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Number of A alleles in one population

Number of A alleles in one population

Figure 3.10 Genetic drift modeled by a Markov chain. In this case, the sample size is two diploid genotypes (2N = 2) or four gametes per generation. Initial allele frequencies in all populations are p = q = 0.5. In one generation, sampling error shifts some proportion of the initial populations that contain two copies of each allele to states of zero, one, two, three, or four copies of one allele. Between generations one and two, sampling error again shifts some proportion of the initial populations to states of zero, one, two, three, or four copies of one allele. However, in generation one there are populations present with all allelic states. The arrows represent the possible allelic states produced by sampling error in the third generation for each of the states in the second generation. The bars in the histogram for the third generation are divided by horizontal lines to show the contributions of each second generation allelic state to the total frequency of populations with a given allelic state (some contributions are very small and are difficult to see). As the Markov process continues, the frequency distribution accumulates more and more of the populations at states of zero and four alleles, eventually reaching fixation or loss for all populations.

The proportion of all populations with one A allele at t = 1 is 4/16 or 0.25. Therefore, (0.422)(0.25) = 0.1055 is the proportion of many replicate populations that should transition from one A allele at t = 1 to one A allele at t = 2. Figure 3.10 shows how all such transitions over three generations add together to determine the overall proportions of populations with each allelic state.

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