standard model that we discussed earlier, where the activity of scientific inquiry is one that alternates between deduction and induction, is not accurate.
Abduction, Deduction & Induction A More Accurate View of Their Relations d
data
abduction 1
h
h
d abduction 1
h
hypothesis
(1) Abduction1: observed, unexpected or surprising effects provide part of the premises for abductions to new hypotheses.
As we have seen, abduction is a fundamentally important part of scientific inquiry. We are continually confronted with surprising or unexpected observatoins that are in need of being explained. Abductive inference is the process of providing hypotheses that give us at least inital understanding of what we observe. In other words, we attempt to make the surprising not so surprising by bringing it into the realm of what is already familiar to us, or what we already understand, via our established theories.
Abduction, Deduction & Induction A More Accurate View of Their Relations d
data
d
abduction 1 deduction
h
abduction 1
deduction
h
h
hypothesis
(1) Abduction1: observed, unexpected or surprising effects provide part of the premises for abductions to new hypotheses. (2) Deduction: predictions of potential test consequences derived from the hypothesis to be tested.
Deduction then serves to predict potential test evidence that can serve to evaluate the hypothesis. Recall, however, that deduction is not the actual act of testing - that is a process that is inductive.
Abduction, Deduction & Induction A More Accurate View of Their Relations data
d
d
abduction 1 deduction
h
induction
deduction
h
abduction 1 induction
h
hypothesis
(1) Abduction1: observed, unexpected or surprising effects provide part of the premises for abductions to new hypotheses. (2) Deduction: predictions of potential test consequences derived from the hypothesis to be tested. (3) Induction:
performing the test; observations of test consequences, providing either confirming or disconfirming evidence.
Then, the act of seeking the predicted test evidence is a matter of induction, where the observations of the consequences of the test serve as part of the premises from which one concludes that the hypothesis being tested has either been confirmed or disconfirmed, or is in need of revision.
Abduction, Deduction & Induction A More Accurate View of Their Relations data
d
d
abduction 1 deduction
induction
deduction
induction
abduction 2
abduction 2
h
abduction 1
h
h
hypothesis (1) Abduction1: observed, unexpected or surprising effects provide part of the premises for abductions to new hypotheses. (2) Deduction: predictions of potential test consequences derived from the hypothesis to be tested. (3) Induction:
performing the test; observations of test consequences, providing either confirming or disconfirming evidence.
(4) Abduction2: in the case that test evidence disconfirms a hypothesis, then this new information could provide part of the premises for abductions to new or revised hypotheses.
And finally, in the case of a hypothesis being disconfirmed, then we have new observations from the test that will then need to be considered as part of the premises for a new abductive inference to a new or revised hypothesis.
Beware of ‘Normal Science’
“...‘normal science’ means research firmly based upon one or more past scientific achievements, achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice.” T.S. Kuhn (1970: 10), The Structure of Scientific Revolutions
Now that we have examined the goal of scientific inquiry, and established that biological systematics must be consistent with that goal, and that there are three recognized classes of reasoning used in the sciences, we need to be cautious of what is known as 'normal science.' 'Normal science' is a phrase coined by philosopher of science, Thomas Kuhn, to describe the day-to-day activities of scientists. This involves the routine and accepted protocols within a particular field of science that practioners use in the course of inquiry.
‘Normal Science’
‘Scientific Revolution’
factual discoveries
paradigm shift(s) conceptual
methodological
What might be regarded as 'normal science' in the present was at some point in the past part of some 'scientific revolution' that replaced what was earlier the standard of 'normal science.' Kuhn referred to these moments of scientific revolution as paradigm shifts, where a scientific community comes to a point of being faced with conceptual and/or methodological changes, that result in a new and somewhat different stage of 'normal science.' A classic example of a conceptual paradigm shift was Charles Darwin's introduction of his theory of natural selection. More specifically, within biological systematics, we might regard Willi Hennig's emphasis on distinguishing para- from monophyly, and the sole advocation of the latter, as a conceptual paradigm shift that especially started after 1966. And with the advent of computer algorithms we have seen methodological paradigm shifts with respect to the inferences of phylogenetic hypotheses, as cladograms.
“‘Normal’ science... is the activity of the non-revolutionary, or more precisely, the not-too-critical professional: of the science student who accepts the ruling dogma of the day; who does not wish to challenge it; and who accepts a new revolutionary theory only if almost everybody else is ready to accept it – if it becomes fashionable by a kind of bandwagon effect. To resist a new fashion needs perhaps as much courage as was needed to bring it about.” K. Popper (1970: 52), Normal science and its dangers. In: Criticism and the Growth of Knowledge
But it is instructive to consider the warning offered by the philosopher of science, Karl Popper, who tells us that 'normal science' can be dangerous. This danger derives from workers passively and uncritically accepting conceptual or methodological approaches. The danger is increased within a scientific community if practitioners have little or no understanding of the more general foundations by which scientific inquiry is supposed to follow. The result can be the development of conceptual and methological protocols that are inconsistent and maybe even contradictory to established scientific inquiry. Ineed, what we will see in much of this course is that while biological systematics has developed its own community of 'normal science,' most of it has been developed in a vacuum, largely isolated from the basic principles of inference and testing that are required in the sciences.
Systematics as a ‘Normal Science’
Finding answers without consideration of questions.
One of the most significant dangers of the 'normal science' of systematics that we see today is that it is a field of study in which the routine is to seek answers, e.g. cladograms and taxa, without actually considering the questions we are supposed to be asking. Throughout this course we will attempt to link our why-questions with the inferences of answers to those questions. It is this relation between questions and answers, between evidence and hypotheses, that forms the foundation for critically assessing biological systematics.
The Philosophy of Biological Systematics Course Outline – Part 2
1.
Systematics involves abductive inference.
2.
Inferences of systematics hypotheses, i.e. taxa.
3.
Some implications for “phylogenetic” methods.
In Part 1 of this course, we first identified that the goal of all the sciences, including biological systematics, is to continually acquire causal understanding of the objects and events we encounter. We then examined the three fundamental classes of reasoning used in the sciences, as well as everyday life. Among these classes of reasoning, we found that abduction is the most common. What we will now find throughout the remainder of this course is that abduction is the mode of reasoning that binds together all of biological systematics. This means we will need to carefully examine how abductive inference is used in all facets of systematics, and from this we can discover some significant implications for nearly all systematics methods.
SOME OF THE RELATIONSHIPS WITHIN BIOLOGICAL SYSTEMATICS
When we speak of ‘relationships,’ we mean causal relationships. Determining the status of species, and all taxa, can best be accomplished by first recognizing the basic unit to which these causal relationships refer. Then, examining the inferential basis for each of these classes of causal relationships.
To begin our examination of these issues, we need to understand what we mean when we speak of 'relationships' in biological systematics. We use the term relationship on a regular basis, but the word is often not clearly understood when it is used in systematics. We first need to recognize that when we speak of relationships, we are speaking of causal relations. For example, we say we are related to our parents, we are related to our sisters or brothers, we are related to our grand parents. In every instance, the relations we are talking about are causal relations, because it is that type of relationship that gives one understanding. And, as we will see in the rest of this course, the units to which those causal relationships refer are individual organisms. Then, we can specifically look at the way in which we infer each of the types of causal relationships that are used in biological systematics. And again, it needs to be emphasized that it is causal relationships that we are interested in, because it is those types of relations that best serve the overall goal of doing science.
(1913-1976)
Hennig, W. 1966. Phylogenetic Systematics
Recall that we saw earlier that one of the best examinations of the nature of causal relationships in systematics can be found in Willi Hennig's (1966) book, Phylogenetic Systematics.
Classes of Relationships 1. ontogenetic
6
2. cyclomorphic 3. sexual dimorphic
7 4
2
4. tokogenetic 5. polymorphic 6. specific
1
3 5
Hennig, W. 1966. Phylogenetic Systematics
7. phylogenetic
Each of these classes of relationships refer to the different classes of explanatory hypotheses we call taxa.
As was noted in Part 1 of this course, Hennig's (1966) well known figure 6 depicts the fundamental classes of relationships used in biological systematics. Clearly, the only way to interpret the relationships represented in this diagram is in a causal context.
Observation statement
Intraspecific hypothesis
Tokogenetic hypothesis
present
Species hypothesis
Phylogenetic hypothesis A-us a-us
adult b-us
(semaphoront)
Cyclomorphic hypothesis
juvenile (semaphoront)
embryo (semaphoront)
%&
Ontogenetic hypothesis
Sexual dimorphic hypothesis
This diagram is redrawn from Hennig's (1966) fig. 6. Notice that when we refer to a cladogram, it summarizes at least two classes of explanatory hypotheses: specific (species) and phylogenetic, as are named here with formal names, A-us, a-us, and b-us. But what is especially clear is that how we obtain such diagrams is not by way of regarding species as classes or individuals. Each of the branches in this diagram are the products of particular inferential actions as reactions to observing in the present particular characters of organisms, and attempting to answer why-questions related to those observations by way of past causal events. What is also important to remember is that in addition to the cladogram in this diagram, there are a wide range of explanatory hypotheses used in biological systematics that assist us in understanding the organisms we observe. What exists in nature are organisms, not taxa, not species. And, what might be obvious at this point is that to say taxa are shown here is to say we have hypotheses addressing particular questions regarding the organisms we have observed.
Causal Relationships (Taxa) in Biological Systematics Some preliminary examples
Let's now look at very simple examples of how we actually engage in the abductive inferences of some of the causal relationships we just examined in the diagrams.
Observation statement
Inference of Observation Statement
First we will consider how we infer an observation statement, which is itself an explanatory hypothesis.
Inference of Observation Statement
“Why do I have these sense data about this object?” sense data
Let's say we observe the organisms shown here. At each instance that we perceive an object, such as the individual circled here. We might then ask why we have these particular sense perceptions or sense data in our brains? In other words, we are asking for an explanation that provides the cause of our sense data.
Inference of Observation Statement Observation statement (=Perceptual hypothesis)
“Why do I have these sense data about this object?” sense data theory of perception + sense data
ˆ “Because this object exists separate from me.”
We therefore infer, by way of abduction, an answer to our why-question that says the object exists separate from ourselves. In other words, we explain the sense data in our brains by our observation statement that this object does in fact exist, rather than giving an alternative explanation. For example, that we might be hallucinating.
Inference of Ontogenetic Hypothesis (Semaphoront)
present
“Why is this individual an adult?”
Another type of question that might be asked regarding this individual is why it shows the characters of being an adult.
Inference of Ontogenetic Hypothesis (Semaphoront)
present
adult (semaphoront)
juvenile (semaphoront)
embryo (semaphoront)
“Why is this individual an adult?” theory of ontogeny + observation statement
ˆ “Because it is the product of ontogeny.”
The explanation would be that this individual is the product of an ontogenetic process, that could be illustrated as shown here. We place our observations of this individual into the context of what we know of the life history of these types of organisms, based on our application of some ontogenetic theory to our observations. And this ontogenetic hypothesis then gives us understanding of some of the particular characters we observe of this individual. The individual is what Willi Hennig (1966) referred to as a semaphoront.
Inference of Tokogenetic Hypothesis
present
“Why does this individual have black spots?”
A third type of why-question we often ask is in relation to unique characters of a particular individual. For instance, the black spots we only observe on this individual, as opposed to no spots on other individuals.
Inference of Tokogenetic Hypothesis
Tokogenetic hypothesis
present
“Why does this individual have black spots?”
theory of tokogeny + observation statement
ˆ “This individual has black spots because the condition was inherited, as the product of past interbreeding events.”
The relevant explanation could then be one pointing out the inheritance of the feature of black dots as the result of past reproductive (interbreeding) events (= tokogeny). For example, the type of relations are tokogenetic, that exist between parents and the offspring that are produced as a result of reproductive events.
Inference of a Specific (Species) Hypothesis present
“Why do these individuals have antennae in contrast to a smooth dorsum?”
A more general question we might ask is in regard to characters shared among a group of individuals. For instance, why do these individuals have antennae in contrast to a smooth dorsum, as is the case in other individuals we have observed? Notice again that we are asking this why-question because it is surprising or unexpected to find specimens with antennae; because from our past experience, we would expect to see more individuals with a smooth dorsum. So we have new observations that are in need of being explained.
Inference of a Specific (Species) Hypothesis present
Species hypothesis (b-us)
“Why do these individuals have antennae in contrast to a smooth dorsum?” species theory (mutation + tokogeny + fixation)
ˆ “These individuals have antennae because the character originated in the population in the past, and became fixed in the population.”
