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.

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 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 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: The analysis of the case wherein a different player has a different benefit and a different cost

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Shun Kurokawa
Keyword(s):  
Natural Selection ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Evolution Of Cooperation ◽  
Cost Ratio ◽  
Personal Cost ◽  
Model Setting

The existence of cooperation demands explanation in terms of natural selection. Prisoner’s dilemma is a framework often used when studying the evolution of cooperation. In prisoner’s dilemma, most previous studies consider the situation wherein an individual who cooperates will give an opponent an amount b at a personal cost of c, where b > c > 0 while an individual who defects will give nothing. This model setting is convenient; however, previous studies have not considered the case wherein a different player has a different benefit and different cost while in reality, it is natural to consider that a different player has a different benefit and different cost. Here, we raise the following question: Taking that a different individual has a different benefit and a different cost into consideration, what strategy is likely to evolve? In this paper, we focus on the direct reciprocity and analyze the case wherein a different player has a different benefit and a different cost. We obtain the condition for the evolution in the general case. And in addition, we have revealed that under a specific condition as the interaction repeats longer and the benefit-to-cost ratio is larger and the cooperating probability is more sensitive to the benefit the opponent provides, the establishment of cooperation is more likely.

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 Kin and multilevel selection in social evolution: a never-ending controversy?

F1000Research ◽  
2016 ◽  
Vol 5 ◽  
pp. 776 ◽  
Author(s):  
Jos Kramer ◽  
Joël Meunier
Keyword(s):  
Kin Selection ◽  
Group Selection ◽  
Evolutionary Biology ◽  
Social Evolution ◽  
Selection Process ◽  
Structured Populations ◽  
Multilevel Selection ◽  
Current Debate ◽  
The Relationship ◽  
Shed Light

Kin selection and multilevel selection are two major frameworks in evolutionary biology that aim at explaining the evolution of social behaviors. However, the relationship between these two theories has been plagued by controversy for almost half a century and debates about their relevance and usefulness in explaining social evolution seem to rekindle at regular intervals. Here, we first provide a concise introduction into the kin selection and multilevel selection theories and shed light onto the roots of the controversy surrounding them. We then review two major aspects of the current debate: the presumed formal equivalency of the two theories and the question whether group selection can lead to group adaptation. We conclude by arguing that the two theories can offer complementary approaches to the study of social evolution: kin selection approaches usually focus on the identification of optimal phenotypes and thus on the endresult of a selection process, whereas multilevel selection approaches focus on the ongoing selection process itself. The two theories thus provide different perspectives that might be fruitfully combined to promote our understanding of the evolution in group-structured populations.

scholarly journals Negotiation and appeasement can be more effective drivers of sociality than kin selection

2016 ◽  
Vol 371 (1687) ◽  
pp. 20150089 ◽  
Author(s):  
Andrés E. Quiñones ◽  
G. Sander van Doorn ◽  
Ido Pen ◽  
Franz J. Weissing ◽  
Michael Taborsky
Keyword(s):  
Genetic Relatedness ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Conditional Cooperation ◽  
Negotiation Strategies ◽  
Structured Population ◽  
The Face ◽  
Kin Structure ◽  
Invasion Analysis ◽  
Individual Based Simulation

Two alternative frameworks explain the evolution of cooperation in the face of conflicting interests. Conflicts can be alleviated by kinship, the alignment of interests by virtue of shared genes, or by negotiation strategies, allowing mutually beneficial trading of services or commodities. Although negotiation often occurs in kin-structured populations, the interplay of kin- and negotiation-based mechanisms in the evolution of cooperation remains an unresolved issue. Inspired by the biology of a cooperatively breeding fish, we developed an individual-based simulation model to study the evolution of negotiation-based cooperation in relation to different levels of genetic relatedness. We show that the evolution of negotiation strategies leads to an equilibrium where subordinates appease dominants by conditional cooperation, resulting in high levels of help and low levels of aggression. This negotiation-based equilibrium can be reached both in the absence of relatedness and in a kin-structured population. However, when relatedness is high, evolution often ends up in an alternative equilibrium where subordinates help their kin unconditionally. The level of help at this kin-selected equilibrium is considerably lower than at the negotiation-based equilibrium, and it corresponds to a level reached when responsiveness is prevented from evolving in the simulations. A mathematical invasion analysis reveals that, quite generally, the alignment of payoffs due to the relatedness of interaction partners tends to impede selection for harsh but effective punishment of defectors. Hence kin structure will often hamper rather than facilitate the evolution of productive cooperation.

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.

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