Читать книгу Principles of Plant Genetics and Breeding - George Acquaah - Страница 176

The genetic advance achieved through selection depends on three factors:

1 The total variation (phenotypic) in the population in which selection will be conducted.

2 Heritability of the target character.

3 Selection pressure to be imposed by the plant breeder (i.e. the proportion of the population that is selected for the next generation).

A large phenotypic variance would provide the breeder a wide range of variability from which to select. Even when the heritability of the trait of interest is very high, genetic advance would be small without a large amount of phenotypic variation (Figure 4.3). When the heritability is high, selecting and advancing only the top few performers is likely to produce a greater genetic advance than selecting many moderate performers. However, such a high selection pressure would occur at the expense of a rapid loss in variation. When heritability is low, the breeder should impose a lower selection pressure in order to advance as many high‐potential genotypes as possible.

Figure 4.3 The effect of phenotypic variance on genetic advance. If the phenotypic variance is too small, the genetic variability from which to select will be limited, resulting in a smaller genetic gain. The reverse is true when the phenotypic variance is large.

In principle, the prediction of response is valid for only one generation of selection. This is because a response to selection depends on the heritability of the trait estimated in the generation from which parents are selected. To predict the response in subsequent generations, heritabilities must be determined in each generation. Heritabilities are expected to change from one generation to the next because, if there is a response, it must be accompanied by change in gene frequencies on which heritability depends. Also, selection of parents reduces the variance and the heritability, especially in the early generations. It should be pointed out that heritability changes are not usually large.

If heritability is unity (V_A = V_P; no environmental variance) progress in a breeding program would be perfect, and the mean of offspring would equal the mean of the selected parents. On the other hand, if heritability is zero, there would be no progress at all (R = 0).

The response in one generation may be mathematically expressed as

where

 Xo = mean phenotype of the offspring of selected parents;

 Xp = mean phenotype of the whole parental generation;

 R = the advance in one generation of selection;

 h2 = heritability;

 σ = phenotypic standard deviation of the parental population;

 i = intensity of selection;

 ∆G = genetic gain or genetic advance.

This equation has been suggested by some to be one of the fundamental equations of plant breeding that must be understood by all breeders, hence called the breeder's equation. The equation is graphically illustrated in Figure 4.4. The factor “i,” the intensity of selection (standardized selection differential), is a statistical factor that depends on the fraction of the current population retained to be used as parents for the next generation. If the entire population is used, the selection intensity is 0. The breeder may consult statistical tables for specific values (e.g. at 1% = 2.668; at 5% i = 2.06; at 10% i = 1.755). The breeder must decide the selection intensity to impose to achieve a desired objective. The selection differential can be predicted if the phenotypic values of the trait of interest are normally distributed, and the selection is by truncation (i.e. the individuals are selected solely in order of merit according to their phenotypic value – no individual being selected is less good than any of those rejected).

Figure 4.4 Genetic gain or genetic advance from selection indicates the progress plant breeders make from one generation to another based on the selection decisions they make.

The response equation is effective in predicting response to selection, provided the heritability estimate (h²) is fairly accurate. In terms of practical breeding, the parameters for the response equation are seldom available and hence not widely used. It is instructive to state that predicted response (theoretical estimate based on heritability and tabulated selection intensity) is different from realized response (what the breeder actually observes in the next generation following selection). Over the long haul, repeated selection tends to fix favorable genes, resulting in a decline in both heritability and phenotypic standard deviation. Once genes have been fixed, there will be no further response to selection.

 Example:

	X	σp	VP	VA	VE
Parents	15	2	6	4	3
Offspring	20.2	15	4.3	2.5	3

 Parents for i at p = 10% = 1.755 (read from tables and assuming a very large population)

 Offspring

Generally, as selection advances to higher generations, genetic variance and heritability decline. Similarly, the advance from one generation to the next declines, while the mean value of the trait being improved increases.