The answer to this question could be in the form of a hypothesis that antennae arose in the past in a reproductively isolated population and as a consequence of natural selection the feature eventually became fixed throughout the population. What is important to recognize here is that we inferred this answer to the question by applying at least three different theories: mutation, tokogeny, and natural selection. And it is this combination of theories that we would refer to by the shorthand phrase of specific or species theory. This hypothesis is illustrated in the diagram shown here, and is the class of hypothesis we typically call species. Notice that this diagram would traditionally be referred to as a lineage. But, all we are doing is providing a summary of past causal events that explain our present observations. Once again, it is important to stress that what we here call a species, is nothing more than a particular class of explanatory hypothesis.
Inference of a Polymorphism Hypothesis
present
Species hypothesis (b-us)
“Why are individuals in this population polymorphic for body color?”
A somewhat less general question we might ask is in regard to the variations among characters shared among a group of individuals. Here we might ask why members of this population are polymorphic for body color?
Inference of a Polymorphism Hypothesis Intraspecific hypothesis present
Species hypothesis (b-us)
“Why are individuals in this population polymorphic for body color?” polymorphism theory (mutation/pleiotropy + tokogenetic)
ˆ “The polymorphism originated in the past in the population with the introduction of red, and the two conditions have been maintained during tokogeny.” The answer to this why-question would be by way of another class of hypothesis, pointing to the fact that subsequent to the introduction of the red condition because of some mutation, both red and blue forms have been maintained by way of tokogeny. What we might call a theory of polymorphism actually means we are applying at least two fundamental theories to our observations in order to answer this question. The hypothesis would then be illustrated as shown in the diagram, and is the class of hypothesis we often call intraspecific.
Inference of a Phylogenetic Hypothesis a-us present
b-us
“Why do these individuals have appendages as opposed to a smooth ventrum?”
And finally, we have the most general class of hypothesis we use in systematics: phylogenetic. We notice that all of the individuals we observe here have ventral appendages, whereas all other types of individuals we have seen have a smooth ventrum.
Inference of a Phylogenetic Hypothesis a-us present
b-us
“Why do these individuals have appendages as opposed to a smooth ventrum?” phylogenetic theory (mutation + tokogeny + fixation + population splitting)
Phylogenetic hypothesis (A-us)
ˆ “These individuals have appendages because the character originated in the past and became fixed in the ancestral population, followed by a splitting of the population .”
Answering the question of why these individuals have appendages in contrast to a smooth ventrum could be in the form of what we usually refer to as 'descent with modification,' followed by the process of population splitting. Unlike a species theory, which at a minimum relies upon the conjunction of theories of mutation, tokogeny, and character fixation, a phylogenetic-based inference also applies a theory of population splitting. This splitting event is traditionally referred to as 'speciation,' but this term is not an accurate description because it implies that species are things that come into existence, which as we will see, is not the case. The hypothesis that is our answer to the why-question is represented by the illustration. And it would be this type of hypothesis we typically refer to as being a phylogenetic hypothesis.
Inference of a Phylogenetic Hypothesis a-us present
b-us
“Why do these individuals have appendages as opposed to a smooth ventrum?” phylogenetic theory (mutation + tokogeny + fixation + population splitting)
Phylogenetic hypothesis (A-us)
ˆ “These individuals have appendages because the character originated in the past and became fixed in the ancestral population, followed by a splitting of the population .” A-us a-us
b-us
This phylogenetic hypothesis is just one part of the diagrams we refer to as cladograms.
Causal Relationships (Taxa) in Biological Systematics If the goal of biological systematics is to provide causal explanations for the phenomena of differentially shared characters among organisms, then... the inferential structure of almost all of systematics is ABDUCTIVE.
From the simple examples we have just seen, it should be apparent that since the goal of biological systematics is consistent with the goal of all scientific inquiry, then the most important class of reasoning throughout all systematics is going to be abduction.
The Philosophy of Biological Systematics Course Outline – Part 2
1.
Systematics involves is abductive inference.
2.
Inferences of systematics hypotheses, i.e. taxa.
3.
Some implications for “phylogenetic” methods.
We are now at a point that we can examine in greater detail the actual structure of abduction used in biological systematics to infer the hypotheses that we typically refer to as taxa. The main focus here will be on the inferences of specific (species) and phylogenetic hypotheses.
A Formal Definition of TAXON
Any of a set of classes of hypotheses used in biological systematics for the purpose of explaining particular characters of observed organisms.
First, a formal definition of the word taxon. This definition is consistent with the goal in any field of science, which is that we attempt to acquire causal understanding by way of our hypotheses explaining our observations of phenomena. The observations we make relative to systematics are of organisms, and our whyquestions are in regard to the properties of those organisms. A taxon is just a term referring to a particular class of explanatory hypotheses, and our systematics hypotheses are our attempts at answering certain of our why-questions.
Abduction: The Inference of Explanatory Hypotheses The inferential structure that leads to all taxa (including species)
• background knowledge • causal theory, stating relations between particular causes and effects • observed effect(s) in need of explanation
• hypothesis of possible past causal condition(s)
= a taxon All of the classes of relationships Hennig (1966) referred to in the diagram presented earlier comprise hypotheses that are derived by way of abduction. Abductive inference begins when we have surprising or unexpected observations that are in need of explanation. We then ask why-questions as the start to understanding what we encounter. What is shown here is what we have already discussed, that an abductive inference consists of observed effects in need of explanation. We apply a particular theory, or theories, to those effects. It is here that we assume that a theory that has been successful in the past at giving us causal understanding will be useful in this instance. It is from these premises that we conclude an explanatory hypothesis that states at least tentative past causal conditions that account for the observed effects. In other words, we have an initial answer to the why-question regarding the observed effects. In the case of biological systematics, we often refer to these hypotheses as 'taxa.'
Inferences of Taxa
Specific (Species) Hypotheses
Let's now look in greater depth at the point of view that, like all taxa, species are nothing more than abductively-inferred explanatory hypotheses.
What are Species? species A
species B
The Solution to the ‘Species Problem’ (actually, the problem is worse than you think!)
Species... We speak of them all the time. Whether as scientists or in our everyday lives, we and most of society refer to species. We talk of endangered species, species diversity, and the conservation of species. But there is a little problem that we too often ignore or do not want face. The problem is that we do not all mean the same thing when we use the word species. For several years now, part of my research has focused on the question of what are species, and can a formal definition be provided that solves what is often referred to as 'the species problem.'
1928
2003
1957
2010
For much of the 20th century, and now into the 21st century, we have seen books and other publications trying to determine the nature of species. Here are four examples from the past 80+ years, each with the same title, from the large literature on the subject, all attempting to solve 'the species problem.' Yet, at the present time, biologists do not have a consensus on what they mean by the term species.
My own attempt to deal with the issue of species began in 2005, when I published a small paper in the journal Marine Ecology of what I thought was a novel solution. In this paper, I pointed out that species are actually just one of the many hypotheses we infer to help understand particular properties or characters of organisms.
And later I published a larger paper in the journal Acta Biotheoretica that provides more details on how my definition of species is related to the overall goal of doing biological systematics. It was in this paper that I showed that all aspects of biological systematics are derived from the same type of reasoning - all with the purpose of meeting our goal as scientists, which is to acquire causal understanding of observations of organisms.
In: The Species Problem: Ongoing Issues (in press) And this chapter, to appear in an edited book in early 2013, expands further on the subject of species being explanatory hypotheses. I point out that the one term species entails at least five separate classes of explanatory hypotheses, which we will examine later. Interestingly, because of the nature of some of these hypotheses, phylogenetic-level hypotheses cannot also be applied to the same organisms.
“[DNA barcoding] provides a way to identify the species to which a plant, animal or fungus belongs.”
Especially with the growing interest in the procedure known as DNA barcoding, which claims that with nucleotide sequences we can place specimens in the appropriate species, it is obvious that the biological community needs to seriously address the question of what we mean when we use the term species. If we do not agree on what we mean by species, then there are no scientific advantages to spending large amounts of money and time using technology that will not satisfy our goals as scientists. Unfortunately, we seem to be more excited about applying technology to provide us with what we think are answers. But, the reality is that we too often do not have a clear idea of what why-questions we are actually asking.
Indeed, I pointed out a few years ago that DNA barcoding is lacking in clear scientific justification because of the very fact that biologists have not yet agreed on what they mean when they use the word species. Once again, the consequence is that we are producing a lot of results, but we do not talk about what why-questions those results are supposed to be answering, and if we are even asking the right questions.
Problem One Class versus individual
• If species are classes – organisms are members based on their characters • If species are individuals – organisms are just the parts that make the whole
To consider a definition of species, there are two fundamental problems we first need to recognize, as these have contributed to misunderstandings of the nature of species and other taxa. The first problem is that discussions about species have mainly focused on deciding whether species are classes or individuals. The arguments that are usually presented state that... ...if species are classes, then organisms are assigned as members of a class according to particular characters; ...alternatively, if species are individuals or things that exist in nature, then organisms form the parts that make up a species. The view that species are individuals or things is probably the most common opinion among systematists. We very often hear people speak of species as though they are objects that exist in time and space, beyond the organisms we observe on a daily basis.
Problem Two: Species -Take Your Pick! Species ‘concepts’ rather than definition 1.
Agamospecies
12.
Hennigian
2.
Biological
13.
Internodal
3.
Cohesion
14.
Morphological
4.
Cladistic
15.
Non-dimensional
5.
Composite
16.
Phenetic
6.
Ecological
17.
Phylogenetic
7.
Evolutionary Significant Unit
18.
Polythetic
8.
Evolutionary
19.
Recognition
9.
Genealogical Concordance
20.
Reproductive Competition
10. Genetic
21.
Successional
11. Genotypic Cluster Definition
22.
Taxonomic
1997
The second problem that has contributed to misunderstanding the nature of species is that emphasis is almost always placed on species 'concepts' rather than a formal definition of the term species in terms of our reactions to observations of organisms. The consequence is that we have over 20 'concepts' that tell us what species are supposed to be, but they do not give us a formal definition.
Species - Take Your Pick! Species ‘concepts’ rather than definition
26 species ‘concepts’
Wilkins (2009)
In the recent book by Wilkins, the number of species 'concepts' has increased to 26.
Problem Two: Species -Take Your Pick! Species ‘concepts’ rather than definition 1.
Agamospecies
12.
Hennigian
2.
Biological
13.
Internodal
3.
Cohesion
14.
Morphological
4.
Cladistic
15.
Non-dimensional
5.
Composite
16.
Phenetic
6.
Ecological
17.
Phylogenetic
7.
Evolutionary Significant Unit
18.
Polythetic
8.
Evolutionary
19.
Recognition
9.
Genealogical Concordance
20.
Reproductive Competition
10. Genetic
21.
Successional
11. Genotypic Cluster Definition
22.
Taxonomic
1997
During much of the 20th century, Enst Mayr's 'biological species concept' has been popular among biologists. But more recently, especially with the development of cladistics, there has been the view that the 'evolutionary species concept' is more appropriate.
Evolutionary Species !
‘... a lineage (an ancestral-descendant sequence of populations) evolving separately from others and with its own unitary evolutionary role and tendencies.’ (Simpson 1961: 153)
!
‘... a single lineage of ancestor-descendant populations which maintains its identity from other such lineages and which has its own evolutionary tendencies and historical fate.’ (Wiley 1978)
!
‘... an entity composed of organisms which maintains its identity from other such entities through time and over space, and which has its own independent evolutionary fate and historical tendencies.’ (Wiley & Mayden 1997)
The evolutionary species concept promotes the view that species are things or individuals, and organisms are the parts that make up species.
Species as Individuals “...there are reasons to favor what has become known as the species-asindividuals thesis.” Richards (2010: 14)
Can, or should, species be treated as individuals, entities, or things?
As the view that species are individuals, things, or entities that exist in time and space has become a prominent point of view, we need to look more closely at the criteria used to consider species as individuals, which will help us to see why this point of view is incorrect.
Can, or should, species be treated as individuals, entities, or things? Individuals versus Classes: Some Criteria
• Individuals can be experienced, but classes cannot.
• Individuals can change, whereas classes do not.
• Individuals are involved in events, which is not possible for classes.
• Classes are composed of individuals, and represent concepts regarding those individuals. Thus, classes are mental constructs.
