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 Decision‐making in breeding based on biometrical genetics
Biometrical genetics is concerned with the inheritance of quantitative traits. As previously stated, most of the genes of interest to plant breeders are controlled by many genes. In order to effectively manipulate quantitative traits, the breeder needs to understand the nature and extent of their genetic and environmental control. M.J. Kearsey summarized the salient questions that need to be answered by a breeder who is focusing on improving quantitative (and also qualitative) traits:
1 Is the character inherited?
2 How much variation in the germplasm is genetic?
3 What is the nature of the genetic variation?
4 How is the genetic variation organized?
By having answers to these basic genetic questions, the breeder will be in a position to apply the knowledge to address certain fundamental questions in plant breeding.
What is the best cultivar to breed?
As will be discussed later in the book, there are several distinct types of cultivars that plant breeders develop – pure lines, hybrids, synthetics, multilines, composites, etc. The type of cultivar is closely related to the breeding system of the species (self‐ or cross‐pollinated), but more importantly on the genetic control of the traits targeted for manipulation. As breeders have more understanding of and control over plant reproduction, the traditional grouping between types
