The genetic description of a population can be done at three different levels, the locus, the gamete or the individual genotype, by specifying the different variants in each case (allelic, gametic or genotypic) and their respective frequencies. A population of a diploid species is composed of individuals (genotypes) that reproduce by the union of their gametes to form zygotes that will give rise to the individuals of the next generation, hence the interest of a genotypic and gametic description. But genotypes and gametes are sets of alleles, two for each locus in the first case and one in the second, hence the interest of the allelic description.

Consider the simplest case: a biallelic locus A with alleles A and a, therefore, genotypes AA, Aa and aa, and suppose that in a population formed by 100 individuals, the number of those corresponding to each genotype is 40, 50 and 10, respectively (Table 2.1).

As we saw in Chapter 2, natural selection is the main force for the change of allelic frequencies and the driving factor behind the evolution of living beings and their adaptation to the incessant environmental changes. Although there are other evolutionary agents that modify the allelic frequencies, only selection produces changes that promote adaptation. We also indicated that natural selection acts directly on a single character, fitness, and the changes occurred on the different quantitative traits of an individual depend on the genetic correlation between them and fitness. Probably, all quantitative characteristics (and also qualitative ones) are more or less related to fitness, since selection acts at all levels, from the cellular to the population (Endler, 1986). In previous chapters we indicated that some traits, the so-called main components, have a strong relationship with fitness. In fact, the empirical evaluation of this is carried out by its components, mainly viability, fecundity and mating success.

In Chapter 3 we studied the partition of the phenotypic value of a quantitative trait, deviated from the population mean, in its genetic and environmental components, and the first in its additive, dominance and epistatic components. The corresponding partition was extended to the components of the phenotypic variance. It was also indicated that the additive values of the individuals are the main responsible for the resemblance between relatives and that this, therefore, can be quantified by the heritability, that is, the ratio of the variance of the additive values and the phenotypic variance, h2 = VA/VP. This intimate relationship between additive variance and resemblance between relatives is what allows us to estimate the first one from the phenotypic values of related individuals.

As we saw in Chapter 4, inbreeding produces changes in the genotypic frequencies that imply an increase in the frequency of homozygotes and a reduction in that of heterozygotes (equations (4.15)–(4.17)). These changes usually alter the mean and variance of the quantitative traits, sometimes with important consequences for the population. Inbreeding depression, that is, the change generated by inbreeding in the mean of quantitative traits, is one of those consequences, and it is manifested as a deterioration of fitness of consanguineous individuals relative to non-consanguineous ones (Charlesworth and Charlesworth, 1999; Charlesworth and Willis, 2009). Inbreeding depression is a phenomenon well known by plant and animal breeders and conservation managers, who generally try to prevent matings between related individuals in order to avoid an increase in inbreeding.