Principles of Plant Breeding

Components of Genetic Variance

• Breeder 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. By knowing the components of variance, one may estimate the relative importance of the various determinants of phenotype. phenotypic value of quantitative traits:

  P (phenotype) = G (genotype) = E (environment)
• 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).
• Total variance of a quantitative trait may be mathematically expressed as follows:

  VP = VG +VE +VGE
• where VP = total phenotypic variance of the segregating population, VG = genetic variance, VE = environmentalvariance, and VGE = variance associated with the genetic and environmental interaction. The genetic component of variance may be further partitioned into three components as follows:

  VG = VA + VD + VI
• where VA = additive variance (variance from additive gene effects), VD = dominance variance (variance fromdominance gene action), and VI = 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 resemblancebetween relatives. Hence VA is the primary determinant of the observable genetic properties of the population,and of the response of the population to selection. Further, VA is the only component that the researchercan most readily estimate from observations made on the population. Consequently, it is common to partitiongenetic variance into two – additive versus all other kinds of variance. This ratio, VA/VP, gives what is calledthe heritability of a trait, an estimate that is of practicalimportance in plant breeding. The total phenotypic variance may then be rewritten as:

  VP = VA + VD + VI + VE + VGE
• To obtain environmental variance, individuals from the same genotype are used. An inbred line (essentially homozygous) consists ofindividuals with the same genotype. An F1 generationfrom a cross of two inbred lines will be heterozygous butgenetically uniform. The variance from the parents andthe F1 may be used as a measure of environmental variance(VE). The procedure for obtaininggenotypic variance from F2 and backcross data. In sum,variances from additive, dominant, and environmentaleffects may be obtained as follows:

  VP1 = E; VP2 = E; VF1 = E

  VF2 = 1/2A + 1/4D + E
VB1 = 1/4A + 1/4D + E
VB2 = 1/4A + 1/4D + E
VB1 + VB2 = 1/2A + 1/2D +2E