Population Genetics. Matthew B. Hamilton

is evidence that inbreeding depression exhibits environmental dependence due to variation among environments in phenotypic expression, dominance, and natural selection (Armbruster and Reed 2005; Cheptou and Donohue 2011). The social and economic correlates of inbreeding depression in humans mentioned above are a specific example of environmental effects on phenotypes. Inbreeding depression can be more pronounced when environmental conditions are more severe or limiting. For example, in the plant rose pink ( Sabatia angularis ) progeny from self‐fertilizations showed decreasing performance when grown in the greenhouse, a garden, and their native habitat, consistent with environmental contributions to the expression of inbreeding depression (Dudash 1990). In another study, the number of surviving progeny for inbred and random‐bred male wild mice (Mus domesticus) was similar under laboratory conditions, but male progeny of matings between relatives sired only 20% of the surviving progeny that males from matings between unrelated individuals did when under semi‐natural conditions due to male–male competition (Meagher et al. 2000). However, not all studies show environmental differences in the expression of inbreeding depression. As an example, uniform levels of inbreeding depression were shown by mosquitoes grown in the laboratory and in natural tree holes where they develop as larvae and pupae in the wild (Armbruster et al. 2000).

Figure 2.17 A graphical depiction of the predictions of the dominance and overdominance hypotheses for the genetic basis of inbreeding depression. The line for dominance shows purging and recovery of the population mean under continued consanguineous mating expected if deleterious recessive alleles cause inbreeding depression. However, the line for overdominance as the basis of inbreeding depression shows no purging effect since heterozygotes continue to decrease in frequency. The results of an inbreeding depression experiment with mice show that litter size recovers under continued brother–sister mating as expected under the dominance hypothesis (Lynch 1977). Only two of the original 14 pairs of wild‐caught mice were left at the sixth generation. Not all of the mouse phenotypes showed patterns consistent with the dominance hypothesis.

      The degree of inbreeding depression also depends on the phenotype being considered. In plants, traits early in the life cycle such as germination less often show inbreeding depression than traits later in the life cycle such as growth and reproduction (Husband and Schemske 1996). A similar pattern is apparent in animals, with inbreeding depression most often observed for traits related to survival and reproduction.

      Inbreeding depression is a critical concept when thinking about the evolution of mating patterns in plants and animals. Suppose that a single locus determines whether an individual will self or outcross and the only allele present in a population is the outcrossing allele. Then imagine that mutation produces an allele at that locus, which, when homozygous, causes an individual to self‐fertilize. Such a selfing allele would have a transmission advantage over outcrossing alleles in the population. To see this, consider the number of allele copies at the mating locus transmitted from parents to progeny. Parents with outcrossing alleles mate with another individual and transmit one allele to their progeny. Self‐fertilizing parents, however, are both mom and dad to their offspring and transmit two alleles to their progeny. In a population of constant size where each individual contributes an average of one progeny to the next generation, the selfing allele is reproduced twice as fast as an outcrossing allele and would rapidly become fixed in the population (see Lande and Schemske 1985; Fisher 1999). Based on this twofold higher rate of increase of the selfing allele, complete self‐fertilization would eventually evolve unless some disadvantage counteracted the increase of selfed progeny in the population. Inbreeding depression where the average fitness of outcrossed progeny exceeds the average fitness of selfed progeny by a factor of two could play this role. If outcrossed progeny are at a twofold advantage due to inbreeding depression, then complete outcrossing would evolve. Explaining the existence of populations that engage in intermediate levels of selfing and outcrossing, a mating system common in plants, remains a challenge under these predictions (Byers and Waller 1999).

       The many meanings of inbreeding

      Unfortunately, the word inbreeding is used as a generic term to describe multiple distinct, although interrelated, concepts in population genetics (Jacquard 1975; Templeton and Read 1994). Inbreeding can apply to:

       consanguinity or kinship of two different individuals based on two alleles sampled at random;

       autozygosity of two alleles within an individual;

       the fixation index and Hardy–Weinberg expected and observed genotype frequencies, especially when there is an excess of homozygotes;

       inbreeding depression caused by deleterious recessive alleles or by overdominance;

       the description of the mating system of a population or species (as in inbred);

       genetic subdivision of a species into populations that exchange limited levels of gene flow such that individual populations increase in autozygosity;

       the increase in homozygosity in a population due to its finite size.

These different concepts all relate in some way to either the probability of allele being identical by descent or to expected genotype frequencies in a population, so the connection to inbreeding is clear. Awareness of the different ways the word inbreeding is used as well as an understanding of these different uses will prevent confusion, which can often be avoided simply by using more specific terminology. Remembering that the concepts are interrelated under the general umbrella of inbreeding can also help in realizing the equivalence of the population genetic processes in operation. The next chapter will show how finite population size is equivalent in its effects to inbreeding. Chapter 4 will take up the topic of population subdivision.

2.7 Hardy–Weinberg for two loci

       Expected genotype frequencies with two loci.

       Quantifying gametic disequilibrium with D.

       Approach to gametic equilibrium over time.

       Causes of gametic disequilibrium.

       Gametic disequilibrium

      We saw earlier in the chapter that Hardy–Weinberg could be extended to give expected genotype frequencies for two loci using via the product rule. While this is accepted without question now, in the early days of population genetics, it was a challenge to explain. In 1902, Walter Sutton and Theodor Boveri advanced the chromosome theory of heredity. They observed cell division and hypothesized that the discrete bodies seen separating into sets at meiosis and mitosis contained hereditary material that was transmitted from parents to offspring. At the time, the concept of chromosomal inheritance presented a paradox. Mendel's second law says that gamete haplotypes (haploid genotype) should appear in frequencies proportional to the product of allele frequencies. This prediction conflicted with the chromosome theory of heredity since there are not enough chromosomes to represent each hereditary trait.

To see the problem, take the example of Homo sapiens with a current estimate of about 20 000 protein coding genes in the nuclear genome. However, humans have only 23 pairs of chromosomes, or a large number of loci but only a small number of chromosomes. So, if chromosomes are indeed hereditary molecules, many genes must be on the same chromosome (on average about 870 genes per chromosome for humans if there are 20 000 genes). This means that some genes are physically linked by being located on the same chromosome.