Quantifying the effects of migration and mutation on adaptation and demography in spatially heterogeneous environments

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.

Evolution and spread of multiadapted pathogens in a spatially heterogeneous environment

Pathogen adaptation to multiple selective pressures challenges our ability to control their spread. Here we analyze the evolutionary dynamics of pathogens spreading in a heterogeneous host population where selection varies periodically in space. We study both the transient dynamics taking place at the front of the epidemic and the long-term evolution far behind the front. We identify five types of epidemic profiles arising for different levels of spatial heterogeneity and different costs of adaptation. In particular, we identify the conditions where a generalist pathogen carrying multiple adaptations can outrace a coalition of specialist pathogens. We also show that finite host populations promote the spread of generalist pathogens because demographic stochasticity enhances the extinction of locally maladapted pathogens. But higher mutation rates between genotypes can rescue the coalition of specialists and speed up the spread of epidemics for intermediate levels of spatial heterogeneity. Our work provides a comprehensive analysis of the interplay between migration, local selection, mutation, and genetic drift on the spread and on the evolution of pathogens in heterogeneous environments. This work extends our fundamental understanding of the outcome of the competition between two specialists and a generalist strategy (single- vs. multiadapted pathogens). These results have practical implications for the design of more durable control strategies against multiadapted pathogens in agriculture and in public health.

Adaptation in a heterogeneous environment II: to be three or not to be

We propose a model to describe the adaptation of a phenotypically structured population in a H-patch environment connected by migration, with each patch associated with a different phenotypic optimum, and we perform a rigorous mathematical analysis of this model. We show that the large-time behaviour of the solution (persistence or extinction) depends on the sign of a principal eigenvalue, [Formula: see text], and we study the dependency of [Formula: see text] with respect to H. This analysis sheds new light on the effect of increasing the number of patches on the persistence of a population, which has implications in agroecology and for understanding zoonoses; in such cases we consider a pathogenic population and the patches correspond to different host species. The occurrence of a springboard effect, where the addition of a patch contributes to persistence, or on the contrary the emergence of a detrimental effect by increasing the number of patches on the persistence, depends in a rather complex way on the respective positions in the phenotypic space of the optimal phenotypes associated with each patch. From a mathematical point of view, an important part of the difficulty in dealing with [Formula: see text], compared to [Formula: see text] or [Formula: see text], comes from the lack of symmetry. Our results, which are based on a fixed point theorem, comparison principles, integral estimates, variational arguments, rearrangement techniques, and numerical simulations, provide a better understanding of these dependencies. In particular, we propose a precise characterisation of the situations where the addition of a third patch increases or decreases the chances of persistence, compared to a situation with only two patches.

Extending eco-evolutionary theory with oligomorphic dynamics

Understanding the interplay between ecological processes and the evolutionary dynamics of quantitative traits in natural systems remains a major challenge. Two main theoretical frameworks are used to address this question, adaptive dynamics and quantitative genetics, both of which have strengths and limitations and are often used by distinct research communities to address different questions. In order to make progress, new theoretical developments are needed that integrate these approaches and strengthen the link to empirical data. Here, we discuss a novel theoretical framework that bridges the gap between quantitative genetics and adaptive dynamics approaches. 'Oligomorphic dynamics' can be used to analyse eco-evolutionary dynamics across different time scales and extends quantitative genetics theory to account for multimodal trait distributions, the dynamical nature of genetic variance, the potential for disruptive selection due to ecological feedbacks, and the non-normal or skewed trait distributions encountered in nature. Oligomorphic dynamics explicitly takes into account the effect of environmental feedback, such as frequency- and density-dependent selection, on the dynamics of multi-modal trait distributions and we argue it has the potential to facilitate a much tighter integration between eco-evolutionary theory and empirical data.

A Theoretical Framework for Trait-Based Eco-Evolutionary Dynamics: Population Structure, Intraspecific Variation, and Community Assembly

AbstractHow is trait diversity in a community apportioned between and within coevolving species? Disruptive selection may result in either a few species with large intraspecific trait variation (ITV) or many species with different mean traits but little ITV. Similar questions arise in spatially structured communities: heterogeneous environments could result in either a few species that exhibit local adaptation or many species with different mean traits but little local adaptation. To date, theory has been well-equipped to either include ITV or to dynamically determine the number of coexisting species, but not both. Here, we devise a theoretical framework that combines these facets and apply it to the above questions of how trait variation is apportioned within and between species in unstructured and structured populations, using two simple models of Lotka-Volterra competition. For unstructured communities, we find that as the breadth of the resource spectrum increases, ITV goes from being unimportant to crucial for characterizing the community. For spatially structured communities on two patches, we find no local adaptation, symmetric local adaptation, or asymmetric local adaptation, depending on how much the patches differ. Our framework provides a general approach to incorporate ITV in models of eco-evolutionary community assembly.

