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2P(IBD)

The first equation is used to determine what to expect for the packaging of alleles into genotypes. The expected value of the probability of identity by descent depends on the size of the population. The flip side of this same coin is that we can determine what to expect for the effective population size based on the probability of identity by descent in a population, as shown in the second equation. In big populations the chances that two alleles are identical by descent is low whereas in small populations the chances of identity by descent are high. When the effective population size is defined by reference to autozygosity or inbreeding, the result is the inbreeding effective population size.

The change in allele frequencies in many replicate populations over generations was the focus of the Markov and diffusion models of genetic drift (section 3.2). The range of change in allele frequency in these models among many populations could also be expressed as a variance. Earlier in the chapter (equation 3.6) the standard error of the mean allele frequency among replicate populations was derived. This leads to the variance in the change in allele frequencies from one generation to the next (Ap = pt-1 - pt) taken among replicate populations:

Variance(Ap) =

pt-Ht-1 2NV

where p and q are allele frequencies at a diallelic locus and the subscripts indicate the generation. As we did above, this equation can be restated by solving for the effective population size:

e 2 x variance(Ap)

In an ideal finite population (under the infinite alleles model), the chances of sampling two copies of the same allele depend on the size of the population and 1

e probability that two alleles are identical by descent (IBD) in a pedigree (see section 2.6). So we have:

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