5 10 15 20 25 30 35 40 45 50 Generation

Figure 3.3 The results of genetic drift continued every generation in populations of N = 4 and N = 20. In the top panels, the six lines represent independent replicates or independent populations experiencing genetic drift starting at the same initial allele frequency (p = 0.5). The random nature of genetic drift can be seen by the zig-zag changes in allele frequency that have no apparent direction. Allele frequencies that reach the upper or lower axes represent cases of fixation or loss. In the bottom panels, the genotype frequencies are shown for the allele frequencies represented by the black and blue lines under the assumption of random mating within each generation. The changes in genotype frequencies are a consequence of changes in allele frequencies due to genetic drift.

cycle in actual biological populations. The implications of relaxing other assumptions such as constant population size are topics of later chapters.

A major limitation of the micro-centrifuge tube demonstration is that it shows the effects of genetic drift over only one generation. A more general model of the effect of sampling error is needed to predict what may happen to allele frequencies over many generations. A general model would sample from one generation to found the next generation, then build a large pool of gametes (like the beakers of microcentrifuge tubes) with those new allele frequencies. The sampling process would then be continued for many generations. Figure 3.3 shows computer-simulated allele frequencies based on this more general model for many generations under the assumptions of the Wright-Fisher model (note that the populations in Fig. 3.3 are twice as large as the samples of micro-centrifuge tubes). The effects of genetic drift are more obvious over longer periods of time. Allele frequencies over a few generations change at random, both increasing and decreasing, sometimes changing very little in one generation and other times changing more substantially. There is a clear trend that over time in these genetic drift simulations that the frequency of one allele reaches either fixation (p = 1.0) or loss (p = 0.0), identical to loss (q = 0.0) and fixation (q = 1.0) for the alternate allele. There is also a trend that fixation or loss occurs in fewer generations with the smaller between-generation sample size and more slowly with the larger between-generation sample size. Since these simulations do not include any processes that could reintroduce genetic variation, once a population has reached fixation or loss there can be no further change in allele frequency.

The bottom panels of Fig. 3.3 show genotype frequencies based on random mating for one of the populations represented in the top panels. Genetic drift clearly causes genotype frequencies to change over time along with the changes in allele frequency. This is in contrast to the processes considered in Chapter 2, such as consanguineous mating, that result in changes in genotype frequency only but do not alter allele frequency. Genetic drift is most commonly modeled and demonstrated from the perspective of

N = 25, initial allele frequency p0 = 0.2

N = 25, initial allele frequency p0 = 0.8

N = 25, initial allele frequency p0 = 0.2

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