Genetic populations

• Genetic versus geographic organization of populations.

• Isolation by distance and divergence of populations.

• Gene flow and migration.

• Direct and indirect measures of gene flow.

The expectation that genotypes will be present in Hardy-Weinberg frequencies, covered in detail in Chapter 2, depends on the assumption of random mating throughout a population. Implicit is the view that a population is a single entity where processes such as mating and movement of individuals are uniform throughout, a condition often called panmixia. Several processes and features at work in actual populations make this initial perspective of population uniformity unlikely to hold true for many populations. It is often the case that within large populations the chances of mating are not uniform as assumed by Hardy-Weinberg. Instead, the chance that two individuals mate often depends on their location within the population. This leads to what is called population structure, or heterogeneity across a population in the chances that two randomly chosen individuals will mate. The first section of this chapter will introduce biological phenomena that contribute to population structure in mating and migration that can lead to differences in allele and genotype frequencies in different parts of a population. The goal of the entire chapter is to develop expectations for the impact of population structure on genotype and allele frequencies along with methods to measure patterns of population structure.

To get an initial idea of how a population might be divided into smaller units that behave independently, consider the hypothetical population in Fig. 4.1. Initially, all individuals in the population have equal chances of mating regardless of their location. Since mating is random, genotype frequencies in the entire population match Hardy-Weinberg expectations and allele frequencies are equal on both sides of the creek. Then imagine that the creek bisecting the population changes permanently into a large river that serves as a barrier to movement of individuals from one side to the other side. Although some individuals still cross the river on occasion, the rate of genetic mixing or gene flow between the two subpopulations bisected by the river is reduced. Lowered levels of gene flow mean that the two subpopulations have allele and genotype frequencies that tend to be independent through time. At the later time points in Fig. 4.1, the two subpopulations have increasingly different allele frequencies over time due to genetic drift, even though there are Hardy-Weinberg expected genotype frequencies within each subpopulation. In the last time period in Fig. 4.1, the allele frequencies in the subpopulations separated by the river are quite different and the genotype frequencies in the total population no longer meet Hardy-Weinberg expectations. In this example, a reduction in gene flow allows the two subpopulations to be acted on independently by genetic drift, ultimately resulting in population differentiation of allele frequencies. The appearance of a geographic barrier that restricts gene flow among populations like that in Fig. 4.1 is sometimes called a vicariance event. Subpopulations - entities recognized with names such as herds, flocks, prides, schools, and even cities - can be formed by a wide range of temporal, behavioral, and geographic barriers that ultimately result in subpopulation allele frequencies that differ from the average allele frequency of the total population.

Another cause of population structure is more subtle, but easy to understand with a thought experiment. Think of one common species of animal or plant that you encounter regularly at home or work. Think of individuals of this species seeking out mates completely at random. Where would individuals likely find mates? They would probably find mates among the other individuals nearby rather than far away. I thought of the trees that are near my home and also

Time

^^ = aa genotype Aa genotype

I = AA genotype

Figure 4.1 An example of population structure and allele-frequency divergence produced by limited gene flow. The total population (large ovals) is initially in panmixia and has Hardy-Weinberg expected genotype frequencies. Then the stream that runs through the population grows into a large river, restricting gene flow between the two sides of the total population. Over time allele frequencies diverge in the two subpopulations through genetic drift. In this example, you can imagine that the two subpopulations drift toward fixation for different alleles but neither reaches fixation due to an occasional individual that is able to cross the river and mate. Note that there is random mating (panmixia) within each subpopulation so that Hardy-Weinberg expected genotype frequencies are maintained within subpopulations. However, after the initial time period genotype frequencies in the total population do not meet Hardy-Weinberg expectations.

on the university campus where I work. When these trees flower and mate via the movement of pollen, it seems likely to me that trees that are closer together are more likely to be mates. I would not expect two trees that are tens or hundreds of kilometers apart to have a good chance of mating. Imagine the species that you thought of and the distances over which mating events might take place. Even if individuals can find mates very far away, there is usually some spatial scale at which the chances of mating are limited. This varies with the species and could be distances as small as a few meters or as large as thousands of kilometers depending on the range of movement of individuals and their gametes.

