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Fontanari JF, Santos M. The dynamics of casual groups can keep free-riders at bay. Math Biosci 2024; 372:109188. [PMID: 38570010 DOI: 10.1016/j.mbs.2024.109188] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2024] [Revised: 03/07/2024] [Accepted: 03/27/2024] [Indexed: 04/05/2024]
Abstract
Understanding the conditions for maintaining cooperation in groups of unrelated individuals despite the presence of non-cooperative members is a major research topic in contemporary biological, sociological, and economic theory. The N-person snowdrift game models the type of social dilemma where cooperative actions are costly, but there is a reward for performing them. We study this game in a scenario where players move between play groups following the casual group dynamics, where groups grow by recruiting isolates and shrink by losing individuals who then become isolates. This describes the size distribution of spontaneous human groups and also the formation of sleeping groups in monkeys. We consider three scenarios according to the probability of isolates joining a group. We find that for appropriate choices of the cost-benefit ratio of cooperation and the aggregation-disaggregation ratio in the formation of casual groups, free-riders can be completely eliminated from the population. If individuals are more attracted to large groups, we find that cooperators persist in the population even when the mean group size diverges. We also point out the remarkable similarity between the replicator equation approach to public goods games and the trait group formulation of structured demes.
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Affiliation(s)
- José F Fontanari
- Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil.
| | - Mauro Santos
- Departament de Genètica i de Microbiologia, Grup de Genòmica, Bioinformàtica i Biologia Evolutiva (GBBE), Universitat Autònoma de Barcelona, Spain; cE3c - Centre for Ecology, Evolution and Environmental Changes & CHANGE - Global Change and Sustainability Institute, Lisboa, Portugal.
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2
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Károlyi A, Scheuring I. Cooperation in public goods game does not require assortment and depends on population density. J Evol Biol 2024; 37:451-463. [PMID: 38459964 DOI: 10.1093/jeb/voae029] [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: 12/11/2023] [Revised: 03/01/2024] [Accepted: 03/06/2024] [Indexed: 03/11/2024]
Abstract
The threshold public goods game is one of the best-known models of non-linear public goods dilemmas. Cooperators and defectors typically coexist in this game when the population is assumed to follow the so-called structured deme model. In this article, we develop a dynamical model of a general N-player game in which there is no deme structure: Individuals interact with randomly chosen neighbours and selection occurs between randomly chosen pairs of individuals. We show that in the deterministic limit, the dynamics in this model leads to the same replicator dynamics as in the structured deme model, i.e., coexistence of cooperators and defectors is typical in threshold public goods game even when the population is completely well mixed. We extend the model to study the effect of density dependence and density fluctuation on the dynamics. We show analytically and numerically that decreasing population density increases the equilibrium frequency of cooperators till the fixation of this strategy, but below a critical density cooperators abruptly disappear from the population. Our numerical investigations show that weak density fluctuations enhance cooperation, while strong fluctuations suppress it.
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Affiliation(s)
- Adél Károlyi
- Department of Zoology, University of Veterinary Medicine, Budapest, Rottenbiller utca 50, Hungary
- University of Potsdam, Institute of Biochemistry and Biology, 14469 Potsdam, Germany
| | - István Scheuring
- HUN-REN, Centre for Ecological Research, Institute of Evolution, Budapest, Konkoly-Thege Miklós út 29-33, Hungary
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3
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Sheng A, Su Q, Wang L, Plotkin JB. Strategy evolution on higher-order networks. NATURE COMPUTATIONAL SCIENCE 2024; 4:274-284. [PMID: 38622347 DOI: 10.1038/s43588-024-00621-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Accepted: 03/12/2024] [Indexed: 04/17/2024]
Abstract
Cooperation is key to prosperity in human societies. Population structure is well understood as a catalyst for cooperation, where research has focused on pairwise interactions. But cooperative behaviors are not simply dyadic, and they often involve coordinated behavior in larger groups. Here we develop a framework to study the evolution of behavioral strategies in higher-order population structures, which include pairwise and multi-way interactions. We provide an analytical treatment of when cooperation will be favored by higher-order interactions, accounting for arbitrary spatial heterogeneity and nonlinear rewards for cooperation in larger groups. Our results indicate that higher-order interactions can act to promote the evolution of cooperation across a broad range of networks, in public goods games. Higher-order interactions consistently provide an advantage for cooperation when interaction hyper-networks feature multiple conjoined communities. Our analysis provides a systematic account of how higher-order interactions modulate the evolution of prosocial traits.
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Affiliation(s)
- Anzhi Sheng
- Center for Systems and Control, College of Engineering, Peking University, Beijing, China
- Department of Biology, University of Pennsylvania, Philadelphia, PA, USA
| | - Qi Su
- Department of Automation, Shanghai Jiao Tong University, Shanghai, China.
- Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China.
- Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai, China.
| | - Long Wang
- Center for Systems and Control, College of Engineering, Peking University, Beijing, China.
- Center for Multi-Agent Research, Institute for Artificial Intelligence, Peking University, Beijing, China.
| | - Joshua B Plotkin
- Department of Biology, University of Pennsylvania, Philadelphia, PA, USA.
- Center for Mathematical Biology, University of Pennsylvania, Philadelphia, PA, USA.
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Henriques GJB, Osmond MM. Cooperation can promote rescue or lead to evolutionary suicide during environmental change. Evolution 2020; 74:1255-1273. [PMID: 32614158 DOI: 10.1111/evo.14028] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Revised: 02/05/2020] [Accepted: 05/23/2020] [Indexed: 12/20/2022]
Abstract
The adaptation of populations to changing conditions may be affected by interactions between individuals. For example, when cooperative interactions increase fecundity, they may allow populations to maintain high densities and thus keep track of moving environmental optima. Simultaneously, changes in population density alter the marginal benefits of cooperative investments, creating a feedback loop between population dynamics and the evolution of cooperation. Here we model how the evolution of cooperation interacts with adaptation to changing environments. We hypothesize that environmental change lowers population size and thus promotes the evolution of cooperation, and that this, in turn, helps the population keep up with the moving optimum. However, we find that the evolution of cooperation can have qualitatively different effects, depending on which fitness component is reduced by the costs of cooperation. If the costs decrease fecundity, cooperation indeed speeds adaptation by increasing population density; if, in contrast, the costs decrease viability, cooperation may instead slow adaptation by lowering the effective population size, leading to evolutionary suicide. Thus, cooperation can either promote or-counterintuitively-hinder adaptation to a changing environment. Finally, we show that our model can also be generalized to other social interactions by discussing the evolution of competition during environmental change.
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Affiliation(s)
- Gil J B Henriques
- Department of Zoology, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada
| | - Matthew M Osmond
- Center for Population Biology, University of California, Davis, Davis, California, 95616
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5
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Schimit PHT, Pattni K, Broom M. Dynamics of multiplayer games on complex networks using territorial interactions. Phys Rev E 2019; 99:032306. [PMID: 30999523 DOI: 10.1103/physreve.99.032306] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Indexed: 06/09/2023]
Abstract
The modeling of evolution in structured populations has been significantly advanced by evolutionary graph theory, which incorporates pairwise relationships between individuals on a network. More recently, a new framework has been developed to allow for multiplayer interactions of variable size in more flexible and potentially changing population structures. While the theory within this framework has been developed and simple structures considered, there has been no systematic consideration of a large range of different population structures, which is the subject of this paper. We consider a large range of underlying graphical structures for the territorial raider model, the most commonly used model in the new structure, and consider a variety of important properties of our structures with the aim of finding factors that determine the fixation probability of mutants. We find that the graphical temperature and the average group size, as previously defined, are strong predictors of fixation probability, while all other properties considered are poor predictors, although the clustering coefficient is a useful secondary predictor when combined with either temperature or group size. The relationship between temperature or average group size and fixation probability is sometimes, however, nonmonotonic, with a directional reverse occurring around the temperature associated with what we term "completely mixed" populations in the case of the hawk-dove game, but not the public goods game.
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Affiliation(s)
- Pedro H T Schimit
- Informatics and Knowledge Management Graduate Program, Universidade Nove de Julho, Rua Vergueiro, 235/249, CEP 01504-000, São Paulo, São Paulo, Brazil
| | - Karan Pattni
- Department of Mathematical Sciences, University of Liverpool, Mathematical Sciences Building, Liverpool L69 7ZL, United Kingdom
| | - Mark Broom
- Department of Mathematics, City, University of London, Northampton Square, London EC1V 0HB, United Kingdom
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Broom M, Pattni K, Rychtář J. Generalized Social Dilemmas: The Evolution of Cooperation in Populations with Variable Group Size. Bull Math Biol 2018; 81:4643-4674. [PMID: 30560442 PMCID: PMC6874626 DOI: 10.1007/s11538-018-00545-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2017] [Accepted: 11/28/2018] [Indexed: 11/03/2022]
Abstract
Evolutionary game theory is an important tool to model animal and human behaviour. A key class of games is the social dilemmas, where cooperation benefits the group but defection benefits the individual within any group. Previous works have considered which games qualify as social dilemmas, and different categories of dilemmas, but have generally concentrated on fixed sizes of interacting groups. In this paper, we develop a systematic investigation of social dilemmas on all group sizes. This allows for a richer definition of social dilemmas. For example, while increasing a group size to include another defector is always bad for all existing group members, extra cooperators can be good or bad, depending upon the particular dilemma and group size. We consider a number of commonly used social dilemmas in this context and in particular show the effect of variability in group sizes for the example of a population comprising negative binomially distributed group sizes. The most striking effect is that increasing the variability in group sizes for non-threshold public goods games is favourable for the evolution of cooperation. The situation for threshold public goods games and commons dilemmas is more complex.