Here are some of the criteria commonly used to claim that species are individuals, and not classes: *** We can experience the existence of individuals, but we cannot experience a class. We can only experience members of a class, not the class itself. *** Individuals can change through time, but classes do not change. Individuals are involved in events or phenomena, but this cannot occur with classes. *** Classes are simply composed of individuals and represent some concept related to those individuals. In other words, classes are concepts that only exist in the human mind. But, let's ask this question: Have you ever seen a species? If species are things or individuals, then obviously they must have emergent characters or properties that allow us to perceive them. Have you ever observed a species by way of its characters or properties? The answer has to be 'no.' We need to stop thinking about species as objects. We need to shift our thinking so that it actually reflects our actions as scientists, in relation to our observations of organisms.
Species a-us
Species b-us
present
‘Individuals change over time and can only be described [as opposed to defined]’ (Mayden 1997: 388).
Contrary to what is claimed, species cannot change through time.
past
This is not ‘change in a lineage.’ There are only differences between organisms.
Let's first address the popular myth that species or lineages 'change through time.' If species are in fact individuals then they should be able to change or evolve. It is rather easy to show that that is not the case. In the example shown here, we observe two groups of organisms in the present. Let's say we know two different species hypotheses apply to these organisms because we know the exact histories, shown here, that occurred in the past to result in the observed individuals. Among these past events we can summarize the transformation series of body colors as shown here. The question is, however, can we say that species a-us and species b-us have exhibited changes over time with regard to body color? In other words, do we see a 'change' or 'evolution' from one color to another? No, not at all. What we observe here is not 'change,' since change is a phenomenon that is only possible with an individual. Instead, all we observe are differences in color between individual organisms. While the diagram suggests that there were mutations, reproductive events, and maybe natural selection in the past, these are all events that occurred with regard to individual organisms, not to a lineage or species. Each of the branches we see here are not individuals in themselves. What we are calling branches or lineages in this diagram are simply summaries of a series of past events involving individual organisms. A species, or lineage, cannot change through time, and they cannot change through time for the very fact that they are not individuals.
a-us
b-us
present
Are these really individuals? Or, simply representations of past causal events?
A-us
So when we see a diagram like this, and formal names are applied, in the form of two species and one genus, we should ask are these individuals? Or, are we simply illustrating our hypotheses (i.e. two specific and one phylogenetic) of possible past events that help give us causal understanding of the characters we observe among individual organisms in the present? As we will see in this course, formal names are not referring to classes or individuals. Rather, they refer to our explanatory hypotheses.
Individuals versus Classes: Neither! • Why do systematists refer to species in relation to organisms? • What is the inferential basis for species? • How does the concept of ‘species’ differ from the concept of any ‘subsepecific’ or ‘supraspecific taxon?’ • The real issue is not to ask, “What is the best species concept?”, but rather to ask, “What is the most appropriate definition for the term species?”
An important consequence is that the ‘individual / class’ distinction is not entirely accurate. The real distinction that needs to be considered is between ‘individual’ and ‘explanatory hypothesis.’
The claim in this course, that all taxa are explanatory hypotheses, and not individuals, things, entities, or classes, will be justified by answering the questions shown here. By answering these questions we will readily see that species, indeed all taxa, are not individuals or things that exist in time and space. Rather, they are our explanatory hypotheses that we develop to give us understanding of what we observe, which are organisms, or past traces of organisms, in the form of fossils.
Q1: Why do some individuals have a white spot in contrast to a completely blue body? Q2: Why do some individuals have antennae in contrast to a smooth dorsum?
The inferential basis for species will be outlined in this example. We observe individuals with unexpected or surprising characters. These new observations can be represented by the two why-questions shown here.
Abductive Inference of Species Hypotheses Q1 Species Theory: If character x(1) originates by mechanisms a, b, cJn, among gonochoristic or cross-fertilizing hermaphroditic individuals of a reproductively isolated population with character x(0), and x(1) subsequently becomes fixed throughout the population during tokogeny by mechanisms d, e, f n, then individuals observed in the present will exhibit character x(1). Observations (effects): Individuals have a white spot in contrast to a completely blue body as seen among individuals to which other species hypotheses refer (a-us, b-us, etc.).
Causal Conditions (specific hypothesis x-us) : The white spot condition originated by unspecified mechanisms within a reproductively isolated population with completely blue bodies and eventually became fixed throughout the population during tokogeny by additional unspecified mechanisms.
With regard to why-question Q1, the answer is abductively inferred by applying a 'species theory' to what are observed among individuals with the white spot condition. What is important to recognize here is that the 'theory' refers to at least three theories: mutation, tokogeny, and natural selection. The conclusion, outlining causal conditions accounting for the presence of white spots, is the hypothesis we have formally called 'species x-us.'
Abductive Inference of Species Hypotheses Q2 Species Theory: If character x(1) originates by mechanisms a, b, cJn, among gonochoristic or cross-fertilizing hermaphroditic individuals of a reproductively isolated population with character x(0), and x(1) subsequently becomes fixed throughout the population during tokogeny by mechanisms d, e, f n, then individuals observed in the present will exhibit character x(1). Observations (effects): Individuals have a dorsal margin with antennae in contrast to a smooth dorsal margin as seen among individuals to which other species hypotheses refer (a-us, b-us, etc.).
Causal Conditions (specific hypothesis y-us) : The antennate dorsal margin condition originated by unspecified mechanisms within a reproductively isolated population with smooth dorsal margins and eventually became fixed throughout the population during tokogeny by additional unspecified mechanisms.
With regard to why-question Q2, the same inferential form used for Q1 is applied to explain the presence of antennae.
Abductive Inference of Species Hypotheses
present
Species hypothesis (x-us)
Causal Conditions (specific hypothesis x-us) : The white spot condition originated by unspecified mechanisms within a reproductively isolated population with completely blue bodies and eventually became fixed throughout the population during tokogeny by additional unspecified mechanisms.
Species hypothesis (y-us)
Causal Conditions (specific hypothesis y-us) : The antennate dorsal margin condition originated by unspecified mechanisms within a reproductively isolated population with smooth dorsal margins and eventually became fixed throughout the population during tokogeny by additional unspecified mechanisms.
The two species hypotheses can be illustrated in the form shown here. Notice that this diagram would traditionally be referred to as two 'lineages.' But, all we are doing is providing a summary of past events that explain our present observations. Once again, it is important to stress that what we here call a species, is nothing more than a particular class of explanatory hypothesis among those classes of hypotheses we refer to as taxa.
A (preliminary) Formal Definition of ‘SPECIES’ An explanatory account of the occurrences of the same character or characters among gonochoristic or crossfertilizing hermaphroditic individuals by way of character origin and subsequent fixation during tokogeny. Important consequences: We do not ‘indentify,’ ‘describe,’ or ‘discover’ species. We discover and describe individual organisms. We present formal names to some of our hypotheses (taxa), and those names should be defined in terms of our hypotheses. Species hypotheses do not apply to strictly asexual or self-fertilizing hermaphroditic organisms.
Based on the examples just presented, here is a formal definition of species. The definition is, however, preliminary. This is the case because the definition only considers gonochoristic and cross-fertilizing hermaphroditic organisms. As we will see later, we also need to consider hypotheses regarding organisms with other modes of tokogeny. Given the definition presented here, a species is simply one class of explanatory hypothesis, that uses a set of theories that differs from what are used among the other types of hypotheses we refer to in biological systematics. In the case of species hypotheses, we speak of character origin and subsequent fixation through evolutionary processes during tokogeny. The theories applied to infer phylogenetic hypotheses, on the other hand, not only include those of character origin and fixation, but also population splitting (which will be presented later). From this definition, there are several important practical consequences. One is that we do not 'identify' or 'describe' species. Rather, we describe individual organisms by way of their properties or characters, and we associate a species hypothesis with those individuals. We present formal names to some of our hypotheses, and those names are then defined in terms of those hypotheses. Another very interesting consequence is that species hypotheses cannot be applied to strictly asexual organisms, or organisms that are strictly self-fertilizing hermaphroditic. In these latter cases, character origin/fixation shows a pattern that is somewhat similar to what is seen for phylogenetic hypotheses. Later we will identify these different hypotheses traditionally entailed by the one term, species.
In saying that species are relations, I mean that when biologists correctly delimit species and when the rest of us correctly use species words... we are all in effect referring neither to entities abstract or concrete nor to their members or parts; instead we are referring to the individual organisms and the relations between them that together constitute their reality as species.
Stamos (2003: 25)
The view that species are abductively inferred hypotheses is similar to the view developed by philosopher of science, David Stamos, in his book, 'The Species Problem.' Stamos claims that species refer to causal relations. As he points out, that as relations, species are not classes or individuals, but rather, we are speaking of the past causal events that give us the organisms we observe. Where the development of my ideas differ from those of Stamos is that I have attempted to investigate to a much greater depth the nature of the reasoning we use as systematists to infer all of the types of hypotheses we call taxa, not just species. Just as important is the fact that all taxa, or more correctly hypotheses, are inferred by use of the same type of reasoning process: abduction.
Definitions of SPECIES1–5 Species1 hypothesis: character origin, with subsequent fixation via tokogeny by sexual reproductive events. Species2 hypothesis: simultaneous character origin/fixation via tokogeny by sexual reproductive events, i.e. hybridization, polyploidy. Species3 hypothesis: simultaneous character origin/fixation, with subsequent tokogeny by asexual, apomictic/ parthenogenetic, or self-fertilizing hermaphroditic reproductive events. Species4 hypothesis: character origin, with subsequent fixation via tokogeny by alternations of sexual and asexual reproductive events. Species5 hypothesis: immediate character origin/fixation via horizontal genetic exchange.
Up to this point, we have acknowledged that... (1) all taxa refer to explanatory hypotheses, as answers to why-questions; (2) these hypotheses are inferred by way of abductive reasoning; and, (3) there are a variety of classes of hypotheses/taxa, depending on the combination of theories that are applied to observed properties of organisms. Clearly, based on what we saw earlier in the example of inferring a species hypothesis, the one term 'species' cannot accommodate the different connotations to which the term species have been applied. In addition to the theory used to infer the hypothesis shown earlier, we can recognize at least four additional theories that have been used in conjunction with species, shown here. Ideally, these five classes of hypotheses should be distinguished as separate taxa beyond the one word of 'species.' After we examine the inferential structure leading to phylogenetic hypotheses, we will see that specific hypotheses 3 and 5 cannot be used in conjunction with phylogenetic hypotheses.
The Fundamental Misunderstanding of DNA Barcoding
“[DNA barcoding] provides a way to identify the species to which a plant, animal or fungus belongs.”
Let's return to the topic of DNA barcoding. Since we do not 'identify' or 'describe' species by way of the characters of organisms, but instead, we apply species hypotheses to our observations of organisms, DNA barcoding is not an acceptable approach in biological systematics. We can look a simple example to see why this is the case.
body:
green (as opposed to brown)
dorsum:
antennae (as opposed to smooth)
ventrum:
legs (as opposed to smooth)
DNA sequence:
CCAGAGGCCCAA (as opposed to C-AAAGGCGCAT)
In this example, we observe these new specimens, with characters we have never seen before compared to the characters we have previously observed of this group. The new specimens have green bodies, as opposed to brown. The dorsum has antennae, as opposed to being smooth. The ventrum has legs, as opposed to being smooth. And, we have some DNA sequence data that shows unique differences, shown here in red, compared to what have been previously observed.
a-us
body:
green (as opposed to brown)
dorsum:
antennae (as opposed to smooth)
ventrum:
legs (as opposed to smooth)
DNA sequence:
CCAGAGGCCCAA (as opposed to C-AAAGGCGCAT)
Definition of a-us: A species hypothesis, accounting for the presence of (1) body is green, (2) dorsum with antennae, (3) ventrum with legs, and (4) unique nucleotides for positions 151, 153, 158, and 161, among observed individuals, as consequences of past mutations, tokogenetic events, and selection / drift among past members of the population.
Based on these observations, we decide to explain the new characters with a new species hypothesis, illustrated here, showing origins and fixation of characters during past tokogeny. The formal definition of species a-us would be written out as shown here, which reflects what is shown in the diagram. The name a-us refers to an explanatory hypothesis for the new characters we have observed among these individuals. We can ask this question: Would DNA barcoding be a proper way to apply the hypothesis we call a-us to the individuals we observe? The answer would be 'no.' Since what we call species a-us is a hypothesis, and not a thing, a sequence of DNA cannot represent all of the observations to which that hypothesis serves as an explanation. There are other characters to which the hypothesis also refers, and these must be taken into consideration.
