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The inbreeding coefficient for an individual gives the probability that the individual has two alleles at a locus that are IBD. What interpretation does the inbreeding coefficient have on the population level? Is it the average inbreeding value in the population?

It is possible to derive the genotype frequencies in the population when the population inbreeding coeeficient is given by F. These are given by:

$A_1A_1$: $p_{A_1}F+p_{A_1}^2(1-F)$

$A_1A_2$: $2p_{A_1}p(1-F)$

$A_2A_2$: $p_{A_2}F+p_{A_2}^2(1-F)$

Is seems like F gives the probability that the two alleles in an individual in the population are IBD. Does this mean that F is the average inbreeding coefficient in the population?

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