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

Genome-Wide Allele Frequency Changes Reveal That Dynamic Metapopulations Evolve Differently

Two important characteristics of metapopulations are extinction-(re)colonization dynamics and gene flow between subpopulations. These processes can cause strong shifts in genome-wide allele frequencies that are generally not observed in "classical" (large, stable, and panmictic) populations. Subpopulations founded by one or a few individuals, the so-called propagule model, are initially expected to show intermediate allele frequencies at polymorphic sites until natural selection and genetic drift drive allele frequencies toward a mutation-selection-drift equilibrium characterized by a negative exponential-like distribution of the site frequency spectrum. We followed changes in site frequency spectrum distribution in a natural metapopulation of the cyclically parthenogenetic pond-dwelling microcrustacean Daphnia magna using biannual pool-seq samples collected over a 5-yr period from 118 ponds occupied by subpopulations of known age. As expected under the propagule model, site frequency spectra in newly founded subpopulations trended toward intermediate allele frequencies and shifted toward right-skewed distributions as the populations aged. Immigration and subsequent hybrid vigor altered this dynamic. We show that the analysis of site frequency spectrum dynamics is a powerful approach to understand evolution in metapopulations. It allowed us to disentangle evolutionary processes occurring in a natural metapopulation, where many subpopulations evolve in parallel. Thereby, stochastic processes like founder and immigration events lead to a pattern of subpopulation divergence, while genetic drift leads to converging site frequency spectrum distributions in the persisting subpopulations. The observed processes are well explained by the propagule model and highlight that metapopulations evolve differently from classical populations.

Predicting emergent animal biodiversity patterns across multiple scales

Restoring biodiversity-based resilience and ecosystem multi-functionality needs to be informed by more accurate predictions of animal biodiversity responses to environmental change. Ecological models make a substantial contribution to this understanding, especially when they encode the biological mechanisms and processes that give rise to emergent patterns (population, community, ecosystem properties and dynamics). Here, a distinction between 'mechanistic' and 'process-based' ecological models is established to review existing approaches. Mechanistic and process-based ecological models have made key advances to understanding the structure, function and dynamics of animal biodiversity, but are typically designed to account for specific levels of biological organisation and spatiotemporal scales. Cross-scale ecological models, which predict emergent co-occurring biodiversity patterns at interacting scales of space, time and biological organisation, is a critical next step in predictive ecology. A way forward is to first capitalise on existing models to systematically evaluate the ability of scale-explicit mechanisms and processes to predict emergent patterns at alternative scales. Such model intercomparisons will reveal mechanism to process transitions across fine to broad scales, overcome approach-specific barriers to model realism or tractability and identify gaps which necessitate the development of new fundamental principles. Key challenges surrounding model complexity and uncertainty would need to be addressed, and while opportunities from big data can streamline the integration of multiple scale-explicit biodiversity patterns, ambitious cross-scale field studies are also needed. Crucially, overcoming cross-scale ecological modelling challenges would unite disparate fields of ecology with the common goal of improving the evidence-base to safeguard biodiversity and ecosystems under novel environmental change.

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.

Genetic Drift Shapes the Evolution of a Highly Dynamic Metapopulation

The dynamics of extinction and (re)colonization in habitat patches are characterizing features of dynamic metapopulations, causing them to evolve differently than large, stable populations. The propagule model, which assumes genetic bottlenecks during colonization, posits that newly founded subpopulations have low genetic diversity and are genetically highly differentiated from each other. Immigration may then increase diversity and decrease differentiation between subpopulations. Thus, older and/or less isolated subpopulations are expected to have higher genetic diversity and less genetic differentiation. We tested this theory using whole-genome pool-sequencing to characterize nucleotide diversity and differentiation in 60 subpopulations of a natural metapopulation of the cyclical parthenogen Daphnia magna. For comparison, we characterized diversity in a single, large, and stable D. magna population. We found reduced (synonymous) genomic diversity, a proxy for effective population size, weak purifying selection, and low rates of adaptive evolution in the metapopulation compared with the large, stable population. These differences suggest that genetic bottlenecks during colonization reduce effective population sizes, which leads to strong genetic drift and reduced selection efficacy in the metapopulation. Consistent with the propagule model, we found lower diversity and increased differentiation in younger and also in more isolated subpopulations. Our study sheds light on the genomic consequences of extinction-(re)colonization dynamics to an unprecedented degree, giving strong support for the propagule model. We demonstrate that the metapopulation evolves differently from a large, stable population and that evolution is largely driven by genetic drift.

