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Phenotypic value

Figure 9.9 General types of natural selection on quantitative traits. Directional selection occurs when phenotypic values at the upper or lower end of the distribution have the highest fitness. Stabilizing selection occurs when intermediate trait values have the highest fitness. Disruptive selection occurs when trait values at the edges of the phenotypic distribution have the highest fitness. Response to directional selection increases or decreases the population mean phenotype. Response to stabilizing or disruptive selection does not change the mean but decreases or increases the variance of the phenotypic distribution.

in phenotypic value decreases over time since individuals with phenotypic values at the upper and lower extremes have lower fitness values and do not contribute to future generations. Similarly, the mean phenotypic value in a population does not change with response to disruptive selection. Disruptive selection causes the variance in phenotypic values to increase since individuals at the upper and lower extremes of the distribution have higher fitness than individuals with phenotypic values near the mean. Disruptive selection results in the phenotypic distribution widening over time, and the distribution of phenotypic values can eventually become bimodal.

The heritability provides the basis for predicting the outcome of natural selection on quantitative traits according to

where R is the response to selection, h2 is the narrowsense heritability, and s is the selection differential that measures the strength of natural selection. R and s are measured in the same units used to measure phenotypic value (e.g. kilograms, centimeters). Equation 9.11 is commonly called the breeder's equation because it predicts the change in mean phenotype in a population that will occur due to one generation of artificial selection as often employed by animal and plant breeders. The response to selection predicted by the breeder's equation is intuitive. Stronger natural selection or phenotypic variation that has a greater basis in additive genetic variance will result in a greater change in the mean pheno-type in a population.

To better understand how natural selection changes the mean phenotypic value, let's work through an example of directional selection based on pheno-typic value. The change in mean phenotype in a population caused by natural or artificial selection depends both on the force or amount of selection that is applied to the population and on genetic variation in the trait. The selection differential is one way to measure the strength of directional natural selection on quantitative traits. The selection differential is the difference between the phenotypic mean of the entire population and the phenotypic mean of that subset of individuals selected on the basis of their phenotypic value to be parents of the next generation. The selection threshold (sometimes called the truncation point) seen in Fig. 9.10 is the lower bound of phenotypic values in the group of parents selected to mate. The selection differential is com puted as the difference in the phenotypic mean of the selected parents (ps) and the phenotypic mean of the entire P1 population (p):

As shown in Fig. 9.10, the selection differential for this case is s = 12.5 - 10.0 = 2.5 (9.13)

which expresses that the selected parents have a 2.5-unit greater average phenotypic value than the full population that they were sampled from. Larger selection differential values indicate stronger selection. Although not true in this example, selection differentials are often expressed in units of standard deviations by standardizing phenotypic values in the parental population to have a mean of zero and a variance of one.

Imagine now that those individuals with pheno-typic values above the selection threshold in the P1 population mate at random and then produce a large population of progeny that are reared in the same environment as the parents. The phenotypic distribution of the progeny is shown in the lower panel of Fig. 9.10. The progeny have a mean phenotypic value of p'= 11.0. The difference between the F1 population phenotypic mean and the pheno-typic mean of the entire P1 population expresses how much the phenotypic mean was changed by selection for larger trait values in the parents. The response to selection is

The phenotypic mean in this example was increased one unit by directional selection in the P1 population.

The response to selection is a function of the amount of phenotypic variation that is due to additive genetic variation according to the breeder's equation. Since both the response to selection and the selection differential are known, it is then possible to estimate the heritability by rearranging the breeder's equation:

When estimated in this way, P2 is called the realized heritability since it is estimated from the observed response to selection rather than predicted by resemblance of parents and progeny in the absence of selection. Using the selection differential

P1 mean

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