Population-genomic inference of the strength and timing of selection against gene flow

Abstract

The interplay of divergent selection and gene flow is key to understanding how populations adapt to local environments and how new species form. Here, we use DNA polymorphism data and genome-wide variation in recombination rate to jointly infer the strength and timing of selection, as well as the baseline level of gene flow under various demographic scenarios. We model how divergent selection leads to a genome-wide negative correlation between recombination rate and genetic differentiation among populations. Our theory shows that the selection density (i.e., the selection coefficient per base pair) is a key parameter underlying this relationship. We then develop a procedure for parameter estimation that accounts for the confounding effect of background selection. Applying this method to two datasets from Mimulus guttatus, we infer a strong signal of adaptive divergence in the face of gene flow between populations growing on and off phytotoxic serpentine soils. However, the genome-wide intensity of this selection is not exceptional compared with what M. guttatus populations may typically experience when adapting to local conditions. We also find that selection against genome-wide introgression from the selfing sister species M. nasutus has acted to maintain a barrier between these two species over at least the last 250 ky. Our study provides a theoretical framework for linking genome-wide patterns of divergence and recombination with the underlying evolutionary mechanisms that drive this differentiation.

Keywords: Mimulus; divergence; local adaptation; recombination; speciation with gene flow.

Fig. 1.

Divergent selection reduces gene flow and increases genetic divergence. (A) Selection against locally maladapted alleles at MSPs (black triangles) reduces the effective migration rate $m_e$. The effect is stronger in regions of low recombination (red; A, Left Upper) and decreases the probability that lineages sampled in different populations migrate and coalesce. Realizations of the coalescence process are shown in A, Left Lower for the (MS)P scenario (SI Appendix, Fig. S1). In regions of high recombination, $m_e$ is higher (blue; A, Right Upper), such that migration and earlier coalescences are more likely (A, Right Lower). (B) The predicted between-population diversity ${\pi }_B=2u𝔼[T_B]$ (curves) matches individual-based simulations (dots); error bars ($\pm \text{𝖲𝖤}$) are too short to be visible. The (MS)M scenario was used with $N_2=5,000$, $u={10}^{-9}$, $\nu =2.5\times {10}^{-7}$, $m=m_0=5\times {10}^{-4}$, $\tau =4N_2$. (C) Approximately linear contour lines with slope $-1$ in the surface of ${\pi }_B$ as a function of log₁₀(s) and log₁₀(ν) support the compound parameter selection density, $\sigma =s\nu$. Here, $r_{\mathrm{bp}}={10}^{-8}$ (1 cM/Mb); other parameters are as in B.

Fig. 2.

Geographic context of serpentine dataset and quasi-likelihood surfaces. (A) Sampling sites in California (modified from ref. with permission from Taylor and Francis Ltd.), and unrooted population phylogeny based on linearized genetic divergence (24). (B) The negative SSD ($-$SSD) for the selection coefficient $s$ and the genomic density $\nu$ of MSPs, conditional on point estimates $\widehat{m}\approx 5.6\times {10}^{-4}$ and $\widehat{\tau }\approx 5\times {10}^7$. The ridge with slope $-$1 confirms the compound parameter selection density, $\sigma =s\nu$. A cross denotes the point estimate and black hulls the 95% bootstrap confidence area. (C) Joint profile surface of the $-$SSD for the baseline migration rate $m$ and the selection density $\sigma$, maximized over $\tau$. Results are shown for the population pair REM$\times$SOD under the (MS)M scenario with genomic windows of 500 kb.

Fig. 3.

Parameter estimates and model fit for the serpentine dataset. (A and C) Profile curves of the quasi-likelihood ($-$SSD) for each parameter, maximizing over the two remaining parameters, for the serpentine$\times$off-serpentine comparisons REM$\times$SOD (A) and SLP $\times$ TUL (C) (Fig. 2). Vertical red and black dashed lines indicate the point estimate and 95% bootstrap CIs, respectively. (B and D) Raw data (blue dots) and model fit (red curve) with 95% CI (gray shading). The corresponding ratio of the effective to the baseline migration rate is shown on the right (red shading: 95% CI). The 95% CI of the distribution of the relative difference between the maximum and minimum $m_e$ across all bootstrap samples, ${\delta }_{m_e}$, is given on top. Other details are as in Fig. 2 B and C. For other population pairs, see SI Appendix, Fig. S26. Between-popul., between population.