Eco-evolutionary model on spatial graphs reveals how habitat structure affects phenotypic differentiation

Differentiation mechanisms are influenced by the properties of the landscape over which individuals interact, disperse and evolve. Here, we investigate how habitat connectivity and habitat heterogeneity affect phenotypic differentiation by formulating a stochastic eco-evolutionary model where individuals are structured over a spatial graph. We combine analytical insights into the eco-evolutionary dynamics with numerical simulations to understand how the graph topology and the spatial distribution of habitat types affect differentiation. We show that not only low connectivity but also heterogeneity in connectivity promotes neutral differentiation, due to increased competition in highly connected vertices. Habitat assortativity, a measure of habitat spatial auto-correlation in graphs, additionally drives differentiation under habitat-dependent selection. While assortative graphs systematically amplify adaptive differentiation, they can foster or depress neutral differentiation depending on the migration regime. By formalising the eco-evolutionary and spatial dynamics of biological populations on graphs, our study establishes fundamental links between landscape features and phenotypic differentiation.

A research agenda for scaling up agroecology in European countries

A profound transformation of agricultural production methods has become unavoidable due to the increase in the world's population, and environmental and climatic challenges. Agroecology is now recognized as a challenging model for agricultural systems, promoting their diversification and adaptation to environmental and socio-economic contexts, with consequences for the entire agri-food system and the development of rural and urban areas. Through a prospective exercise performed at a large interdisciplinary institute, INRAE, a research agenda for agroecology was built that filled a gap through its ambition and interdisciplinarity. It concerned six topics. For genetics, there is a need to study genetic aspects of complex systems (e.g., mixtures of genotypes) and to develop breeding methods for them. For landscapes, challenges lie in effects of heterogeneity at multiple scales, in multifunctionality and in the design of agroecological landscapes. Agricultural equipment and digital technologies show high potential for monitoring dynamics of agroecosystems. For modeling, challenges include approaches to complexity, consideration of spatial and temporal dimensions and representation of the cascade from cropping practices to ecosystem services. The agroecological transition of farms calls for modeling and observational approaches as well as for creating new design methods. Integration of agroecology into food systems raises the issues of product specificity, consumer behavior and organization of markets, standards and public policies. In addition, transversal priorities were identified: (i) generating sets of biological data, through research and participatory mechanisms, that are appropriate for designing agroecological systems and (ii) collecting and using coherent sets of data to enable assessment of vulnerability, resilience and risk in order to evaluate the performance of agroecological systems and to contribute to scaling up. The main lessons learned from this collective exercise can be useful for the entire scientific community engaged in research into agroecology.

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)'.

Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal?

When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to close the resulting system of equations, they often assume the local trait distributions are Gaussian [see for instance Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 )]. The aim of this paper is to introduce a mathematical framework that follows the whole trait distribution (without prior assumption) to study evolutionary dynamics of sexually reproducing populations. Specifically, it focuses on complex traits, whose inheritance can be encoded by the infinitesimal model of segregation (Fisher in Trans R Soc Edinb 52(2):399-433, 1919. https://doi.org/10.1017/S0080456800012163 ). We show that it allows us to derive a regime in which our model gives the same dynamics as when assuming Gaussian local trait distributions. To support that, we compare the stationary problems of the system of moments derived from our model with the one given in Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 ) and show that they are equivalent under this regime and do not need to be otherwise. Moreover, under this regime of equivalence, we show that a separation bewteen ecological and evolutionary time scales arises. A fast relaxation toward monomorphism allows us to reduce the complexity of the system of moments, using a slow-fast analysis. This reduction leads us to complete, still in this regime, the analytical description of the bistable asymmetrical equilibria numerically found in Ronce and Kirkpatrick (Evolution 55(8):1520-1531, 2001. https://doi.org/10.1111/j.0014-3820.2001.tb00672.x.37 ). More globally, we provide explicit modelling hypotheses that allow for such local adaptation patterns to occur.

Spatial structure and dispersal dynamics in a house sparrow metapopulation

The effects of spatial structure on metapopulation dynamics depend upon the interaction between local population dynamics and dispersal, and how this relationship is affected by the geographical isolation and spatial heterogeneity in habitat characteristics. Our aim is to examine how emigration and immigration of house sparrows Passer domesticus in a Norwegian archipelagic metapopulation are affected by key factors predicted by classic metapopulation models to affect dispersal-spatial and temporal variation in population size, inter-island distance, local demography and habitat characteristics. This metapopulation can be divided into two major habitat types: (a) islands closer to the mainland where sparrows breed in colonies on farms, and (b) islands without farms, situated farther away from the mainland where sparrows are exposed to harsher environmental conditions. Dispersal was spatially structured within the metapopulation; there was proportionally and numerically less emigration and immigration involving farm islands, as compared to non-farm islands. Furthermore, emigration and immigration occurred mostly between nearby islands. Moreover, emigration in response to spatial differences in mean population size differed between the habitat types, but populations with large mean received more immigrants in both habitat types. The number of emigrants and immigrants was negatively related to long-term recruit production, which was not the case in non-farm islands. The proportion and number of emigrants was positively related to temporal increases in recruit production on farm islands, however not on non-farm islands. Our results demonstrate that spatial heterogeneity in environmental conditions influences how spatial variation in long-term mean population size, and temporal and spatial variation in recruit production, affects dispersal dynamics. The spatial structure of this metapopulation is therefore best described by a spatially explicit model in which the exchange of individuals within each habitat type is strongly affected by the degree of geographical isolation, population size and recruit production. However, these relationships differed between the two habitat types; non-farm islands showing similarities to a mainland-island model type of structure, whereas farm islands showed features more associated with source-sink or balanced dispersal models. Such differential dispersal dynamics between habitat types are expected to have important consequences for the ecological and evolutionary dynamics within this metapopulation.

Adaptation in a heterogeneous environment I: persistence versus extinction

Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens is a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under the effects of mutation, selection and migration in a two-patch environment, each patch being associated with a different phenotypic optimum. We consider two types of growth functions that depend on the n-dimensional phenotypic trait: either local and linear or nonlocal nonlinear. In both cases, we obtain existence and uniqueness results as well as a characterization of the large-time behaviour of the solution (persistence or extinction) based on the sign of a principal eigenvalue. We show that migration between the two environments decreases the chances of persistence, with in some cases a 'lethal migration threshold' above which persistence is not possible. Comparison with stochastic individual-based simulations shows that the PDE approach accurately captures this threshold. Our results illustrate the importance of cultivar mixtures for disease prevention and control.

Evolution of Specialization in Heterogeneous Environments: Equilibrium Between Selection, Mutation and Migration

Adaptation in spatially heterogeneous environments results from the balance between local selection, mutation, and migration. We study the interplay among these different evolutionary forces and demography in a classical two-habitat scenario with asexual reproduction. We develop a new theoretical approach that goes beyond the Adaptive Dynamics framework, and allows us to explore the effect of high mutation rates on the stationary phenotypic distribution. We show that this approach improves the classical Gaussian approximation, and captures accurately the shape of this equilibrium phenotypic distribution in one- and two-population scenarios. We examine the evolutionary equilibrium under general conditions where demography and selection may be nonsymmetric between the two habitats. In particular, we show how migration may increase differentiation in a source-sink scenario. We discuss the implications of these analytic results for the adaptation of organisms with large mutation rates, such as RNA viruses.

Bayesian inference of natural selection from spatiotemporal phenotypic data

Spatiotemporal variations of natural selection may influence the evolution of various features of organisms such as local adaptation or specialisation. This article develops a method for inferring how selection varies between locations and between generations from phenotypic data. It is assumed that generations are non-overlapping and that individuals reproduce by selfing or asexually. A quantitative genetics model taking account of the effects of stabilising natural selection, the environment and mutation on phenotypic means and variances is developed. Explicit results on the evolution of populations are derived and used to develop a Bayesian inference method. The latter is applied to simulated data and to data from a wheat participatory plant breeding programme. It has some ability to infer evolutionary parameters, but estimates may be sensitive to prior distributions, for example when phenotypic time series are short and when environmental effects are large. In such cases, sensitivity to prior distributions may be reported or more data may be collected.

Quantifying the efficacy of genetic shifting in control of mosquito-borne diseases

Many of the world's most prevalent diseases are transmitted by animal vectors such as dengue transmitted by mosquitoes. To reduce these vector-borne diseases, a promising approach is "genetic shifting": selective breeding of the vectors to be more resistant to pathogens and releasing them to the target populations to reduce their ability to transmit pathogens, that is, lower their vector competence. The efficacy of genetic shifting will depend on possible counterforces such as natural selection against low vector competence. To quantitatively evaluate the potential efficacy of genetic shifting, we developed a series of coupled genetic-demographic models that simulate the changes of vector competence during releases of individuals with low vector competence. We modeled vector competence using different genetic architectures, as a multilocus, one-locus, or two-locus trait. Using empirically determined estimates of model parameters, the model predicted a reduction of mean vector competence of at least three standard deviations after 20 releases, one release per generation, and 10% of the size of the target population released each time. Sensitivity analysis suggested that release efficacy depends mostly on the vector competence of the released population, release size, release frequency, and the survivorship of the released individuals, with duration of the release program less important. Natural processes such as density-dependent survival and immigration from external populations also strongly influence release efficacy. Among different sex-dependent release strategies, releasing blood-fed females together with males resulted in the highest release efficacy, as these females mate in captivity and reproduce when released, thus contributing a greater proportion of low-vector-competence offspring. Conclusions were generally consistent across three models assuming different genetic architectures of vector competence, suggesting that genetic shifting could generally apply to various vector systems and does not require detailed knowledge of the number of loci contributing to vector competence.

Linking local adaptation with the evolution of sex differences

Many conspicuous forms of evolutionary diversity occur within species. Two prominent examples include evolutionary divergence between populations differentially adapted to their local environments (local adaptation), and divergence between females and males in response to sex differences in selection (sexual dimorphism sensu lato). These two forms of diversity have inspired vibrant research programmes, yet these fields have largely developed in isolation from one another. Nevertheless, conceptual parallels between these research traditions are striking. Opportunities for local adaptation strike a balance between local selection, which promotes divergence, and gene flow-via dispersal and interbreeding between populations-which constrains it. Sex differences are similarly constrained by fundamental features of inheritance that mimic gene flow. Offspring of each sex inherit genes from same-sex and opposite-sex parents, leading to gene flow between each differentially selected half of the population, and raising the question of how sex differences arise and are maintained. This special issue synthesizes and extends emerging research at the interface between the research traditions of local adaptation and sex differences. Each field can promote understanding of the other, and interactions between local adaptation and sex differences can generate new empirical predictions about the evolutionary consequences of selection that varies across space, time, and between the sexes.This article is part of the theme issue 'Linking local adaptation with the evolution of sex differences'.

Spatiotemporal dynamics of fungicide resistance in the wheat pathogen Zymoseptoria tritici in France

BACKGROUND

Management of pesticide resistance is a major issue in modern agricultural systems, particularly in the context of the broader challenge of reducing pesticide use. However, such management must be adapted to resistance dynamics, which remains challenging to predict due to its dependence on many biological traits of pests, interactions with the environment and pesticide use. We retrospectively studied the evolution of reported resistances to four modes of action (benzimidazoles, quinone outside inhibitors, sterol demethylation inhibitors and succinate dehydrogenase inhibitors), in French populations of the wheat pathogen Zymoseptoria tritici.

RESULTS

We used statistical models to analyse the Performance trial network data set (2004-2017; ∼ 70 locations in France yearly). They highlighted contrasting behaviours between phenotypes, for example: (i) stable spatial distributions and colonization front structures over time, and (ii) different frequency growth rates at the national scale and between regions.

CONCLUSION

We provide a quantitative description of the spatiotemporal patterns of resistance evolution for fungicides with several modes of action. Moreover, we highlight some unexpected resistance dynamics in France, with major differences between the north and south. This complex pattern of resistance evolution in French populations is consistent with previous descriptions of dynamics at the European scale. These results should make it easier to anticipate evolution locally and to improve the management of resistance. © 2019 Society of Chemical Industry.

Adaptive diversification in heterogeneous environments

The role of environmental heterogeneity in the evolution of biological diversity has been studied only for simple types of heterogeneities and dispersals. This article broadens previous results by considering heterogeneities and dispersals that are structured by several environmental factors. It studies the evolution of a metapopulation, living in a network of patches connected by dispersal, under the effects of mutation, selection and migration. First, it is assumed that patches are equally connected and that they carry habitats characterized by several factors exerting selection pressures on several individual traits. Habitat factors may vary in the environment independently or they may be correlated. It is shown that correlations between habitat factors promote adaptive diversification and that this effect may be modified by trait interactions on survival. Then, it is assumed that patches are structured by two crossed factors, called the row and column factors, such that patches are more connected when they occur in the same row or in the same column. Environmental patterns in which each habitat appears in each row the same number of times and appears in each column the same number of times are found to hinder adaptive diversification.

Evolutionary dynamics of a quantitative trait in a finite asexual population

In finite populations, mutation limitation and genetic drift can hinder evolutionary diversification. We consider the evolution of a quantitative trait in an asexual population whose size can vary and depends explicitly on the trait. Previous work showed that evolutionary branching is certain ("deterministic branching") above a threshold population size, but uncertain ("stochastic branching") below it. Using the stationary distribution of the population's trait variance, we identify three qualitatively different sub-domains of "stochastic branching" and illustrate our results using a model of social evolution. We find that in very small populations, branching will almost never be observed; in intermediate populations, branching is intermittent, arising and disappearing over time; in larger populations, finally, branching is expected to occur and persist for substantial periods of time. Our study provides a clearer picture of the ecological conditions that facilitate the appearance and persistence of novel evolutionary lineages in the face of genetic drift.

How do cold-sensitive species endure ice ages? Phylogeographic and paleodistribution models of postglacial range expansion of the mesothermic drought-tolerant conifer Austrocedrus chilensis

In view of global climate change, it is important to understand the responses of tree species to climate changes in the past. Combinations of phylogeographic analysis of genetic evidence, coupled with species distribution models (SDMs), are improving our understanding on this subject. We combined SDMs and microsatellite data from populations of the entire range of Austrocedrus chilensis, a dominant mesotherm (cold-sensitive) conifer of dryland forests of the southern Andes, to test the hypothesis of long-distance postglacial migration from northern and warmer refugia at the Last Glacial Maximum (LGM). The SDM indicated suitable conditions for Austrocedrus in northern Chile (western) at the LGM and largely unsuitable conditions in Argentina (eastern). Population genetic diversity and effective population sizes within populations decreased southward along the Andes, consistent with the hypothesis of long-distance dispersal from a northern refugium. Results support the hypothesis of one (or a few) warmer (low latitude) refugia in Chile for Austrocedrus. On balance, the evidence suggests that in contrast to cold-tolerant tree taxa with the capacity to fast-track postglacial warming thanks to local refugia, cold-sensitive species might have undergone long-distance range expansion, lagging behind progressive climate change throughout the Holocene.

Evolution of Quantitative Traits under a Migration-Selection Balance: When Does Skew Matter?

Quantitative-genetic models of differentiation under migration-selection balance often rely on the assumption of normally distributed genotypic and phenotypic values. When a population is subdivided into demes with selection toward different local optima, migration between demes may result in asymmetric, or skewed, local distributions. Using a simplified two-habitat model, we derive formulas without a priori assuming a Gaussian distribution of genotypic values, and we find expressions that naturally incorporate higher moments, such as skew. These formulas yield predictions of the expected divergence under migration-selection balance that are more accurate than models assuming Gaussian distributions, which illustrates the importance of incorporating these higher moments to assess the response to selection in heterogeneous environments. We further show with simulations that traits with loci of large effect display the largest skew in their distribution at migration-selection balance.

Multidimensional (co)evolutionary stability

The complexity of biotic and abiotic environmental conditions is such that the fitness of individuals is likely to depend on multiple traits. Using a synthetic framework of phenotypic evolution that draws from adaptive dynamics and quantitative genetics approaches, we explore how the number of traits under selection influences convergence stability and evolutionary stability in models for coevolution in multidimensional phenotype spaces. Our results allow us to identify three different effects of trait dimensionality on stability. First are (i) a "combinatorial effect": without epistasis and genetic correlations, a higher number of trait dimensions offers more opportunities for equilibria to be unstable; and (ii) epistatic interactions, that is, fitness interactions between traits, which tend to destabilize evolutionary equilibria; this effect increases with the dimension of phenotype space. These first two effects influence both convergence stability and evolutionary stability, while (iii) genetic correlations (due, e.g., to pleiotropy or linkage disequilibrium) can affect only convergence stability. We illustrate the general prediction that increased dimensionality destabilizes evolutionary equilibria using examples drawn from well-studied classical models of frequency-dependent competition for resources, adaptation to a spatially heterogeneous environment, and antagonistic coevolution. In addition, our analyses show that increased dimensionality can favor diversification, for example, in the form of local adaptation, as well as evolutionary escape.