Principles of Plant Genetics and Breeding. George Acquaah

variety) will display additive, dominance, and epistatic gene action. F₁ hybrid material will have no additive gene action and no genetic variation.

      In terms of pollination, self‐pollinated species exhibit additive gene action since this gene action is associated with homozygosity. On the contrary, non‐additive gene action is associated with heterozygosity and hence is more prevalent in cross‐pollinated species than self‐pollinated ones. Simply inherited (qualitative, oligogenic) traits predominantly exhibit non‐additive and epistatic gene action, while polygenic traits are governed predominantly by additive gene action.

      Gene action estimates are affected by the presence of genetic linkage. Estimates of additive gene action and dominance gene action can be biased up when the genes of interest are in the coupling phase (AB/ab). In the repulsion phase (Ab/aB), genes can cause estimates of dominance gene action to be biased upwards and additive action downwards.

      4.2.8 Variance components of a quantitative trait

      The genetics of a quantitative trait centers on the study of its variation. As D.S. Falconer stated, it is in terms of variation that the primary genetic questions are formulated. Further, the researcher is interested in partitioning variance into its components that are attributed to different causes or sources. The genetic properties of a population are determined by the relative magnitudes of the components of variance. In addition, by knowing the components of variance, one may estimate the relative importance of the various determinants of phenotype.

      K. Mather expressed the phenotypic value of quantitative traits in this commonly used expression:

Individuals differ in phenotypic value. When the phenotypes of a quantitative trait are measured, the observed value represents the phenotypic value of the individual. The phenotypic value is variable because it depends on genetic differences among individuals, as well as environmental factors and the interaction between genotypes and the environment (called G × E interaction). A third factor (GE) is therefore added to the previous conceptual equation so that the total variance of a quantitative trait may be mathematically expressed as follows:

      where V_P = total phenotypic variance of the segregating population; V_G = genetic variance; V_E = environmental variance; and V_GE = variance associated with the genetic and environmental interaction.

      The genetic component of variance may be further partitioned into three components as follows:

      where V_A = additive variance (variance from additive gene effects); V_D, = dominance variance (variance from dominance gene action); and V_I = interaction (variance from interaction between genes). Additive genetic variance (or simply additive variance) is the variance of breeding values and is the primary cause of resemblance between relatives. Hence V_A is the primary determinant of the observable genetic properties of the population, and of the response to the population to selection. Further, V_A is the only component that the researcher can most readily estimate from observations made on the population. Consequently, it is common to partition genetic variance into two – additive versus all other kinds of variance. This ratio, V_A/V_P, gives what is called the heritability of a trait, an estimate that is of practical importance in plant breeding.

      The total phenotypic variance may then be rewritten as follows:

      To estimate these variance components, the researcher uses carefully designed experiments and analytical methods. To obtain environmental variance, individuals from the same genotype or replicates are used.

      An inbred line (essentially homozygous) consists of individuals with the same genotype. An F₁ generation from a cross of two inbred lines will be heterozygous but genetically uniform. The variance from the parents and the F₁ may be used as a measure of environmental variance (V_E). K. Mather provided procedures for obtaining genotypic variance from F₂ and backcross data. In sum, variances from additive, dominant, and environmental effects may be obtained as follows:

      (where V_P1 and V_P2 are variances for the parents in a cross; V_F1 is the variance of the resulting hybrid; F₂ is the variance of the F₂ population; A and D are additive and dominant effects, respectively; E is the environmental effect; V_B1 and V_B2 are backcross variances). This represents the most basic procedure for obtaining components of genetic variance since it omits the variances due to epistasis, which are common with quantitative traits. More rigorous biometric procedures are needed to consider the effects of interlocular interaction.

      It should be pointed out that additive variance and dominance variance are statistical abstractions rather than genetical estimates of these effects. Consequently, the concept of additive variance does not connote perfect additivity of dominance or epistasis. To exclude the presence of dominance or epistasis, all the genotypic variance must be additive.

      4.2.9 The concept of heritability

      Genes are not expressed in a vacuum but in an environment. A phenotype observed is an interaction between genes that encode it and the environment in which the genes are being expressed. Plant breeders typically select plants based on the phenotype of the desired trait, according to the breeding objective. Sometimes, a genetically inferior plant may appear superior to other plants only because it is located in a more favorable region of the soil. This may mislead the breeder. In other words, the selected phenotype will not give rise to the same progeny. If the genetic variance is high and the environmental variance is low, the progeny will be like the selected phenotype. The converse is also true. If such a plant is selected for advancing the breeding program, the expected genetic gain will not materialize. Quantitative traits are more difficult to select in a breeding program because they are influenced to a greater degree by the environment than are qualitative traits. If two plants are selected randomly from a mixed population, the observed difference in a specific trait may be due to the average effects of genes (hereditary differences), or differences in the environments in which the plants grew up, or both. The average effects of genes are what determines the degree of resemblance between relatives (parents and offspring), and hence is what is transmitted to the progenies of the selected plants.

       Definition

      The concept of the reliability of the phenotypic value of a plant as a guide to the breeding value (additive genotype) is called the heritability of the metrical trait. As previously indicated, plant breeders are able to measure phenotypic values directly, but it is the breeding value of individuals that determines their influence on the progeny. Heritability is the proportion of the observed variation in a progeny that is inherited. The bottom line is that if a plant breeder selects plants