scholarly journals Ordering structured populations in multiplayer cooperation games

2016 ◽  
Vol 13 (114) ◽  
pp. 20150881 ◽  
Author(s):  
Jorge Peña ◽  
Bin Wu ◽  
Arne Traulsen
Keyword(s):  
Population Structure ◽  
Spatial Structure ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Multiplayer Games ◽  
Spatial Games ◽  
Population Structures ◽  
Single Structure ◽  
Containment Order ◽  
Update Rules

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.

scholarly journals Ordering structured populations in multiplayer cooperation games

2015 ◽  
Author(s):  
Jorge Peña ◽  
Bin Wu ◽  
Arne Traulsen
Keyword(s):  
Population Structure ◽  
Spatial Structure ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Multiplayer Games ◽  
Spatial Games ◽  
Population Structures ◽  
Single Structure ◽  
Containment Order ◽  
Update Rules

AbstractSpatial 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 𝒮1 is greater than population structure 𝒮2 in the containment or the volume order, then 𝒮1 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.

scholarly journals Parent-preferred dispersal promotes cooperation in structured populations

2019 ◽  
Vol 286 (1895) ◽  
pp. 20181949 ◽  
Author(s):  
Xiaojie Chen ◽  
Åke Brännström ◽  
Ulf Dieckmann
Keyword(s):  
Pairwise Comparison ◽  
Small World ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Pair Approximation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Different Types ◽  
Population Structures ◽  
Update Rules

Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth–death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.

scholarly journals Evolutionary games of multiplayer cooperation on graphs

2016 ◽  
Author(s):  
Jorge Peña ◽  
Bin Wu ◽  
Jordi Arranz ◽  
Arne Traulsen
Keyword(s):  
Spatial Structure ◽  
Computer Simulations ◽  
Evolutionary Games ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Pair Approximation ◽  
Regular Graphs ◽  
Multiplayer Games ◽  
Cooperative Interactions ◽  
Analytical Approximations

AbstractThere has been much interest in studying evolutionary games in structured populations, often modelled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering.Author SummaryCooperation can be defined as the act of providing fitness benefits to other individuals, often at a personal cost. When interactions occur mainly with neighbors, assortment of strategies can favor cooperation but local competition can undermine it. Previous research has shown that a single coefficient can capture this trade-off when cooperative interactions take place between two players. More complicated, but also more realistic models of cooperative interactions involving multiple players instead require several such coefficients, making it difficult to assess the effects of population structure. Here, we obtain analytical approximations for the coefficients of multiplayer games in graph-structured populations. Computer simulations show that, for particular instances of multiplayer games, these approximate coefficients predict the condition for cooperation to be promoted in random graphs well, but fail to do so in graphs with more structure, such as lattices. Our work extends and generalizes established results on the evolution of cooperation on graphs, but also highlights the importance of explicitly taking into account higher-order statistical associations in order to assess the evolutionary dynamics of cooperation in spatially structured populations.

scholarly journals Evolution of cooperation in an epithelium

2019 ◽  
Vol 16 (152) ◽  
pp. 20180918 ◽  
Author(s):  
Jessie Renton ◽  
Karen M. Page
Keyword(s):  
Social Interactions ◽  
Voronoi Tessellation ◽  
Evolutionary Game ◽  
Cellular Level ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Animal Kingdom ◽  
Population Structures ◽  
Fixation Probabilities ◽  
Evolutionary Graph Theory

Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom but also on the cellular level. In cancer, for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory (EGT). The population structures arising due to cellular arrangement in tissues, however, are dynamic and thus cannot be accurately represented by either of these frameworks. In this work, we compare the conditions for cooperative success in an epithelium modelled using EGT, to those in a mechanical model of an epithelium—the Voronoi tessellation (VT) model. Crucially, in this latter model, cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the VT model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the EGT model.

scholarly journals Accounting for spatial complexities in the calculation of biological reference points: effects of misdiagnosing population structure for stock status indicators

2017 ◽  
Vol 74 (11) ◽  
pp. 1878-1894 ◽  
Author(s):  
Daniel R. Goethel ◽  
Aaron M. Berger
Keyword(s):  
Population Structure ◽  
Spatial Structure ◽  
Reference Points ◽  
Stock Status ◽  
Spatial Population ◽  
Management Procedures ◽  
Population Structures ◽  
Explicit Simulation ◽  
The One ◽  
Source Sink

Misidentifying spatial population structure may result in harvest levels that are unable to achieve management goals. We developed a spatially explicit simulation model to determine how biological reference points differ among common population structures and to investigate the performance of management quantities that were calculated assuming incorrect spatial population dynamics. Simulated reference points were compared across a range of population structures and connectivity scenarios demonstrating the influence of spatial assumptions on management benchmarks. Simulations also illustrated that applying a harvest level based on misdiagnosed spatial structure leads to biased stock status indicators, overharvesting, or foregone yield. Across the scenarios examined, incorrectly specifying the connectivity dynamics (particularly misdiagnosing source–sink dynamics) was often more detrimental than ignoring spatial structure altogether. However, when the true dynamics exhibited spatial structure, incorrectly assuming panmictic structure resulted in severe depletion if harvesting concentrated on more productive population units (instead of being homogeneously distributed). Incorporating spatially generalized operating models, such as the one developed here, into management strategy evaluations will help develop management procedures that are more robust to spatial complexities.

