## The effects of sampling lead to genetic drift

• Biological populations are finite.

• A simple sampling experiment with microcentrifuge tube "populations."

• The Wright-Fisher model of sampling.

• Sampling error and genetic drift in biological populations.

In Chapter 2, that population size is very large, effectively infinite, was among the assumptions listed for Hardy-Weinberg expected genotype frequencies to be realized. This entire chapter will be devoted to the changes in allele and genotype frequency that occur when this assumption is not met and populations are small or at least finite. Population size has profound effects on allele frequencies in biological populations and has a specific definition in the context of population genetics. A variable for population size in one form or another appears in many of the fundamental equations used to predict genotype or allele frequencies in populations. In those expectations where no explicit variable for population size appears there is an assumption instead, just as in the Hardy-Weinberg expectation for genotype frequencies. There is a strong biological motivation behind this attention to population size. All biological populations, without exception, are finite. Therefore, no actual population ever exactly meets the population size assumption of Hardy-Weinberg, although some may be large enough to show few genetic effects of finite size over relatively short periods of time. There is also a tremendous range of population sizes in the biological world. An understanding of the population genetic effects of population size will help to explain why some populations and species violate the assumptions to a greater degree than others, making sense of both the factors that cause differences in population size and the consequences of such differences. The causes and allele-frequency consequences of finite population size can be understood and modeled in a variety of ways. Those models and concepts critical to understanding the population genetic impacts of finite population size will be the topics of this chapter.

A simple, hands-on demonstration can be used to show the role that population size plays in allele frequency in a population from one generation to the next. A plastic beaker filled with micro-centrifuge tubes can be used to represent gametes (Fig. 3.1). The micro-centrifuge tubes are of two different colors, say blue and clear, and there are 50 of each per beaker. Each beaker approximates a population with one diallelic locus where the allele frequencies are p = q = 0.5. Imagine sampling four tubes from a beaker and recording the resulting frequencies of the blue and clear tubes. Then imagine (after returning the four tubes and mixing the contents of the beaker) drawing out a sample of 20 tubes and recording the frequency of the blue and clear tubes. These handfuls of micro-centrifuge tubes represent the sampling process that occurs during reproduction and can be used to understand what happens to allele frequencies over time in a finite population.

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