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Hauert C, Doebeli M. Spatial social dilemmas promote diversity. Proc Natl Acad Sci U S A 2021; 118:e2105252118. [PMID: 34649992 PMCID: PMC8594579 DOI: 10.1073/pnas.2105252118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/19/2021] [Indexed: 11/18/2022] Open
Abstract
Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.
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Affiliation(s)
- Christoph Hauert
- Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada;
- Department of Zoology, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - Michael Doebeli
- Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
- Department of Zoology, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
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The components of directional and disruptive selection in heterogeneous group-structured populations. J Theor Biol 2020; 507:110449. [PMID: 32814071 DOI: 10.1016/j.jtbi.2020.110449] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Revised: 08/05/2020] [Accepted: 08/07/2020] [Indexed: 11/23/2022]
Abstract
We derive how directional and disruptive selection operate on scalar traits in a heterogeneous group-structured population for a general class of models. In particular, we assume that each group in the population can be in one of a finite number of states, where states can affect group size and/or other environmental variables, at a given time. Using up to second-order perturbation expansions of the invasion fitness of a mutant allele, we derive expressions for the directional and disruptive selection coefficients, which are sufficient to classify the singular strategies of adaptive dynamics. These expressions include first- and second-order perturbations of individual fitness (expected number of settled offspring produced by an individual, possibly including self through survival); the first-order perturbation of the stationary distribution of mutants (derived here explicitly for the first time); the first-order perturbation of pairwise relatedness; and reproductive values, pairwise and three-way relatedness, and stationary distribution of mutants, each evaluated under neutrality. We introduce the concept of individual k-fitness (defined as the expected number of settled offspring of an individual for which k-1 randomly chosen neighbors are lineage members) and show its usefulness for calculating relatedness and its perturbation. We then demonstrate that the directional and disruptive selection coefficients can be expressed in terms individual k-fitnesses with k=1,2,3 only. This representation has two important benefits. First, it allows for a significant reduction in the dimensions of the system of equations describing the mutant dynamics that needs to be solved to evaluate explicitly the two selection coefficients. Second, it leads to a biologically meaningful interpretation of their components. As an application of our methodology, we analyze directional and disruptive selection in a lottery model with either hard or soft selection and show that many previous results about selection in group-structured populations can be reproduced as special cases of our model.
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Wickman J, Dieckmann U, Hui C, Brännström Å. How geographic productivity patterns affect food-web evolution. J Theor Biol 2020; 506:110374. [PMID: 32634386 DOI: 10.1016/j.jtbi.2020.110374] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Revised: 02/25/2020] [Accepted: 06/11/2020] [Indexed: 11/26/2022]
Abstract
It is well recognized that spatial heterogeneity and overall productivity have important consequences for the diversity and community structure of food webs. Yet, few, if any, studies have considered the effects of heterogeneous spatial distributions of primary production. Here, we theoretically investigate how the variance and autocorrelation length of primary production affect properties of evolved food webs consisting of one autotroph and several heterotrophs. We report the following findings. (1) Diversity increases with landscape variance and is unimodal in autocorrelation length. (2) Trophic level increases with landscape variance and is unimodal in autocorrelation length. (3) The extent to which the spatial distribution of heterotrophs differ from that of the autotroph increases with landscape variance and decreases with autocorrelation length. (4) Components of initial disruptive selection experienced by the ancestral heterotroph predict properties of the final evolved communities. Prior to our study reported here, several authors had hypothesized that diversity increases with the landscape variance of productivity. Our results support their hypothesis and contribute new facets by providing quantitative predictions that also account for autocorrelation length and additional properties of the evolved communities.
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Affiliation(s)
- Jonas Wickman
- Integrated Science Lab, Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden.
| | - Ulf Dieckmann
- Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria; Department of Evolutionary Studies of Biosystems, The Graduate University for Advanced Studies (Sokendai), Hayama, Kanagawa 240-0193, Japan
| | - Cang Hui
- Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University, Matieland 7602, South Africa; Mathematical and Physical Biosciences, African Institute for Mathematical Sciences, Cape Town 7945, South Africa
| | - Åke Brännström
- Integrated Science Lab, Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden; Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, 2361 Laxenburg, Austria
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Mullon C, Lehmann L. An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal, with an application to socially synergistic traits. Evolution 2019; 73:1695-1728. [PMID: 31325322 DOI: 10.1111/evo.13803] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Accepted: 06/03/2019] [Indexed: 01/03/2023]
Abstract
Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance-covariances between traits that experience frequency-dependent selection. Assuming a multivariate-normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within-individuals depends on the fitness effects of such associations between-individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within-individuals is costly but synergistically beneficial between-individuals. As dispersal becomes limited and relatedness increases, associations between-traits between-individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal.
