Predictions of patterns of response to artificial selection in lines derived from natural populations

Abstract

The pattern of response to artificial selection on quantitative traits in laboratory populations can tell us something of the genetic architecture in the natural population from which they were derived. We modeled artificial selection in samples drawn from natural populations in which variation had been maintained by recurrent mutation, with genes having an effect on the trait, which was subject to real stabilizing selection, and a pleitropic effect on fitness (the joint-effect model). Natural selection leads to an inverse correlation between effects and frequencies of genes, such that the frequency distribution of genes increasing the trait has an extreme U-shape. In contrast to the classical infinitesimal model, an early accelerated response and a larger variance of response among replicates were predicted. However, these are reduced if the base population has been maintained in the laboratory for some generations by random sampling prior to artificial selection. When multiple loci and linkage are also taken into account, the gametic disequilibria generated by the Bulmer and Hill-Robertson effects are such that little or no increase in variance and acceleration of response in early generations of artificial selection are predicted; further, the patterns of predicted responses for the joint-effect model now become close to those of the infinitesimal model. Comparison with data from laboratory selection experiments shows that, overall, the analysis did not provide clear support for the joint-effect model or a clear case for rejection.

Figure 1.—

Distributions of gene frequencies corresponding to the three models, with parameters as given in Table 1. The distributions are symmetrical about 0.5 and only the left half is displayed. (a) Distributions shown for recently captured populations (thin solid line) and for populations maintained for 32 generations at size of 160 individuals (dashed line). For comparison the distribution for neutral genes in a captured populations of size 250 is also shown (thick solid line). (b) Distribution conditional on the effect (a) on the trait for captured populations. Thick solid line in b is the same for neutral genes as in a.

Figure 2.—

Influences of linkage and the Bulmer effects on (a) response, (b) standard deviation of response among replicate lines, and (c) the within-line genetic variance. The base population was assumed to sample from natural populations at mutation-selection balance, with its initial gene frequency distribution given by Equation 5. The natural population size M was 10⁴ and the equilibrium genetic variance was . A cage population of size M_c = 160 was drawn from this before artificial selection of intensity i = 0.966 (i.e., 40% selected) and size N = 40. Two methods are used: transition matrix for independent individual loci (dashed lines), and Monte Carlo simulation for genome comprising three chromosomes, each with a map length 0, ¹/₄, ¹/₂, 1, 4, and ∞ morgans (M; thin solid lines). Simulations for one completely linked genome (thick solid lines) are included for comparison.

Figure 3.—

Effects of population size (with 40% selected; left) and selection intensity (with a selection population size N = 40; right) on (a and d) expected response, (b and e) standard deviation of response among replicates, and (c and f) the within-line genetic variance. Two linkage structures are considered: each chromosome of map length 1 M (dashed line) and free recombination (solid line). In f, note that with free recombination, selection of 20% (thick solid line) produced a higher V_G than selection of 70%, between generations 3 and 21. The population was previously under natural selection as in Figure 2.

Figure 4.—

Influence of maintenance of the base population prior to artificial selection on (a) response, (b) standard deviation of response among replicate lines, and (c) the within-line genetic variance. Base populations for artificial selection are either drawn immediately from the wild (“NS”) or maintained captive for 32 generations at a constant size of 160 individuals (“NS-c”) under two recombination rates: free recombination between loci (thin solid lines) and three chromosomes each of length 1 M (dashed lines). Also shown for comparison are the predictions of the infinitesimal model including the Bulmer effect (thick solid lines) and simulation results for the neutrality model (“neutral”). Artificial selection is as in Figure 2 (N = 40, 40% selected).

Figure 5.—

Influence of new mutation and comparison between predictions from the natural selection model (left) and from the infinitesimal model and modification of it (right). For the natural selection model (a–c), effects of new mutations were sampled from a reflected gamma ¹/₄ distribution with mutation rate λ = 0.3 per generation per haploid genome. For the infinitesimal model (d–f), effects of mutations within each locus are sampled from a normal distribution of mean 0 and variance V_G0/(2 × 5740) with a rate 2 × 5740 × (V_M/V_G0) per generation per genome, where V_M = 10⁻³V_E and . Artificial selection is as in Figure 2 (N = 40, 40% selected). Three linkage patterns are considered: each chromosome of map length 0, 1, and ∞ M. Solid lines represent predictions without new mutations while dashed lines show prediction with contribution from new mutation. For comparison, d–f also show the Robertsonian formulas, where genetic drift alone affects frequencies (thin solid lines) and also predictions with incorporation of linkage disequilibrium due to the Bulmer effect (thick solid lines).

Figure 6.—

Comparison between predicted and experimental values of the total response after 50 generations, relative to the initial response (R₅₀/R₁), plotted against the effective size of the population under artificial selection. Theoretical predictions are based on selection of 20% (dotted lines), 40% (dashed lines), and 70% (solid lines) selection, assuming three chromosomes each of length 1 M. Data points (diamonds, i > 1.0; circles, i < 1.0) are experimental results on selection in Drosophila, from Weber and Diggins (1990). (a) Artificial selection starting from base populations drawn immediately from a natural population at mutation-selection balance under the joint pleiotropic and stabilizing selection model, with contributions from new mutations (thick solid lines) and without new mutations (thin solid lines). (b) Artificial selection starting from base populations taken from nature and kept for 32 generations at a size 160, including contributions from new mutations. (c) The predictions from the infinitesimal model, modified to include new mutation and linkage. Robertsonian predictions with new mutation and the Bulmer effect (thick solid line, assuming 40% selected) are shown in c for comparison.