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Laurie et al. 2004

PTC, phenylthiocarbamide.

effects on phenotypic variation (dog body size, human stature) to a large number of OTLs with individual small effects on phenotypic variation (kernel oil content). This mirrors the overall trend in OTL mapping results, where the number of OTLs and their effect sizes are strongly dependent on the species, population, and phenotype studied. Whereas part of this diversity in OTL mapping results is likely caused by methodological and statistical power differences among studies, some of it likely reflects actual variability in the number and effects of OTLs that cause phenotypic variation.

OTL mapping studies not only identify effect sizes, but can also quantify the degree of dominance and epistasis for OTLs. OTLs have been observed to have dominance that ranges from zero (additive gene action), through all degrees of partial dominance to complete dominance, to cases of overdominance. One classic example is the wide range of the d/a ratio (a is the estimated additive effect of an allele and d is the estimated heterozygote value), spanning -2.0 to +2.0, observed for 74 OTLs detected for 11 phenotypes in tomato (de Vincente & Tanksley 1993). Based on these results, dominance frequently contributes to the genotypic variation of quantitative traits. Evidence for interaction variance caused by epistasis has been equivocal. Interactions between or among loci did not often explain much of the observed genotypic variation in early OTL mapping studies. However, it is generally more difficult to detect epistasis for OTLs due to statistical and sample size limitations (see Carlborg & Haley 2004). Recently, more effort has been directed toward testing for epistasis in OTL studies and numerous empirical studies have identified statistically meaningful interactions between two or more OTLs as often as additive effects of OTLs (reviewed by Malmberg & Mauricio 2005).

The genetic architecture of quantitative traits - the effect size and gene action (additivity, dominance, or epistasis) of OTL underlying a trait - plays a crucial role in how quantitative traits will respond to natural selection. As an illustration, imagine that dog body mass is under natural selection for larger size such that s = 0.3 with h2 = 1.0. The breeder's equation R = h2s predicts response to selection without reference to the genetic architecture of the quantitative trait. In this example, R = (1.0)(0.3) = 0.3, or a predicted increase of 0.3 standard deviations per generation. Now imagine that the additive genetic variation in body mass is caused by a number of OTLs. The strength of selection on the trait is divided across the independent loci that cause the additive genetic variation in the trait. The pressure of natural selection on one OTL is then only as large as its role in causing additive genetic variance in the phenotype. Said another way, the selection experienced by one OTL is proportional to its effect size. The breeder's equation can be modified for a single OTL by adjusting the selection differential for the proportion of additive genetic variation explained by a OTL according to

To see how this modified breeder's equation works, let's return to the example of the OTL that explains 38% of the total body mass difference between large and small dog breeds. That one OTL experiences 38% of the selection pressure that is exerted on the entire phenotype because it causes 38% of the additive genetic variation. Response to selection will be accomplished by relatively large changes in the allele frequencies at that one OTL with a 38% effect. In fact, the selection differential on that one OTL is s = (0.3)(0.38) = 0.114. This also leads to a predicted response to selection of 0.144 standard deviations for that one OTL alone.

The predictions of the nearly neutral theory (see Chapter 8) show the consequences of this division of the selection differential among OTL in proportion to their effect size. In finite populations, the balance between genetic drift and natural selection can be predicted with the quantity 4Nes where s is the selection differential. When 4Nes >> 1 then selection is the primary determinant of allele frequency, when 4Nes << 1 then genetic drift is the main process influencing allele frequency, and when 4Nes is on the order of one then both selection and genetic drift determine allele frequency. For a OTL of 38% effect experiencing a selection differential of s = 0.114, the response to selection will depend on Ne. In the context of an effective population size greater than about 25, the frequencies of the alleles at a OTL with a 38% effect would be expected to be dictated exclusively by natural selection. Only if the effective population size were less than 10 would we expect genetic drift to exclusively dictate the fate of allele frequencies at the OTL.

Under more realistic circumstances, many OTLs will have effect sizes much smaller than 38% and traits will most commonly have heritabilities less than 1.0. To take another example, imagine a OTL with a 2% effect for a trait with h2 = 0.3 that is experiencing an identical selection differential of s = 0.3.

The effective response to selection for this QTL of small effect is R = (0.3)((0.3)(0.02)) = 0.0018, or a predicted increase of 0.0018 standard deviations per generation. This QTL of small effect experiences a very weak pressure from natural selection precisely because it is a weak cause of additive genetic variation in a trait that has a low heritability. According to the 4Nes rule, this QTL would have to experience selection in the context of an effective population size greater than about 2000 for natural selection alone to dictate allele frequencies over time.

