– making it possible to distinguish between haploid and diploid selections. The coefficient of selection is designated s, and has values between 0 and 1. Generally, the contribution of a favorable genotype is given a score of 1, while a less favorable (less fit) genotype is scored 1 − s.
An s = 0.1 means for every 100 zygotes produced with the favorable genotype, there will be 90 individuals with the unfavorable genotype. Fitness can exhibit complete dominance, partial dominance, no dominance, or overdominance. Consider a case of complete dominance of the A allele. The relative fitness of genotypes will be:
| Genotypes | AA | Aa | aa | Total |
| Initial frequency | p 2 | 2pq | q 2 | 1 |
| Relative fitness | 1 | 1 | 1 − s | |
| After selecting | p 2 | 2pq | q 2 (1 − s) | 1 − sq 2 |
The total after selection is given by:
To obtain the gene frequency in the next generation, use
where
The relationship between any two generations may be generalized as:
Similarly, the difference in gene frequency, Δq, between any two generations can be shown to be:
Other scenarios of change in gene frequency are possible.
Plant breeders use artificial selection to impose new fitness values on genes that control traits of interest in a breeding program.
3.5 Summary of key plant breeding applications
Selection is most effective at intermediate gene frequency (q = 0.5) and least effective at very large or very small frequencies (q = 0.99 or q = 0.01). Further, selection for or against a rare allele is ineffective. This is so because a rare allele in a population will invariably occur in the heterozygote and be protected (heterozygote advantage).
Migration increases variation of a population. Variation of a population can be expanded in a breeding program through introductions (impact of germplasm). Migration also minimizes the effects of inbreeding.
In the absence of the other factors or processes, any one of the frequency altering forces will eventually lead to fixation of one allele or the other.
The forces that alter gene frequencies are usually balanced against each other (e.g. mutation to a deleterious allele is balanced by selection).
Gene frequencies attain stable values called equilibrium points.
In both natural and breeding populations, there appears to be a selective advantage for the heterozygote (hybrid). Alleles with low selection pressure may persist in the population in heterozygote state for many generations.
As population size decreases, the effect of random drift increases. This effect is of importance in germplasm collection and maintenance. The original collection can be genetically changed if a small sample is taken for growing to maintain the accession.
3.6 Modes of selection
There are three basic forms of selection – stabilizing, disruptive, and directional – the last form being the one of most concern to plant breeders. These forms of selection operate to varying degrees under both natural and artificial selection. A key difference lies in the goal. In natural selection, the goal is to increase the fitness of the species, whereas in plant breeding, breeders impose artificial selection usually to direct the population toward a specific goal (not necessarily the fittest).
3.6.1 Stabilizing selection
Selection as a process is ongoing in nature. Regarding characters that directly affect the fitness of a plant (i.e. viability, fertility), selection will always be directionally toward optimal phenotype for a given habitat. However, for other characters, once optimal phenotype has been attained, selection will act to perpetuate it as long as the habitat remains stable. Selection will be for the population mean and against either extreme expression of the phenotype. This mode of selection is called stabilizing selection (or also called balancing or optimum selection). Taking flowering for example; stabilizing selection will favor neither early flowering nor late flowering. In terms of genetic architecture, dominance will be low or absent or ambidirectional, whereas epistasis will not generally be present. Stabilizing selection promotes additive variation.
3.6.2 Disruptive selection
Natural habitats are generally not homogeneous but consist of a number of “ecological niches” that are distinguishable in time (seasonal or long‐term cycles), space (microniches), or function. These diverse ecological conditions favor diverse phenotypic optima in form and function. Disruptive selection is a mode of selection in which extreme variants have higher adaptive value than those around the average mean value. Hence, it promotes diversity (polymorphism). The question then is how the different optima relate (dependent or independent) for maintenance and functioning. Also, at what rate does gene exchange occur between the differentially selected genotypes? These two factors (functional relationship and rate of gene exchange) determine the effect of genetic structure of a population. In humans, for example, a polymorphism that occurs is sex (female and male). The two sexes are 100% interdependent in reproduction (gene exchange is 100%). In plants, self‐incompatibility is an example of such genetically controlled polymorphism. The rarer the self‐incompatibility allele at a locus, the higher the chance of compatible mating (and vice versa). Such frequency‐dependent selection is capable of building up a large number of self‐incompatibility alleles in a population. As previously indicated, several hundreds of alleles have been found in some species.
3.6.3 Directional selection
Plant breeders, as previously stated, impose directional selection to change existing populations or varieties (or other genotypes) in a predetermined way. Artificial selection is imposed on the targeted character(s) to achieve maximal or optimal expression. To achieve this, the breeder employs techniques (crossing) to reorganize the genes form the parents in a new genetic matrix
