Establishment of new mutations under divergence and genome hitchhiking

Abstract

Theoretical models addressing genome-wide patterns of divergence during speciation are needed to help us understand the evolutionary processes generating empirical patterns. Here, we examine a critical issue concerning speciation-with-gene flow: to what degree does physical linkage (r < 0.5) of new mutations to already diverged genes aid the build-up of genomic islands of differentiation? We used simulation and analytical approaches to partition the probability of establishment for a new divergently selected mutation when the mutation (i) is the first to arise in an undifferentiated genome (the direct effect of selection), (ii) arises unlinked to any selected loci (r = 0.5), but within a genome that has some already diverged genes (the effect of genome-wide reductions in gene flow for facilitating divergence, which we term 'genome hitchhiking'), and (iii) arises in physical linkage to a diverged locus (divergence hitchhiking). We find that the strength of selection acting directly on a new mutation is generally the most important predictor for establishment, with divergence and genomic hitchhiking having smaller effects. We outline the specific conditions under which divergence and genome hitchhiking can aid mutation establishment. The results generate predictions about genome divergence at different points in the speciation process and avenues for further work.

Figure 1.

(a–f) A summary of previous theory on equilibrium levels of neutral genetic differentiation under DH and GH. Shown are equilibrium levels of divergence (F_ST) at neutral sites linked at various recombination distances to a locus under divergent selection. DH can generate and maintain regions of neutral differentiation extending away from a selected site, but only under certain conditions. Note that when numerous, unlinked loci in addition to the original site are also under selection, genome-wide divergence can occur via GH such that genomic islands are erased (e.g. in (c) compare scenarios with one to three loci to those with four to six loci under selection); pop., population. Reproduced with permission from Feder & Nosil [46]. Copyright © John Wiley and Sons Inc.

Figure 2.

Schematic depiction of different scenarios for the establishment of a new mutation. In all cases, black dots represent genomic locations where new mutations arise. (a) If the mutation is the first to arise, in a completely undiverged genome, it receives no aid in establishment from hitchhiking effects (noH). This can be thought of as the baseline probability of establishment of the mutation all on its own. The establishment of the mutation might be facilitated in two ways. First, establishment might be facilitated by DH if the new mutation arises in physical linkage to a locus already diverged via selection. Second, establishment might be facilitated by GH if the new mutation arises unlinked to any selected loci, but within a genome that has some diverged loci. (b) Divergence before (dashed line) versus after (solid line) establishment of the new mutations.

Figure 3.

Partitioning the probability of establishment for a new mutation into relative contributions owing to noH, GH and DH (see figure 2 and main text for abbreviations). Shown is an example with conditions favourable for DH with a high migration rate (m) = 0.1, strong selection on the initially diverged locus (s_o = 0.5), selection on the new mutation less than the migration rate (s_n = 0.05) and tight linkage (r = 0.001) between the already selected locus and new mutation. Given are the probabilities of establishment for the mutation alone (0.00675), for the new mutation unlinked to the previously existing selected locus (0.0108), and for the new mutations at various recombination distances from r = 0.5 to r = 0.001 to the selected locus (dark line = mean for the new mutation arising in the favoured and disfavoured populations). For r = 0.001, the probability of establishment for a new mutation under these conditions equals 0.0188. Based on these values, the relative contributions to establishment are 35.9% for the new mutation on its own, 21.6% for the GH effect and 42.5% for DH. Thus, even under these favourable conditions with very tight linkage, there is a less than two times increase for the effect of DH on the establishment of a new mutation above that for GH and the effect of the mutation on its own in the absence of linkage (0.0188/0.0108 = 1.74).

Figure 4.

The effects of selection strength on the probability of establishment of new mutations; s_n is the strength of selection on a new mutation and s_o is the strength of selection on an originally pre-diverged locus. The strength of selection acting directly on mutations was of greater importance for establishment than either DH or GH, as evidenced by the fact that the probability of establishment of a new mutation was similar when: (i) it is the first and only mutation to arise in an undifferentiated genome (no hitchhiking is noH, probability of establishment denoted at r = 0.50), (ii) it arises in physical linkage to a locus already diverged via selection (DH is the probability of establishment for each recombination rate represented by the solid line in each panel), and (iii) it arises unlinked to any selected loci, but within a genome that has a single locus already diverged (GH is probability of establishment denoted at r = 0.50). In essence, noH = DH = GH. Results are shown for m = 0.001. Highly comparable results were observed when migration rates were higher (see electronic supplementary material).

Figure 5.

(a–f) The effects of varying selection strength from very strong (s_n = 0.5) to weak (s_n = 0.01) on the probability of establishment of a new mutation linked at various recombination distances to an original locus under very strong divergent selection (s_o = 0.5). Probabilities of establishment are given for conditions of high migration rate (m = 0.1) for a new mutation arising in the favoured population (dashed line), in the disfavoured population (stippled line) and the mean for the favoured and disfavoured populations together (solid line). Also shown are the baseline probabilities of establishment for a new mutation on its own not influenced by selection on any other loci in the genome (noH) and when the new mutation was unlinked (r = 0.5) to the other locus in the genome under divergent selection (GH). Note that the probabilities for the favoured and disfavoured populations tend to counterbalance one another, especially when selection on the new mutation is not lower than the migration rate, reducing the effect of DH in facilitating mutation establishment.

Figure 6.

The effect of increasing numbers of unlinked loci in the genome each under very strong divergent selection (s_o = 0.5) on the probability of establishment of a new mutation under weak selection (s_n = 0.01) relative to the migration rate (m = 0.1). Shown are the results for the mean probabilities of establishment of a new mutation averaged across the favoured and disfavoured populations when one, two, three and five loci are under very strong divergent selection. Also given in parentheses are the effective migration rates (m_e) for a neutral unlinked locus in the genome estimated by the method of Feder & Nosil [46] for when no, one, two, three and five loci are already under very strong divergent selection.