Why do species have a skin? Investigating mutational constraint with a fundamental population model

Evolving mutation rate advances the invasion speed of a sexual species

Background

Many species are shifting their ranges in response to global climate change. Range expansions are known to have profound effects on the genetic composition of populations. The evolution of dispersal during range expansion increases invasion speed, provided that a species can adapt sufficiently fast to novel local conditions. Genetic diversity at the expanding range border is however depleted due to iterated founder effects. The surprising ability of colonizing species to adapt to novel conditions while being subjected to genetic bottlenecks is termed ‘the genetic paradox of invasive species’. Mutational processes have been argued to provide an explanation for this paradox. Mutation rates can evolve, under conditions that favor an increased rate of adaptation, by hitchhiking on beneficial mutations through induced linkage disequilibrium. Here we argue that spatial sorting, iterated founder events, and population structure benefit the build-up and maintenance of such linkage disequilibrium. We investigate if the evolution of mutation rates could play a role in explaining the ‘genetic paradox of invasive species’ for a sexually reproducing species colonizing a landscape of gradually changing conditions.

Results

We use an individual-based model to show the evolutionary increase of mutation rates in sexual populations during range expansion, in coevolution with the dispersal probability. The observed evolution of mutation rate is adaptive and clearly advances invasion speed both through its effect on the evolution of dispersal probability, and the evolution of local adaptation. This also occurs under a variable temperature gradient, and under the assumption of 90% lethal mutations.

Conclusions

In this study we show novel consequences of the particular genetic properties of populations under spatial disequilibrium, i.e. the coevolution of dispersal probability and mutation rate, even in a sexual species and under realistic spatial gradients, resulting in faster invasions. The evolution of mutation rates can therefore be added to the list of possible explanations for the ‘genetic paradox of invasive species’. We conclude that range expansions and the evolution of mutation rates are in a positive feedback loop, with possibly far-reaching ecological consequences concerning invasiveness and the adaptability of species to novel environmental conditions.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-017-0998-8) contains supplementary material, which is available to authorized users.

Limits to adaptation along environmental gradients

Why do species not adapt to ever-wider ranges of conditions, gradually expanding their ecological niche and geographic range? Gene flow across environments has two conflicting effects: although it increases genetic variation, which is a prerequisite for adaptation, gene flow may swamp adaptation to local conditions. In 1956, Haldane proposed that, when the environment varies across space, "swamping" by gene flow creates a positive feedback between low population size and maladaptation, leading to a sharp range margin. However, current deterministic theory shows that, when variance can evolve, there is no such limit. Using simple analytical tools and simulations, we show that genetic drift can generate a sharp margin to a species' range, by reducing genetic variance below the level needed for adaptation to spatially variable conditions. Aided by separation of ecological and evolutionary timescales, the identified effective dimensionless parameters reveal a simple threshold that predicts when adaptation at the range margin fails. Two observable parameters determine the threshold: (i) the effective environmental gradient, which can be measured by the loss of fitness due to dispersal to a different environment; and (ii) the efficacy of selection relative to genetic drift. The theory predicts sharp range margins even in the absence of abrupt changes in the environment. Furthermore, it implies that gradual worsening of conditions across a species' habitat may lead to a sudden range fragmentation, when adaptation to a wide span of conditions within a single species becomes impossible.

Chromosome inversions, adaptive cassettes and the evolution of species' ranges

A chromosome inversion can spread when it captures locally adapted alleles or when it is introduced into a species by hybridization with adapted alleles that were previously absent. We present a model that shows how both processes can cause a species range to expand. Introgression of an inversion that carries novel, locally adapted alleles is a particularly powerful mechanism for range expansion. The model supports the earlier proposal that introgression of an inversion triggered a large range expansion of a malaria mosquito. These results suggest a role for inversions as cassettes of genes that can accelerate adaptation by crossing species boundaries, rather than protecting genomes from introgression.

Evolutionary rescue by beneficial mutations in environments that change in space and time

A factor that may limit the ability of many populations to adapt to changing conditions is the rate at which beneficial mutations can become established. We study the probability that mutations become established in changing environments by extending the classic theory for branching processes. When environments change in time, under quite general conditions, the establishment probability is approximately twice the 'effective selection coefficient', whose value is an average that gives most weight to a mutant's fitness in the generations immediately after it appears. When fitness varies along a gradient in a continuous habitat, increased dispersal generally decreases the chance a mutation establishes because mutations move out of areas where they are most adapted. When there is a patch of favourable habitat that moves in time, there is a maximum speed of movement above which mutations cannot become established, regardless of when and where they first appear. This critical speed limit, which is proportional to the mutation's maximum selective advantage, represents an absolute constraint on the potential of locally adapted mutations to contribute to evolutionary rescue.

Theoretical perspectives on the statics and dynamics of species' borders in patchy environments

Understanding range limits is a fundamental problem in ecology and evolutionary biology. In 1963, Mayr argued that "contaminating" gene flow from central populations constrained adaptation in marginal populations, preventing range expansion, while in 1984, Bradshaw suggested that absence of genetic variation prevented species from occurring everywhere. Understanding stability of range boundaries requires unraveling the interplay of demography, gene flow, and evolution of populations in concrete landscape settings. We walk through a set of interrelated spatial scenarios that illustrate interesting complexities of this interplay. To motivate our individual-based model results, we consider a hypothetical zooplankter in a landscape of discrete water bodies coupled by dispersal. We examine how patterns of dispersal influence adaptation in sink habitats where conditions are outside the species' niche. The likelihood of observing niche evolution (and thus range expansion) over any given timescale depends on (1) the degree of initial maladaptation; (2) pattern (pulsed vs. continuous, uni- vs. bidirectional), timing (juvenile vs. adult), and rate of dispersal (and hence population size); (3) mutation rate; (4) sexuality; and (5) the degree of heterogeneity in the occupied range. We also show how the genetic architecture of polygenic adaptation is influenced by the interplay of selection and dispersal in heterogeneous landscapes.