The Fundamental Misunderstanding of DNA Barcoding
a-us Species only defined by sequence data, ignoring all other relevant observations.
DNA sequence:
CCAGAGGCCCAA (as opposed to
C-AAAGGCGCAT )
Here is a simple example to illustrate the problem. We previously defined species a-us as a hypothesis that explains the occurrences of three morphological characters and particular nucleotides. But, what if we only rely on the sequence data, as is claimed is all that is necessary for DNA barcoding of species? Let's say that with future collecting, one finds more specimens that have the same nucleotide sequence.
The Fundamental Misunderstanding of DNA Barcoding
a-us Species only defined by sequence data, ignoring all other relevant observations. Additional specimens observed, with the same ‘barcode.’
DNA sequence:
CCAGAGGCCCAA (as opposed to
C-AAAGGCGCAT )
But, if we actually examine the other characters to which hypothesis a-us applies, we notice that some of these characters are different.
The Fundamental Misunderstanding of DNA Barcoding
a-us - revised
Species only defined by sequence data, ignoring all other relevant observations.
b-us
Additional specimens observed, with the same ‘barcode.’ Sequence data are now explained phylogenetically, not by species hypotheses. DNA sequence:
CCAGAGGCCCAA (as opposed to
C-AAAGGCGCAT )
In fact, we would have to infer a completely new species hypothesis to account for these new observations. And as a consequence, we also would have to completely revise the hypothesis we call a-us. The sequence data would no longer be part of the species hypothesis, but instead would be explained by a new phylogenetic hypothesis. So clearly DNA barcoding is not a proper scientific procedure for applying species hypotheses to the organisms we observe. Since what we call species are hypotheses, and not things, a sequence of DNA alone cannot represent that hypothesis if there are other characters that the hypothesis also refers to. It is when we stop thinking of species as objects we are trying to find in nature, and instead recognize that species are just one type of hypothesis we apply to organisms, we see that DNA barcoding is a technique with very serious problems.
Inferences of Taxa
Phylogenetic Hypotheses
Continuing with the earlier example, let's look at the form abductive inference takes to produce phylogenetic hypotheses.
Q1: Why do some of these individuals have a white spot in contrast to completely black? Q2: Why do some of these individuals have antennae in contrast to a smooth dorsum?
Q3: Why do individuals to which species hypotheses x-us and y-us refer have ventral appendages? Recall that the two previous why-questions were answered by way of abductive inferences to respective species hypotheses. Question Q3, however, addresses the occurrence of ventral appendages among individuals to which species hypotheses xus and y-us refer. Note that this question is still contrastive, in that we are asking why some individuals have ventral appendages in contrast to a smooth ventrum.
The Relation Between Why-Questions and Phylogenetic Hypotheses The most fundamental basis for the inference of phylogenetic hypotheses is the application of a causal theory which is appropriate to the why-questions being asked.
All phylogenetic-level questions (as opposed to ontogenetic, tokogenetic, specific, etc.) have the form, “Why do individuals to which species hypotheses x-us and y-us refer have character x(1), in contrast to members of other species with character x(0)?”. The only appropriate theory, relative to such a question, is one which accounts for shared similarities by way of a common cause. This requirement has distinct implications for most “phylogenetic” methods.
Since biological systematics is about seeking causal understanding by way of the abductive inferences of explanatory hypotheses, we have to be aware of the relations between the forms of why-questions we ask and the hypotheses that serve as answers to those questions. An important component to these relations is knowing what causal theories are appropriate for answering questions. With regard to questions that are to be answered by way of phylogenetic hypotheses, we must clearly understand the form of the questions we ask. Plus, because we are asking questions about our observations of shared characters, the only rational approach is to use theories that provide us with common causes, such that the integrity of our observation statements is maintained as much as possible.
present new observations
Q3: Why do individuals to which species hypotheses x-us and y-us refer have ventral appendages? Phylogenetic Theory: If character x(0) exists among individuals of a reproductively isolated, gonochoristic or cross-fertilizing hermaphroditic population and character x(1) originates by mechanisms a, b, cJ n, and becomes fixed within the population by mechanisms d, e, fJ n (=ancestral species hypothesis), followed by event(s) g, h, iJ n, wherein the population is divided into two or more reproductively isolated populations, then individuals to which descendant species hypotheses refer would exhibit x(1).
To answer question Q3 requires use of a 'descent with modification' theory that will explain the presence of shared characters by way of a common cause. The phylogenetic theory shown here consists of three theories: (1) mutation, (2) fixation, and (3) population splitting. It is important to notice that the phylogenetic theory is very vague - it says nothing specific about the causal mechanisms that might have occurred. We will see later that this vague quality has significant implications.
Abductive Inference of Phylogenetic Hypotheses Phylogenetic Theory: If character x(0) exists among individuals of a reproductively isolated, gonochoristic or cross-fertilizing hermaphroditic population and character x(1) originates by mechanisms a, b, cJ n, and becomes fixed within the population by mechanisms d, e, fJ n (=ancestral species hypothesis), followed by event(s) g, h, iJ n, wherein the population is divided into two or more reproductively isolated populations, then individuals to which descendant species hypotheses refer would exhibit x(1). Observations (effects): Individuals to which specific hypotheses x-us and y-us refer have ventrolateral margins with appendages in contrast to smooth as seen among individuals to which other species hypotheses (a-us, b-us, etc.) refer.
Causal Conditions (phylogenetic hypothesis X-us): Ventrolateral margin appendages originated by some unspecified mechanism(s) within a reproductively isolated population with smooth ventrolateral margins, and the appendage condition became fixed in the population by some unspecified mechanism(s) (= ancestral species hypothesis), followed by an unspecified event(s) that resulted in two or more reproductively isolated populations.
Based on question Q3, we would apply the phylogenetic theory to the observed effects in need of explanation, and abductively infer the hypothesized set of past causal conditions shown here. Notice that because the theory applied is vague, the hypothesis too is lacking in detail.
x-us
y-us
present
Causal Conditions (phylogenetic hypothesis X-us): Ventrolateral margin appendages originated by some unspecified mechanism(s) within a reproductively isolated population with smooth ventrolateral margins, and the appendage condition became fixed in the population by some unspecified mechanism(s) (= ancestral species hypothesis), followed by an unspecified event(s) that resulted in two or more reproductively isolated populations.
X-us
The written form of the hypothesis, formally named X-us, can be illustrated as shown here. You might notice that the two species hypotheses, x-us and y-us, are also shown, even though they were separately inferred from previous abductive inferences.
x-us
y-us
present X-us x-us
y-us
A-us
This detailed illustration of the written form of the hypothesis is what we typically represent in the much more simplified form known as a 'cladogram.' Notice that a cladogram can do no more than imply the already vague causal conditions provided by the written hypothesis. As we will see, this is a problem because systematists commonly do not understand all of the causal aspects implied by cladograms.
Definitions of SPECIES1–5
*Species hypothesis: 1
*Species hypothesis: 2
character origin, with subsequent fixation via tokogeny by sexual reproductive events. simultaneous character origin/fixation via tokogeny by sexual reproductive events, i.e. hybridization, polyploidy.
Species3 hypothesis: simultaneous character origin/fixation, with subsequent tokogeny by asexual, apomictic/ parthenogenetic, or self-fertilizing hermaphroditic reproductive events.
*Species hypothesis: 4
character origin, with subsequent fixation via tokogeny by alternations of sexual and asexual reproductive events.
Species5 hypothesis: immediate character origin/fixation via horizontal genetic exchange.
* Phylogenetic hypotheses can only be applied to individuals to which these hypotheses are applied. Recall in the example just shown for inference of a phylogenetic hypothesis, as a cladogram, that the species hypotheses would have been separately inferred. We also found earlier that the one term 'species' refers to at least five classes of hypotheses, each with distinctly different causal conditions. There is the added implication that phylogenetic hypotheses are not applicable to all organisms to which these species hypotheses apply. In fact, only species1, species2, and species4 hypotheses can be used in conjunction with phylogenetic hypotheses. Since population spitting events are a necessary part of phylogenetic hypotheses for causally accounting for shared characters, such splitting events are simply not applicable to species3- and species5-type hypotheses.
A-us
X-us
a-us b-us x-us y-us z-us
A cladogram. What does it imply? Converting the diagram into words.
Let's look at an example that further illustrates the relations between cladograms and the explanatory hypotheses they imply. Such relations must exist if we are to claim that biological systematics is a field of science, and it is the case that systematics has the goal of acquiring causal understanding of the occurrences of characters among organisms.
As will be discussed in a later lecture on character coding, a data matrix is more than just a summary of one's observations of characters among organisms. It also summarizes our why-questions associated with those observations. Indeed, it is a necessity that our why-questions be present in a data matrix if we are to claim that cladograms serve in some capacity as explanations. Thus, when we see the standard cladogram with 'character state changes on branches,' these are actually vaguely implying the series of explanatory hypotheses that are answers for the separate why-questions implied by a data matrix. In the following slides, we can identify each of the explanatory hypotheses that are implied by this cladogram.
a-us Formally named specific hypothesis:
6(1)
Definition of a-us: A specific hypothesis, accounting for the presence of character 6(1) among observed individuals. Character 6(1) originated in a population of individuals with 6(0) by unspecified mechanisms, subsequent to which 6(1) became fixed in the population by unspecified mechanisms, leading to individuals observed in the present, all with 6(1).
First, let's identify each of the species hypotheses on the cladogram, referred to as aus, b-us, x-us, y-us, and z-us. Once again, keep in mind that species hypotheses are inferred separately from phylogenetic hypotheses. For each species hypothesis indicated on the cladogram, we can present the formal definition of each name. Note, however, that these formal definitions are nothing like what is required by the international codes of nomenclature or the PhyloCode. Problems associated with these nomenclatural issues will be addressed in a later lecture. For now, the important thing is that we recognize the variety of explanatory hypotheses that are represented by the cladogram. Notice that the formal definition here provides an explanation for character 6(1) among individuals. Similar definitions are shown next for remaining species hypotheses.
b-us Formally named specific hypothesis:
7(1)
Definition of b-us: A specific hypothesis, accounting for the presence of character 7(1) among observed individuals. Character 7(1) originated in a population of individuals with 7(0) by unspecified mechanisms, subsequent to which 7(1) became fixed in the population by unspecified mechanisms, leading to individuals observed in the present, all with 7(1).
x-us Formally named specific hypothesis:
8(1)
Definition of x-us: A specific hypothesis, accounting for the presence of character 8(1) among observed individuals. Character 8(1) originated in a population of individuals with 8(0) by unspecified mechanisms, subsequent to which 8(1) became fixed in the population by unspecified mechanisms, leading to individuals observed in the present, all with 8(1).
y-us Formally named specific hypothesis:
10(1)
Definition of y-us: A specific hypothesis, accounting for the presence of character 10(0) among observed individuals. Character 10(0) originated in a population of individuals with 10(1) by unspecified mechanisms, subsequent to which 10(0) became fixed in the population by unspecified mechanisms, leading to individuals observed in the present, all with 10(0). Hypothesis y-us is an ad hoc hypothesis, as a consequence of inferring phylogenetic hypothesis X-us.
Species hypothesis y-us might appear unusual for the fact that it is defined as an ad hoc hypothesis of homoplasy relative to the phylogenetic hypotheses implied by the cladogram. While in the context of phylogenetic hypotheses in the cladogram the definition is an instance of homoplasy, hypothesis y-us still would have been defined prior to the phylogenetic inference.
z-us Formally named specific hypothesis:
2(1)
Definition of z-us: A specific hypothesis, accounting for the presence of character 9(1) among observed individuals. Character 9(1) originated in a population of individuals with 9(0) by unspecified mechanisms, subsequent to which 9(1) became fixed in the population by unspecified mechanisms, leading to individuals observed in the present, all with 9(1). Inclusive of ad hoc hypothesis (required as part of definition of phylogenetic hypothesis X-us): Character 2(0) originated by unspecified mechanisms among a poulation of individuals with 2(1), subsequent to which 2(0) became fixed in the population.
A-us a-us b-us
Formally named phylogenetic hypothesis:
1(1)
Definition of A-us: A phylogenetic hypothesis, accounting for the presence of character 1(1) among observed individuals. Character 1(1) originated in a population of individuals with 1(0) by unspecified mechanisms, subsequent to which 1(1) became fixed in the population by unspecified mechanisms, subsequent to which there was an unspecified population splitting event, leading to individuals observed in the present, all with 1(1), and to which specific hypotheses a-us and b-us also apply.
