Principles of Plant Genetics and Breeding. George Acquaah

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 genes determine the quantitative trait.

      2 These genes lack dominance.

      3 The action of the genes is additive.

Nilsson‐Ehle crossed two varieties of wheat, one with deep red grain of genotype R₁R₁R₂R₂, and the other white grain of genotype r₁r₁r₂r₂. The results are summarized in Table 4.1. He observed that all the seed of the F₁ was medium red. The F₂ showed about 1/16 dark red and 1/16 white seed, the remainder being intermediate. The intermediates could be classified into 6/16 medium red (like the F₁), 4/16 red, and 4/16 light red. The F₂ distribution of phenotypes may be obtained as an expansion of the binomial (a + b)⁴, where a = b = ½ (a binomial coefficient is the number of combinations of r items that can be selected from a set of n items).

Table 4.1 Transgressive segregation.

P1
F1	R 1 r 1 R 2 r 2
F2	1/16 = R1R1R2R2
	4/16 = R1R1R2r2, R1r1R2R2
	6/16 = R1R1r2r2, R1r1R2r2, r1r1R2R2
	4/6 = R1r1r2r2, r1r1R2r2
	1/16 = r1r1r2r2

His interpretation was that the two genes each had a pair of alleles that exhibited cumulative effects. In other words, the genes lacked dominance and their action was additive. Each allele R₁ or R₂ added some red to the phenotype so that the genotypes of white contained neither of these alleles, while the dark red genotype contained only R₁ and R₂. The phenotypic frequency ratio resulting from the F₂ was 1 : 4 : 6 : 4 : 1 (i.e. nine genotypes and five classes) (Figure 4.2).

      

Figure 4.2 (a)Nilsson‐Ehle's classical work involving wheat color provided the first formal evidence of genes with cumulative effect. (b) An illustration of gene action using numeric values.

      The study involved only two loci. However, most polygenic traits are conditioned by genes at many loci. The number of genotypes that may be observed in the F₂ is calculated as 3ⁿ, where n = number of loci (each with two alleles). Hence, for 3 loci, the number of genotypes = 27, and for 10 loci, it will be 3¹⁰ = 59 049. Many different genotypes can have the same phenotype; consequently, there is no strict one‐to‐one relationship between genotype. For n loci, there are 3ⁿ genotypes and 2n + 1 phenotypes. Many complex traits such as yield may have dozens and conceivably even hundreds of loci.

      Other difficulties associated with studying the genetics of quantitative traits are dominance, environmental variation, and epistasis. Not only can dominance obscure the true genotype, but both the amount and direction can vary from one gene to another. For example, allele A may be dominant to a, but b may be dominant to B. It has previously been mentioned that environmental effects can significantly obscure genetic effects. Non‐allelic interaction is a clear possibility when many genes are acting together.

       Number of genes controlling a quantitative trait

      Polygenic inheritance is characterized by segregation at a large number of loci affecting a trait as previously discussed. Biometrical procedures have been proposed to estimate the number of genes involved in a quantitative trait expression. However, such estimates, apart from not being reliable, have limited practical use. Genes may differ in the magnitude of their effects on traits, not to mention the possibility of modifying gene effects on certain genes.

       Modifying genes

      One gene may have a major effect on one trait, and a minor effect on another. There are many genes in plants without any known effects besides the fact that they modify the expression of a major gene by either enhancing or diminishing it. The effect of modifier genes may be subtle, such as slight variations in traits like shape and shades of color of flowers, or variation in aroma and taste in fruits. Those trait modifications are of concern to plant breeders as they conduct breeding programs to improve quantitative traits involving many major traits of interest.

      4.2.4