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Determining Selection across Heterogeneous Landscapes: A Perturbation-Based Method and Its Application to Modeling Evolution in Space
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Ecology and Environmental Sciences.
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2017 (English)In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 189, no 4, p. 381-395Article in journal (Refereed) Published
Abstract [en]

Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.

Place, publisher, year, edition, pages
UNIV CHICAGO PRESS , 2017. Vol. 189, no 4, p. 381-395
Keywords [en]
evolution, spatial, reaction-diffusion models, adaptive dynamics, quantitative genetics, metacommunities
National Category
Evolutionary Biology
Identifiers
URN: urn:nbn:se:umu:diva-134209DOI: 10.1086/690908ISI: 000398685600006PubMedID: 28350499OAI: oai:DiVA.org:umu-134209DiVA, id: diva2:1112502
Available from: 2017-06-20 Created: 2017-06-20 Last updated: 2019-01-08Bibliographically approved
In thesis
1. Evolution of Ecological Communities in Spatially Heterogeneous Environments
Open this publication in new window or tab >>Evolution of Ecological Communities in Spatially Heterogeneous Environments
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Evolution av ekologiska samhällen i rumsligt heterogena miljöer
Abstract [en]

Evolutionarily stable communities are the endpoints of evolution, and ecological communities whose traits are under selection will eventually settle into them. Hence, the properties of such communities are of particular interest, as they can persist over long evolutionary time scales. The notion of an evolutionarily stable strategy - an evolved strategy that cannot be beat by any other once established - has now been part of theoretical ecology for almost 50 years, and the theory for evolutionarily stable strategies and communities, and how they are reached has become increasingly versatile. However, for environments where conditions vary in space, so-called heterogeneous environments, efficient analytical and numerical tools for studying evolutionarily stable communities and how they come about have been lacking. Hence, many questions regarding how evolutionarily stable diversity is generated and maintained when ecological and evolutionary forces vary in space remain unexplored. In particular, how spatially averaged selection and selective forces derived from spatial variability can act together to either promote or inhibit evolutionarily stable diversity is not well understood.  

In this thesis, I use a two-pronged approach towards answering such questions by developing the necessary analytical and numerical tools for assembling and analyzing evolutionarily stable communities in heterogeneous environments, and by then employing these tools to study communities of resource competitors and food webs. Specifically, I derive expressions for directional and stabilizing/disruptive selection when the spatially heterogeneous ecological dynamics of a community are described by reaction-diffusion equations. These expressions allow us to understand selection across an environment in terms of local selection pressures, and also enable efficient numerical implementations of evolutionary community assembly procedures that lead to evolutionarily stable communities.  

Applied to the communities of resource competitors and food webs I find that the selective forces derived from spatially averaged selection and those derived from spatial variability can act both in concert or in opposition. If these forces act in opposition and if the spatial variability of local selection is high, a high diversity of organisms can form even when spatially averaged selection is stabilizing. In contrast, if spatially averaged selection is disruptive, it can prevent more diverse communities from forming by creating few globally unbeatable strategies. However, these forces can also act disruptively in concert to create more diverse communities. Together, these results demonstrate a surprising variety of qualitatively different outcomes when evolutionarily stable communities are assembled in heterogeneous environments.

Abstract [sv]

Evolutionärt stabila samhällen är slutpunkten för evolution, och ekologiska samhällen vars egenskaper är under selektion kommer till slut att bli ett sådant. Således är egenskaperna hos sådana samhällen särskilt intressanta, då dessa kan bestå oförändrade under långa evolutionära tidsskalor. Idén om evolutionärt stabila strategier - strategier som är oslagbara när de väl evolverat - är sedan nästan 50 år tillbaka ett väl etablerat koncept inom teoretisk ekologi. Under dessa år har teorin för evolutionärt stabila strategier och samhällen blivit alltmer välutvecklad. Denna utveckling till trots saknas fortfarande effektiva analytiska och numeriska verktyg för att studera evolutionärt stabila samhällen i heterogena miljöer, där de ekologiska betingelserna - och således även krafterna från naturligt urval - varierar från punkt till punkt i rummet. På grund av detta har många frågor rörande hur evolutionärt stabil mångfald blir till och bevaras när ekologiska och evolutionära krafter varierar i rummet förblivit outforskade. I synnerhet är kännedomen låg om hur rumsligt genomsnittlig selektion och selektion som härstammar från rummets variabilitet samverkar för att antingen förstärka eller förhindra mångfald.

I den här avhandlingen använder jag ett dubbelt grepp för att närma mig svar på dessa frågor, dels genom att utveckla de nödvändiga analytiska och numeriska verktygen för att sätta samman och analysera evolutionärt stabila samhällen i heterogena miljöer, och dels genom att använda dessa metoder för att studera samhällen av resurskonkurenter och näringsvävar. För att åstadkomma detta härleder jag uttryck för riktad och stabiliserande/disruptiv selektion när den rumsligt heterogena ekologiska dynamiken beskrivs av reaktion-diffusion ekvationer. Dessa uttryck möjliggör förståelse för selektion i en heterogen miljö i termer av hur selektion verkar lokalt i rummet, och möjliggör effektiva numeriska implementationer av metoder för att evolutionärt sätta samman samhällen.

När dessa metoder appliceras på samhällena av resurskonkurenter och näringsvävar kan jag utröna att de selektiva krafterna som härstammar från rumsligt genomsnittlig selektion och de som härstammar från rumslig variabilitet både kan samverka och motverka varandra. Om de motverkar varandra, och graden av rumslig variabilitet är hög kan hög mångfald uppstå, även när genomsnittlig selektion är stabiliserande. I kontrast till detta kan disruptiv genomsnittlig selektion motverka mångfald genom att selektera för ett fåtal globalt dominanta strategier. Dessa krafter kan dock också samverka disruptivt och tillsammans bilda en stor mångfald. Tillsammans påvisar dessa resultat en stor variation av kvalitativt olika utfall när evolutionärt stabila samhällen sätts samman i rumsligt heterogena miljöer.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 2019. p. 87
Series
Research report in mathematics, ISSN 1653-0810 ; 64/19
Keywords
Spatial models, reaction-diffusion equations, eco-evolutionary models, adaptive dynamics, evolutionarily stable communities
National Category
Evolutionary Biology Ecology Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-155133 (URN)978-91-7601-992-4 (ISBN)
Public defence
2019-02-01, N430, Naturvetarhuset, Umeå, 09:00 (English)
Opponent
Supervisors
Available from: 2019-01-11 Created: 2019-01-08 Last updated: 2019-01-10Bibliographically approved

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Wickman, JonasDiehl, SebastianBrännström, Åke

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