Principles of Plant Genetics and Breeding. George Acquaah

Figure 3.2 The approach to linkage equilibrium under random mating of two loci considered together. The value of “c” gives the linkage frequency between two loci. The effect of linkage is to slow down the rate of approach, the closer the linkage, the slower the rate. For c = 5, there is no linkage. The equilibrium value is approached slowly and theoretically unattainable.

3.3 Factors affecting changes in gene frequency

      Gene frequency in a population may be changed by one of two primary types of processes: systematic or dispersive. A systematic process causes a change in gene frequency that is predictable in both direction and amount. A dispersive process, associated with small populations, is predictable only in amount, not direction. D.S. Falconer listed the systematic processes as migration, mutation, and selection.

      3.3.1 Migration

      Migration is important in small populations. It entails the entry of individuals into an existing population from outside. Because plants are sedentary, migration, when it occurs naturally, is via pollen transfer (gamete migration). The impact of this immigration will have on the recipient population will depend on the immigration rate and the difference in gene frequency between the immigrants and natives. Mathematically, ∆q = m(q _m − q _o), where ∆q = the changes in the frequency of genes in the new mixed population, m = the number of immigrants, q _m = the gene frequency of the immigrants, and q _o = gene frequency of the host. Plant breeders employ this process to change frequencies when they undertake introgression of genes into their breeding populations. The breeding implication is that for open‐pollinated (outbreeding) species, the frequency of the immigrant gene may be low, but its effect on the host gene and genotypes could be significant.

      3.3.2 Mutation

      Natural mutations are generally rare. A unique mutation (non‐recurrent mutation) would have little impact on gene frequencies. Mutations are generally recessive in gene action, but the dominant condition may also be observed. Recurrent mutation (occurs repeatedly at a constant frequency) may impact gene frequency of the population. Natural mutations are of little importance to practical plant breeding. However, breeders may artificially induce mutation to generate new variability for plant breeding.

      3.3.3 Selection

      Selection is the most important process for altering population gene frequencies by plant breeders. Its effect is to change the mean value of the progeny population from that of the parental population. This change may be greater or lesser than the population mean, depending on the trait of interest. For example, breeders aim for higher yield but may accept and select for less of a chemical factor in the plant that may be toxic in addition to the high yield. For selection to succeed there must be:

      1 Phenotypic variation for the trait to allow differences between genotypes to be observed.

      2 The phenotypic variation must at least be partly genetic.

3.4 Frequency dependent selection

      Selection basically concerns the differential rate of reproduction by different genotypes in a population. The concept of fitness describes the absolute or relative reproductive rate of genotypes. The contribution of genotypes to the next generation is called the fitness (or adaptive value or selective value). The relative fitness of genotypes in a population may depend on its frequency relative to others. Selection occurs at different levels in the plant – phenotype, genotype, zygote, and gamete – 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