Dominance theory

The dominance theory assumes that vigor in plants is conditioned by dominant alleles, recessive alleles being deleterious or neutral in effect. It follows then that a genotype with more dominant alleles will be more vigorous than one with few dominant alleles. Consequently, crossing two parents with complementary dominant alleles will concentrate more favorable alleles in the hybrid than either parent. The dominance theory is the more favored of the two theories by most scientists, even though neither is completely satisfactory. In practice, linkage and a large number of genes prevent the breeder from developing inbred lines that contain all homozygous dominant alleles. If too many deleterious alleles are present it makes it difficult to inbreed to recover sufficient loci with homozygous dominant alleles. Inbreeding depression occurs upon selfing because the deleterious recessive alleles that are protected in the heterozygous condition become homozygous and are expressed. It should be pointed out that highly productive inbred lines have continued to be produced for hybrid production, the reason why single-cross hybrids have returned to dominance in corn hybrid production.To illustrate this theory, assume a quantitative trait is conditioned by four loci. Assume that each dominant genotype contributes two units to the phenotype, while a recessive genotype contributes one unit. A cross between two inbred parents could produce the following outcome With dominance, each locus will contribute two units to the phenotype. The result is that the F1 would be more productive than either parent. D.L. Falconer developed a mathematical expression for the relationship between the parents in a cross that leads to heterosis as follows where HF1 is the the deviation of the hybrid from the

mid-parent value, d is the the degree of dominance, and y is the the difference in gene frequency in the parents of the cross. From the expression, maximum mid-parent heterosis will occur when the values of the two factors are each unity. That is, the populations to be crossed are fixed for opposite alleles and there is complete dominance.

Over dominance theory

The phenomenon of the heterozygote being superior to the homozygote is called overdominance. The overdominance theory assumes thatthe alleles of a gene are contrasting but each has a different favorable effect in the plant. Consequently, a heterozygous locus would have greater positive effect than a homozygous locus and, by extrapolation, a genotype with more heterozygous loci would be more vigorous than one with less heterozygotes.To illustrate this phenomenon, consider a quantitative trait conditioned by four loci. Assume that recessive, heterozygote, and homozygote dominants contribute 1, 2, and 1½ units to the phenotypic value,respectively:

Biometrics of heterosis

Heterosis may be defined in two basic ways:

Better-parent heterosis. This is calculated as the degree by which the F1 mean exceeds the better parent in the cross.

 Mid-parent heterosis. Previously defined as the superiority of the F1 over the mean of the parents.

For breeding purposes, the breeder is most interested to know whether heterosis can be manipulated for crop improvement. To do this, the breeder needs to understand the types of gene action involved in the phenomenon as it operates in the breeding population of interest. As Falconer indicated, in order for heterosis to manifest for the breeder to exploit, some level of dominance gene action must be present, in addition to the presence of relative difference in gene frequency in the two parents. Given two populations, in Hardy–Weinberg equilibrium, with genotypic values and frequencies for one locus with two alleles p and q for population A, and r and s for population B as follows

From the foregoing, if, heterosis. On the other hand, if in population A pผ0 or 1 and by the same token in population B rผ0 or 1 for the same locus, depending on whether the allele is in homozygous recessive or dominant state, there will be a heterotic response. In the first generation, the heterotic response will be due to the loci where pผ1 and rผ0, or vice versa. Consequently, heterosis manifested will depend on the number of loci that have contrasting loci as well as the level of dominance at each locus. The highest heterosis will occur when one allele is fixed in one population and the other allele in the other. If gene action is completely additive, the average response would be equal to the mid-parent, and hence heterosis will be zero. On the other hand, if there is dominance and/or epistasis, heterosis will manifest.

Plant breeders develop cultivars that are homozygous.When there is complete or partial dominance, the best genotypes to develop are homozygotes orheterozygous, where there could be opportunities todiscover transgressive segregates. On the other hand,when non-allelic interaction is significant, the bestgenotype to breed would be a heterozygote. Some recent views on heterosis have been published. Some maize researchers have provided evidence to the effect that the genetic basis of heterosis is partial dominance to complete dominance. A number of research data supporting overdominance suggest that it resulted from pseudo-overdominance arising from dominant alleles in repulsion phase linkage.

Yet, still, some workers in maize research have suggested epistasis between linked loci to explain the terosis.