Allele Frequencies: Staying Constant Chapter 14
What is Allele Frequency? How frequent any allele is in a given population: – Within one race – Within one nation – Within one town/school/research project
• Calculated by genotyping a large sample of the population • Or – estimated by phenotype frequency in entire population (recessive disease only)
Example: PKU allele
Population Genetics Considers all alleles within a given population: • Allele is the version of the gene that a person carries (Allele frequency) • Gene pool = all alleles that are possible within population’s gametes • Genotype frequency = proportion of the population that has each type of genotype • Phenotype frequency = percentage of population that have phenotype
Bi-allelic Gene • In bi-allelic gene there are only two alleles possible – T or t – for tall or short pea plants – R or r – for wrinkled or round seeds
• p = frequency of the more common of the two alleles • q = frequency of the less common of the two alleles
Commonly… • Many genes have more than two alleles • Most common diseases/disorders are multifactorial: – More than one gene – each with more than two alleles – Environment and genetics
• Therefore – phenotype will not equal genotype
Rare cases are still useful… • Even though most genes and most diseases don’t follow these rules we are about to learn • There are still many cases where these rules are important and useful for genetics • Next class we’ll learn some of the complications
Hardy-Weinberg Equilibrium Where the allele frequencies stay constant from one generation to the next • Often calculated with a bi-allelic gene (p and q) Therefore… • p and q remaining constant
Changing Allele Frequencies 1. Mutation – introduces new alleles into population 2. Natural Selection – specific alleles are more likely to be passed down because they are somehow advantageous 3. Non-random Mating – individuals of one genotype are more likely to mate with individuals of same genotype – Think of an example of this happening?
Changing Allele Frequencies 4. Migration – individuals with specific genotypes move in or out of a population 5. Genetic Drift – random changes in allele frequencies – Caused by random sampling of specific genotypes – Often seen in small, isolated populations Can you think of why? – Nothing to do with natural selection
Hardy-Weinberg Equilibrium • Requires that none of these things are happening in a population: – No mutation – No selection – No migration – No genetic drift – Random mating – Large population
• Obviously this is VERY rare in real life
Hardy-Weinberg Equilibrium 1908 • Hardy – an English mathematician • Weinberg – a German physician • Both derived, independently, an algebra calculation for what happens to allele frequencies within a population • Assuming all those false conditions
Hardy-Weinberg Equilibrium 1. If there are only two alleles then the following must be true: p+q=1 The frequency of the two alleles added together must equal the entire population (a frequency of 1)
Hardy-Weinberg Equilibrium 2. The genotype frequencies can also be calculated: p2 + 2pq + q2 = 1 The frequency of each homozygote equals the frequency of the allele squared The frequency of heterozygote is 2 times p times q Product Rule These three genotypes must add to one Product and Addition Rules
Hardy-Weinberg Equilibrium 1. Allele frequencies add to one: p+q=1 2. The genotype frequencies can be calculated from the allele frequencies: p2 + 2pq + q2 = 1
Hardy-Weinberg Equilibrium 1. Allele frequencies add to one: p+q+r=1 2. The genotype frequencies can be calculated from the allele frequencies: p2 + 2pq + 2pr + 2rq + q2 + r2 = 1
How it was derived:
A (p) a (q)
A (p)
a (q)
AA (pp)
Aa (pq)
Aa (pq)
aa (qq)
Frequencies: Allele A =p Allele a =q Genotype AA = p2 Genotype Aa = 2pq Genotype aa = q2
Let’s work through HWE: • Autosomal recessive trait – (middle finger is shorter than 2 and 4) • All we know is this: In 100 individuals there are 9 that show the recessive shorter finger • Use HWE to figure out: Both allele frequencies All three genotype frequencies
Let’s work through HWE: • Know: 9/100 show recessive phenotype • Calculate: p= q= Homozygous Dominant = Heterozygous = Homozygous Recessive = 0.09
Let’s work through HWE: • 9/100 = recessive phenotype • Know this is an autosomal recessive trait Therefore: • Recessive phenotype = qq genotype • q2 = 0.09 Therefore: • q = 0.3 • p must equal 1 - q = 1 - .3 = 0.7
Let’s work through HWE: • p = 0.7 and q = 0.3 • Homozygous Dominant = p2 (.7)(.7) = .49 or 49% • Heterozygous = 2 pq 2(.7)(.3) = .42 or 42% • Homozygous Recessive = q2 (.3)(.3) = .09 or 9% (which is what we based all of these calculations on)
Solved HWE: • Know: 9/100 show recessive phenotype • Calculate: p = .7 q = .3 Homozygous Dominant (p2) = 49% Heterozygous (2pq) = 42% Homozygous Recessive (q2) = 9% • What about in the next generation?