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Affiliation(s)
- Mark Broom
- Department of Mathematics, City, University of London, Northampton Square, London, EC1V 0HB, UK.
| | - Karan Pattni
- Department of Mathematical Sciences, The University of Liverpool, Mathematical Sciences Building, Liverpool, L69 7ZL, UK
| | - Jan Rychtář
- Department of Mathematics and Statistics, The University of North Carolina at Greensboro, Greensboro, NC, 27412, USA
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Rodrigues AMM. Ecological succession, patch age and the evolution of social behaviour and terminal investment. OIKOS 2018. [DOI: 10.1111/oik.05341] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- António M. M. Rodrigues
- Dept of Zoology, Univ. of Cambridge; Downing Street Cambridge CB2 3EJ UK
- Wolfson College; Barton Road Cambridge UK
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Wu B, Arranz J, Du J, Zhou D, Traulsen A. Evolving synergetic interactions. J R Soc Interface 2017; 13:rsif.2016.0282. [PMID: 27466437 PMCID: PMC4971219 DOI: 10.1098/rsif.2016.0282] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2016] [Accepted: 06/30/2016] [Indexed: 11/12/2022] Open
Abstract
Cooperators forgo their own interests to benefit others. This reduces their fitness and thus cooperators are not likely to spread based on natural selection. Nonetheless, cooperation is widespread on every level of biological organization ranging from bacterial communities to human society. Mathematical models can help to explain under which circumstances cooperation evolves. Evolutionary game theory is a powerful mathematical tool to depict the interactions between cooperators and defectors. Classical models typically involve either pairwise interactions between individuals or a linear superposition of these interactions. For interactions within groups, however, synergetic effects may arise: their outcome is not just the sum of its parts. This is because the payoffs via a single group interaction can be different from the sum of any collection of two-player interactions. Assuming that all interactions start from pairs, how can such synergetic multiplayer games emerge from simpler pairwise interactions? Here, we present a mathematical model that captures the transition from pairwise interactions to synergetic multiplayer ones. We assume that different social groups have different breaking rates. We show that non-uniform breaking rates do foster the emergence of synergy, even though individuals always interact in pairs. Our work sheds new light on the mechanisms underlying such synergetic interactions.
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Affiliation(s)
- Bin Wu
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, People's Republic of China
| | - Jordi Arranz
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany
| | - Jinming Du
- Liaoning Key Laboratory of Manufacturing Systems and Logistics, Institute of Industrial Engineering and Logistics Optimization, Northeastern University, Shenyang 110819, People's Republic of China Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Da Zhou
- School of Mathematical Sciences, Xiamen University, Xiamen 361005, People's Republic of China
| | - Arne Traulsen
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, 24306 Plön, Germany
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Abstract
Spatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure is greater than population structure in the containment or the volume order, then can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.
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Affiliation(s)
- Jorge Peña
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany
| | - Bin Wu
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany
| | - Arne Traulsen
- Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, Plön 24306, Germany
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10
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Yoshioka H. Mathematical analysis and validation of an exactly solvable model for upstream migration of fish schools in one-dimensional rivers. Math Biosci 2016; 281:139-148. [PMID: 27693303 DOI: 10.1016/j.mbs.2016.09.014] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2016] [Revised: 09/16/2016] [Accepted: 09/20/2016] [Indexed: 11/15/2022]
Abstract
Upstream migration of fish schools in 1-D rivers as an optimal control problem is formulated where their swimming velocity and the horizontal oblateness are taken as control variables. The objective function to be maximized through a migration process consists of the biological and ecological profit to be gained at the upstream-end of a river, energetic cost of swimming against the flow, and conceptual cost of forming a school. Under simplified conditions where the flow is uniform in both space and time and the profit to be gained at the goal of migration is sufficiently large, the optimal control variables are determined from a system of algebraic equations that can be solved in a cascading manner. Mathematical analysis of the system reveals that the optimal controls are uniquely found and the model is exactly solvable under certain conditions on the functions and parameters, which turn out to be realistic and actually satisfied in experimental fish migration. Identification results of the functional shapes of the functions and the parameters with experimentally observed data of swimming schools of Plecoglossus altivelis (Ayu) validate the present mathematical model from both qualitative and quantitative viewpoints. The present model thus turns out to be consistent with the reality, showing its potential applicability to assessing fish migration in applications.
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Affiliation(s)
- Hidekazu Yoshioka
- Faculty of Life and Environmental Science, Shimane University, Nishikawatsu-cho 1060, Matsue, Shimane 690-8504, Japan.
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