Perturbation responses in co-evolved model meta-communities

A spatially explicit eco-evolutionary model assembles simulated meta-communities which are subjected to species and community perturbation experiments to determine factors affecting the stability of the global ecosystem. Spatial structure and resource variety increase the persistence of the ensembles against the removal of an individual species, yet they remain vulnerable to re-invasion by an existing member of the meta-community if it is introduced to all patches with minimal population. Optimal reserve placement strategies are identified for maximally preserving global biodiversity from the effects of sequences of patch disruption, and targeted reserve placement that shields the most or the rarest biodiversity is usually effective. However, if disturbed populations are permitted to re-settle in neighboring patches, then reserves should also be situated remotely to isolate their residents from invasion.

Selection on modifiers of genetic architecture under migration load

Gene flow between populations adapting to differing local environmental conditions might be costly because individuals can disperse to habitats where their survival is low or because they can reproduce with locally maladapted individuals. The amount by which the mean relative population fitness is kept below one creates an opportunity for modifiers of the genetic architecture to spread due to selection. Prior work that separately considered modifiers changing dispersal, recombination rates, or altering dominance or epistasis, has typically focused on the direction of selection rather than its absolute magnitude. We here develop methods to determine the strength of selection on modifiers of the genetic architecture, including modifiers of the dispersal rate, in populations that have previously evolved local adaptation. We consider scenarios with up to five loci contributing to local adaptation and derive a new model for the deterministic spread of modifiers. We find that selection for modifiers of epistasis and dominance is stronger than selection for decreased recombination, and that selection for partial reductions in recombination are extremely weak, regardless of the number of loci contributing to local adaptation. The spread of modifiers that reduce dispersal depends on the number of loci, epistasis and extent of local adaptation in the ancestral population. We identify a novel effect, that modifiers of dominance are more strongly selected when they are unlinked to the locus that they modify. These findings help explain population differentiation and reproductive isolation and provide a benchmark to compare selection on modifiers under finite population sizes and demographic stochasticity.

When populations of a species are spread over different habitats the populations can adapt to their local conditions, provided dispersal between habitats is low enough. Natural selection allows the populations to maintain local adaptation, but dispersal and gene flow create a cost called the migration load. The migration load measures how much fitness is lost because of dispersal between different habitats, and also creates an opportunity for selection to act on the arrangement and interaction between genes that are involved in local adaptation. Modifier genes can spread in these linked populations and cause functional, local adaptation genes, to become more closely linked on a chromosome, or change the way that these genes are expressed so that the locally adapted gene copy becomes dominant. We modeled this process and found that selection on modifiers that create tighter linkage between locally adapted genes is generally weak, and modifiers that cause gene interactions are more strongly selected. Even after these gene interactions have begun to evolve, further selection for increased gene interaction is still strong. Our results show that populations are more likely to adapt to local conditions by evolving new gene interactions than by evolving tightly linked gene clusters.

