# Chapter 23. (Mendelian) Population. Gene Pool. Genetic Variation. Population Genetics

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1 30 25 Chapter 23 Population Genetics Frequency A B C D F Grade = 57 Avg = 79.5 % (Mendelian) Population A group of interbreeding, sexually reproducing organisms that share a common set of genes Gene Pool For a given gene (or set of genes), the set of alleles present in a population. Genetic Variation Ubiquitous (its everywhere!) Genetic variation is the raw material for evolution What forces shape and limit genetic variation? 1

2 We need a mathematical model! Genotypic Frequencies Single locus, two alleles: f(aa) = f(aa) = umber of AA individuals umber of Aa individuals f(aa) = umber of aa individuals = Population Size Allelic Frequencies Allelic Frequencies f(allele) = umber of copies of Allele umber of copies of all Alleles f(allele) = umber of copies of Allele umber of copies of all Alleles p = f(a) = 2n AA + n Aa 2 p + q = 1 q = f(a) = 2n aa + n Aa 2 q = 1 - p n AA = number of AA individuals Making it More Complicated: Mathematical Expansions M Blood Type Antigens in Humans Multiple alleles at a locus Phenotype Genotype umber X linked loci MM L M L M 182 Multiple loci M L M L 172 L L 44 2

3 Calculate Genotypic and Allelic Frequencies at this locus Genotypic Frequencies: Calculate Genotypic and Allelic Frequencies at this locus Genotypic Frequencies: f(mm) = umber of MM individuals f(mm) = umber of MM individuals 182 = 398 = f(m) = umber of M individuals f(m) = umber of M individuals 172 = = f() = umber of individuals f() = umber of individuals 44 = 398 = Calculate Genotypic and Allelic Frequencies at this locus Allelic Frequencies: Calculate Genotypic and Allelic Frequencies at this locus Allelic Frequencies: f(allele) = umber of copies of Allele umber of copies of all Alleles f(allele) = umber of copies of Allele umber of copies of all Alleles p = f(m) = 2n MM + n M 2 p = f(m) = 2n MM + n M 2 2(182) = = (398) q = f() = 2n + n M 2 q = f() = 2n + n M 2 2(44) = = (398) Hardy Weinberg Law Describes how reproduction and Mendelian principles affect allelic and genotypic frequencies of a population Assumptions Infinitely large population Random mating o selection, mutation, migration 3

4 Predictions Allelic frequencies of the population do not change Hardy Weinberg Equilibrium Genotypes are in the expected proportions of : Genotypic frequencies reach equilibrium after one generation p 2 = f(aa) 2pq = f(aa) q 2 = f(aa) Hardy Weinberg Equilibrium p 2 + 2pq + q 2 = 1 When a population is in HWE, proportions of genotypes are determined by allele frequencies. Implications of the Hardy- Weinberg Law Population cannot evolve if it meets HW assumptions. Genotype frequencies predictable (determined by allelic frequencies). A single generation of random mating results in equilibrium frequencies. Figure

5 Hardy Weinberg Provides a framework for studying population genetics. Estimating Allelic Frequencies We can estimate Allelic frequencies in a population when dominance is present. It is a ULL MODEL that describes what happens in a population that is only subject to the rules of Mendelian inheritance. This is useful for diseases that are recessive traits, such as Cystic Fibrosis. We must assume H-W equilibrium Cystic Fibrosis in Humans Cystic Fibrosis in Humans Frequency of Cystic Fibrosis in orth American Caucasians is 1 in 2000 q 2 = f(aa) = f(aa) = p 2 = = q = 0.02 f(aa) = 2pq = 2(.02)(.98) = p = 1 - q = 0.98 This is the frequency of carriers in the population Assumptions Infinitely large population Random mating o selection, mutation, migration onrandom Mating Positive Assortative Mating Like individuals mate (eg height in humans) egative Assortative Mating Unlike individuals mate Inbreeding Preferential mating between relatives 5

6 Figure 23.4 onrandom mating alters genotypic frequencies, but not allelic frequencies Identical by state Identical by descent Inbreeding Frequency of homozygotes increases. Frequency of heterozygotes decreases. Inbreeding Coefficient Measures the probability that two alleles are identical by descent (IBD). Ranges from 0 (Random mating) to 1 (All alleles IBD) F Inbreeding Depression Increase in frequency of lethal and deleterious traits with inbreeding. 6

7 Figure 23.5 Figure 23.6 Assumptions Infinitely large population Random mating o selection, mutation, migration Mutation All genetic variation ultimately arises through mutation. Mutation rates are low. Effect PER GEERATIO is small Mutation Mutation rate: µ = forward mutation rate ν = reverse mutation rate When mutation is incorporated into the model, the forward and reverse mutation rates determine the equilibrium allele frequencies. 7

8 Assumptions Infinitely large population Random mating o selection, mutation, migration Migration Influx of alleles from other populations Also called gene flow Decreases genetic differences among populations Increases genetic variation within populations Assumptions Infinitely large population Then what good is Hardy Weinberg? There are no IFIITELY LARGE populations. Random mating o selection, mutation, migration Sampling Error Genetic Drift In a finite population, only a sample of alleles are transmitted to the next generation By chance, the frequency of the alleles in the gametes may be different than the parental frequencies The smaller the sample, the larger the potential deviation Sampling error may lead to changes in allelic frequency Direction of change is random Magnitude depends on population size 8

9 Magnitude of Genetic Drift Depends on the population size Magnitude of Genetic Drift Depends on the population size BUT: Only individuals who contribute alleles to the next generation are counted Effective Population Size e The size of an idealized population that would undergo the same magnitude of genetic drift as the population under consideration e < Uneven sex ratio Variance in reproductive success Fluctuations in over time on random mating Effect of Uneven Sex Ratio: e = 4 x n males x n females n males + n females 9

10 Causes of Genetic Drift I Chronicly low population size caused by ecological limitations Limited space, food, etc Example: Desert pupfish Causes of Genetic Drift II Founder Effect: a population is established from a small number of founders Causes of Genetic Drift III Genetic Bottleneck: a population undergoes a drastic reduction in size Effects of Drift Change in allelic frequencies in a population Elephant Seals went through a bottleneck in the late 1880s. As few as 20 existed in Loss of genetic variation within populations Genetic divergence among populations 107 populations, e = 16 Genetic Drift can cause divergence among populations! Figure e = 20 Figure

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