These observations about how the effective population size influences response to selection on individual OTLs shed light on an implicit assumption of the infinitesimal model of the genetic basis of quantitative traits. It is only in the context of large effective population sizes that the allele frequencies of OTLs with small effect sizes will respond to natural selection. In a finite population, as the number of OTLs grows large and the effect size approaches zero, the net response to selection will shrink and each locus will be subject to genetic drift rather than natural selection. Therefore, the infinitesimal model must also assume that the effective population size is inversely related to the OTL effect size. Drift-selection balance for OTLs in finite populations also serves to explain the simulation results in Fig. 9.12 that relate to long-term response to selection. In Fig. 9.12b there are many OTLs of small effect that clearly remain segregating for a longer period of time than the OTLs of large effect in Fig. 9.12a. The reason why the OTLs of small effect remain segregating longer is that they experience a relatively weak net selection pressure. The allele frequencies at the loci in Fig. 9.12b are clearly spreading out toward fixation and loss as we would expect of many replicate neutrally evolving loci (see Chapter 3), although perhaps the probability of fixation is greater than it would be under pure genetic drift.

The expected behavior of OTLs under the processes of genetic drift and natural selection has lead to a possible test for the action of natural selection on quantitative traits. Under the influence of natural selection alone, OTL alleles that fix in a population should all cause the trait value to change in the same direction (Orr 1998b; Anderson & Slatkin 2003). For example, if natural selection is acting to increase the trait mean then only OTL alleles that increase the trait value should be fixed in the population. Alternatively, under pure genetic drift OTL alleles that both increase and decrease the trait value should fix with equal frequency. Based on this logic, Rieseberg et al. (2002) used OTL effects estimated from 42 traits with greater than six OTLs to test for the action of directional selection. They concluded that alleles at OTLs are very often under the influence of natural selection and that life-history traits experience stronger natural selection than morphological traits. Interpreting this test for natural selection on OTLs is problematic, however, since quantitative traits in general are not sampled at random for OTL mapping studies. Rather, quantitative traits in domesticated organisms that have been under

Interact box 9.5 Effect sizes and response to selection at QTLs

Use the QTL module in PopGene.S2 to simulate response to selection for a quantitative trait that has QTL with variable effect sizes. The key parameter to vary is the percentage of genotypic variation explained by each QTL. Select the option for Some loci have large effects and the rest have equal small effects, set Number of large effect loci = 3, and VG explained by each large effect locus = 0.20. Set the other simulation parameters at Natural selection phenotypic value truncation point = 0.5 (only individuals in the upper 50% of phenotypic value reproduce), N = 250, mutation rate = 0.0, generations = 100, VE = 0.1, and Maximum genotypic va lue = 10.0.

Use the modified breeder's equation given in equation 9.42 to compute the net response to selection for the QTL with large and small effects in this simulation. When the selection truncation point is 0.50 in the simulation, the selection differential is s ~ 0.399 (see the text web page for more details). The heritability is also h2 > 0.5. Using these parameter values, what would you predict about the patterns of allele frequency change for QTL of large and small effect sizes?

Try out different values for the Natural selection phenotypic value truncation point or N and predict the consequences using equation 9.42. Then run the simulation to test your predictions.

long-term selection are most likely to be subject to OTL mapping since the effort to map OTLs is justified by the potential for improvements in selective breeding. While Rieseberg et al. (2002) showed that OTL alleles do tend to cause the trait value to change in the same direction as expected under selection, it is not clear whether the sample of taxa and phenotypes used for the test is representative of taxa and pheno-types in general.

Other results suggest that OTLs experience a combination of both genetic drift and natural selection. The OTLs of small effect identified from the Illinois Long-Term Selection study clearly show the effects of both genetic drift and natural selection. Among the OTLs identified for kernel oil concentration, about 20% show effects that are opposite to the direction of natural selection, such as OTLs that reduce oil concentration segregating in the lines selected for high oil concentration (Laurie et al. 2004). Since selection is acting against these OTLs with opposite effects, they must have escaped loss due to strong genetic drift in the context of an effective population size of about 10. Results similar to kernel oil concentration have been observed for tomato OTLs.

The results of OTL mapping studies can also be used to estimate the distribution of effect sizes for numerous OTLs. Figure 9.18 shows distributions of OTL effect sizes estimated for numerous phenotypes in dairy cows, pigs, and D. melanogaster. The distributions show the difference in phenotypic values for alternative homozygous genotypes (or the equivalent of 2a) at OTLs in units of phenotypic standard deviations. OTLs with smaller effect sizes explain a smaller proportion of the additive variance in a quantitative trait. OTLs at the right-hand edge of the x axis have a large effect on the genotypic variance.

These distributions of OTL effect sizes can be related to the models of mutation considered in Chapter 5. In particular, Fisher's geometric model of mutation (refer to Fig. 5.5) predicts that mutations of smaller phenotypic effect are more likely to improve fitness. Extending this model to OTLs, we can now think of OTLs with larger and smaller effects on genotypic variation (refer to Fig. 5.6). Kimura's version of Fisher's geometric model of mutation predicts that the genetic drift-natural selection balance will lead to fixation of alleles with the same effect on trait value (all either increasing or decreasing the trait mean) for those OTL of medium to large effect. Orr's (1998a) version of the geometric model considers a series of OTL mutations over time (but only one mutation segregates at a time) that take the popula

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