Next, there are three phylogenetic hypotheses implied by the cladogram. As shown in each definition, character origin and fixation within a reproductively isolated ancestral population is indicated, followed by a population splitting event. Once again, notice how vague these hypotheses are with regard to presenting past causal conditions.
X-us y-us z-us 10(0)* 2(0)*
Formally named phylogenetic hypothesis:
10(1) 4(1) 3(1) 2(1)
Definition of X-us: A phylogenetic hypothesis, accounting for the presence of characters 2(1), 3(1), 4(1), and 10(1) among observed individuals. Characters 2(1), 3(1), 4(1), and 10(1) originated by unspecified mechanisms among a population of individuals with 2(0), 3(0), 4(0), and 10(0), subsequent to which 2(1), 3(1), 4(1), and 10(1) became fixed in the population by unspecified mechanisms, followed by a population splitting event, leading to individuals with 2(1), 3(1), 4(1), and 10(1), and to which specific hypotheses x-us, y-us, and z-us also apply. Required ad hoc hypothesis: Character 2(0) originated by unspecified mechanisms among a poulation of individuals with 2(1), subsequent to which 2(0) became fixed in the population. This hypothesis is a subset to the specific hypothesis, z-us. Required ad hoc hypothesis: Character 10(0) originated by unspecified mechanisms among a poulation of individuals with 10(1), subsequent to which 10(0) became fixed in the population. This hypothesis is referred to as specific hypothesis, y-us.
It is important to notice in this example that the phylogenetic hypothesis accounting for the presence of 2(1) and 10(1) also requires two ad hoc hypotheses (homoplasy). Formally, defining X-us should not only include the causal conditions explaining the occurrences of 2(1), 3(1), 4(1), and 10(1), but also include the required instances of homoplasy.
y-us z-us Unnamed phylogenetic hypothesis: 5(1)
Definition:
A phylogenetic hypothesis, accounting for the presence of character 5(1) among observed individuals. Character 5(1) originated by unspecified mechanisms among a population of individuals with 5(0), subsequent to which 5(1) became fixed in the population by unspecified mechanisms, followed by a population splitting event, leading to individuals with 5(1), and to which specific hypotheses y-us and z-us also apply.
The Philosophy of Biological Systematics Course Outline – Part 2
1.
Systematics involves is abductive inference.
2.
Inferences of systematics hypotheses, i.e. taxa.
3.
Some implications for “phylogenetic” methods.
At this point, we have examined relations between the goals of scientific inquiry and biological systematics, finding that in both instances the acquisition of causal understanding is fundamentally important. We then looked at the nature of the reasoning process, known as abduction, used to go from our why-questions regarding observations, to explanatory hypotheses that provide some degree of initial understanding. The structure of abductive inference was then examined in relation to systematics. Given that most of what is done in biological systematics in terms of methods is related to the inferences of phylogenetic hypotheses, as cladograms, it will be useful to consider some significant implications for these methods in relation to abductive reasoning.
The Limits of Phylogenetic Hypotheses Phylogenetic hypotheses are ‘explanation sketches,’ not complete, formal explanations.
“What the explanatory analyses of historical events offer is, then, in most cases not an explanation..., but something that might be called an explanation sketch. Such a sketch consists of a more or less vague indication of the laws and initial conditions considered as relevant, and it needs ‘filling out’ in order to turn into a full-fledged explanation.” Hempel (1965: 238), Aspects of Scientific Explanation
One fundamental implication that we need to consider is the basic limitation of cladograms as explanatory vehicles. You will recall that earlier we found that the abductive inferences of phylogenetic hypotheses, in the form of cladograms, only allow one to present extremely vague causal accounts of the distributions of observed characters among individuals. The vague nature of such explanations are certainly characterized by what little is conveyed in cladograms. This means that cladograms, as implying a set of phylogenetic hypotheses, are nothing more than what philosopher of science Carl G. Hempel referred to as 'explanation sketches.'
x-us
y-us
present X-us x-us
X-us
y-us
Phylogenetic hypotheses offer very vague explanations of our observations.
Obviously, when we examine either a cladogram (right) or a slightly more detailed causal account (left), we find that nothing is indicated with regard to the specific past events of how a character originated in an ancestral population, how that character subsequently became fixed in that population, or the cause of the later population splitting event.
The Limits of Phylogenetic Hypotheses Phylogenetic hypotheses present very limited causal events.
Phylogenetic hypotheses, as graphically represented by ‘cladograms,’ are explanation sketches consisting of two classes of causal conditions: 1.
character origin and fixation by unspecified causal events among members of an ancestral population/species, and...
2.
subsequent population splitting events by unspecified causal events.
The explanatory depth of cladograms is extremely limited. Cladograms do not provide specific information regarding causal conditions which can serve as complete explanations.
Indeed, it is infrequent that we see hypothesized causal events actually referred to in the context of cladograms. Unfortunately, cladograms are too often only referred to in terms of being branching diagrams, composed of 'terminal branches,' 'nodes,' and 'internal branches' or 'internodes.' None of these terms are appropriate from an explanatory perspective. A 'terminal branch' is actually a previously inferred species hypothesis. A 'node' is a hypothesized population splitting event. An 'internal branch' denotes the events of character origin and fixation. But in all instances, the explanatory depth provided by a cladogram is extremely limited. This is why cladograms are no more than explanation sketches. From a scientific perspective, they actually are not particularly significant, and certainly not worthy of the importance too often given to them by systematists. As we shall see later in the course, such vague explanatory accounts offer no means to effectively engage in hypothesis testing.
present
x-us
y-us h1, 2: origin/fixation X-us
h3b: population splitting
X-us
h3a: origin/fixation
x-us
y-us
Phylogenetic hypotheses, as cladograms, only state two classes of vague causal events: (1) character origin/fixation, and (2) population splitting.
The diagram presented here summarizes what was discussed in the previous two slides, indicating the very vague causal events typically implied by cladograms.
The Explanatory Components of Cladograms
0 a-us
1 x-us
1 y-us Hypothesis accounting for origin/fixation of population-level character(s)
Population splitting hypothesis Hypothesis accounting for origin/fixation of character 1
‘Phylogenetic hypothesis’
To solve the problem of systematics hypotheses being explanation sketches, rather than full explanations that can be empirically tested, we first need to identify what these sketches actually have to offer. Using the cladogram shown here, we can identify three classes of hypotheses. One of these is said to be a species hypothesis, e.g. y-us. The other two classes of hypotheses comprise what would be more generally called a phylogenetic hypothesis. In the example shown here, the phylogenetic hypothesis is summarized by the cladogram, but two hypotheses are indicated - what are commonly known as the 'internode' and 'node.' The species hypotheses would have been inferred separately from the phylogenetic hypothesis. What you should notice for the three hypotheses shown on the cladogram is that all of them are extremely vague. None of them provides full explanatory accounts. As such, there would be no way to proceed with testing any of these hypotheses. It first would be necessary to fill out the causal conditions within each. This is a fundamental condition that is usually ignored in systematics.
‘Phylogenetic trees’
Unfortunately, the lack of emphasis on the explanatory components of cladograms have led to the inappropriate focus on what are called 'phylogenetic trees.'
“Evidence [sic] from morphological, biochemical, and gene sequence data suggests that all organisms on Earth are genetically related, and... can be represented by a vast evolutionary tree, the Tree of Life. The Tree of Life then represents the phylogeny of organisms, i. e., the history of organismal lineages as they change through time.”
And this emphasis on seeking 'the tree of life' has contributed to his misunderstanding of our real goal in biological systematics.
‘Phylogenetic trees’ ~ Fallacy of reification ~ “Constructing the Tree of Life (ToL), a diagrammatic depiction of the evolutionary relationships among all extinct and extant taxa, is one of biology’s most important tasks.” Novick et al. (2012: 757) BioScience
The result has been what is called the fallacy of reification. Phylogenetic trees are treated as if they are the objects we seek, when in fact they are supposed to simply represent components of only some of our explanatory hypotheses.
‘Phylogenetic trees’ ~ Fallacy of reification ~ • tree topology comparisons (violation of requirement of total evidence)
• statistical consistency (ignoring nature of abductive inference)
Some of the unfortunate, and quite significant, consequences of this reification has been the incorrect view that (1) phylogenetic trees can be compared with one another simply as a matter of comparing 'tree topologies; (2) that 'branch lengths' are of some importance, when in fact they are not; and (3) that statistical consistency is important when it comes to comaring tree topologies. As we will see when we examine the 'requirement of total evidence,' tree topologies cannot be meaningfully compared. And this has consequences for the incorrect view that statistical consistency matters. We will address this misconception when we look at 'maximum likelihood' as a method of inferring phylogenetic hypotheses. Related to likelihood, we will see that 'branch lengths' are misinterpretations of the causal components implied by cladograms. In all, these are problems directly related to the reification of cladograms as abstract things that have lost contact with our real goal in systematics: to causally understand our observations of the properties of organisms.
‘Phylogenetic trees’ ~ Fallacy of reification ~
“Hypothesis of the protostome tree of life, placing Arthropoda within the ecdysozoan phyla. This tree is a summary of diverse sources, with emphasis on groups recognized in phylogenomic analyses.” Giribet, G. & G.D. Edgecombe. 2012. Reevaluating the arthropod tree of life. Annual Review of Entomology 57: 167186.
Not only the common practice of tree/cladogram comparisons is mistaken, but also diagrams like that shown here. Such 'summaries' are diagrams that are empirically meaningless. There are no explanatory components to be found because the requirement of total evidence is violated. As a field of science, biological systematics should not tolerate such illustrations for the fact that the illustrations show no relation to our goal of acquiring causal understanding.
Phylogenetic Inference is Not Deductive Causes cannot be deduced from effects
1.
The inference from effects to cause(s) in phylogenetics is ampliative. The non-ampliative nature of deduction only provides for inferences from cause to effect(s).
2.
Multiple conclusions are possible in phylogenetic inference – it is impossible to have multiple conclusions in deduction.
3.
The requirement of total evidence must be specifically considered, which is not necessary in deduction.
Thus far in this course we have seen that the inference from observed effects to an hypothesis offering an explanation of those effects is not a matter of deductive inference. It is instead, abductive. You will, however, sometimes encounter biological systematics publications in which authors claim phylogenetic inference is deductive. The rules of deductive reasoning would not allow this. The three main reasons are shown in this slide.
Evidence and Inference For any inference, the evidence for a conclusion will be the premises.
evidence
1o Premise...
1o Premise... 2o Premise... Conclusion
or
2o Premise... Conclusion
Another common misunderstanding lies in use of the term 'evidence.' Recall from our examination of the different classes of reasoning, that for any inference, the premises serve as evidence for their respective conclusions. Regardless of the class of reasoning being deductive or non-deductive (abductive or inductive), the relation between evidence and conclusion remains the same. It is the relation between premises and allow for a particular conclusion or set of conclusions. Systematists often speak of evidence. They speak of 'evidence supporting' particular cladograms or taxa. But as we will see, especially when we examine the nature of hypothesis testing, systematists are routinely confused when it comes to correctly referring to 'evidence' in the proper context.
Relations Between the Types of ‘Evidence’ in Biological Systematics Evidence 1: the basis for initially suggesting a hypothesis . Since a hypothesis is abductively inferred, the evidence consists of character data and the causal theory. The relation of evidence 1 to the hypothesis is that of premises to conclusion. Evidence 2: the basis for judging a hypothesis to be true . This is the evidence obtained during the actual test of the hypothesis. The relation of evidence 2 to the hypothesis is that of premises to conclusion. The evidence suggesting a hypothesis is not the same as the evidence used to test the hypothesis.
We can broadly identify notions of evidence as follows: (1) The evidence that initially suggests a hypothesis, and (2) the evidence for judging a hypothesis to be true. The evidence in (1) is that used in abduction from observed effects to hypothesized past causal events. The evidence in (2) is that used in induction, thus consists of observations or outcomes of actual test conditions. Considerations of (1) and (2) in biological systematics are too often confused - it is common to see claims that character data, i.e. evidence in (1), can serve as evidence used to test phylogenetic hypotheses, (2). As we will see later when we examine the testing of phylogenetic hypotheses, evidence in the form of shared characters, i.e. (1), cannot serve as test evidence, i.e. (2). To claim character data can be used to both infer hypotheses explaining those data as well as serve as test evidence for those hypotheses would be circular. More technically, any given phylogenetic hypothesis cannot be used to deduce the occurrences of novel characters. Thus, what becomes important to recognize is that while shared characters are evidence used to abductively infer phylogenetic hypotheses, as explanatory accounts for the occurrences of those characters, new character data cannot be used as premises to serve as test evidence for those hypotheses.
