Further models of natural selection

7.1 Viability selection with three alleles or two loci

Mean fitness surfaces.

Natural selection on one locus with three alleles.

Natural selection on two diallelic loci.

Chapter 6 established a series of general predictions about the action of natural selection when fitness is equivalent to genotype-specific viability determined by a single locus with two alleles. The conditions required for the basic diallelic locus model of natural selection are quite restrictive and are probably not met often in biological populations. The goal of this chapter is to extend our understanding of the model of natural selection to increasingly complex and general genetic situations. In a sense then, this chapter explores the process of natural selection under assumptions that might better approximate conditions found in some natural populations. In the first section, we will retain the viability natural selection model and its assumptions but modify the numbers of alleles at a locus and the number of loci. The goal is to examine the outcomes of viability selection when fitness is determined by either a single locus with three alleles or two loci each with two alleles.

A useful tool that we will employ to understand the dynamics of genotype frequencies, allele frequencies, and mean fitness under natural selection is called a fitness surface. A fitness surface is a graph that shows genotype frequencies of a population on some axes along with the mean fitness of the population at each possible point in the range of genotype frequencies. For one locus with two or three alleles, a De Finetti diagram can be used as a fitness surface, as shown in Fig. 7.1. The three axes represent genotype frequencies of a population on the plot. Each point inside the triangle defines three genotype frequencies that are then used to compute the mean fitness of the population. The mean fitness is represented by shading as well as contour lines that connect points of equal mean fitness. Since contour plots of mean fitness are interpreted exactly like topographic maps where contour lines are used to represent elevation, they are also called fitness landscapes or adaptive landscapes. The highest point on a fitness surface represents equilibrium genotype frequencies under natural selection. A fitness surface also shows how natural selection will change genotype frequencies over time if the process of natural selection operates like a hiker who can only travel uphill. For any point on a fitness surface, natural selection will act to increase mean fitness of the population and shift genotype frequencies in a direction that increases the mean fitness. Once the population is at a point where mean fitness cannot increase, natural selection has reached an equilibrium and stops changing genotype frequencies, in Fig. 7.1, the entire surface is a tilted plane that is has its highest point at the

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