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Avila P, Mullon C. Evolutionary game theory and the adaptive dynamics approach: adaptation where individuals interact. Philos Trans R Soc Lond B Biol Sci 2023; 378:20210502. [PMID: 36934752 PMCID: PMC10024992 DOI: 10.1098/rstb.2021.0502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 01/16/2023] [Indexed: 03/21/2023] Open
Abstract
Evolutionary game theory and the adaptive dynamics approach have made invaluable contributions to understanding how gradual evolution leads to adaptation when individuals interact. Here, we review some of the basic tools that have come out of these contributions to model the evolution of quantitative traits in complex populations. We collect together mathematical expressions that describe directional and disruptive selection in class- and group-structured populations in terms of individual fitness, with the aims of bridging different models and interpreting selection. In particular, our review of disruptive selection suggests there are two main paths that can lead to diversity: (i) when individual fitness increases more than linearly with trait expression; (ii) when trait expression simultaneously increases the probability that an individual is in a certain context (e.g. a given age, sex, habitat, size or social environment) and fitness in that context. We provide various examples of these and more broadly argue that population structure lays the ground for the emergence of polymorphism with unique characteristics. Beyond this, we hope that the descriptions of selection we present here help see the tight links among fundamental branches of evolutionary biology, from life history to social evolution through evolutionary ecology, and thus favour further their integration. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.
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Affiliation(s)
- Piret Avila
- Institute for Advanced Studies in Toulouse, Université Toulouse 1 Capitole, 31080 Toulouse, France
| | - Charles Mullon
- Department of Ecology and Evolution, University of Lausanne, 1015 Lausanne, Switzerland
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2
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Uchiumi Y, Sato M, Sasaki A. Evolutionary double suicide in symbiotic systems. Ecol Lett 2023; 26:87-98. [PMID: 36331163 DOI: 10.1111/ele.14136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2021] [Revised: 08/31/2022] [Accepted: 10/13/2022] [Indexed: 11/06/2022]
Abstract
Mutualism is thought to face a threat of coextinction cascade because the loss of a member species could lead to the extinction of the other member. Despite this common emphasis on the perils of such knock-on effect, hitherto, the evolutionary causes leading to extinction have been less emphasised. Here, we examine how extinction could be triggered in mutualism and whether an evolutionary response to partner loss could prevent collateral extinctions, by theoretically examining the coevolution of the host exploitation by symbionts and host dependence on symbiosis. Our model reveals that mutualism is more vulnerable to co-extinction through adaptive evolution (evolutionary double suicide) than parasitism. Additionally, it shows that the risk of evolutionary double suicide rarely promotes the backward evolution to an autonomous (non-symbiotic) state. Our results provide a new perspective on the evolutionary fragility of mutualism and the rarity of observed evolutionary transitions from mutualism to parasitism.
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Affiliation(s)
- Yu Uchiumi
- Department of Evolutionary Studies of Biosystems, The Graduate University of Advanced Studies, SOKENDAI, Hayama, Kanagawa, Japan.,Department of Liberal Arts, Nihon University School of Medicine, Itabashi-ku, Tokyo, Japan
| | - Masato Sato
- Department of Evolutionary Studies of Biosystems, The Graduate University of Advanced Studies, SOKENDAI, Hayama, Kanagawa, Japan.,Bioproduction Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan
| | - Akira Sasaki
- Research Center for Integrative Evolutionary Science, The Graduate University for Advanced Studies, SOKENDAI, Hayama, Kanagawa, Japan.,Evolution and Ecology Program, International Institute for Applied Systems Analysis, Laxenburg, Austria
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3
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Alharbi W, Sandhu SK, Areshi M, Alotaibi A, Alfaidi M, Al-Qadhi G, Morozov AY. Revisiting implementation of multiple natural enemies in pest management. Sci Rep 2022; 12:15023. [PMID: 36056142 PMCID: PMC9440112 DOI: 10.1038/s41598-022-18120-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2022] [Accepted: 08/05/2022] [Indexed: 11/23/2022] Open
Abstract
A major goal of biological control is the reduction and/or eradication of pests using various natural enemies, in particular, via deliberate infection of the target species by parasites. To enhance the biological control, a promising strategy seems to implement a multi-enemy assemblage rather than a single control agent. Although a large body of theoretical studies exists on co-infections in epidemiology and ecology, there is still a big gap in modelling outcomes of multi-enemy biological control. Here we theoretically investigate how the efficiency of biological control of a pest depends on the number of natural enemies used. We implement a combination of eco-epidemiological modelling and the Adaptive Dynamics game theory framework. We found that a progressive addition of parasite species increases the evolutionarily stable virulence of each parasite, and thus enhances the mortality of the target pest. However, using multiple enemies may have only a marginal effect on the success of biological control, or can even be counter-productive when the number of enemies is excessive. We found the possibility of evolutionary suicide, where one or several parasite species go extinct over the course of evolution. Finally, we demonstrate an interesting scenario of coexistence of multiple parasites at the edge of extinction.