Reproductive isolation via polygenic local adaptation in sub-divided populations: Effect of linkage disequilibria and drift

This paper considers how polygenic local adaptation and reproductive isolation between hybridizing populations is influenced by linkage disequilibria (LD) between loci, in scenarios where both gene flow and genetic drift counteract selection. It shows that the combined effects of multi-locus LD and genetic drift on allele frequencies at selected loci and on heterozygosity at neutral loci are predicted accurately by incorporating (deterministic) effective migration rates into the diffusion approximation (for selected loci) and into the structured coalescent (for neutral loci). Theoretical approximations are tested against individual-based simulations and used to investigate conditions for the maintenance of local adaptation on an island subject to one-way migration from a differently adapted mainland, and in an infinite-island population with two habitats under divergent selection. The analysis clarifies the conditions under which LD between sets of locally deleterious alleles allows these to be collectively eliminated despite drift, causing sharper and (under certain conditions) shifted migration thresholds for loss of adaptation. Local adaptation also has counter-intuitive effects on neutral (relative) divergence: F_ST is highest for a pair of subpopulations belonging to the same (rare) habitat, despite the lack of reproductive isolation between them.

Environmental adaptation often involves spatially heterogeneous selection at many genetic loci. Thus, the evolutionary consequences of hybridisation between populations adapted to different environments depend on the coupled dynamics of multiple loci under selection, migration and genetic drift, making them challenging to predict. Here, I introduce theoretical approximations that accurately capture the effect of such coupling on allele frequencies at individual loci, while also accounting for the stochastic effects of genetic drift. I then use these approximations to study hybridisation in a metapopulation consisting of many interconnected subpopulations, where each subpopulation belongs to one of two habitats under divergent selection. The analysis clarifies how subpopulations belonging to a rare habitat can maintain local adaptation despite high levels of migration if net selection against multi-locus genotypes is stronger than a threshold which depends on the relative abundances of the two habitats. Further, local adaptation in a metapopulation can significantly elevate F_ST between subpopulations belonging to the same habitat, even though these are not reproductively isolated. These findings highlight the importance of carefully considering the genetic architecture and spatial context of divergence when interpreting patterns of genomic differentiation between speciating populations.

Inversions and parallel evolution

Local adaptation leads to differences between populations within a species. In many systems, similar environmental contrasts occur repeatedly, sometimes driving parallel phenotypic evolution. Understanding the genomic basis of local adaptation and parallel evolution is a major goal of evolutionary genomics. It is now known that by preventing the break-up of favourable combinations of alleles across multiple loci, genetic architectures that reduce recombination, like chromosomal inversions, can make an important contribution to local adaptation. However, little is known about whether inversions also contribute disproportionately to parallel evolution. Our aim here is to highlight this knowledge gap, to showcase existing studies, and to illustrate the differences between genomic architectures with and without inversions using simple models. We predict that by generating stronger effective selection, inversions can sometimes speed up the parallel adaptive process or enable parallel adaptation where it would be impossible otherwise, but this is highly dependent on the spatial setting. We highlight that further empirical work is needed, in particular to cover a broader taxonomic range and to understand the relative importance of inversions compared to genomic regions without inversions.

This article is part of the theme issue ‘Genomic architecture of supergenes: causes and evolutionary consequences’.

The response of a metapopulation to a changing environment

A species distributed across diverse environments may adapt to local conditions. We ask how quickly such a species changes its range in response to changed conditions. Szép et al. (Szép E, Sachdeva H, Barton NH. 2021 Polygenic local adaptation in metapopulations: a stochastic eco-evolutionary model. Evolution75, 1030-1045 (doi:10.1111/evo.14210)) used the infinite island model to find the stationary distribution of allele frequencies and deme sizes. We extend this to find how a metapopulation responds to changes in carrying capacity, selection strength, or migration rate when deme sizes are fixed. We further develop a 'fixed-state' approximation. Under this approximation, polymorphism is only possible for a narrow range of habitat proportions when selection is weak compared to drift, but for a much wider range otherwise. When rates of selection or migration relative to drift change in a single deme of the metapopulation, the population takes a time of order m-1 to reach the new equilibrium. However, even with many loci, there can be substantial fluctuations in net adaptation, because at each locus, alleles randomly get lost or fixed. Thus, in a finite metapopulation, variation may gradually be lost by chance, even if it would persist in an infinite metapopulation. When conditions change across the whole metapopulation, there can be rapid change, which is predicted well by the fixed-state approximation. This work helps towards an understanding of how metapopulations extend their range across diverse environments. This article is part of the theme issue 'Species' ranges in the face of changing environments (Part II)'.