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Affiliation(s)
- Charles Mullon
- Department of Ecology and Evolution, University of Lausanne, 1015, Lausanne, Switzerland
| | - Laurent Lehmann
- Department of Ecology and Evolution, University of Lausanne, 1015, Lausanne, Switzerland
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Spatial heterogeneity and evolution of fecundity-affecting traits. J Theor Biol 2018; 454:190-204. [DOI: 10.1016/j.jtbi.2018.06.005] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Revised: 06/01/2018] [Accepted: 06/04/2018] [Indexed: 11/23/2022]
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Nurmi T, Parvinen K, Selonen V. Joint evolution of dispersal propensity and site selection in structured metapopulation models. J Theor Biol 2018; 444:50-72. [PMID: 29452172 DOI: 10.1016/j.jtbi.2018.02.011] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Revised: 02/06/2018] [Accepted: 02/12/2018] [Indexed: 11/30/2022]
Abstract
We propose a novel mathematical model for a metapopulation in which dispersal occurs on two levels: juvenile dispersal from the natal site is mandatory but it may take place either locally within the natal patch or globally between patches. Within each patch, individuals live in sites. Each site can be inhabited by at most one individual at a time and it may be of high or low quality. A disperser immigrates into a high-quality site whenever it obtains one, but it immigrates into a low-quality site only with a certain probability that depends on the time within the dispersal season. The vector of these low-quality-site-acceptance probabilities is the site-selection strategy of an individual. We derive a proxy for the invasion fitness in this model and study the joint evolution of long-distance-dispersal propensity and site-selection strategy. We focus on the way different ecological changes affect the evolutionary dynamics and study the interplay between global patch-to-patch dispersal and local site-selection. We show that ecological changes affect site-selection mainly via the severeness of competition for sites, which often leads to effects that may appear counterintuitive. Moreover, the metapopulation structure may result in extremely complex site-selection strategies and even in evolutionary cycles. The propensity for long-distance dispersal is mainly determined by the metapopulation-level ecological factors. It is, however, also strongly affected by the winter-survival of the site-holders within patches, which results in surprising non-monotonous effects in the evolution of site-selection due to interplay with long-distance dispersal. Altogether, our results give new additional support to the recent general conclusion that evolution of site-selection is often dominated by the indirect factors that take place via density-dependence, which means that evolutionary responses can rarely be predicted by intuition.
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Affiliation(s)
- Tuomas Nurmi
- Department of Biology, FIN-20014 University of Turku, Finland.
| | - Kalle Parvinen
- Department of Mathematics and Statistics, FIN-20014 University of Turku, Finland; Evolution and Ecology Program, International Institute for Applied Systems Analysis, A-2361 Laxenburg, Austria
| | - Vesa Selonen
- Department of Biology, FIN-20014 University of Turku, Finland
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Nurmi T, Parvinen K, Selonen V. The evolution of site-selection strategy during dispersal. J Theor Biol 2017; 425:11-22. [PMID: 28478118 DOI: 10.1016/j.jtbi.2017.05.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2016] [Revised: 04/19/2017] [Accepted: 05/03/2017] [Indexed: 11/16/2022]
Abstract
We propose a mathematical model that enables the evolutionary analysis of site-selection process of dispersing individuals that encounter sites of high or low quality. Since each site can be inhabited by at most one individual, all dispersers are not able to obtain a high-quality site. We study the evolutionary dynamics of the low-quality-site acceptance as a function of the time during the dispersal season using adaptive dynamics. We show that environmental changes affect the evolutionary dynamics in two ways: directly and indirectly via density-dependent factors. Direct evolutionary effects usually follow intuition, whereas indirect effects are often counter-intuitive and hence difficult to predict without mechanistic modeling. Therefore, the mechanistic derivation of the fitness function, with careful attention on density- and frequency dependence, is essential for predicting the consequences of environmental changes to site selection. For example, increasing fecundity in high-quality sites makes them more tempting for dispersers and hence the direct effect of this ecological change delays the acceptance of low-quality sites. However, increasing fecundity in high-quality sites also increases the population size, which makes the competition for sites more severe and thus, as an indirect effect, forces evolution to favor less picky individuals. Our results indicate that the indirect effects often dominate the intuitive effects, which emphasizes the need for mechanistic models of the immigration process.
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Affiliation(s)
- Tuomas Nurmi
- Department of Biology, University of Turku, FIN-20014, Finland.
| | - Kalle Parvinen
- Department of Mathematics and Statistics, University of Turku, FIN-20014, Finland; Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg A-2361, Austria
| | - Vesa Selonen
- Department of Biology, University of Turku, FIN-20014, Finland
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