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Affiliation(s)
- Weam Alharbi
- Department of Mathematics, Faculty of science, University of Tabuk, Tabuk, 71491, Saudi Arabia
| | - Simran K Sandhu
- School of Computing and Mathematical Sciences, University of Leicester, Leicester, LE1 7RH, UK
| | - Mounirah Areshi
- Department of Mathematics, Faculty of science, University of Tabuk, Tabuk, 71491, Saudi Arabia
| | - Abeer Alotaibi
- Department of Mathematics, Faculty of science, University of Tabuk, Tabuk, 71491, Saudi Arabia
| | - Mohammed Alfaidi
- Department of Biology, University College of Duba, University of Tabuk, Tabuk, 71491, Saudi Arabia
| | - Ghada Al-Qadhi
- Department of Mathematics, Faculty of science, University of Tabuk, Tabuk, 71491, Saudi Arabia
| | - Andrew Yu Morozov
- School of Computing and Mathematical Sciences, University of Leicester, Leicester, LE1 7RH, UK.
- Laboratory of Behaviour of Lower Vertebrates, Institute of Ecology and Evolution, Moscow, 119071, Russia.
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4
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Nguyen VAT, Vural DC. Extinction in complex communities as driven by adaptive dynamics. J Evol Biol 2021; 34:1095-1109. [PMID: 33973303 DOI: 10.1111/jeb.13796] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Revised: 04/08/2021] [Accepted: 04/20/2021] [Indexed: 11/30/2022]
Abstract
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. 'Adaptive dynamics' is the standard mathematical framework to describe evolutionary changes in community interactions, and in particular, predict adaptation driven extinction. Unfortunately, most authors implement the equations of adaptive dynamics through computer simulations that require assuming a large number of questionable parameters and fitness functions. In this study, we present analytical solutions to adaptive dynamics equations, thereby clarifying how outcomes depend on any computational input. We develop general formulas that predict equilibrium abundances over evolutionary time scales. Additionally, we predict which species will go extinct next, and when this will happen.
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Liu B, Song L, Wang X, Kang B. Effects of pollution on individual size of a single species. INT J BIOMATH 2020. [DOI: 10.1142/s1793524520500795] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species. The invasion fitness function of a monomorphic species is given, which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system, which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate. We conclude that the pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size, while the opposite is more likely to generate evolutionary branching and promote species diversity. The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.
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Affiliation(s)
- Bing Liu
- College of Mathematics and Information Science, Anshan Normal University, Anshan 114007, Liaoning, P. R. China
| | - Le Song
- Department of Mathematics, Liaoning Normal University, Dalian 116029, Liaoning, P. R. China
| | - Xin Wang
- College of Mathematics and Information Science, Anshan Normal University, Anshan 114007, Liaoning, P. R. China
| | - Baolin Kang
- College of Mathematics and Information Science, Anshan Normal University, Anshan 114007, Liaoning, P. R. China
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Janoušková E, Berec L. Fecundity-Longevity Trade-Off, Vertical Transmission, and Evolution of Virulence in Sterilizing Pathogens. Am Nat 2019; 195:95-106. [PMID: 31868533 DOI: 10.1086/706182] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
Sterilizing pathogens are common, yet studies focused on how such pathogens respond adaptively to fecundity reductions caused in their hosts are rare. Here we assume that the infected hosts, as a result of redistributing energy resources saved by reduced fecundity, have increased longevity and focus on exploring the consequences of such a fecundity-longevity trade-off on sterility virulence evolution in the pathogens. We find that the trade-off itself cannot prevent the evolution of full sterilization. Therefore, we allow for vertical transmission and reveal that the fecundity-longevity trade-off strongly determines the threshold efficiency of vertical transmission above which partial host sterilization evolves. Partial sterilization may appear as an intermediate level of sterility virulence or as a stable dimorphism at which avirulent and highly virulent strains coexist. The fecundity-longevity trade-off significantly contributes to determining the actual outcome, in many cases countering predictions made in the absence of this trade-off. It is known that in well-mixed populations, partial sterilization may evolve in pathogens under a combination of horizontal and vertical transmission. Our study highlights that this is independent of the form of horizontal transmission and the type of density dependence in host demography and that the fecundity-longevity trade-off is an important player in sterility virulence evolution.
