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Modern Genetic Analysis Chapter 18. Quantitative Genetics
More on Analyzing Variance

Knowledge of the broad heritability (H2) of a trait in a population is not very useful in itself, but a finer subdivision of phenotypic variance can provide important information for plant and animal breeders. The genetic variation and the environmental variation can themselves each be further subdivided to provide information about gene action and the possibility of shaping the genetic composition of a population.

Additive and Dominance Variance

When a heterozygote A / a is not exactly intermediate in phenotype between the two homozygotes A / A and a / a, then all the genetic variation for phenotype cannot be accounted for by differences in the average effect in the population of A and a alleles. Some of the genetic variance is the result of the deviation of the heterozygote from the phenotype expected from a simple averaging of the two allelic effects. The total genetic variance in the population can then be subdivided into additive genetic variation,S 2a the variance that arises because there is an average difference between the carriers of a alleles and the carriers of A alleles, and a component called the dominance variance, S 2d which results from the fact that heterozygotes are not exactly intermediate between the monozygotes. Thus

The total phenotypic variance can now be written as

We define a new kind of heritability, the heritability in the narrow sense (h2), as

It is this heritability, not to be confused with H2, that is useful in determining whether a program of selective breeding will succeed in changing the population. The greater the h2 is, the greater the difference is between selected parents and the population as a whole, which will be preserved in the offspring of the selected parents.

To see why it is this heritability that matters for selection response, consider an extreme case where the two homozygotes are equal in phenotypesay, with a score of 10but the heterozygote is overdominant, with a score of 12. Further, suppose the population is in random-mating proportions

If we now select the largest individuals to breed for the next generation, they will all be heterozygotes, and, when they are bred together, they will exactly reproduce once again the 1:2:1 distribution of genotypes in the preceding generation. Selection will have been completely ineffective despite the existence of genetic variance in the population, because all the variance was due to dominance and there was no additive variance.

MESSAGE
The effect of selection depends on the amount of additive genetic variance and not on the genetic variance in general. Therefore, the narrow heritability, h2, not the broad heritability, H2, is relevant for a prediction of response to selection.

What has been described as the "dominance" variance is really more complicated. It is all the genetic variation that cannot be explained by the average effect of substituting A for a. If there is more than one locus affecting the character, then any epistatic interactions between loci will appear as variance not associated with the average effect of substituting alleles at the A locus. In principle, we can separate this interaction varianceS2i from the dominance variance S2d In practice, however, this cannot be done with any semblance of accuracy, so all the nonadditive variance appears as "dominance" variance.

Estimating Genetic Variance Components

Genetic components of variance can be estimated from covariance between relatives, but the derivation of these estimates is beyond the scope of an elementary text.

There is, however, another way to estimate h2 that reveals its real meaning. If we plot the phenotypes of the offspring against the average phenotypes of their two parents (the midparent value), we may observe a relation like the one illustrated in Figure 18-11. The regression line will pass through the mean of all the parents and the mean of all the offspring, which will be equal to each other because no change has occurred in the population between generations. Moreover, taller parents have taller children and shorter parents have shorter children, so that the slope of the line is positive. But the slope is not unity; very short parents have children who are somewhat taller and very tall parents have children who are somewhat shorter than they themselves are. This slope of less than unity for the regression line arises because heritability is less than perfect. If the phenotype were additively inherited with complete fidelity, then the height of the offspring would be identical with the midparent value and the slope of the line would be 1. On the other hand, if the offspring had no heritable similarity to their parents, all parents would have offspring of the same average height and the slope of the line would be 0. This suggests that the slope of the regression line of the offspring value on the midparent value is an estimate of additive heritability. In fact, the relation is precise.

The fact that the slope equals the additive heritability now allows us to use h2 to predict the effects of artificial selection. Suppose that we select parents for the next generation who are on the average 2 units above the general mean of the population from which they were chosen. If h2 = 0.5 then the offspring who form the next, selected generation will lie 0.5(2.0) = 1.0 unit above the mean of the present population, because the regression coefficient predicts how much increase in y will result from a unit increase in x. We can define the selection differential as the difference between the selected parents and the unselected mean and the selection response as the difference between their offspring and the preceding generation. Then

or

The second expression provides us with yet another way to estimate h2: by selecting for one generation and comparing the response with the selection differential. Usually this is carried out for several generations, and the average response is used.

Remember that any estimate of h2, just as for H2, depends on the assumption of no greater environmental correlation between closer relatives. Moreover, h2 in one population in one set of environments will not be the same as h2 in a different population at a different time. Figure 18-12 shows the range of heritabilities reported in various studies for a number of traits in chickens. The very small ranges are generally close to zero. For most traits for which a substantial heritability has been reported in some population, there are big differences from study to study.

The Use of h2 in Breeding

Even though h2 is a number that applies only to a particular population and a given set of environments, it is still of great practical importance to breeders. A poultry geneticist interested in increasing, say, growth rate is not concerned with the genetic variance over all possible flocks and all environmental distributions. Given a particular flock (or a choice between a few particular flocks) under the environmental conditions approximating present husbandry practice, the question becomes: Can a selection scheme be devised to increase growth rate and, if so, how fast? If one flock has a lot of genetic variance and another only a little, the breeder will choose the former to carry out selection. If the heritability in the chosen flock is very high, then the mean of the population will respond quickly to the selection imposed, because most of the superiority of the selected parents will appear in the offspring. The higher h2 is, the higher the parentoffspring correlation is. If, on the other hand, h2 is low, then only a small fraction of the increased growth rate of the selected parents will appear in the next generation.

If h2 is very low, some alternative scheme of selection or husbandry may be needed. In this case, H2 together with h2 can be of use to the breeder. Suppose that h2 and H2 are both low, which means that there is a lot of environmental variance compared with genetic variance. Some scheme of reducing S2e must be used. One method is to change the husbandry conditions so that environmental variance is lowered. Another is to use family selection. Rather than choosing the best individuals, the breeder allows pairs to produce several progeny, and the mating is selected on the basis of the average performance of the progeny. Averaging over progeny allows uncontrolled environmental and developmental noise variation to be canceled out, and a better estimate of the genotypic difference between pairs can be made so that the best pairs can be chosen as parents of the next generation.

If, on the other hand, h2 is low but H2 is high, then there is not much environmental variance. The low h2 is the result of a small amount of additive genetic variance compared with dominance and interaction variance. Such a situation calls for special breeding schemes that make use of nonadditive variance. One such scheme is the hybrid-inbred method, which is used almost universally for corn. A large number of inbred lines are created by selfing. These inbred lines are then crossed in many different combinations (all possible combinations, if this is economically feasible), and the cross that gives the best hybrid is chosen. Then new inbred lines are developed from this best hybrid, and again crosses are made to find the best second-cycle hybrid. This scheme selects for dominance effects, because it takes the best heterozygotes; it has been the basis of major genetic advances in hybrid maize yield in North America since 1930. Yield in corn does not appear to have large amounts of nonadditive genetic variance, so it is debatable whether this technique ultimately produces higher-yielding varieties than those that would have resulted from years of simple selection techniques based on additive variance.

The hybrid method has been introduced into the breeding of all kinds of plants and animals. Tomatoes and chickens, as examples, are now almost exclusively hybrids. Attempts also have been made to breed hybrid wheat, but thus far the wheat hybrids obtained do not yield consistently better than the nonhybrid varieties now used.

MESSAGE
The subdivision of genetic variation and environmental variation provides important information about gene action that can be used in plant and animal breeding.

© 1999 by W. H. Freeman and Company. All rights reserved.