Practical Applications of HWE 1. Genotyping error – If your genotypes are grossly off of the expected from HWE calculations
2. Artificial Selection 3. Population Genetics – Determining genetic risk in different populations
4. Disease risk 5. Forensic Biology
Genotyping Error Are genotypes present in expected proportions with allele frequencies? Allele freq. p(1) = 0.62 q(2) = 0.38
Expected:
Genotype 1/1 1/2 2/2
Observed 123 131 50 304
Expected 116.9 143.2 43.9 304
1/1 = p2 * total # genotypes 1/2 = 2pq * total # genotypes 2/2 = q2 * total # genotypes
HWE Calculations: CHI2: 2.207 df: 1 p-value: 0.137
Artificial Selection This is the human act of purposely selecting certain traits over others: • Changing phenotype frequencies • Agriculture – What examples can you think of?
• Pure breed dogs (other animals) • HWE calculations will tell you: – How many mating pairs to set up – How many generations to get desired result
Population Genetics • Estimate genotype frequency from phenotype frequency • Based on known percentage of population that shows a recessive phenotype • That percent must be homozygous for the recessive allele right? (q2) • What are problems here? – Multifactorial, more than two alleles, etc
Disease Risk Couple wants to know their risk of having a child with a specific disease • If one (or both) parents have phenotype in question – run genetic tests • If neither have phenotype then question is about being a carrier (2pq) • Based on population genetics calculations and therefore their assumptions
Disease Risk Couple wants to know their risk of being carriers for disease (2pq) • Population genetics tells us how frequent phenotype is in population • That’s q2 • Square root – calculate q • Calculate p • Calculate 2 pq – That’s carrier frequency
Carrier Frequencies:
X-linked is different… • Females follow same HWE formula: p2 + 2pq + q2 = 1 • Males however only carry one allele: Therefore • In males phenotype frequency is allele frequency (not genotype) • Therefore frequency of recessive phenotype gives you q, not q2
Forensic Biology Using biology to add to the forensics of a crime scene • Although we all share 99.9 percent of our DNA with every other human • That 0.1 % equals about 3 million base pairs of difference • Product rule means that this can ID more than there are humans on the planet
Forensic Biology Identifying individuals with DNA: 1. Genotype a few polymorphisms (~10) 2. All on different chromosomes 3. All highly polymorphic – More than two alleles – More alleles, more information per polymorphism
4. Match to crime scene – Or body, or baby to father in paternity
Forensic Biology Identifying individuals with DNA: • Match to crime scene – Or body, or baby to father in paternity
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Calculating the chance of seeing the DNA profile is calculated based on Hardy-Weinberg Equilibrium Exact calculations depend on how frequent alleles are in given population How likely genotypes will be
Polymorphisms: • SNPs: – Single Nucleotide Polymorphism – More common, but only have two alleles
• RFLPs: – Restriction Fragment Length Polymorphism – Many alleles
• Microsatellites: – Polymorphic repeats in non-coding sequence – Most alleles possible (avg. around 8)
How is HWE involved? • Determine genotype of individual • Use HWE to calculate probability of seeing specific genotype: – Het. = 2pq = 2(.6)(.4) = 0.36 – Homo = q2 = (.25)(.25) = 0.0625
• Then use product rule to calculate final probability that another person has the same combination of genotypes: – (.36)(.06) = 0.0225 or 2.25% chance
HWE and Product Rule: Genotype Five Bi-allelic Polymorphism
Het = 2pq = 2(.6)(.3)
= .36
Het = 2pq = 2(.5)(.3)
= .30
Het = 2pq = 2(.15)(.8) = .24 Homo = q2 = (.2)(.2)
= .04
Het = 2pq = 2(.80)(.18)= .29
HWE and Product Rule:
= .36
(.36)(.3)(.24)(.04)(.29) = 0.00031
= .30 = .24 = .04 = .29
Or 1/3,226 Therefore, the chance of this matching the wrong person is 1/3,226
Summary • Hardy-Weinberg Equilibrium(HWE) states: p+q=1 p2 + 2pq + q2 = 1 • HWE is unlikely to exist in a real population • But it is still useful for many fields of genetics – know how and when to use it • Know how to calculate it for biallelic genes
Next Class: • Read Chapter Fifteen • Homework – Chapter Fourteen Problems; – Review: 1, 2, 3, 5 – Applied: 1, 2, 6, 7, 11
• Happy Halloween!