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Vitale C, Best A. The paradox of tolerance: Parasite extinction due to the evolution of host defence. J Theor Biol 2019; 474:78-87. [PMID: 31051178 DOI: 10.1016/j.jtbi.2019.04.024] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Revised: 04/24/2019] [Accepted: 04/29/2019] [Indexed: 10/26/2022]
Abstract
Host defence against parasite infection can rely on two broad strategies: resistance and tolerance. The spread of resistance traits usually lowers parasite prevalence and decreases selection for higher defence. Conversely, tolerance mechanisms increase parasite prevalence and foster selection for more tolerance. Here we examine the potential for the host to drive parasites to extinction through the evolution of one or other defence mechanism. We analysed theoretical models of resistance and tolerance evolution in both the absence and the presence of a trade-off between defence and reproduction. In the absence of costs, resistance evolves towards maximisation and, consequently, parasite extinction. Tolerance also evolves towards maximisation but the positive feedback between tolerance and disease prevents the disappearance of the parasite. On the contrary, when defence comes with costs it is impossible for the host to eliminate the infection through resistance, because costly resistance is selected against when parasites are at low prevalence. We uncover that the only path to disease clearance in the presence of costs is through tolerance. Paradoxically, however, it is by lowering tolerance -and hence increasing disease-induced mortality- that extinction can occur. We also show that such extinction can occur even in the case of parasite counter-adaptation. Our results emphasise the importance of tolerance as a defence strategy, and identify key questions for future research.
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Affiliation(s)
- Caterina Vitale
- School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, United Kingdom.
| | - Alex Best
- School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, United Kingdom.
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Abrams PA. How Does the Evolution of Universal Ecological Traits Affect Population Size? Lessons from Simple Models. Am Nat 2019; 193:814-829. [PMID: 31094600 DOI: 10.1086/703155] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
This article argues that adaptive evolutionary change in a consumer species should frequently decrease (and maladaptive change should increase) population size, producing adaptive decline. This conclusion is based on analysis of multiple consumer-resource models that examine evolutionary change in consumer traits affecting the universal ecological parameters of attack rate, conversion efficiency, and mortality. Two scenarios are investigated. In one, evolutionary equilibrium is initially maintained by opposing effects on the attack rate and other growth rate parameters; the environment or trait is perturbed, and the trait then evolves to a new (or back to a previous) equilibrium. Here evolution exhibits adaptive decline in up to one-half of all cases. The other scenario assumes a genetic perturbation having purely fitness-increasing effects. Here adaptive decline in the consumer requires that the resource be self-reproducing and overexploited and requires a sufficient increase in the attack rate. However, if the resource exhibits adaptive defense via behavior or evolution, adaptive decline may characterize consumer traits affecting all parameters. Favorable environmental change producing parameter shifts similar to those produced by adaptive evolution has similar counterintuitive effects on consumer population size. Many different food web models have already been shown to exhibit such counterintuitive changes in some species.
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Evolutionary Suicide of Prey: Matsuda and Abrams’ Model Revisited. Bull Math Biol 2018; 81:4778-4802. [DOI: 10.1007/s11538-018-0472-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Accepted: 07/16/2018] [Indexed: 10/28/2022]
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Impacts of infection avoidance for populations affected by sexually transmitted infections. J Theor Biol 2018; 455:64-74. [PMID: 29981756 DOI: 10.1016/j.jtbi.2018.06.030] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2017] [Revised: 06/17/2018] [Accepted: 06/27/2018] [Indexed: 11/22/2022]
Abstract
Sexually transmitted infections are ubiquitous in nature and affect many populations. The key process for their transmission is mating, usually preceded by mate choice. Susceptible individuals may avoid mating with infected individuals to prevent infection provided it is recognizable. We show that accounting for infection avoidance significantly alters host population dynamics. We observe bistability between the disease-free and endemic or disease-induced extinction equilibria, significant abrupt reduction in the host population size and disease-induced host extinction. From the population persistence perspective, the best strategy is either not to avoid mating with the infected individuals, to prevent disease-induced host extinction, or to completely avoid mating with the infected individuals, to prevent pathogen invasion. Increasing sterilization efficiency of the infection leads to lower population sizes and reduced effect of mating avoidance. We also find that the disease-free state is more often attained by populations with strong polyandry, whereas a high-density endemic state is more often observed for populations with strong polygyny, suggesting that polygamy rather than monogamy may be promoted in denser host populations.