This phenomenon of decreasing chances of mating with increasing distance separating individuals is termed isolation by distance (Wright 1943a, 1943b, 1946). Sewall Wright was motivated by data on the spatial frequencies of blue and white flowers of the plant Linanthus parryae (Fig. 4.2) to develop

(b)

Figure 4.2 The plant Linanthus parryae, or desert snow, is found in the Mojave Desert region of California. (a) L. parryae can literally cover thousands of hectares of desert during years with rainfall sufficient to allow widespread germination of dormant seeds present in the soil. This tiny plant has either blue or white flowers. (b) In some locations most plants have blue or most have white flowers whereas in other locations more equal frequencies of the two flower colors are found. Reproduced with permission of Barbara J. Collins. For a color version of this image see Plate 4.2.

expectations for populations experiencing isolation by distance. The patchwork spatial pattern of flower color frequencies in L. parryae was considered by Wright as a prime example of the consequences of isolation by distance in continuous populations. However, as flower-color frequencies were followed over more and more years, the interpretation that flower-color frequencies were primarily due to genetic drift made possible by isolation by distance has been challenged (e.g. Turelli et al. 2001). Wright carried out a series of detailed analyses of L. parryae data (Wright 1978) but the nature of the processes that affect the spatial distributions of L. parryae flower colors is a controversy that has continued for more than 50 years (see Schemske & Bierzychudek 2001). Regardless of the specific situation in L. parryae, the phenomenon of isolation by distance is ubiquitous in natural populations. One biologist described isolation by distance as a given in the genetics of natural populations, likening it to the force of gravity in physics, with the only question being the geographic scale at which it impacts genotype and allele frequencies.

Computer simulations are a convenient way to explore how isolation by distance influences allele and genotype frequencies. Figure 4.3 shows two simulated populations where each point on a grid represents the geographic location of a diploid individual. In one case, the population exhibits panmixia and indviduals find a mate at random from all individuals within a 99 x 99 individual mating area. In the contrasting case where there is strong isolation by distance, each individual mates at random within a much smaller 3 x 3 individual area. Both populations start off looking very similar, with Hardy-Weinberg expected genotype frequencies and randomly scattered locations of the three genotypes. After 200 generations the population with a 99 x 99 individual mating area (Fig. 4.3 a) still shows random locations of the three genotypes. However, the population with a 3 x 3 mating area (Fig. 4.3b) has distinct clumps of identical genotypes and fewer heterozygotes (represented by blue squares). One effect of isolation by distance is clearly local changes in allele frequency in a population, with local regions approaching fixation or loss, akin to the impact of reducing the effective population size (see the breeding effective population size in section 3.5). Alternatively, isolation by distance can be thought of as a form of inbreeding, since restricted mating distances cause homozygosity within subpopulations to increase. The patterns of genotypes in the simulated populations bear this out, with an obvious decline in the overall frequency of heterozygotes over time with isolation by distance (Fig. 4.3b) but no such decline when there is panmixia (Fig. 4.3 a).

Isolation by distance Decreasing chances of mating or gene flow as the geographic distance between individuals or populations increases.

Gene flow The successful movement of alleles into populations through the movement of individuals (migration) or the movement of gametes. Panmixia Random mating, literally meaning "all mixed."

Population structure Heterogeneity in allele frequencies across a population caused by limited gene flow.

Subpopulation A portion of the total population that experiences limited gene flow from other parts of the total population so that its allele frequencies evolve independently to some degree; synonymous with deme.

Population structure has profound implications for genotype and allele frequencies. Subdivision breaks up a population into smaller units that are each genetically independent to some degree. One consequence is that each subpopulation has a smaller effective population size than the effective size of the entire population if there were random mating. The genetic variation found in a single large panmictic population and a population subdivided into many smaller demes is organized in a different manner. Think of the simple case of a diallelic locus. A single large population may take a very long time to experience fixation or loss due to genetic drift and thus maintain both alleles. In a highly subdivided population each deme may quickly reach fixation or loss, but both alleles can be maintained in the overall population since half of the subpopulations are expected to reach fixation and half loss for a given allele. Processes that cause population structure can also be thought of as both creative and constraining in evolutionary change (Slatkin 1987a). The genetic isolation among demes caused by subdivision can prevent novel and even advantageous alleles from spreading throughout a population. But, at the same time, genetic isolation allows subpopulations to evolve independent allele frequencies and maintain unique

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