Population Genetics. Matthew B. Hamilton

Figure 2.11 An allozyme gel stained to show alleles at the phosphoglucomutase or PGM locus in striped bass and white bass. The right‐most three individuals are homozygous for the faster migrating allele (FF genotype), while the left‐most four individuals are homozygous for the slower migrating allele (SS genotype). No double‐banded heterozygotes (FS genotype) are visible on this gel. The + and – indicate the anode and cathode, respectively, ends of the gel. Wells where the individual samples were loaded into the gel can be seen at the bottom of the picture. Gel picture kindly provided by J. Epifanio.

      (2.12)

      where k is the number of alleles at the locus, the p_i ² and 2p_ip_j terms represent the expected homozygote genotype frequencies with random mating based on allele frequencies, and indicates summation of the frequencies of the k homozygous genotypes. Under random mating, . This quantity was called the gene diversity by Nei (1973) to distinguish it from the heterozygosity when there is non‐random mating within populations and to recognize that it is a quantity that can be applied to polyploids (see Meirmans et al. 2018). The expected heterozygosity can be adjusted for small samples by multiplying H_e by 2N/(2N − 1) where N is the total number of genotypes (Nei and Roychoudhury 1974), a correction that makes little difference unless N is about 50 or fewer individuals. In a similar manner, the observed heterozygosity (H_o) is the sum of the frequencies of all heterozygotes observed in a sample of genotypes:

      (2.13)

      where the observed frequency of each heterozygous genotype H_i is summed over the h = k(k − 1)/2 heterozygous genotypes possible with k alleles. Both H_e and H_o can be averaged over multiple loci to obtain mean heterozygosity estimates for two or more loci. Heterozygosity provides one of the basic measures of genetic variation, or more formally genetic polymorphism, in population genetics.

      The fixation index as a measure of deviation from expected levels of heterozygosity is a critical concept that will appear in several places later in this text. The fixation index plays a conceptual role in understanding the effects of population size on heterozygosity (Chapter 3) and also serves as an estimator of the impact of population structure on the distribution of genetic variation (Chapter 4).

2.6 Mating among relatives

      The previous section of this chapter showed how non‐random mating can increase or decrease the frequency of heterozygote genotypes compared to the frequency that is expected with random mating. The last section also introduced the fixation index as well as ways to quantify heterozygosity in a population. This section will build on that foundation to show two concepts: (i) the consequences of non‐random mating on allele and genotype frequencies in a population and (ii) the probability that two alleles are identical by descent. The focus will be on positive genotypic assortative mating (like genotypes mate) or inbreeding since this will eventually be helpful to understand genotype frequencies in small populations. The end of this section will consider some of the consequences of inbreeding and the evolution of autogamy.

       Impacts of non‐random mating on genotype and allele frequencies

Let's develop an example to understand the impact of mating among relatives on genotype and allele frequencies in a population. Under complete positive assortative mating or selfing, an individual mates with another individual possessing an identical genotype. Figure 2.12 diagrams the process of positive genotypic assortative mating for a diallelic locus, following the frequencies of each genotype through time. Initially, the frequency of the heterozygote is H but this frequency will be halved each generation. A Punnett square for two heterozygotes shows that half of the progeny are heterozygotes (H/2). The other half of the progeny are homozygotes (H/2), composed of one‐quarter of the original heterozygote frequency of each homozygote genotype (H/2[1–1/2]). It is obvious that matings among like homozygotes will produce only identical homozygotes, so the homozygote genotypes each yield a constant frequency of homozygous progeny each generation. In total, however, the frequency of the homozygous genotypes increases by a factor of each generation due to homozygous progeny of the heterozygous genotypes. If the process of complete assortative mating continues, the population rapidly loses heterozygosity and approaches a state where the frequency of heterozygotes is zero.

      As an example, imagine a population where p = q = 0.5 that has Hardy–Weinberg genotype frequencies D = 0.25, H = 0.5, and R = 0.25. Under complete positive assortative mating, what would be the frequency of heterozygotes after five generations? Using Figure 2.12, at time t = 5, heterozygosity would be H(1/2)⁵ = H(1/32) = 1/64 or 0.016. This is a drastic reduction in only five generations.