Читать книгу Principles of Plant Genetics and Breeding - George Acquaah - Страница 181

A breeder has a specific objective for conducting a breeding project. However, selection is seldom made on the basis of one trait alone. For example, if the breeding project is for disease resistance, the objective will be to select a genotype that combines disease resistance with the qualities of the elite adapted cultivar. Invariably, breeders usually practice selection on several traits simultaneously. The problem with this approach is that as more traits are selected for, the less the selection pressure that can be exerted on any one trait. Therefore, the breeder should select on the basis of two or three traits of the highest economic value. It is conceivable that a trait of high merit may be associated with other traits of less economic value. Hence, using the concept of selection on total merit, the breeder would make certain compromises, selecting individuals that may not have been selected, were it based on a single trait.

In selecting on a multivariate phenotype, the breeder explicitly or implicitly assigns a weighting scheme to each trait, resulting in the creation of a univariate trait (an index) that is then selected. The index is the best linear prediction of an individual's breeding value. It takes the form of a multiple regression of breeding values on all the sources of information available for the population.

The methods used for constructing an index usually include heritability estimates, relative economic importance of each trait, and genetic and phenotypic correlation between the traits. The most common index is a linear combination that is mathematically expressed as follows:

where z is the vector of phenotypic values in an individual, and b is a vector of weights. For three traits, the form may be

where a, b, and c are coefficients correcting for relative heritability and the relative economic importance of traits A, B, and C, respectively, and A¹, B¹, and C¹ are the numerical values of traits A, B, and C expressed in standardized form. A standardized variable (X¹) is calculated as

where, X is the record of performance made by an individual; X is the average performance of the population; and σ_x is the standard deviation of the trait.

The classical selection index has the following form:

where x₁, x₂, x₃, x_n are the phenotypic performance of the traits of interest, and b₁, b₂, and b₃ are the relative weights attached to the respective traits. The weights could be simply the respective relative economic importance of each trait, the resulting index called the basic index, and may be used in cultivar assessment in official registration trials.

An index by itself is meaningless, unless it is used in comparing several individuals on a relative basis. Further, in comparing different traits, the breeder is faced with the fact that the mean and variability of each trait is different, and frequently, the traits are measured in different units. Standardization of variables resolves this problem.