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Evolution of Amphimixis and Recombination Under Fluctuating Selection in One and Many Traits

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Evolution of Amphimixis and Recombination Under Fluctuating Selection in One and Many Traits Genet. Res., Camb. (1996), 68, pp. 165-173 With 7 text-figures Copyright © 1996 Cambridge University Press 165 Evolution of amphimixis and recombination under fluctuating selection in one and many traits ALEXEY S. KONDRASHOV* AND LEV YU. YAMPOLSKY Section of Ecology and Systematics, Cornell University, Ithaca, NY 14853, USA (Received 6 June 1995 and in revised form 14 May 1996) Summary Both stabilizing and directional selection acting on one or many quantitative traits usually reduce the genetic variance in a polymorphic population. Amphimixis and recombination restore the variance, pushing it closer to its value under linkage equilibrium. They thus increase the response of the population to fluctuating selection and decrease the genetic load when the mean phenotype is far from optimum. Amphimixis can have a short-term advantage over apomixis if selection fluctuates frequently and widely, so that every genotype often has a low fitness. Such selection causes high genetic variance due to frequent allele substitutions, and a high load even with amphimixis. Recombination in an amphimictic population is maintained only if selection is usually strong and effectively directional. A modifier allele causing free recombination can have a significant advantage only if fluctuations of selection are such that the load is substantial. With smaller fluctuations, an intermediate recombination rate can be established, either due to fixation of alleles that cause such a rate or due to the stable coexistence of alleles causing high and low recombination. If many traits simultaneously are under fluctuating selection, amphimixis and recombination can be maintained when selection associated with individual traits is weaker and the changes in their mean values are smaller than with a single trait. Still, the range of changes of the fitness optima in each trait must be at least of the order of the trait's standard deviation, and the total load must be high. 1. Introduction Amphimixis and recombination can be beneficial in an infinite population under a changing environment because they destroy linkage disequilibria created by epistatic selection (see Kondrashov, 1993). The corresponding Environmental Deterministic (ED) hypotheses can be subdivided into two subclasses. Non-responsiveness hypotheses claim that destruction of disequilibria is beneficial because it reduces the response of a population to frequent and relatively small fluctuations of selection, while better re- sponsiveness hypotheses postulate that this destruction is beneficial because it increases the response to rarer and wider fluctuations, or to invariant directional Trait selection (Barton, 1995). 'Narrowing' selection (Shnol & Kondrashov, 1993) Fig. 1. Under selection with fluctuating fitness function amphimixis can be advantageous only if every genotype acting on a quantitative trait reduces the genetic sometimes has a low fitness. With all-or-nothing variance below its linkage equilibrium level by creating truncation selection, this is the case when there is at least a pair of fitness functions, w^x) and w2(.v), each • Corresponding author. Telephone: +1(607) 254-4221. Fax: describing selection at some moments of time, which do + 1(607) 255-8088. e-mail: [email protected]. not overlap. Downloaded from https://www.cambridge.org/core. IP address: 170.106.34.90, on 01 Oct 2021 at 03:18:47, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0016672300034054 A. S. Kondrashov and L. Yu. Yampolsky 166 Fig. 2. The average deviation of the mean value (ji) of the trait from m (a) and from o (b), and the genetic load corresponding to the geometric mean fitness (c) with w = 1, S = 1-5, and r = 20 (circles), 80 (squares), and 320 (diamonds) in the amphimictic (filled markers) and apomictic (open markers) populations as functions of d (compare with figure 3 in KY-96). repulsion linkage disequilibria, while amphimixis and mean reaches the fitness optimum. Under invariant recombination move it closer to this level by destroying directional selection strong enough to provide a short- them and thus increase the resulting changes in the term (Maynard Smith, 1978) advantage for trait mean value (Mather, 1943; Fraser, 1957; amphimixis, the higher variance is beneficial but the Felsenstein, 1965; Eshel & Feldman, 1970; Crow, mean value of the trait changes rapidly and 1992; Charlesworth, 1993). Both directional selection irreversibly. Apparently this is not common in nature, (if the increase in fitness caused by two beneficial although if many traits are selected simultaneously a alleles in the same genotype is less than the product of short-term advantage may be consistent with slow their individual effects, i.e. if they interact sub- evolution in each of them (Maynard Smith, 1988, multiplicatively or with