Understanding the biology of species' ranges: when and how does evolution change the rules of ecological engagement?

Understanding processes that limit species' ranges has been a core issue in ecology and evolutionary biology for many decades, and has become increasingly important given the need to predict the responses of biological communities to rapid environmental change. However, we still have a poor understanding of evolution at range limits and its capacity to change the ecological 'rules of engagement' that define these communities, as well as the time frame over which this occurs. Here we link papers in the current volume to some key concepts involved in the interactions between evolutionary and ecological processes at species' margins. In particular, we separate hypotheses about species' margins that focus on hard evolutionary limits, which determine how genotypes interact with their environment, from those concerned with soft evolutionary limits, which determine where and when local adaptation can persist in space and time. We show how theoretical models and empirical studies highlight conditions under which gene flow can expand local limits as well as contain them. In doing so, we emphasize the complex interplay between selection, demography and population structure throughout a species' geographical and ecological range that determines its persistence in biological communities. However, despite some impressively detailed studies on range limits, particularly in invertebrates and plants, few generalizations have emerged that can predict evolutionary responses at ecological margins. We outline some directions for future work such as considering the impact of structural genetic variants and metapopulation structure on limits, and the interaction between range limits and the evolution of mating systems and non-random dispersal. This article is part of the theme issue 'Species' ranges in the face of changing environments (Part II)'.

The costs and benefits of dispersal in small populations

Dispersal has three major effects on adaptation. First, gene flow mixes alleles adapted to different environments, potentially hindering (swamping) adaptation. Second, it brings in other variants and inflates genetic variance: this aids adaptation to spatially (and temporally) varying environments but if selection is hard, it lowers the mean fitness of the population. Third, neighbourhood size, which determines how weak genetic drift is, increases with dispersal-when genetic drift is strong, increase of the neighbourhood size with dispersal aids adaptation. In this note, I focus on the role of dispersal in environments that change gradually across space, and when local populations are quite small such that genetic drift has a significant effect. Using individual-based simulations, I show that in small populations, even leptokurtic dispersal benefits adaptation by reducing the power of genetic drift. This has implications for management of fragmented or marginal populations: the beneficial effect of increased dispersal into small populations is stronger than swamping of adaption under a broad range of conditions, including a mixture of local and long-distance dispersal. However, when environmental gradient is steep, heavily fat-tailed dispersal will swamp continuous adaptation so that only patches of locally adapted subpopulations remain. This article is part of the theme issue 'Species' ranges in the face of changing environments (Part II)'.

Genetic load and extinction in peripheral populations: the roles of migration, drift and demographic stochasticity

We analyse how migration from a large mainland influences genetic load and population numbers on an island, in a scenario where fitness-affecting variants are unconditionally deleterious, and where numbers decline with increasing load. Our analysis shows that migration can have qualitatively different effects, depending on the total mutation target and fitness effects of deleterious variants. In particular, we find that populations exhibit a genetic Allee effect across a wide range of parameter combinations, when variants are partially recessive, cycling between low-load (large-population) and high-load (sink) states. Increased migration reduces load in the sink state (by increasing heterozygosity) but further inflates load in the large-population state (by hindering purging). We identify various critical parameter thresholds at which one or other stable state collapses, and discuss how these thresholds are influenced by the genetic versus demographic effects of migration. Our analysis is based on a 'semi-deterministic' analysis, which accounts for genetic drift but neglects demographic stochasticity. We also compare against simulations which account for both demographic stochasticity and drift. Our results clarify the importance of gene flow as a key determinant of extinction risk in peripheral populations, even in the absence of ecological gradients. This article is part of the theme issue 'Species' ranges in the face of changing environments (part I)'.

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.