Wahlund+effect

=Wahlund effect=

The **Wahlund effect** is the reduction in the overall heterozygosity of a population as a result of subpopulation structures. Essentially, if two or more subpopulations have independent allele frequencies then the overall heterozygosity is reduced, irrespective of whether those subpopulations are in Hardy-Weinberg equilibrium. The most common cause is a geographical barrier to gene flow between the subpopulations, followed by independent genetic drift in each subpopulation.

The simplest example is where you have a population, P, with the allele frequencies of **A** and **a** given by //p// and //q//, respectively (where //p// + //q// = 1). Suppose this population is split into two subpopulations, P1 and P2, and that all the dominant **A** alleles are in subpopulation P1 and all the recessive **a** alleles are in subpopulation P2 (this is a feasible consequence of genetic drift). This means there are no heterozygotes, even though the subpopulations are in Hardy-Weinberg equilibrium.

To make a slight generalisation of the above example, let //p// 1  and //p// 2  represent the allele frequencies of **A** in P1 and P2 (and likewise let //q// 1  and //q// 2  represent the frequencies of **a**). Suppose the allele frequencies in the two subpopulations P1 and P2 are unequal (i.e. //p// 1 does not equal //p//2  and //q// 1 does not equal //q// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">) and suppose that each subpopulation is in Hardy-Weinberg equilibrium, so that the genotype frequencies in each subpopulation are //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: super;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">, 2//pq// and //q// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: super;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> (where the sum of these is 1). Then the heterozygosity of the overall population is given by the mean of the two:

= (2//p//1//q//1) + (2//p//2//q//2) / 2

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">Which cancels out to give //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">1 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">//q// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">1 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> + //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">//q// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">, or //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">1 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">(1 - //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">1 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">) + //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">(1 - //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">2 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;">), which is always smaller than 2//p//(1 − //p//) ( = 2//pq//) unless //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">1 <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%;"> = //p// <span style="font-family: Arial,Helvetica,sans-serif; font-size: 90%; vertical-align: sub;">2