using equation 3.13. For populations that are at fixation or loss, sampling cannot change the allele frequency. Therefore, populations initially fixed for A (Pt=0(2)) all transition to populations fixed for A (P2^2 = 1) but none of the populations initially lost for A (Pt=0(0)) can transition to any other state, so

P0—2 is zero. Lastly, the Pt=0(2), Pt=0(1), and Pt=0(0) terms each represent the frequencies of populations that possess a given allelic state. This means that the transition probabilities are multiplied by the frequency of populations in a given allelic state to determine the expected frequency of populations with a given allelic state in the next generation.

Using this same logic, the expected frequencies of populations with zero, one, and two A alleles after one generation of sampling error are shown in Table 3.2. Using these transition probabilities, the expected population frequencies over four generations of sampling are shown in Fig. 3.9. The result of the equations in Table 3.2 is a generation-by-generation prediction for the average behavior of populations under genetic drift when there is an infinite number of replicate populations. This method of modeling the action of genetic drift is known as a Markov chain model. It is important to recognize that the outcome of genetic drift for a single population cannot be predicted. Rather, we can only know the probability that a single population experiences a given change in allele frequency such as going from one to zero copies of the A allele. If many replicate populations are experiencing genetic drift, then the Markov chain predicts the proportion of populations that have a given allelic state in each generation.

Figure 3.10 shows the first two steps in the Markov chain for a population of two diploid individuals or four gametes, similar to the micro-centrifuge tube sampling experiment from the first section of this chapter. With a slightly larger population size than in Fig. 3.9, there are a larger number of allelic state transitions to account for between generations.

Table 3.2 The equations used to calculate the expected frequency of populations with zero, one, or two A alleles in generation one (t = 1) based on the previous generation (t = 0). Frequencies at t = 1 depend both on transition probabilities due to sampling error (constant terms like 0, 1, or 1/2) and population frequencies in the previous generation (Pt=0(x) terms). The transition probabilities are calculated with the binomial formula

0 0

Post a comment