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The development of genotyping platforms with high-density of SNP markers makes possible today a detailed analysis of the variation along the genome. Advances in genomic sequencing techniques have allowed access to more than 80 million SNPs in humans (Auton et al., 2015: 1000 Genomes Project Consortium) and several million in model species (Mackay et al., 2012). In parallel, there has been a great development of statistical methods for the estimation of genetic effects and mapping of quantitative trait loci (QTL). Among the new applications of genomic information is the search and mapping of QTLs, the detection of the selection footprint and genomic selection, methods that we will outline throughout the chapter.
Artificial selection is perhaps the most important application of quantitative genetics, being the main agent of the genetic improvement of plants and animals. Carried out, sometimes inadvertently, from the starts of domestication, artificial selection consists of using as reproducers only the most suitable individuals in relation to a specific objective, generally of interest for human consumption or welfare. Artificial selection is the tool with which most of the increase in the production of domestic animals has been achieved, such as the duplication of milk production in cattle and the four-fold increase of the weight in chickens in the last 50 years (Hill, 2014). But artificial selection is also a basic experimental tool for genetic research (Hill and Caballero, 1992).
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.
In Chapter 2 we analysed the process of genetic drift, or random change of allele frequencies in populations of small size due to the sampling of gametes, and in Chapter 4 we considered the inbreeding generated in these populations by the inevitable mating between relatives. We studied these phenomena under the simplified conditions of the ideal population of Wright–Fisher, which are described in Section 2.5. Under this simple model, we derived the expressions of the expected variance of allele frequencies by genetic drift (equations (2.8) and (2.9)) and the expected inbreeding coefficient and its rate of increase per generation (equations (4.12) and (4.13)), all of them being a function of the population census size, N. However, real populations may fail to meet one or more of the ideal conditions, so that the mentioned expressions would no longer hold.
Some heritable characteristics are qualitative, with an expression clearly identifiable in discrete classes. Such is the case of attributes like some differences in colour, shape or structure, by which individuals of a population or species can be classified. The analysis of this type of simple character was what allowed Mendel to describe the bases of inheritance and many other geneticists, later, to understand the relation between this and the chromosomal behaviour during reproduction, as well as the interactions between genes. However, most of the traits that we find in nature present a continuous variation. Even some of the seemingly discrete attributes, such as colour, may show gradual variation if analysed in detail. These types of characters with gradual variation are called quantitative traits and, sometimes, metric or continuous traits.
Mutation is the source of genetic variation of populations on which natural or artificial selection act to produce genetic changes leading to adaptive evolution or economic improvement of plants and animals. In the case of single loci affecting qualitative traits or genes of major effect on quantitative traits the estimation of the frequency or rate at which mutations appear per generation is relatively simple for dominant mutations, since it is based directly on the count. For example, if from 1 million births of phenotypically normal parents for the achondroplasia allele (a dominant mutation producing dwarfism) 10 individuals appear with the disease, the mutation rate per locus and generation will be u = 10/(2 × 106) = 0.5 × 10−5, where the factor 2 of the denominator stems from the fact that each individual carries two alleles.
Quantitative genetics is the study of continuously varying traits which make up the majority of biological attributes of evolutionary and commercial interest. This book provides a much-needed up-to-date, in-depth yet accessible text for the field. In lucid language, the author guides readers through the main concepts of population and quantitative genetics and their applications. It is written to be approachable to even those without a strong mathematical background, including applied examples, a glossary of key terms, and problems and solutions to support students in grasping important theoretical developments and their relevance to real-world biology. An engaging, must-have textbook for advanced undergraduate and postgraduate students. Given its applied focus, it also equips researchers in genetics, genomics, evolutionary biology, animal and plant breeding, and conservation genetics with the understanding and tools for genetic improvement, comprehension of the genetic basis of human diseases, and conservation of biological resources.
As already indicated in Chapter 1, the phenotypic value (P) of an individual for a quantitative trait, deviated from the population mean, is decomposed into the genotypic value (G), determined by the genetic endowment of the individual, and the environmental deviation (E), that is, P = G + E.
Inbreeding is a consequence of the mating between relatives. This is an inevitable phenomenon in populations of small census size even when crossing between their individuals is ‘random’. But inbreeding can also exist in large populations, when relatives mate with each other naturally or forcedly. In this chapter we will analyse the conceptual and mathematical treatment of inbreeding, whose bases are largely due to Sewall Wright. We will address the concepts of coefficient of inbreeding and coancestry, the ways in which these are calculated from genealogical information and genetic markers data, as well as their modulation by the different population forces of change in the allelic frequencies that act in the populations.
The fit between observed (O) and expected (E) frequencies is statistically contrasted by a χ2 test, since the summation Σ(O − E)2/E is distributed as a χ2 distribution with a number of degrees of freedom equal to the number of genotypic classes that are compared less the number of parameters that are needed to obtain the expected values. In this case there are six classes and to obtain the expected values two of the three allele frequencies are needed (the third is determined once the first two are known) and the total number of individuals in the sample. Therefore, the number of degrees of freedom is d.f. = 6 − 2 − 1 = 3.