was developed as a measure of the probability that two alleles in a genotype are autozygous or identical by descent in a single finite population. We can extend this equation to include the influence of migration on autozygosity when there are numerous subpopulations that experience limited gene flow each generation. The goal is to develop an expression for the fixation index that accounts for both population size and migration. Finite population size causes autozygosity to increase over time in individual subpopulations. Migration counteracts this trend, bringing in alleles from other subpopulations that are not identical by descent, thereby decreasing the autozygosity. Therefore, in general in subdivided populations, the net autozygosity is the balance of the processes of genetic drift and migration.

When there is gene flow, two modifications need to be made to the probabilities of autozygosity given in the two terms of equation 4.51. The first modification involves the probability of autozygosity or-.

With migration, some proportion m of the alleles in a subpopulation arrived via gene flow from other subpopulations while 1 - m of the alleles are contributed by individuals and gametes that did not leave their subpopulation. Therefore, there is some chance that one or both of a pair of alleles was introduced to a subpopulation by migration. A randomly sampled pair of alleles in a subpopulation with zero, one, or two alleles due to gene flow each generation have probabilities of (1 - m)2, 2m(1 - m),and m2, respectively. Only the (1 - m)2 proportion of genotypes with no alleles introduced by gene flow can contribute to the pool of alleles that may become identical by descent

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