Population Genetics. Matthew B. Hamilton

non‐random mating that can be utilized to estimate mating patterns in natural populations.

      Mating among related individuals, termed consanguineous mating or biparental inbreeding, increases the probability that the resulting progeny are homozygous compared to random mating. This occurs since relatives, by definition, are more likely than two random individuals to share one or two alleles that were inherited from ancestors they share in common (this makes mating among relatives a form of assortative mating). Therefore, when related individuals mate, their progeny have a higher chance of receiving the same allele from both parents, giving them a greater chance of having a homozygous genotype. Sexual autogamy or self‐fertilization is an extreme example of consanguineous mating where an individual can mate with itself by virtue of possessing reproductive organs of both sexes. Many plants and some animals, such as the nematode Caenorhabditis elegans, are hermaphrodites that can mate with themselves.

There are also cases of disassortative mating, where individuals with unlike genotypes have a higher probability of mating. A classic example in mammals is mating based on genotypes at major histocompatibility complex (MHC) loci, which produce proteins involved in self/non‐self recognition in immune response. Mice are able to recognize individuals with similar MHC genotypes via odor, and based on these odors, avoid mating with individuals possessing a similar MHC genotype. Experiments where young mice were raised in nests of either their true parents or foster parents (called cross‐fostering) showed that mice learn to avoid mating with individuals possessing odor cues similar to their nest‐mates' rather than avoiding MHC‐similar individuals per se (Penn and Potts 1998). This suggests that mice learn the odor of family members in the nest and avoid mating with individuals with similar odors, indirectly leading to disassortative mating at MHC loci as well as the avoidance of consanguineous mating. One hypothesis to explain the evolution of disassortative mating at MHC loci is that the behavior is adaptive since progeny with higher heterozygosity at MHC loci may have more effective immune response. There is evidence that some animals prefer mates with dissimilar MHC genotypes (e.g. Miller et al. 2009), while, in humans, the possibility remains controversial (Qiao et al. 2018).

      The effects of non‐random mating on genotype frequencies can be measured by comparing Hardy–Weinberg expected frequency of heterozygotes, which assumes random mating, with observed heterozygote frequencies in a population. A quantity called the fixation index, symbolized by F (f is reserved for the coancestry coefficient introduced later in Section 2.6.), is commonly used to compare how much heterozygosity is present in an actual population relative to the expected levels of heterozygosity under random mating

(2.9)

where H_e is the Hardy–Weinberg expected frequency of heterozygotes based on population allele frequencies and H_o is the observed frequency of heterozygotes. Dividing the difference between the expected and observed heterozygosity by the expected heterozygosity expresses the difference in the numerator as a percentage of the expected heterozygosity. Even if the difference in the numerator may seem small, it may be large relative to the expected heterozygosity. Dividing by the expected heterozygosity also puts F on a convenient scale of −1 and + 1. Negative values indicate heterozygote excess and positive values indicate homozygote excess relative to Hardy–Weinberg expectations. In fact, the fixation index can be interpreted as the correlation between the two alleles sampled to make a diploid genotype (see the Appendix for an introduction to correlation if necessary). Given that one allele has been sampled from the population, if the second allele tends to be identical, there is a positive correlation (e.g. A and then A or a and then a); if the second allele tends to be different, there is a negative correlation (e.g. A and then a or a and then A); and if the second allele is independent, there is no correlation (e.g. equally likely to be A or a). With random mating, no correlation is expected between the first and second allele sampled to make a diploid genotype.

      Interact box 2.2 Assortative mating and genotype frequencies

      The impact of assortative mating on genotype and allele frequencies can be simulated on the text simulation website. Use the Simulation menu and select de Finetti. The program models several non‐random mating scenarios based on the settings in the Mating Model box. Start with Random Mating, set the initial genotype frequencies using the sliders for the frequencies of AA and Aa, and set Generations to simulate to 20. The genotype frequencies over time will be plotted on the triangle. Recall that if the points for each generation change position only vertically, then only genotype frequency is changing, while a movement to the left or right means that allele frequencies have changed. Try a set of three or four initial genotype frequencies that vary both allele and genotype frequencies. Under random mating, why does it appear that there are only two points even though 20 generations are simulated? How long does it take for a population to reach equilibrium with random mating?

      Select the Positive Assortative radio button and repeat the simulations using the same initial genotype frequencies you used for random mating. Then, select the Negative Assortative radio button and again run the simulation using the same initial genotype frequencies that you employed for the other two mating models. How do the two types of non‐random mating affect genotype frequencies? Allele frequencies?

      Assortative mating: Mating patterns where individuals do not mate in proportion to their genotype frequencies in the population; mating that is more (positive assortative mating) or less (negative assortative mating) frequent with respect to genotype or genetically based phenotype than expected by random combination.

      Consanguineous mating: Mating between related individuals that can take the form of biparental inbreeding (mating between two related individuals) or sexual autogamy (self‐fertilization).

      Fixation index (F): The proportion by which heterozygosity is reduced or increased relative to the heterozygosity in a randomly mating population with the same allele frequencies.

Let's work through an example of genotype data for one locus with two alleles that can be used to estimate the fixation index. Table 2.8 gives observed counts and frequencies of the three genotypes in a sample of 200 individuals. To estimate the fixation index from these data requires an estimate of allele frequencies first. The allele frequencies can then be used to determine expected heterozygosity under the assumptions of Hardy–Weinberg. If p represents the frequency of the B allele,

      (2.10)

      using the genotype counting method to estimate allele frequency (Table 2.8 uses the allele counting method). The frequency of the b allele, q, can be estimated directly in a similar fashion or by subtraction since there are only two alleles in this case. The Hardy–Weinberg expected frequency of heterozygotes is . It is then simple to estimate the fixation index using the observed and expected heterozygosities.

      (2.11)

In this example, there is a clear deficit of heterozygotes relative to Hardy–Weinberg expectations. The population contains 59% fewer heterozygotes than would be expected in a population with the same allele frequencies that was experiencing random mating and the other conditions set out in the assumptions of Hardy–Weinberg. Interpreted as a correlation between the allelic states of