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selection steadily changed oil content to about 22% in the high line and to 0% in the low line. Response to selection was similarly linear for protein content, starting at 10.9% and reaching 32.1% in the high line and 4.2% in the low line.

The Illinois Long-Term Selection experiment shows that response to selection is relatively steady and linear over a long period of time. (Slight fluctuations in the mean phenotype over time may be explained by some variation in the selection differential each generation as well as by environmental variation.) The observed change in phenotypic means in the Illinois Long-Term Selection experiment looks similar to the predicted response to selection on traits with many loci in the simulation results shown in Figs 9.12b and 9.12c. The results are therefore consistent with genetic variation in the oil- and protein-content phenotypes being caused by a relatively large number of loci and the possibility that mutation may have contributed some genetic variation over time.

Another example is long-term selection carried out for 70 generations to increase the percentage of body muscle, measured as protein content, in mice at 42 days old (Bunger et al. 1998). Figure 9.14a shows the mean amount of protein per individual over the course of the experiment. Selection increased protein content rapidly at first, but then response to selection slowed as the experiment continued. This is a classic example of a selection plateau where continued natural selection shows a diminishing response over time such that the trait mean asymptotes toward a constant value even though selection is still being applied to increase the trait mean. The additive genetic variance (VA) and the heritability (h2) shown in Fig. 9.14b explain why response to selection decreased over time. The additive genetic variance, and therefore the herit-ability, decreased through time so that the response to selection was not constant over the 70 generations of the experiment. The observed reduction over time in the response to selection and the selection plateau are similar to the predicted response to selection on traits with few loci of large effects shown in Fig. 9.12 a. The response to long-term selection for protein content in mice is therefore consistent with genetic variation caused by a relatively small number of loci having relatively large effects on the phenotype.

Two additional phenomena can cause limits to selection response. The first process is the accumulation of gametic disequilibrium that alters the amount of additive genetic variance. The additive genetic variance (VA) can be decomposed into two parts:

Figure 9.14 Long-term selection for muscle mass in mice (measured as protein content per individual) over 70 generations. (a) The phenotypic mean over time, with a pronounced asymptote, or selection plateau, that indicates a diminishing response to selection over time. The total phenotypic variance, the additive genetic variance, and the realized heritability are shown in (b). Even though the selection differential is constant over time, the heritability declines steadily, as expected for a quantitative trait where genetic variation is caused by relatively few loci. The dip in protein content during generations 18-20 was an artifact due to an environmental effect. While the phenotypic variance increases over the experiment (b), this is caused largely by the increase in the phenotypic mean (the coefficient of variation of VP stays nearly constant). Redrawn from Bunger, L., Renne, U., Dietl, G., and Kuhla, S. (1998) Long-term selection for protein amount over 70 generations in mice. Genetical Research 72: 93-109. Reprinted with the permission of Cambridge University Press.

Figure 9.14 Long-term selection for muscle mass in mice (measured as protein content per individual) over 70 generations. (a) The phenotypic mean over time, with a pronounced asymptote, or selection plateau, that indicates a diminishing response to selection over time. The total phenotypic variance, the additive genetic variance, and the realized heritability are shown in (b). Even though the selection differential is constant over time, the heritability declines steadily, as expected for a quantitative trait where genetic variation is caused by relatively few loci. The dip in protein content during generations 18-20 was an artifact due to an environmental effect. While the phenotypic variance increases over the experiment (b), this is caused largely by the increase in the phenotypic mean (the coefficient of variation of VP stays nearly constant). Redrawn from Bunger, L., Renne, U., Dietl, G., and Kuhla, S. (1998) Long-term selection for protein amount over 70 generations in mice. Genetical Research 72: 93-109. Reprinted with the permission of Cambridge University Press.

where Va is the additive genic variance that is not impacted by gametic disequilibrium and D is the gametic disequilibrium coefficient. When there is gametic equilibrium (D = 0) then the additive genetic variance is all caused by variance in alleles, or genic variance. However, when there is some level of gametic disequilibrium then the additive genetic variance can be reduced (negative D) or increased (positive D). Directional and stabilizing natural selection tend to cause negative gametic disequilibrium because individuals with similar phenotypic values tend to have a correlated set of alleles at each of the loci that contribute to the trait (also see the example in Chapter 2). In contrast, disruptive selection tends to cause positive gametic disequilibrium. If selection is strong relative to recombination, then gametic disequilibrium will alter the additive genetic variance and thereby the heritability. A reduction in the response to selection or a selection plateau can occur when negative gametic disequilibrium caused by selection has accumulated such that VA declines even though the loci the underlie the trait have not all reached fixation and loss. For more details on this complex topic consult Bulmer (1985) and Lynch and Walsh (in preparation; draft chapters available at http://nitro.biosci.arizona.edu/zbook/book.html).

The other process that can limit response to selection is called antagonistic pleiotropy. It occurs when response to selection changes the mean of one trait (selection for) as well as the mean of a correlated trait (selection of). While selection for increased fitness drives change in the mean of one trait over time, the correlated change in the mean of the other trait may actually decrease fitness. After some response to selection has occurred, the fitness trade offs between the two traits may reach a point where further change in the mean of one trait that increases fitness is offset by the negative fitness consequences of change in the mean of a correlated trait. When such fitness trade offs for correlated traits exist, they will ultimately limit response to selection even when additive genotypic variation exists for both traits. Examples of such trade offs for correlated traits have been hypothesized or observed for a range of traits. One possible trade off maintained by antagonistic pleiotropy involves alleles that tend to increase reproduction at early ages but decrease lifespan (Williams 1957). In support of the hypothesis that survival and reproduction have a fitness trade off, Silbermann and Tatar (2000) have shown that a heat-induced protein expressed by the hsp70 locus influences both egg hatching rate and survival rate in Drosophila melanogaster. Higher levels of hsp 70 expression lead to longer lifespans but at the same time lead to lower rates of egg hatching. If reproduction and survival in D. melanogaster are associated by antagonistic pleiotropy via hsp70, then response to any selection acting on these traits will not be able to exhaust all the additive genetic variation if the highest fitness is a balance of intermediate levels of both traits.

The genetic variance/covariance or G matrix has also become a focus of research to better understand how the genetic basis of potentially non-independent quantitative traits changes over time with selection, genetic drift, and mutation (reviewed by Steppan et al. 2002; Jones et al. 2003). The G matrix represents the genetic inter-relationships among multiple traits, so estimating it in a range of species and for a range of traits is a prerequisite to understand how pheno-types might respond to long-term natural selection. Understanding how the G matrix changes over time is also fundamental to understanding long-term response to selection. The predicted trait means in equation 9.21 rely on the constancy of the G matrix over time. If G changes rapidly or unpredictably over time then predicted changes in trait means are not applicable over long periods of time. Rapid changes in G would also reduce the ability to infer past patterns of response to selection given a current estimate of G.

Neutral evolution of quantitative traits

Considering a quantitative trait as selectively neutral is useful to predict the action of basic processes that will reduce as well as contribute to additive genetic variation. If a quantitative trait is neutral, each locus that contributes to variation in the trait should be neutral as well. Therefore, we can employ expressions already developed to predict the consequences of genetic drift. Additive genotypic variation is expected to decrease with genetic drift over time because the alleles at the loci that form the basis of VA will progress toward fixation and loss. The expected rate of decrease in VA by genetic drift is

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