Problem box answer

Each of the values in the transition matrix is obtained using the binomial formula. The chance that a population at fixation or loss transitions to an allele frequency different than 1 or 0, respectively, is always 0. The chance of transitioning from one to four A alleles is identical to the chance of transitioning from three to no a alleles, since the number of A alleles is four minus the number of a alleles. Using this symmetry permits two columns to be filled out after performing calculations for only one of the columns (see table below). The transition probabilities are a function of the sample size only and so are constant each generation. The total frequency of populations in a given allelic state in the next generation depends on initial frequencies of populations in each state (Pt=0(x)). The expected frequencies of populations in each allelic state therefore changes each generation. This Markov chain model is available as a Microsoft Excel spreadsheet on the textbook website under the link to Problem Box 3.2.

One generation later (t = 1) Initial state: number of A alleles (t = 0)

State

Expected

0 0

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