Election and effect

In population genetics , one speaks of the choice and effect when the heterozygosity of a population is reduced by structuring it into subpopulations. In particular, when two or more subpopulations have different allele frequencies , the overall heterozygosity is reduced even when the subpopulations are in Hardy-Weinberg equilibrium . The reasons why a population is split up into several subpopulations can, for example, be geographical barriers that prevent the exchange of genetic material. Then when genetic drift sets in, the choice and effect arises.

The Wahlund effect was first recognized in 1928 by the Swedish geneticist Sten Wahlund .

A simple example

If a population with the allele frequencies A and a (given by and respectively ) is split into two equally large subpopulations and , and all A alleles in the subpopulation , all a alleles are in the subpopulation , which can easily arise with genetic drift there are no longer any heterozygotes, even if the subpopulations are still in the Hardy-Weinberg equilibrium. ${\displaystyle P}$ ${\displaystyle p}$ ${\displaystyle q}$ ${\displaystyle p+q=1}$ ${\displaystyle P_{1}}$ ${\displaystyle P_{2}}$ ${\displaystyle P_{1}}$ ${\displaystyle P_{2}}$

Example with two alleles and two subpopulations

To top example opposite to generalize, let us and the allelic frequencies of A in and represent. (and as well as represent a ). ${\displaystyle p_{1}}$ ${\displaystyle p_{2}}$ ${\displaystyle P_{1}}$ ${\displaystyle P_{2}}$ ${\displaystyle q_{1}}$ ${\displaystyle q_{2}}$

The allele frequencies in each population are now expressed different, mathematically . ${\displaystyle p_{1}\neq p_{2}}$

If one now imagines that every population is in an internal Hardy-Weinberg equilibrium, this means that the genotypes AA , Aa and aa are p ² , 2 pq , and q ² for each population.

Then the heterozygosity ( ) in the whole population is given by the mean of the two: ${\displaystyle H}$

${\displaystyle H}$	${\displaystyle ={2p_{1}q_{1}+2p_{2}q_{2} \over 2}}$
	${\displaystyle ={p_{1}q_{1}+p_{2}q_{2}}}$
	${\displaystyle ={p_{1}(1-p_{1})+p_{2}(1-p_{2})}}$

and that is always less than (= ) unless: ${\displaystyle 2p(1-p)}$ ${\displaystyle 2pq}$ ${\displaystyle p_{1}=p_{2}}$

Summary

The choice and effect can be applied to a wide variety of subpopulations of different sizes. The heterozygosity of the entire population is given by the average heterozygosity of the subpopulations, weighted according to the size of the subpopulations.