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:

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

       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.