Adaptive Evolution of Cooperation through Darwinian Dynamics in Public Goods Games

Deng, Kangyao; Chu, Tianguang

doi:10.1371/journal.pone.0025496

Cited by 22 publications

(26 citation statements)

References 21 publications

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“…3) of a cooperative strategy to biologically plausible scenarios in which genetic drift, migration, and/or environmental variability allow a mutant strategy to make up a significant part of the population (even if it is not selected for when initially rare). Our analysis also generalizes the results of Deng andChu (2011) (who used Darwinian dynamics, Brown andVincent 2008).…”

Section: Introductionsupporting

confidence: 83%

“…Most often, the effect of how the benefit depends on collective investment is investigated in the context of binary strategies (cooperate or defect) (Motro 1991;Liang et al 2015;Archetti and Scheuring 2011), sometimes with the addition of population structure (e.g., Wu et al 2009). However, Deng and Chu (2011) have investigated how evolutionary dynamics in continuous public goods games are influenced by nonlinearities in how collective investment is translated to the public good, using specific functional forms (linear, step function or sigmoid). While most other studies investigate stability of a homogeneous population against mutations that are close to the resident strategy, Deng and Chu were interested in stability against invasion by any strategy (in line with the original definition of evolutionary stability by Maynard Smith and Price 1973).…”

Section: Introductionmentioning

confidence: 99%

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Evolutionary stability in continuous nonlinear public goods games

Molina

Earn

2016

J. Math. Biol.

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We investigate a type of public goods games played in groups of individuals who choose how much to contribute towards the production of a common good, at a cost to themselves. In these games, the common good is produced based on the sum of contributions from all group members, then equally distributed among them. In applications, the dependence of the common good on the total contribution is often nonlinear (e.g., exhibiting synergy or diminishing returns). To date, most theoretical and experimental studies have addressed scenarios in which the set of possible contributions is discrete. However, in many real-world situations, contributions are continuous (e.g., individuals volunteering their time). The "n-player snowdrift games" that we analyze involve continuously varying contributions. We establish under what conditions populations of contributing (or "cooperating") individuals can evolve and persist. Previous work on snowdrift games, using adaptive dynamics, has found that what we term an "equally cooperative" strategy is locally convergently and evolutionarily stable. Using static evolutionary game theory, we find conditions under which this strategy is actually globally evolutionarily stable. All these results refer to stability to invasion by a single mutant. We broaden the scope of existing stability results by showing that the equally cooperative strategy is locally stable to potentially large population perturbations, i.e., allowing for the possibility that mutants make up a non-negligible proportion of the population (due, for example, to genetic drift, environmental variability or dispersal).

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Section: Introductionsupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Evolutionary stability in continuous nonlinear public goods games

Molina

Earn

2016

J. Math. Biol.

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“…In case all players are equal this simplifies to the critical mass problem [49]. Thresholds, being described by step-like benefit functions, can be considered as an extreme case of a general nonlinear benefit function [50,51], with the other extreme being when the public good depends only slightly (or not at all) on the contributions of the members. The generalized sigmoid function bridges these two extremes and is characterized by two parameters, namely the threshold and the steepness parameter.…”

Section: Introductionmentioning

confidence: 99%

Impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies

et al. 2012

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Cooperation and defection may be considered as two extreme responses to a social dilemma. Yet the reality is much less clear-cut. Between the two extremes lies an interval of ambivalent choices, which may be captured theoretically by means of continuous strategies defining the extent of the contributions of each individual player to the common pool. If strategies are chosen from the unit interval, where 0 corresponds to pure defection and 1 corresponds to the maximal contribution, the question is what is the characteristic level of individual investments to the common pool that emerges if the evolution is guided by different benefit functions. Here we consider the steepness and the threshold as two parameters defining an array of generalized benefit functions, and we show that in a structured population there exist intermediate values of both at which the collective contributions are maximal. However, as the cost-to-benefit ratio of cooperation increases the characteristic threshold decreases, while the corresponding steepness increases. Our observations remain valid if more complex sigmoid functions are used, thus reenforcing the importance of carefully adjusted benefits for high levels of public cooperation.

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“…In evolutionary game theory, in the study of the evolution of public goods, sigmoid functions have been modelled mainly using the logistic equation to analyse the production of non-linear public goods , Deng & Chu 2011, and it is known that concave functions [Motro 1991, Hauert et al 2006, Frank 2010 lead to a different type of dynamics [Archetti & Scheuring 2012]. It is interesting that sigmoid inputoutput functions are not limited to interactions between cells and molecules [e.g.…”

Section: Importance Of the Hill Equationmentioning

confidence: 99%

Evolution of optimal Hill coefficients in nonlinear public goods games

Archetti

Scheuring

2016

Journal of Theoretical Biology

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In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, models of biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function.

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Adaptive Evolution of Cooperation through Darwinian Dynamics in Public Goods Games

Cited by 22 publications

References 21 publications

Evolutionary stability in continuous nonlinear public goods games

Evolutionary stability in continuous nonlinear public goods games

Impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies

Evolution of optimal Hill coefficients in nonlinear public goods games

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