2: Population genetics

A: p=1 a: q=0 A: p=0 a: q=1 In such a case, there are no heterozygous individuals in the population, although according to HW, there should be. There is a deficit in heterozygous. Is this phenomenon general? Two subpopulations

A: p 1 a: q 1 A: p 2 a: q 2 Subpopulation 2Subpopulation 1 We assume panmixia (random mating) in each subpopulation. Two subpopulations

A: p 1 a: q 1 A: p 2 a: q 2 Subpopulation 2Subpopulation 1 We assume N 1 individuals in population 1, N 2 individuals in population 2. Let N=N 1 +N 2. Let K 1 be the fraction of population 1 out of the entire population: K 1 = N 1 /N. K 2 = 1-K 1. Two subpopulations

A: p 1 a: q 1 A: p 2 a: q 2 Subpopulation 2Subpopulation 1 This is also the HW heterozygosity, which is expected since the subpopulation is in panmixia What is the general heterozygosity in subpopulation 1? Two subpopulations

A: p 1 a: q 1 A: p 2 a: q 2 Subpopulation 2Subpopulation 1 What is the expected heterozygosity, under HW in the entire population? To compute this we first have to compute the frequency of A and a in the entire population. Then: Two subpopulations

The frequency of allele A in the entire population is: Two subpopulations

The expected heterozigosity under HW is often also called H exp Two subpopulations

H exp is the probability to sample a heterozygous if one first mix all the alleles of the entire population. The question is what is the different between this expectation and the actual frequency of heterozygous in a sample from the population. Two subpopulations

H exp is the probability to sample a heterozygous if one first mix all the alleles of the entire population. The question is what is the different between this expectation and the actual frequency of heterozygous in a sample from the population. Two subpopulations

A: p 1 a: q 1 A: p 2 a: q 2 K1-K Probability to sample a heterozygous individual in subpopulation 1 Probability to sample subpopulation 1 Two subpopulations

A: p 1 a: q 1 A: p 2 a: q 2 K1-K We will show that H obs is always smaller than H exp and that this is a general phenomenon for subpopulations. Two subpopulations

Heterozygote deficit F= (H exp -H obs )/H exp Heterozygote deficit (also known as Inbreeding coefficient) F measures the fractional reduction in heterozygosity relative to random mating

Rewriting F

Simplifying terms F is always non negative -> reduction in heterozygosity relative to random mating is a general phenomenon when there is non random mating.

A: p 1 a: q 1 A: p 2 a: q 2 K1-K F>0 we have a heterozygote deficit F=0 when p 1 =p 2 (or K=0). F varies depending on the locus considered Heterozygote deficit

p1p1 PnPn p4p4 p3p3 p2p2 … The above argument for two subpopulations also holds true for more than two subpopulations… Heterozygote deficit

Wahlund effect This reduction is called the Wahlund effect

2: Population genetics

Other mechanisms that can cause a heterozygote deficit in a population Non random mating (no panmixia): 1. Autogamy = autofecondation 2. Positive assortative mating = sexually reproducing organisms that tend to mate with individuals that are like themselves in some respect.

Cleistogamy = the character “closed flowers”, which is directly linked to self-pollination. All the genes in the individual will slowly loose genetic diversity. Autogamy: Cleistogamy flowers

Animals that choose partners with a specific character as they have (e.g., a fly with red eye will prefer to mate with a fly with red eye). Not all the genes will loose genetic diversity to the same extent. The genes responsible for the selected type of segregation will be most homozygous. Positive assortative mating

Excess of heterozygote Negative assortative mating = sexually reproducing organisms tend to mate with individuals that are different from themselves in some respect. Advantage of the rare = individual with rare genotypes will reproduce more.

Negative assortative mating: an example The Sporophytic (the diploid form of plants) Self-Incompatibility (SSI) The female part of a plant

Advantage of the rare In some mating systems a male bearing a rare allele will have a mating advantage. Rare allele advantage will tend to increase the frequency of the rare allele and hence increase heterozygosity. This is also true for the human population.