scholarly journals Group size effects in social evolution

2018 ◽  
Author(s):  
Jorge Peña ◽  
Georg Nöldeke
Keyword(s):  
Group Size ◽  
Size Effects ◽  
Evolutionary Biology ◽  
Social Evolution ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Basin Of Attraction ◽  
Evolution Of Cooperation ◽  
Positive Effects ◽  
Public Goods Games

AbstractHow the size of social groups affects the evolution of cooperative behaviors is a classic question in evolutionary biology. Here we investigate group size effects in the evolutionary dynamics of games in which individuals choose whether to cooperate or defect and payoffs do not depend directly on the size of the group. We find that increasing the group size decreases the proportion of cooperators at both stable and unstable rest points of the replicator dynamics. This implies that larger group sizes can have negative effects (by reducing the amount of cooperation at stable polymorphisms) and positive effects (by enlarging the basin of attraction of more cooperative outcomes) on the evolution of cooperation. These two effects can be simultaneously present in games whose evolutionary dynamics feature both stable and unstable rest points, such as public goods games with participation thresholds. Our theory recovers and generalizes previous results and is applicable to a broad variety of social interactions that have been studied in the literature.

scholarly journals Emergence of cooperation in public goods games

2009 ◽  
Vol 276 (1660) ◽  
pp. 1379-1384 ◽  
Author(s):  
Shun Kurokawa ◽  
Yasuo Ihara
Keyword(s):  
Natural Selection ◽  
Public Goods ◽  
Group Size ◽  
Evolutionary Biology ◽  
Basin Of Attraction ◽  
Simple Expression ◽  
Evolution Of Cooperation ◽  
Emergence Of Cooperation ◽  
Third Law ◽  
The One

Evolution of cooperation has been a major issue in evolutionary biology. Cooperation is observed not only in dyadic interactions, but also in social interactions involving more than two individuals. It has been argued that direct reciprocity cannot explain the emergence of cooperation in large groups because the basin of attraction for the ‘cooperative’ equilibrium state shrinks rapidly as the group size increases. However, this argument is based on the analysis of models that consider the deterministic process. More recently, stochastic models of two-player games have been developed and the conditions for natural selection to favour the emergence of cooperation in finite populations have been specified. These conditions have been given as a mathematically simple expression, which is called the one-third law. In this paper, we investigate a stochastic model of n -player games and show that natural selection can favour a reciprocator replacing a population of defectors in the n -player repeated Prisoner's Dilemma game. We also derive a generalized version of the one-third law (the {2/[ n ( n +1)]} 1/( n −1) law). Additionally, contrary to previous studies, the model suggests that the evolution of cooperation in public goods game can be facilitated by larger group size under certain conditions.

scholarly journals Group size effects in social evolution

2018 ◽  
Vol 457 ◽  
pp. 211-220 ◽  
Author(s):  
Jorge Peña ◽  
Georg Nöldeke
Keyword(s):  
Group Size ◽  
Size Effects ◽  
Social Evolution

scholarly journals Extinction rates in tumor public goods games

2017 ◽  
Author(s):  
Philip Gerlee ◽  
Philipp M. Altrock
Keyword(s):  
Population Growth ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Cell Types ◽  
Relative Fitness ◽  
Replicator Equation ◽  
Cellular Interactions ◽  
Cancer Evolution ◽  
Public Goods Games

AbstractCancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumor cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the timescales, in particular in co-evolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell type specific rates have to be accounted for explicitly.

scholarly journals Extinction rates in tumour public goods games

2017 ◽  
Vol 14 (134) ◽  
pp. 20170342 ◽  
Author(s):  
Philip Gerlee ◽  
Philipp M. Altrock
Keyword(s):  
Population Growth ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Cell Types ◽  
Relative Fitness ◽  
Replicator Equation ◽  
Cellular Interactions ◽  
Cancer Evolution ◽  
Public Goods Games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.

scholarly journals Neighborhood size-effects in nonlinear public goods games

2018 ◽  
Author(s):  
Gregory J. Kimmel ◽  
Philip Gerlee ◽  
Joel S. Brown ◽  
Philipp M. Altrock
Keyword(s):  
Public Goods ◽  
Public Good ◽  
Size Effects ◽  
Evolutionary Dynamics ◽  
Logistic Growth ◽  
Neighborhood Size ◽  
Frequency Dependent ◽  
Frequency Dependent Selection ◽  
The Public ◽  
Public Goods Games

Ecological and evolutionary dynamics can be strongly affected by population assortment and frequency-dependent selection. In growing populations, a particular challenge is to disentangle global ecological effects from local frequency-dependent effects. Here we implement a logistic growth and death model on the global scale, coupled to frequency-dependent growth rates influenced by a public goods game between cooperators and defectors. For each individual, the public good is only effective within a neighborhood of other individuals, and the public good-growth rate relationship can be nonlinear. At low numbers of cooperators, increases of public good accumulate synergistically; at high numbers, increases in public good only provide diminishing returns-the inflection point of this pattern is given by the strength of frequency-dependent selection in relation to the background fitness effect. We observed complex critical behavior in the evolutionary dynamics’ equilibria, determined by the relative magnitude of frequency-dependent to constant (background) growth benefits. We predict neighborhood-size-driven state changes, hysteresis between polymorphic and monomorphic equilibria, and observed that type-dependent differences in neighborhood sizes can destabilize monomorphic cooperative states but increase coexistence of cooperators and defectors. Stochastic neighborhood size fluctuations also led to coexistence and could stabilize the purely cooperative equilibrium. Our results quantify the role of assortment through neighborhood-size effects and nonlinearity of the gains function in eco-evolutionary dynamics, which is relevant for a variety of microbial and cellular public goods games.

scholarly journals Group Size Effects and Critical Mass in Public Goods Games

2018 ◽  
Author(s):  
María Pereda ◽  
Valerio Capraro ◽  
Angel Sánchez
Keyword(s):  
Public Goods ◽  
Group Size ◽  
Size Effects ◽  
Critical Mass ◽  
Public Goods Games

scholarly journals Group size effects and critical mass in public goods games

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
María Pereda ◽  
Valerio Capraro ◽  
Angel Sánchez
Keyword(s):  
Public Goods ◽  
Group Size ◽  
Size Effects ◽  
Critical Mass ◽  
Public Goods Games

scholarly journals Author Correction: Group size effects and critical mass in public goods games

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
María Pereda ◽  
Valerio Capraro ◽  
Angel Sánchez
Keyword(s):  
Public Goods ◽  
Group Size ◽  
Size Effects ◽  
Critical Mass ◽  
Public Goods Games
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