diminishing returns epistasis) p. 62; Crow, 1992). and stabilizing selection are usually narrowing (see Thus, the better responsiveness hypotheses are Shnol & Kondrashov, 1993). more plausible under fluctuating selection (Mather, Under invariant stabilizing selection, the higher 1943;Treisman, 1976; Maynard Smith, 1980, 1988; variance becomes deleterious after the population Korol & Preygel 1989; Crow, 1992; Charlesworth, Downloaded from https://www.cambridge.org/core. IP address: 170.106.34.90, on 01 Oct 2021 at 03:18:47, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0016672300034054 Evolution of amphimixis and recombination under fluctuating selection 167 1993; Korol et al. 1994), either directional or stabilizing (when the population mean is far from the 3. Results optimum, stabilizing selection becomes effectively (i) Amphimixis versus apomixis: one trait directional and the increase in variance is beneficial). A short-term advantage of amphimixis requires that When not stated otherwise, we used the default no phenotype has high fitness for a long time (Fig. 1; parameters from KY-96. Figure 2 presents the data on Treisman, 1976). Maintenance of recombination in an the deviations of the mean value of the trait /* from m amphimictic population may require even more (Fig. Id) and o (Fig. 2b), and on the genetic load (Fig. stringent conditions (Charlesworth, 1993). 2 c). In the amphimictic population the deviation of fi from o is smaller, while its deviation from m is larger, Here we will supplement the recent analytical results so that amphimixis facilities the response to selection, of Charlesworth (1993) and Barton (1995) by in- due to higher genetic variance (see KY-96). Figure 2 is vestigating a computer simulational model of the based on the data from a single run, observed from evolution of amphimixis and recombination under generation 3d during 5d generations. The results of fluctuating selection acting on one or many quan- different runs were very similar (data not reported). titative traits. Not surprisingly, this better responsiveness of amphimixis leads to a lower load when d> S. Amphimicts outcompete apomicts with twofold re- 2. Model productive advantage (Maynard Smith, 1978) if (l-^amP)/[2(l-4po)] > 1, where Lamp and Lapo are The basic model was described in Kondrashov & the values of the load, in terms of geometric mean Yampolsky (1996; hereafter KY-96). To consider the fitness, in the two populations. This requires Lap0 > evolution of recombination, we added a modifier 0-5, which does not happen if there is a phenotype locus R, which does not mutate, does not influence which always has high fitness (a compromise strategy), fitness directly, is unlinked to the selectable loci, and i.e. if d<S (Fig. 2c). When selection changes determines the recombination rate. An allele rk caused frequently (T = 20), Lapo grows rapidly when d k cross-overs in independent random places in the becomes larger than S, but Lamp is only slightly lower single linkage group (chromosome) that carried all the than Lapo. In contrast, when selection changes rarely selectable loci. Thus, r0 caused complete linkage in (T = 320) only very large d leads to high Lapo. The this chromosome, while rK caused free recombination. advantage of amphimixis appears most readily with Different modes of dominance at R were studied. an intermediate frequency of fluctuations (T = 80). In In the case of many («) traits, we assumed that each one is controlled by a separate set of / loci, so that the total number of selectable loci was l*n. With limited (a) 1 recombination, all these loci were arranged linearly in one chromosome (/ loci responsible for the first trait Apomixis first, then / loci responsible for the second trait, etc.). The fitness of a phenotype X, w(X), depended on the distance of X from the optimum O (both X and O are, of course, n-dimensional vectors). With Euclidean 2 metrics X= \/'L(xi — o() , while with module metrics X = I.\xt — o,|, where ot and xt are the optimal and the actual values of the rth trait, respectively. The middle phenotype M (with coordinates mt), occupies the centre of the range of changes in O. The maximal deviation of o, from w, is d, and the maximal distance of O from M is D. With Gaussian stabilizing selection w(A0 = exp(-(Ar-O)2/2S'2), while with truncation stabilizing selection w(X) = 1 if \X— 0\ ^ T and 0 otherwise. For periodically fluctuating selection we assumed = m( + dsm{2n[t/T + i/ (1) Fig. 3. The genetic load corresponding to the geometric mean fitness in the amphimictic and apomictic population (compare with equation 1 in KY-96). According to (a) under the same parameters as in Fig. 2 (5 = 1-5, eqn (1), different o deviate maximally from the d = 4-5 and T = 80) but with non-zero environmental t variance, and (b) under the same parameters as in Fig. 2 corresponding mt at different moments, so that the (S = 1-5, T = 80), but with alleles having arbitrary effects distribution of the values of o( does not change much (compared with figures 6 and 7 in KY-96).
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