Example: Relations Between Phylogenetic Inference, Deduction, and Induction Abduction Causal theory: character origin/fixation, with subsequent population splitting events.
observations
I.
why-questions
Observations (effects): individuals to which species hypotheses b-us and c-us refer have character x(1) in contrast to x(0) as seen among individuals to which other species hypotheses refer.
a-us b-us c-us 0 1 1
Explanatory hypothesis: character x(1) origin/fixation, followed by a population splitting event.
a-us b-us c-us 0 1 1
abduction
The next five slides will summarize the relations between evidence and conclusions. What is important to notice is that while character data are used as evidence to abductively infer phylogenetic hypotheses, such data cannot play any part in the subsequent evaluation or testing of those hypotheses. The relations between inferring hypotheses and their being tested will be further examined later when we address the mechanics of hypothesis testing.
Example: Relations Between Phylogenetic Inference, Deduction, and Induction Explanation sketch (deductive) Causal theory: character origin/fixation, with subsequent population splitting events. Explanatory hypothesis: character x(1) origin/fixation, followed by a population splitting event.
a-us b-us c-us 0 1 1
II. Observations (effects): individuals to which species hypotheses b-us and c-us refer have character x(1) in contrast to x(0) as seen among individuals to which other species hypotheses refer.
a-us b-us c-us 0 1 1
Subsequent to our abductive inferences, we can characterize phylogenetic hypotheses (and the same applies to most biological systematics hypotheses) as 'explanation sketches.' Characterized here in the classic deductive-nomological form, we see that the explanatory hypothesis, plus relevant theories, serve to provide us with at least a vague explanation of the observed effects of shared characters.
Example: Relations Between Phylogenetic Inference, Deduction, and Induction Formal explanation (deductive) Causal theory: character origin/fixation by mechanisms a, b, c, ... n, with subsequent population splitting events caused by x, y, z, ... n.
III.
Explanatory hypothesis: detailed descriptions of all causal conditions related to character origin/fixation in ancestral population, and detailed descriptions of events leading to splitting of that population.
Observations (effects): individuals to which species hypotheses b-us and c-us refer have character x(1) in contrast to x(0) as seen among individuals to which other species hypotheses refer.
a-us b-us c-us 0 1 1
a-us b-us c-us 0 1 1
If one wishes to move beyond the overly simplistic 'explanation sketches' that are cladograms, they would have to fill out the causal conditions stated in the explanatory hypothesis. Converting cladograms to full explanatory accounts is very rarely performed, but would be necessary to proceed to testing.
Example: Relations Between Phylogenetic Inference, Deduction, and Induction Deduction of test consequences Causal theory: character origin/fixation by mechanisms a, b, c, ... n, with subsequent population splitting events caused by x, y, z, ... n. Explanatory hypothesis: detailed descriptions of all causal conditions related to character origin/fixation in ancestral population, and detailed descriptions of events leading to splitting of that population.
IV.
Observations (effects): individuals to which species hypotheses b-us and c- us refer have character x(1) in contrast to x(0) as seen among individuals to which other species hypotheses refer.
a-us b-us c-us 0 1 1
Test predictions: effects, related as closely as possible to the hypothesized causal conditions – – effect m – effect n – effect o
The reason it is stressed that cladograms are inadequate as explanatory vehicles is the fact that the only way to actually move forward with considering the formal testing of any explanatory hypothesis is that we must present a detailed causal account. Without these details being provided, there is no opportunity to deduce from the hypothesis the potential test evidence or consequences needed to evaluate the hypothesis. What is shown here is the deduction of potential test evidence. This evidence would consist of effects that are direct consequences of the causal conditions stated in the hypothesis. Such effects should preferably have the lowest probability of occurrence if the hypothesized events did not occur.
Example: Relations Between Phylogenetic Inference, Deduction, and Induction Induction: performing hypothesis test Causal theory: character origin/fixation by mechanisms a, b, c, ...n, with subsequent population splitting events caused by x, y, z, ...n. Explanatory hypothesis: detailed descriptions of all causal conditions related to character origin/fixation in ancestral population, and detailed descriptions of events leading to splitting of that population. Observations (effects): individuals to which species hypotheses b-us and c- us refer have character x(1) in contrast to x(0) as seen among individuals to which other species hypotheses refer.
V.
a-us b-us c-us 0 1 1
Test predictions: effects, related as closely as possible to the hypothesized causal conditions – – effect m – effect n – effect o Actual test conditions: the detailed actions taken to attempt to observe predicted effects m, n, and o. Test outcomes:
– effect m is observed – effect n is observed – effect o is observed
ˆ HYPOTHESIS IS CONFIRMED
The act of actually engaging in hypothesis testing is not deductive, contrary to what is too often presented in the biological systematics (especially 'cladistic') literature. Notice that the premises in this example comprise the test. In order to perform the test, we must acknowledge our applications of relevant theories, the hypothesis being tested, as well as the original effects from which the hypothesis was abductively inferred. We also acknowledge the potential test evidence inferred by deduction. The test conditions that are carried out in accordance with attempting to find the potential test evidence are also part of the premises. And the premises include the actual test results. Notice in this example the test outcomes match what was predicted. From these results (premises) we can conclude that the hypothesis is confirmed. In other words, the test results provide positive support for the hypothesis. The conclusion that the hypothesis has received support is derived from an inductive processs. While the test results might give us a sense that the probability of the hypothesis has been increased, this is no guarantee that the hypothesis is certain.
Systematics and Abduction Some Implications for Phylogenetic Inference Once we acknowledge the formal structure of the why-questions we ask in systematics, and the abductive form of inference to hypotheses, there are distinct implications for the following issues:
1.
‘Parsimony’ vs ‘maximum likelihood’ methods.
2.
‘Bayesian’ inference.
There have been three issues stressed thus far in this course: (1) the goal of science, as well as biological systematics, is the acquisition of causal understanding; (2) the process of seeking that understanding starts with acknowledging our why-questions in relation to our observations of the features of organisms; and (3) the inferential process used to provide at least intitial answers to why-questions is known as abduction. If these three issues form the foundation for all of biological systematics, then there are distinct implications for the subfield known as phylogenetic systematics. The three common methods used to infer cladograms, 'parsimony,' 'maximum likelihood,' and 'Bayesianism,' are typically not examined in the context of the issues mentioned above. This has led to the consequence that systematists have not been sufficiently critical of the methods they use, or when they are critical, the logic of the arguments are usually unsound.
Why-Questions and Abductive Reasoning Why-questions abductive inference
hypothesis(es)
plausibility
An issue surrounding the subject of abductive inference is the plausibility of hypotheses.
Why-Questions and Abductive Reasoning Why-questions abductive inference
hypothesis(es)
parsimony
plausibility
likelihood
Such plausibility is initially determined on the basis of the premises used in the inference, while the more in-depth assessment of plausibility relies on the actions of testing. Regarding initial plausibility, two criteria have been suggested as important: parsimony (or simplicity) and likelihood. It is these two criteria that we need to examine in relation to the inferences of phylogenetic hypotheses.
Parsimony vs Likelihood What is Parsimony?
Simplicity Syntactic (‘elegance’)
Ontological (‘parsimony’)
# of hypotheses
# of entities/causes/processes postulated (it is rational to prefer theories/hypotheses with fewer ontological commitments)
With regard to the use of methods referred to as 'parsimony' and 'maximum likelihood,' we first have to understand what these terms mean, and the relations they have to abductive inference. To answer the question of what is parsimony, it's useful to recognize the more general term, simplicity. The concept of simplicity can be divided into what are referred to as syntactic and ontological forms. The ontological form is also known as parsimony. Parsimony is then the act of minimizing the number of entities, causes, or postulated processes. It is the view that it is more rational to prefer theories and hypotheses that require fewer ontological commitments.
Parsimony vs Likelihood What is Parsimony?
Simplicity “Scientists often appeal to a criterion of simplicity as a consideration that helps them decide which hypotheses are most plausible.” E. Sober (2001: 433), Simplicity (in: A Companion to the Philosphy of Science)
Ontological (‘parsimony’)
# of entities/causes/processes postulated (it is rational to prefer theories/hypotheses with fewer ontological commitments)
There are several different ways in which parsimony has been characterized. Sober (2001) suggests that simplicity/parsimony allows for choosing hypotheses that are most plausible. But, there are several different conceptions regarding how to determine plausibility in relation to simplicity/parsimony.
Parsimony vs Likelihood What is Parsimony?
Simplicity Ontological (‘parsimony’)
# of auxiliary hypotheses – a simpler theory is one with fewer auxiliary hypotheses (sensu Thagard 1988)
For instance, Thagard (1988: "Computational Philosophy of Science") suggests that one should choose theories or hypotheses that rely on the fewest number of auxiliary hypotheses.
Parsimony vs Likelihood What is Parsimony? Parsimony / simplicity: “...simplicity is a function of the size and nature of the [auxiliary hypotheses] needed by a theory T to explain facts F.” P. Thagard (1988: 83), Computational Philosophy of Science The fewer the number of auxiliary hypotheses required by a theory to explain the facts in question, the simpler it is. Auxiliary hypothesis – a statement, not part of the original theory, which is assumed in order to help explain certain aspects of effects.
Parsimony vs Likelihood What is Parsimony?
Simplicity Ontological (‘parsimony’)
testability – a simpler theory is more testable (sensu Popper 1959)
Karl Popper (1959: "The Logic of Scientific Discovery") suggested that parsimony should refer to the testability of theories and hypotheses.
Parsimony vs Likelihood What is Parsimony? Parsimony / simplicity: “Simple statements... are to be prized more highly than less simple ones because they tell us more; because their empirical content is greater; and because they are better testable.” K. Popper (1959: 142), The Logic of Scientific Discovery
Parsimony vs Likelihood What is Parsimony?
Simplicity Ontological (‘parsimony’)
informativeness – a simpler theory is more informative (sensu Sober 1975)
Sober (1975: "Simplicity") offered the view that simplicity/parsimony should be determined according to the informativeness of a theory or hypothesis.
Parsimony vs Likelihood What is Parsimony? Parsimony / simplicity: “...the simplicity of a hypothesis can be measured by... how well it answers certain kinds of questions. [T]he more informative a hypothesis is in answering these questions, the simpler it is.” E. Sober (1975: vii), Simplicity Hypothesis H is more informative than HN with respect to question Q if H requires less extra information than HN to answer Q.
Parsimony vs Likelihood What is Parsimony? Parsimony / simplicity: “To justify simplicity is to show why it should be taken into account in judging how plausible a theory is.” E. Sober (2001: 18), What is the problem of simplicity? Common criteria for plausibility: Popperian –
one theory/hypothesis is better corroborated than another.
Likelihoodist –
one theory/hypothesis has more evidential support than another, L(e | h).
Bayesian –
one theory/hypothesis is more probable than another.
Akaike framework – one theory/hypothesis has more predictive accuracy than another.
In his overview of simplicity/parsimony, Sober (2001) states that there are four common criteria for determining the plausibility of theories and hypotheses in terms of simplicity/parsimony: (1) Popperian, (2) Bayesian, (3) Likelihoodist, (4) and the Akaike framework. What is important to notice is that the Popperian, Bayesian, and Akaike criteria apply to theories or hypotheses subsequent to testing. The concern in biological systematics, however, is the relation of parsimony to abductive inference, not testing. As we will see later, the likelihoodist criterion can be considered important, but this must be in the context of both the auxiliary hypotheses used (sensu Thagard 1988) and informativeness (sensu Sober 1975).
Parsimony vs Likelihood What is Parsimony? ‚ Abductive inference is the reasoning process to provide answers (as explanatory hypotheses) to why-questions. ‚ The simplest/most parsimonious answers are those that require the fewest causes, because they are most informative for the questions asked (sensu Sober 1975), as well as rely on fewer auxiliary hypotheses ( sensu Thagard 1988), and thus result in hypotheses with greatest likelihood. ‚ In other words, the integrity of our observation statements, in the form of why-questions, should be maintained as fully as possible in the hypotheses that serve as answers to those questions.
We can now look at the relation between parsimony and the abductive inferences of hypotheses.
