Effect of partial selfing and polygenic selection on establishment in a new habitat

Genomic implications of the repeated shift to self-fertilization across a species' geographic distribution

The ability to self-fertilize often varies among closely related hermaphroditic plant species, though, variation can also exist within species. In the North American Arabidopsis lyrata, the shift from self-incompatibility (SI) to selfing established in multiple regions independently, mostly since recent postglacial range expansion. This has made the species an ideal model for the investigation of the genomic basis of the breakdown of SI and its population genetic consequences. By comparing nearby selfing and outcrossing populations across the entire species' geographic distribution, we investigated variation at the self-incompatibility (S-)locus and across the genome. Furthermore, a diallel crossing experiment on one mixed-mating population was performed to gain insight into the inheritance of mating system variation. We confirmed that the breakdown of SI had evolved in several S-locus backgrounds. The diallel suggested the involvement of biparental contributions with dominance relations. Though, the population-level genome-wide association study did not single out clear-cut candidate genes but several regions with one near the S-locus. On the implication side, selfing as compared to outcrossing populations had less than half of the genomic diversity, while the number and length of runs of homozygosity (ROHs) scaled with the degree of inbreeding. Selfing populations with a history of long expansion had the longest ROHs. The results highlight that mating system shift to selfing, its genetic underpinning and the likely negative genomic consequences for evolutionary potential can be strongly interlinked with past range dynamics.

Polygenic selection to a changing optimum under self-fertilisation

Many traits are polygenic, affected by multiple genetic variants throughout the genome. Selection acting on these traits involves co-ordinated allele-frequency changes at these underlying variants, and this process has been extensively studied in random-mating populations. Yet many species self-fertilise to some degree, which incurs changes to genetic diversity, recombination and genome segregation. These factors cumulatively influence how polygenic selection is realised in nature. Here, we use analytical modelling and stochastic simulations to investigate to what extent self-fertilisation affects polygenic adaptation to a new environment. Our analytical solutions show that while selfing can increase adaptation to an optimum, it incurs linkage disequilibrium that can slow down the initial spread of favoured mutations due to selection interference, and favours the fixation of alleles with opposing trait effects. Simulations show that while selection interference is present, high levels of selfing (at least 90%) aids adaptation to a new optimum, showing a higher long-term fitness. If mutations are pleiotropic then only a few major-effect variants fix along with many neutral hitchhikers, with a transient increase in linkage disequilibrium. These results show potential advantages to self-fertilisation when adapting to a new environment, and how the mating system affects the genetic composition of polygenic selection.

Limits to species' range: the tension between local and global adaptation

We know that heritable variation is abundant, and that selection causes all but the smallest populations to rapidly shift beyond their original trait distribution. So then, what limits the range of a species? There are physical constraints and also population genetic limits to the effectiveness of selection, ultimately set by population size. Global adaptation, where the same genotype is favoured over the whole range, is most efficient when based on a multitude of weakly selected alleles and is effective even when local demes are small, provided that there is some gene flow. In contrast, local adaptation is sensitive to gene flow and may require alleles with substantial effect. How can populations combine the advantages of large effective size with the ability to specialise into local niches? To what extent does reproductive isolation help resolve this tension? I address these questions using eco-evolutionary models of polygenic adaptation, contrasting discrete demes with continuousspace.

Partial Clonality Expands the Opportunity for Spatial Adaptation

AbstractReproductive mode may strongly impact adaptation in spatially varying populations linked by dispersal, especially when sexual and clonal offspring differ in dispersal. We determined how spatial structure affects adaptation in populations with mixed clonal and sexual reproduction. In a source-sink quantitative genetic deterministic model (with stabilizing selection around different optima), greater clonal reproduction or parent-offspring association (a measure of the part of the parent's phenotype other than the additive genetic component inherited by clonal offspring) increased the selective difference (difference between phenotypic optima) allowing sink populations to adapt. Given dispersal differences between clonally and sexually produced juveniles, adaptation increased with an increasing fraction of clonal dispersers. When considering migrational meltdown, partially clonal reproduction reduced cases where dispersal caused habitat loss. Stochastic individual-based simulations support these results, although the effect of differential dispersal was reversed, with decreased clonal dispersal allowing greater adaptation. These results parallel earlier findings that for an instantaneous shift in phenotypic optimum, increasing clonality allowed population persistence for a greater shift; here, selective change is spatial rather than temporal. These results may help explain the success of many partially clonal organisms in invading new habitats, complementing traditional explanations based on avoiding Allee effects.

The infinitesimal model with dominance

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the "shared" and "residual" components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/M. We illustrate our results with some numerical examples.

Dynamic maximum entropy provides accurate approximation of structured population dynamics

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios in a dynamic environment.

Complex processes in biology and physics have much in common. Collective motion of animals can be well described by models of interacting particles and emergent collective behavior can often be characterized as phase transitions of such a model. When the system is settled to a steady state, statistical physics connects random fluctuations of the process with key macroscopic quantities, using the maximum entropy method. It is thus not surprising that this method is in turn useful in understanding biological systems. However, realistic problems such as structured population dynamics, studied in our work, are set in dynamic environments, caused for instance by fluctuations in food supply. Therefore, we use the dynamical maximum entropy approximation, which allows us to reduce the full problem to simpler dynamics, without the need to track microscopic details. We focus on two processes (one in physics, one in biology) in our study: the motion of a charged particle and the dynamics of structured populations, both in a changing environment. We show that the method is extremely accurate even when the environmental changes are very fast, thus providing a powerful tool to study both biological and physical processes in changing environments.

Polygenic local adaptation in metapopulations: A stochastic eco-evolutionary model

This article analyzes the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat-dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments.