Dynamics of sexual populations structured by a space variable and a phenotypical trait

Mirrahimi, Sepideh; Raoul, G.

doi:10.1016/j.tpb.2012.12.003

Cited by 42 publications

(51 citation statements)

References 39 publications

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“…We consider self-compatible, hermaphroditic plants with no seed bank. Following previous analytical models (18,19,21,23,24,(30)(31)(32), we consider the continuous-time evolution of a population in a continuous space structured by a phenotypic trait, which determines fitness. Population density at time t and at location x is denoted nðx, tÞ; the mean phenotypic trait is denoted zðx, tÞ (see Table 1 for a summary of the notation).…”

Section: Methodsmentioning

confidence: 99%

“…Building on previous quantitative genetic models in continuous space (18,19,21,23,24,(30)(31)(32), we analyze here the effect of the distance of pollen dispersal relative to seed dispersal on the responses of a population to a changing environment. We assume that pollen does not directly limit plant fecundity but that population dynamics depend on local adaptation.…”

Section: Significancementioning

confidence: 99%

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Pollen dispersal slows geographical range shift and accelerates ecological niche shift under climate change

Aguilée

Raoul

Rousset

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Species may survive climate change by migrating to track favorable climates and/or adapting to different climates. Several quantitative genetics models predict that species escaping extinction will change their geographical distribution while keeping the same ecological niche. We introduce pollen dispersal in these models, which affects gene flow but not directly colonization. We show that plant populations may escape extinction because of both spatial range and ecological niche shifts. Exact analytical formulas predict that increasing pollen dispersal distance slows the expected spatial range shift and accelerates the ecological niche shift. There is an optimal distance of pollen dispersal, which maximizes the sustainable rate of climate change. These conclusions hold in simulations relaxing several strong assumptions of our analytical model. Our results imply that, for plants with long distance of pollen dispersal, models assuming niche conservatism may not accurately predict their future distribution under climate change.vidence is accumulating that current climate change has already induced extinctions of species (1, 2), and this phenomenon is predicted to accelerate in the next decades (3). In an environment that is changing both in space and in time, species may escape from extinction by changing their geographical distribution such that they track in space the same climatic conditions, by adapting their phenotype to the new climatic conditions where their currently occur, or by a combination of these strategies (4, 5). Poleward and upward altitudinal spatial range shifts of populations have already been observed in many animals and plants (e.g., refs. 1, 6, and 7). Likewise, there is increasing evidence of phenotypic changes induced by climate change, caused by plastic and/or genetic responses (8). The success or failure of these responses strongly depends on dispersal, which influences both colonization and adaptation (3, 9, 10). For plants, the demographic migration (due to seed dispersal) is partially uncoupled from gene flow (due to both pollen and seed dispersal): pollen and seed dispersal are therefore not expected to have the same consequences on spatial range shifts and on ecological niche shifts (9,(11)(12)(13)(14)(15). In this paper, we investigate how the dispersal distance of pollen specifically affects the evolutionary and demographic responses of populations under climate change.The challenges associated with adaptation to climate change, and how theoretical studies have attempted to model the responses to these challenges, can be concretely illustrated with the example of Picea sitchensis (Sitka spruce). This tree species naturally occurs on a limited geographical range along the Pacific coast of North America. Bud set date, a phenotype linked with adaptation to climate, is genetically differentiated throughout the range, linearly decreasing from south to north, which suggests divergent selection on this trait across the range, associated with temperature (16, 17). Likewise, many theoretica...

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Section: Methodsmentioning

confidence: 99%

Section: Significancementioning

confidence: 99%

Pollen dispersal slows geographical range shift and accelerates ecological niche shift under climate change

Aguilée

Raoul

Rousset

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

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“…This provides a way to study a small adaptation potential while scaling the environment accordingly. This small adaptation limit has already been studied by Mirrahimi and Raoul (2013) and there is an explicit expression for the propagation speed for such low adaptation scenarios, given by:…”

Section: Explicit Approximation Of Propagation Speeds Under Various Amentioning

confidence: 99%

“…The blue hatched area is the zone in the parameter space where the difference between propagation speed in Kirkpatrick and Barton's model and Fisher-KPP's model is at most 0.1, marking the strong adaptation regime; the red hatched area is where propagation speed in Kirkpatrick and Barton's model is well approximated (i.e. the difference is at most 0.1) by the formula by Mirrahimi and Raoul (2013), i.e., given by (3), marking the weak adaptation regime.…”

Section: Relating Propagation Speeds To Adaptation Regimesmentioning

confidence: 99%

Effects of variations in adaptation potential on invasion speeds and species ranges

Méndez-Vera¹,

Raoul²,

Massol³

et al. 2019

Preprint

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Confronted with global changes and their potential impacts on biodiversity, an important question is to understand the ecological and evolutionary determinants of species geographical distributions. In order to understand how adaptation in heterogeneous environments constrains such distributions, we analyze how the potential of adaptation along an environmental cline affects the geographical distribution and propagation dynamics (invasion or extinction) of a single species. We re-analyse a model initially proposed by Kirkpatrick and Barton using propagation speed to assess whether species distribution is spatially limited or not.We found that for big adaptation potentials, the species invades space following Fisher's model, whereas for small adaptation potentials the propagation depends on the evolutionary challenge to overcome. We have explicit approximations for the propagation speeds in both cases. We discuss the utility of these propagation speeds as an eco-evolutionary index based on empirical studies.

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“…The analysis of nonlinear reaction-diffusion systems by maximal exploitation of relations to the ordinary diffusion equation has parallels in recent work of Alfaro and Carles [42] on non-local reaction-diffusion equations, while the notion of interacting, evolving phenotype distributions (in a genetic, rather than epigentic context, and with a somewhat different mathematical formulation) was pursued by May and Nowak two decades ago [43][44][45]. The inclusion of variation across physical space as well as across phenotype space or the incorporation of non-local couplings with more structure than in our simple coupling via the total population could produce a richer class of behaviours [46][47][48][49][50][51][52][53][54][55].…”

Section: Laplace Transform Analysismentioning

confidence: 99%

Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences

Chisholm

Lorenzi

Desvillettes

et al. 2016

Z. Angew. Math. Phys.

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Abstract. Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible, and illustrate that whilst epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of "epigenetic load" and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a "proof of concept" of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage, and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.

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Dynamics of sexual populations structured by a space variable and a phenotypical trait

Cited by 42 publications

References 39 publications

Pollen dispersal slows geographical range shift and accelerates ecological niche shift under climate change

Pollen dispersal slows geographical range shift and accelerates ecological niche shift under climate change

Effects of variations in adaptation potential on invasion speeds and species ranges

Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences

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