style="font-size:15px;"> Population genetics and quantitative genetics are closely related fields, both dealing with the genetic basis of phenotypic variation among the individuals in a population. Population genetics traditionally focuses on frequencies of alleles and genotypes, whereas quantitative genetics focuses on linking phenotypic variation of complex traits to its underlying genetic basis to enable researchers to better understand and predict genetic architecture and long‐term change in populations (to predict the response to selection given data on the phenotype and relationships of individuals in the population). Historically, quantitative genetics has its roots in statistical abstractions of genetic effects, first described by Karl Pearson and Ronald Fisher in the early 1900s. The foregoing represents the classical view of quantitative genetics.
The modern molecular view of quantitative genetics focuses on the use of molecular genetics tools (genomics, bioinformatics, computational biology, etc.) to reveal links between genes and complex phenotypes (quantitative traits). Genes that control quantitative traits are called quantitative trait loci (QTL). Molecular‐based QTL analyses are being used to evaluate the coupling associations of the polymorphic deoxyribonucleic acid (DNA) sites with phenotypic variations of quantitative and complex traits and analyze their genetic architecture. There is evidence of a paradigm shift in the field of quantitative genetics. In this chapter, both classical (Sections 4.2–4.2.19) and molecular (Sections 4.3–4.7) quantitative genetics are discussed. Discussions in this section will include genetic and environmental variances, relationships and genetic diversity, linkage, and epistatic issues in populations.
4.2 Quantitative traits
Most traits encountered in plant breeding are quantitatively inherited. Many genes control such traits, each contributing a small effect to the overall phenotypic expression of a trait. Variation in quantitative trait expression is without natural discontinuities (i.e. the variation is continuous). The traits that exhibit continuous variations are also called metric traits. Any attempt to classify such traits into distinct groups is only arbitrary. For example, height is a quantitative trait. If plants are grouped into tall versus short plants, one could find relatively tall plants in the short group and similarly short plants in the tall group.
4.2.1 Qualitative genetics versus quantitative genetics
The major way in which qualitative genetics and quantitative genetics differ may be summarized as follows:
Nature of traitsQualitative genetics is concerned with traits that have Mendelian inheritance and can be described according to kind, and as previously discussed, can be unambiguously categorized. Quantitative genetic traits are described in terms of the degree of expression of the trait, rather than the kind.
Scale of variabilityQualitative genetic traits provide discrete (discontinuous) phenotypic variation, whereas quantitative genetic traits produce phenotypic variation that spans the full spectrum (continuous).
Number of genesIn qualitative genetics, the effects of single genes are readily detectable, while in quantitative genetics, single gene effects are not discernible. Rather, traits are under polygenic control (genes with small indistinguishable effects).
Mating patternQualitative genetics is concerned with individual matings and their progenies. Quantitative genetics is concerned with a population of individuals that may comprise a diversity of mating kinds.
Statistical analysisQualitative genetic analysis is quite straightforward, and is based on counts and ratios. On the other hand, quantitative analysis provides estimates of population parameters (attributes of the population from which the sample was obtained).
4.2.2 The environment and quantitative variation
All genes are expressed in an environment (phenotype = genotype + environmental effect). However, quantitative traits tend to be influenced to a greater degree than qualitative traits. Under significantly large environmental effects, qualitative traits (controlled by one or a few major genes) can exhibit quantitative trait inheritance pattern. A strong environmental influence causes the otherwise distinct classes to overlap (Figure 4.1).
Figure 4.1 Environmental effect on gene expression. The phenotype = genotype + environment. Some traits are influenced a lot more than others by the environment. Cross (a) has small environmental influence such that the phenotypes are distinguishable in the F2; in cross (b) the environmental influence is strong, resulting in more blurring of the differences among phenotypes in the segregating population.
4.2.3 Polygenes and polygenic inheritance
Quantitative traits are controlled by multiple genes or polygenes.
What are polygenes?
Polygenes are genes with effects that are too small to be individually distinguished. They are sometimes called minor genes. In polygenic inheritance, segregation occurs at a large number of loci affecting a trait. The phenotypic expression of polygenic traits is susceptible to significant modification by the variation in environmental factors to which plants in the population are subjected. Polygenic variation cannot be classified into discrete groups (i.e. variation is continuous). This is because of the large number of segregating loci, each with effects so small that it is not possible to identify individual gene effects in the segregating population or meaningfully describe individual genotypes. Instead, biometrics is used to describe the population in terms of means and variances. Continuous variation is caused by environmental variation and genetic variation due to the simultaneous segregation of many genes affecting the trait. These effects convert the intrinsically discrete variation to a continuous one. Biometrical genetics is used to distinguish between the two factors that cause continuous variability to occur.
Another aspect of polygenic inheritance is that different combinations of polygenes can produce a particular phenotypic expression. Furthermore, it is difficult to measure the role of environment on trait expression because it is very difficult to measure the environmental effect on a plant basis. Consequently, a breeder attempting to breed a polygenic trait should evaluate the cultivar in an environment that is similar to that prevailing in the production region. It is beneficial to plant breeding if a tight linkage of polygenes (called polygenic block; linkage block) that has favorable effects on traits of interest to the breeder is discovered.
In 1910, a Swedish geneticist, Nilsson‐Ehle provided a classic demonstration of polygenic inheritance and in the process helped to bridge the gap between our understanding of the essence of quantitative and qualitative traits. Polygenic inheritance may be explained by making three basic assumptions:
1 That many