Parsimony vs Likelihood What is Parsimony? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• auxiliary hypothesis, hx
• auxiliary hypotheses, hx, hy, hz
• theory, T1
• theory, T2
• shared similarities, e
• shared similarities, e
• phylogenetic hypothesis, h1
• phylogenetic hypothesis, h2
Consider this example of two abductive inferences, both attempting to answer the same set of why-questions. Notice that the principle differences between the two inferences are the number of auxiliary hypotheses, types of theories used, and hypotheses inferred.
Parsimony vs Likelihood What is Parsimony? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• auxiliary hypothesis, hx
• auxiliary hypotheses, hx, hy, hz
• theory, T1
• theory, T2
• shared similarities, e
• shared similarities, e
• phylogenetic hypothesis, h1
• phylogenetic hypothesis, h2
Parsimony is the relation between a question(s) and answer(s). Hypothesis h1 is more informative than h2 with respect to question Q if h1 requires less extra information than h2 to answer Q.
For the question of which hypothesis is most parsimonious, we would take into consideration the relations between why-questions and the answers offered, as well as the respective number of auxiliary hypotheses used.
“Why are there marks in the sand?”
Let's look at a simple example of how parsimony is used in our process of abductively inferring explanatory hypotheses. You encounter these depressions in the sand, leading to the why-question shown here.
“Why are there marks in the sand?”
H1
H2
As answers to this question, you might consider two alternative hypotheses. One hypothesis explains the patterns as being footprints due to a person walking on the beach. The other hypothesis says that Bigfoot walked on the beach.
S(H1 | Q) > S(H2 | Q) H1 is more informative than H2; i.e. H1 requires less extraneous information beyond the observation to answer the question.
“Why are there marks in the sand?”
H1
H2
Obviously, we would say that hypothesis H1 is the more parsimonious (or simpler) answer to the why-question in contrast to H2. In other words, H1 is more informative than H2 because the former requires us to invoke fewer auxiliary hypotheses or extra information. Another way to say this is that H1 is more consistent with our background knowledge, given that we have no useful evidence to rationally consider Bigfoot as a possible causal factor. What is important to notice in this example is that parsimony or simplicity refers to the relation between the why-question and the answer to that question.
Parsimony vs Likelihood What is Parsimony? ‚ Notice that parsimony is not a criterion applied within the abductive inference of a hypothesis. Rather, it is the premises used in the inference that determines what hypotheses can be inferred. [But there is an exception in the case of computer algorithms, as we will see later.] ‚ The criterion of parsimony only applies to choices among hypotheses, as determined by criteria that determine hypothesis plausibility.
Parsimony vs Likelihood What is Parsimony? Why-question Q, leads to...
Abductive inference X:
Abductive inference Y:
• ‘common ancestry’
• ‘common ancestry’ + rate of character evolution
•abcd 0011 0111
•abcd 0011 0111
• phylogenetic hypothesis,
• phylogenetic hypothesis,
a b c d ‘2 steps’
a d c b ‘3 steps’
Let's now look at an example referring to phylogenetic inference. In the two abductive inferences, the premises differ in that one uses strict 'common ancestry,' while the other uses a combination of 'common ancestry' plus consideration of evolutionary rates of character change.
Parsimony vs Likelihood What is Parsimony? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• ‘common ancestry’
• ‘common ancestry’ + rate of character evolution Parsimony: ‘Two-step’ hypothesis is most informative at answering the why-question.
•abcd 0011 0111 • phylogenetic hypothesis,
•abcd 0011 0111 • phylogenetic hypothesis,
a d c b
a b c d ‘2 steps’
‘3 steps’
Which hypothesis is most parsimonious?
In asking which hypothesis is most parsimonious, we have to consider the informativeness of each of the hypotheses relative to the why-questions that were asked. Clearly, the hypothesis requiring two steps provides an explanation that best maintains the integrity of the observations presented in the why-question.
Parsimony vs Likelihood What is Parsimony? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• auxiliary hypothesis,
• auxiliary hypotheses,
(1) all observation statements are true
(2) morphology observation statements are true; (3) DNA sequence observations are not necessarily true
• ‘common ancestry’
• ‘common ancestry’ + rate of character evolution
•abcd 0011 0111
•abcd 0011 0111
• phylogenetic hypothesis,
• phylogenetic hypothesis,
a b c d ‘2 steps’
a d c b ‘3 steps’
We can also consider the auxiliary hypotheses, or background knowledge, required by each inference. Notice that the strict 'common ancestry' theory alone carries with it the auxiliary hypothesis that our observation statements are true. This should seem rational given that the goal of the inference is to answer the why-question regarding our observations, and there is the presupposition that our observations of shared characters are true. The other inference, however, must include two auxiliary hypotheses due to the fact that 'common ancestry' is used in conjunction with consideration of rates of character change. The auxiliary hypotheses are interesting because while one assumes our observations of some characters are true, we must include the second auxiliary hypothesis in order to apply the theory of rates of character evolution. You might notice that to introduce these auxiliaries, as well as the theory of rate change, is at odds with our observation statements as well as the why-question.
Parsimony vs Likelihood What is Parsimony? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• auxiliary hypothesis,
• auxiliary hypotheses,
(1) all observation statements are true
• ‘common ancestry’ •abcd 0011 0111
(2) morphology observation statements are true; (3) DNA sequence observations are not necessarily true
Auxiliary hypothesis (3) is added to only deal with sequence data, whereas • ‘common ancestry’ + rate (1) addresses all data. Note also that (3) is of character evolution inconsistent with both observations and why•abcd questions.
0011 0111
• phylogenetic hypothesis,
a b c d ‘2 steps’
• phylogenetic hypothesis, The likelihood of a(b(c d)) is higher than a(d(c b)).
a d c b ‘3 steps’
We can see in this example that asking which hypothesis is most parsimonious entails considering the following issues: (a) Informativeness of the hypotheses relative to the why-question(s). Clearly the two-step hypothesis is the more informative; (b) The three-step hypothesis was inferred using two as opposed to one auxiliary hypothesis, where auxiliary hypothesis (3) is especially inconsistent with observation statements and why-questions; (c) We can give consideration to the likelihood of each hypothesis, which is actually related to conditions (a) and (b). The likelihood of hypothesis a(b(c d)) [two-step hypothesis] is higher for the fact that the hypothesis makes the observations in need of explanation more probable (from an abductive standpoint).
Parsimony vs Likelihood ‘Maximum Parsimony’ and Algorithms The inferences of phylogenetic hypotheses by ‘maximum parsimony’ computer algorithms do apply parsimony since the algorithms consider all (or as many as possible) cladograms during the process of finding the ‘shortest trees.’ This means that these computer algorithms have an inferential form more like: • D is a collection of character data. • Hypothesis H1 has x steps (= H1 explains D). • Hypothesis H2 has x+n steps (= H2 does not explain D as simply). • Therefore, H1 is preferable.
Note that it was mentioned earlier that parsimony is not a criterion applied *within* an abductive inference. While this generally is the case, the situation is somewhat different with regard to the implementation of abduction by computer algorithms, where there is a process of searching through 'tree space' using the criterion of minimizing the number of 'evolutionary steps' required to account for the distributions of characters. Recall that an abductive inference usually consists of a theory or set of theories that is/are applied to character data. In the case of computer algorithms, the form of abduction is closer to what is shown here, in which case parsimony is in fact applied within the inference.
Parsimony vs Likelihood ‘Maximum Parsimony’ and Algorithms Why-question Q, leads to... Abductive inference X: • ‘common ancestry’ •abcd 0011 0111
We can, however, apply the criteria of informativeness, number of auxiliary hypotheses, and likelihood to the manner in which computer algorithms apply the criterion of parsimony. Consider this example, in standard abductive form.
Parsimony vs Likelihood ‘Maximum Parsimony’ and Algorithms Why-question Q, leads to... Abductive inference X: • ‘common ancestry’ •abcd 0011 0111
a b c d
a b c d a c b d a d b c
2 ‘steps’ 3 ‘steps’
Which hypothesis is most parsimonious?
A computer algorithm will consider the variety of 'tree topologies' with respect to tree 'length.' In an analogous manner, algorithms consider parsimony in the selection process.
Parsimony vs Likelihood ‘Maximum Parsimony’ and Algorithms Why-question Q, leads to... Abductive inference X: • ‘common ancestry’ Parsimony: Two-step hypothesis is most informative at answering the whyquestion, and has the highest likelihood.
•abcd 0011 0111 • phylogenetic hypothesis,
a b c d
a b c d a c b d a d b c
2 ‘steps’ 3 ‘steps’
Which hypothesis is most informative?
Informativeness is the principle criterion in the selection process, especially given that the goal of searching for trees of minimal length is most consistent with the observations in the data matrix. And, as will be shown later with regard to the coding of characters, a data matrix does imply our why-questions. As well, in terms of likelihood, the selection of trees of minimal length will also be those that make our observations most probable.
Parsimony vs Likelihood What is likelihood? The likelihood L of a hypothesis h, given observation e is: L(h1 | e) o L(h2 | e).
The likelihood of hx is the degree to which e supports (abductively, in the present case) hx over hy. Hypothesis hx makes the occurrence of e more probable than hy: P(e | hx) o P(e | hy).
We now need to examine the nature of likelihood as it relates to abductive inference. The standard characterization of likelihood (L) for a hypothesis (h), given evidence (e), is shown here. Recall, however, that evidence (e) can be conceived in two fundamentally different ways. Similarly, to speak of 'support' for a hypothesis by way of evidence can have two very different meanings. The lack of making this distinction is one of the biggest misconceptions in systematics when it comes to speaking of methods, as well as the process of testing. The support for an abductively inferred hypothesis by evidence will be (in part) the characters explained by that hypothesis, i.e. the premises. Remember that such evidence is NOT the same as the evidence one would seek to actually test that hypothesis. Historically, the reference to evidence (e) in the concept of likelihood has been in regard to test evidence, not abductive evidence. As we will see in this section, this has important consequences for the method called 'maximum likelihood' in biological systematics, especially when one attempts to compare that method with what is called 'maximum parsimony.'
Parsimony vs Likelihood What is likelihood? The likelihood L of a hypothesis h, given observation e is: L(h1 | e) o L(h2 | e).
The likelihood of hx is the degree to which e supports (abductively, in the present case) hx over hy. Hypothesis hx makes the occurrence of e more probable than hy: P(e | hx) o P(e | hy). “‘Support’ is used to express the informal idea that some of our beliefs give us evidence for others.”
Sober (1975: 33), Simplicity
“In an argument, the evidence is given in the statements: the premises.”
Salmon (1984: 9), Logic
As we saw earlier, for any inference, it is the premises that provide the evidential support for a conclusion. Thus, one has to know the type of inference they are referring to when speaking of support: abductive support or inductive (testing) support.
Parsimony vs Likelihood What is Likelihood? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• theory, T1
• theory, T2
• shared similarities, e
• shared similarities, e
• phylogenetic hypothesis, h1
• phylogenetic hypothesis, h2
Likelihood is the relation between evidence (premises) and answer(s)
L(h1 | e) = P(e | hx)
Since likelihood refers both to the support for a particular hypothesis, as well as the extent to which a hypothesis makes evidence most probable, likelihood in an abductive context is just the relation between the premises and hypothesis that serves as answer(s) to a why-question(s).
“Why are there marks in the sand?”
L(H1 | e)
L(H2 | e)
We can use the previous example to illustrate likelihood in relation to abductive inference. Based on the observation of the patterns in the beach sand, you have the alternate inferences of causes due to humans or a Bigfoot. We can recognize the likelihood of each hypothesis.
L(H1 | e) = L(H2 | e)
“Why are there marks in the sand?”
L(H1 | e)
L(H2 | e)
Considering just the relations between the evidence (foot prints) and the respective hypotheses, both hypotheses make the presence of the foot prints most probable; both hypotheses are equally supported. The likelihoods are the same.
L(H1 | e, b) > L(H2 | e, b)
“Why are there marks in the sand?”
L(H1 | e)
L(H2 | e)
But we know that we cannot just consider the relation between the foot prints and the alternate hypotheses. We also need to take into consideration our background knowledge. We know there is no legitimate theory of, or evidence for Bigfoots, whereas our experience with humans is well established. It is the inclusion of our background knowledge that enables us to show that hypothesis H1 has higher likelihood over H2.
Parsimony vs Likelihood What is Likelihood? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• auxiliary hypothesis, hx
• auxiliary hypotheses, hx, hy, hz
• theory, T1
• theory, T2
• shared similarities, e
likelihood
• phylogenetic hypothesis, h1
• shared similarities, e • phylogenetic hypothesis, h2
Likelihood is the relation between evidence (premises) and answer(s)
L(h1 | e) = P(e | hx)
Implicitely, our background knowledge comprises part of the premises of the abductive inferences.