scholarly journals The effect of population structure on the rate of evolution

2013 ◽  
Vol 280 (1762) ◽  
pp. 20130211 ◽  
Author(s):  
Marcus Frean ◽  
Paul B. Rainey ◽  
Arne Traulsen
Keyword(s):  
Population Structure ◽  
Evolutionary Process ◽  
Ecological Factors ◽  
Structured Populations ◽  
Fixation Time ◽  
Fixation Probability ◽  
Star Graphs ◽  
Rate Of Evolution ◽  
Population Structures ◽  
Evolution Proceeds

Ecological factors exert a range of effects on the dynamics of the evolutionary process. A particularly marked effect comes from population structure, which can affect the probability that new mutations reach fixation. Our interest is in population structures, such as those depicted by ‘star graphs’, that amplify the effects of selection by further increasing the fixation probability of advantageous mutants and decreasing the fixation probability of disadvantageous mutants. The fact that star graphs increase the fixation probability of beneficial mutations has lead to the conclusion that evolution proceeds more rapidly in star-structured populations, compared with mixed (unstructured) populations. Here, we show that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and draw attention to the importance of fixation time. By comparing population structures that amplify selection with other population structures, both analytically and numerically, we show that evolution can slow down substantially even in populations where selection is amplified.

scholarly journals Evolution of cooperation with asymmetric social interactions

2022 ◽  
Vol 119 (1) ◽  
pp. e2113468118
Author(s):  
Qi Su ◽  
Benjamin Allen ◽  
Joshua B. Plotkin
Keyword(s):  
Social Networks ◽  
Population Structure ◽  
Social Interactions ◽  
Social Stratification ◽  
Practical Problem ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Network Growth ◽  
Indirect Reciprocity ◽  
Organizational Hierarchies

How cooperation emerges in human societies is both an evolutionary enigma and a practical problem with tangible implications for societal health. Population structure has long been recognized as a catalyst for cooperation because local interactions facilitate reciprocity. Analysis of population structure typically assumes bidirectional social interactions. But human social interactions are often unidirectional—where one individual has the opportunity to contribute altruistically to another, but not conversely—as the result of organizational hierarchies, social stratification, popularity effects, and endogenous mechanisms of network growth. Here we expand the theory of cooperation in structured populations to account for both uni- and bidirectional social interactions. Even though unidirectional interactions remove the opportunity for reciprocity, we find that cooperation can nonetheless be favored in directed social networks and that cooperation is provably maximized for networks with an intermediate proportion of unidirectional interactions, as observed in many empirical settings. We also identify two simple structural motifs that allow efficient modification of interaction directions to promote cooperation by orders of magnitude. We discuss how our results relate to the concepts of generalized and indirect reciprocity.

scholarly journals Origin of diversity in spatial social dilemmas

2021 ◽  
Author(s):  
Christoph Hauert ◽  
Michael Doebeli
Keyword(s):  
Spatial Structure ◽  
Adaptive Dynamics ◽  
Social Dilemmas ◽  
Finite Size ◽  
Structured Populations ◽  
Pair Approximation ◽  
Evolutionary Diversification ◽  
Invasion Fitness ◽  
Population Structures ◽  
Mixed Populations

Cooperative investments in social dilemmas can spontaneously diversify into stably co-existing 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 under-stood 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 unfavourable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

Spatial social dilemmas promote diversity

2021 ◽  
Vol 118 (42) ◽  
pp. e2105252118
Author(s):  
Christoph Hauert ◽  
Michael Doebeli
Keyword(s):  
Spatial Structure ◽  
Adaptive Dynamics ◽  
Social Dilemmas ◽  
Finite Size ◽  
Structured Populations ◽  
Pair Approximation ◽  
Evolutionary Diversification ◽  
Invasion Fitness ◽  
Population Structures ◽  
Mixed Populations

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.

scholarly journals Modes of migration and multilevel selection in evolutionary multiplayer games

2015 ◽  
Author(s):  
Yuriy Pichugin ◽  
Chaitanya S. Gokhale ◽  
Julián Garcia ◽  
Arne Traulsen ◽  
Paul B. Rainey
Keyword(s):  
Structured Populations ◽  
Multilevel Selection ◽  
Evolution Of Cooperation ◽  
Cost Ratio ◽  
Fixation Probability ◽  
Multiplayer Games ◽  
Cooperative Strategy ◽  
Individual Actions

The evolution of cooperation in group-structured populations has received much attention, but little is known about the effects of different modes of migration of individuals between groups. Here, we have incorporated four different modes of migration that differ in the degree of coordination among the individuals. For each mode of migration, we identify the set of multiplayer games in which the cooperative strategy has higher fixation probability than defection. The comparison shows that the set of games under which cooperation may evolve generally expands depending upon the degree of coordination among the migrating individuals. Weak altruism can evolve under all modes of individual migration, provided that the benefit to cost ratio is high enough. Strong altruism, however, evolves only if the mode of migration involves coordination of individual actions. Depending upon the migration frequency and degree of coordination among individuals, conditions that allow selection to work at the level of groups can be established.

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