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Koivu-Jolma M, Annila A. Epidemic as a natural process. Math Biosci 2018; 299:97-102. [PMID: 29534891 PMCID: PMC7094378 DOI: 10.1016/j.mbs.2018.03.012] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2017] [Revised: 03/07/2018] [Accepted: 03/09/2018] [Indexed: 12/17/2022]
Abstract
Mathematical epidemiology is a well-recognized discipline to model infectious diseases. It also provides guidance for public health officials to limit outbreaks. Nevertheless, epidemics take societies by surprise every now and then, for example, when the Ebola virus epidemic raged seemingly unrestrained in Western Africa. We provide insight to this capricious character of nature by describing the epidemic as a natural process, i.e., a phenomenon governed by thermodynamics. Our account, based on statistical mechanics of open systems, clarifies that it is impossible to predict accurately epidemic courses because everything depends on everything else. Nonetheless, the thermodynamic theory yields a comprehensive and analytical view of the epidemic. The tenet subsumes various processes in a scale-free manner from the molecular to the societal levels. The holistic view accentuates overarching procedures in arresting and eradicating epidemics.
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Affiliation(s)
- Mikko Koivu-Jolma
- Department of Physics, University of Helsinki, Helsinki, FI-00014, Finland
| | - Arto Annila
- Department of Physics, University of Helsinki, Helsinki, FI-00014, Finland; Department of Biosciences, University of Helsinki, Helsinki, FI-00014, Finland.
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The evolution of parasitic and mutualistic plant-virus symbioses through transmission-virulence trade-offs. Virus Res 2017; 241:77-87. [PMID: 28434906 DOI: 10.1016/j.virusres.2017.04.011] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2016] [Revised: 04/11/2017] [Accepted: 04/12/2017] [Indexed: 12/21/2022]
Abstract
Virus-plant interactions range from parasitism to mutualism. Viruses have been shown to increase fecundity of infected plants in comparison with uninfected plants under certain environmental conditions. Increased fecundity of infected plants may benefit both the plant and the virus as seed transmission is one of the main virus transmission pathways, in addition to vector transmission. Trade-offs between vertical (seed) and horizontal (vector) transmission pathways may involve virulence, defined here as decreased fecundity in infected plants. To better understand plant-virus symbiosis evolution, we explore the ecological and evolutionary interplay of virus transmission modes when infection can lead to an increase in plant fecundity. We consider two possible trade-offs: vertical seed transmission vs infected plant fecundity, and horizontal vector transmission vs infected plant fecundity (virulence). Through mathematical models and numerical simulations, we show (1) that a trade-off between virulence and vertical transmission can lead to virus extinction during the course of evolution, (2) that evolutionary branching can occur with subsequent coexistence of mutualistic and parasitic virus strains, and (3) that mutualism can out-compete parasitism in the long-run. In passing, we show that ecological bi-stability is possible in a very simple discrete-time epidemic model. Possible extensions of this study include the evolution of conditional (environment-dependent) mutualism in plant viruses.
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Abstract
We study the joint adaptive dynamics of n scalar-valued strategies in ecosystems where n is the maximum number of coexisting strategies permitted by the (generalized) competitive exclusion principle. The adaptive dynamics of such saturated systems exhibits special characteristics, which we first demonstrate in a simple example of a host-pathogen-predator model. The main part of the paper characterizes the adaptive dynamics of saturated polymorphisms in general. In order to investigate convergence stability, we give a new sufficient condition for absolute stability of an arbitrary (not necessarily saturated) polymorphic singularity and show that saturated evolutionarily stable polymorphisms satisfy it. For the case [Formula: see text], we also introduce a method to construct different pairwise invasibility plots of the monomorphic population without changing the selection gradients of the saturated dimorphism.
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