‘Maximum likelihood’ in Phylogenetic Inference (A) data matrix of observations
The following five slides illustrate the method of 'maximum likelihood' as applied in the inference of phylogenetic hypotheses.
‘Maximum likelihood’ in Phylogenetic Inference (A) data matrix of observations (B-C) map ‘character states’ on rooted tree
‘Maximum likelihood’ in Phylogenetic Inference (A) data matrix of observations (B-C) map ‘character states’ on rooted tree
(D) likelihood values for each ‘character state’ optimization on tree
‘Maximum likelihood’ in Phylogenetic Inference (A) data matrix of observations (B-C) map ‘character states’ on rooted tree
(D) likelihood values for each ‘character state’ optimization on tree
(E) sum of likelihoods for all ‘characters’
‘Maximum likelihood’ in Phylogenetic Inference (A) data matrix of observations (B-C) map ‘character states’ on rooted tree
(D) likelihood values for each ‘character state’ optimization on tree
(E) sum of likelihoods for all ‘characters’ (F) sum of log of likelihoods for all ‘characers’
Parsimony vs Likelihood The relation between parsimony and likelihood
We can now examine the relation between parsimony and maximum likelihood in the context of abductive inference in biological systematics.
Parsimony vs Likelihood The relation between parsimony and likelihood Why-question Q, leads to... Abductive inference X: • strict common ancestry
likelihood [= L(h | e)]
•abcd 0011 0111 • phylogenetic hypothesis,
a b c d ‘2 steps’
First, recall that likelihood is nothing more than the phenomenon of applying a theory as completely as possible to a set of effects.
Parsimony vs Likelihood The relation between parsimony and likelihood Why-question Q, leads to... Abductive inference X: • strict common ancestry
likelihood [= L(h | e)]
parsimony
•abcd 0011 0111 • phylogenetic hypothesis,
a b c d ‘2 steps’ Hypothesis has maximum likelihood, and is most parsimonious.
Parsimony, on the other hand, refers to the relation between why-questions and the hypothesis that serves as an answer. What should be apparent in this example is that parsimony and likelihood are different concepts. In this example, the inference leads to a hypothesis of maximum likelihood, as well as being most parsimonious.
Parsimony vs Likelihood The relation between parsimony and likelihood Why-question Q, leads to... Abductive inference X: • common ancestry + rate of character evolution
likelihood [= L(h | e)]
•abcd 0011 0111 • phylogenetic hypothesis,
a c b d ‘3 steps’
Consider a different example, where two theories are used: common ancestry plus rates of character evolution. Once again, the hypothesis must be of maximum likelihood for the fact that the theories are applied to effects.
Parsimony vs Likelihood The relation between parsimony and likelihood Why-question Q, leads to... Abductive inference X: • common ancestry + rate of character evolution
likelihood [= L(h | e)]
•abcd 0011 0111
not-parsimonious
• phylogenetic hypothesis,
a c b d ‘3 steps’ Hypothesis has maximum likelihood, but is not parsimonious.
But, with regard to parsimony, we see that the conclusion is not most parsimonious relative to our why-questions. One could just rely on the theory of strict common ancestry, and infer a hypothesis that is more parsimonious. And again, keep in mind that the likelihood obtained is automatic, given the premises. No matter what premises one uses, an abductive inference will produce a hypothesis of maximum likelihood. From the perspective of scientific inquiry, parsimony is the more critical issue since we should place a higher value on hypotheses that best answer our why-questions with the most plausible hypotheses. And, in the case of abductive inference, the most plausible hypotheses will be those that best explain our observations while maintaining the integrity of those observations.
Parsimony vs Likelihood The relation between parsimony and likelihood Why-question Q, leads to...
Abductive inference X:
Abductive inference Y:
• theory, T1
• theory, T2
• shared similarities, e
• shared similarities, e
• phylogenetic hypothesis, h1
• phylogenetic hypothesis, h2
a b c d ‘2 steps’
a c b d ‘3 steps’
If parsimony and likelihood conflict, how does one choose?
We can summarize the relation between parsimony and likelihood when it comes to abductive inference. Consider the two inferences shown here. The premises differ in the theory each uses. If it is the case that parsimony and likelihood are not necessarily consistent with each other, as we saw in the previous example, on what basis should one choose between these conflicting hypotheses?
Parsimony vs Likelihood The relation between parsimony and likelihood Why-question Q, leads to...
• shared similarities, e • phylogenetic hypothesis, h2
‚ Recall that in any abductive inference, the likelihood of the conclusion(s) is trivially maximum.
It makes no sense to attempt to compare the likelihoods of the two hypotheses, since both inferences must, by default, produce hypotheses with respective maximum likelihoods.
Parsimony vs Likelihood The relation between parsimony and likelihood Why-question Q, leads to...
• shared similarities, e • phylogenetic hypothesis, h2
‚ Recall that in any abductive inference, the likelihood of the conclusion(s) is trivially maximum. ˆ Likelihood must be considered within the context of parsimony. The two concepts cannot be weighed against one another.
Where comparison becomes critical is with regard to parsimony. Parsimony is a criterion that does not reside *within* an inference, but instead is determined in relation to our why-questions. The consequence is that parsimony and likelihood are not conditions that can be compared to one another, contrary to what is so commonly claimed in the systematics literature.
Parsimony vs Likelihood Why-question Q, leads to... Abductive inference X:
parsimony
Abductive inference Y:
• auxiliary hypothesis, hx
• auxiliary hypotheses, hx, hy, hz
• theory, T1
• theory, T2
• shared similarities, e • phylogenetic hypothesis, h1
likelihood
• shared similarities, e • phylogenetic hypothesis, h2
Why-questions determine the roles of parsimony and likelihood in abductive inference.
Considering the question of which hypothesis is most parsimonious, we would want to take into consideration the relations between why-questions and the answers offered, as well as the respective auxiliary hypotheses used.
Parsimony vs Likelihood
parsimony
likelihood
Incorrect relationship between parsimony and likelihood.
‚ Recall that in any abductive inference, the likelihood of the conclusion(s) is trivially maximum. ˆ Likelihood must be considered within the context of parsimony. The two concepts cannot be weighed against one another.
Within biological systematics, the relationship between parsimony and likelihood has been seen as one in which parsimony and likelihood are to be compared to one another. But as we have seen, in the context of abductive inference, such a relationship is incorrect.
Parsimony vs Likelihood
parsimony likelihood
Correct relationship between parsimony and likelihood.
‚ Choosing between methods such as ‘maximum parsimony’ and ‘maximum likelihood’ requires careful consideration of the auxiliary hypotheses and theories used in each.
The correct relationship between parsimony and likelihood is where parsimony entails likelihood. The consequence is that we cannot compare methods called 'maximum parsimony' and 'maximum likelihood' on the basis of likelihood. The comparison must be made in terms of parsimony, and that requires that we examine the auxiliary hypotheses and theories used with each approach, as well as the ability of the abductively-inferred hypotheses to serve as answers to our why-questions.
Parsimony vs Likelihood wh
y - quest i o ns
parsimony likelihood
Correct relationship between parsimony and likelihood.
But... it is the nature of our why-questions that dictate phylogenetic inference. And why-questions in conjunction with parsimony (not likelihood) determine hypothesis plausibility. But ultimately, our why-questions will need to be considered in relation to parsimony.
Where does this leave us? Why-question Q, leads to... Abductive inference X:
Abductive inference Y:
• auxiliary hypothesis, hx
• auxiliary hypotheses, hx, hy, hz
• theory, T1
• theory, T2
• shared similarities, e • phylogenetic hypothesis, h1
likelihood
• shared similarities, e • phylogenetic hypothesis, h2
1.
Why-questions seek common-cause explanations of fact(s) and foil(s).
2.
Per (1), abductive inferences require common cause theories.
3.
Per (1) & (2), a phylogenetic hypothesis is most parsimonious relative to why-questions.
4.
Per (1) & (2), likelihood is proximately determined by why-questions, distally by premises.
5.
CONCLUSION: The constraint on phylogenetic inference, and thus methods, comes from why-questions, not parsimony or likelihood.
We can summarize the relations between our why-questions with parsimony and likelhood as follows...
Why-Questions and Abductive Reasoning Why-questions abductive inference
parsimony
likelihood
hypothesis(es)
plausibility
As noted in the previous slide, the plausibility of our hypotheses is primarily determined by our why-questions, and secondarily by the relations of those questions to hypotheses in terms of parsimony.
‘Maximum Likelihood’ Problems with likelihood methods in phylogenetic inference
“The main idea behind phylogeny inference with maximum-likelihood is to determine the tree topology, branch lengths, and parameters of the evolutionary model (e.g. transition/transversion ratio, base frequencies, rate variation among sites)... that maximize the probability of observing the sequences at hand.” Schmidt & von Haeseler (2010: 183), Phylogenetic inference using maximum likelihood methods.
Based on what we have now covered with regard to abductive inference, we can identify several problems with the 'maximum likelihood' method.
‘Maximum Likelihood’ Problems with likelihood methods in phylogenetic inference
1: c-us
a-us: 0
b-us: 0
‘parsimony’ tree
1: d-us
Let's look the standard argument that has been used to defend likelihood as preferable to parsimony. We have the phylogenetic hypothesis shown here, inferred using strict 'common ancestry.' [nb: It is incorrect to refer to this as a 'parsimony' tree. While the hypothesis is most parsimonious, that is only because of the theory applied to observations in the abductive inference. The hypothesis is also of maximum likelihood. As we have already seen, the relevant issue is not parsimony versus likelihood, but rather the theories one chooses, in conjunction with background knowledge, in relation to why-questions.]
‘Maximum Likelihood’ Problems with likelihood methods in phylogenetic inference
a-us: 0
1: c-us
‘parsimony’ tree
b-us: 0
1: d-us
c-us: 1 1: d-us ‘long branch’ attraction
a-us: 0
‘true’ tree
0: b-us
The argument is that 'parsimony' can lead to an 'incorrect' answer. The reason being that we have not taken into consideration the phenomenon known as long branch attraction.
‘Maximum Likelihood’ Problems with likelihood methods in phylogenetic inference
a-us: 0
b-us: 0 The method of ‘maximum likelihood’ inference is claimed to be better than ‘parsimony’ because it...
1: c-us
‘parsimony’ tree
1: d-us
c-us: 1 1: d-us
• considers rates of evolutionary change ‘along branches;’
‘long branch’ attraction
a-us: 0
‘true’ tree
0: b-us
Thus, we are told that 'maximum likelihood' is more effective at inferring 'correct' hypotheses for the fact that (1) the method takes into consideration rates of character evolution, and (2) the method has the property of 'statistical consistency.'
‘Maximum Likelihood’ Problems with likelihood methods in phylogenetic inference
“The main idea behind phylogeny inference with maximum-likelihood is to determine the tree topology, branch lengths , and parameters of the evolutionary model (e.g. transition/transversion ratio, base frequencies, rate variation among sites)... that maximize the probability of observing the sequences at hand.” Schmidt & von Haeseler (2010: 183), Phylogenetic inference using maximum likelihood methods.
Let's first address the related issues of branch length and evolutionary rates.
‘Maximum Likelihood’ Problems with likelihood methods in phylogenetic inference
Branch length:
“...the number of substitutions along each branch of the tree...” Schmidt & von Haeseler (2010: 185), Phylogenetic inference using maximum likelihood methods.
An issue noted earlier, the fallacy of reification, is exemplified by the idea that cladogram branches can be assigned lengths. A notion of branch length works if cladograms have some tangible quality as objects in time and space, where their component parts consist of 'branches,' 'nodes,' and 'leaves.' But this is not the case. As we have already seen, cladograms are nothing more than graphic devices that imply at least three classes of causal events by way of (1) species hypotheses, and (2) phylogenetic hypotheses involving the events of (a) character origin/fixation and (b) subsequent population splittings. The concept of branch length not only ignores the totality of these hypotheses, it incorrectly assigns properties to 'branches' that are irrelevant to our goal of scientific inquiry. The separate hypotheses of character origin/fixation that are implied by, and therefore comprise branches, cannot be meaningfully summarized in terms of 'length.'
‘Maximum Likelihood’ Problems with likelihood methods in phylogenetic inference Rate variation violates the common cause requirement of whyquestions for explaining facts and foil in terms of phylogenetic hypotheses. “Why do members of a-us and b-us have A at position 546 in contrast to T, C, or G?”