Evolutionary games with environmental feedbacks

Tilman, Andrew R.; Plotkin, Joshua B.; Akçay, Erol

doi:10.1038/s41467-020-14531-6

Cited by 172 publications

(157 citation statements)

References 53 publications

(63 reference statements)

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“…2(C), which means the system can finally evolve to many different stable states depending on the initial conditions. This new phenomenon is totally different from the solely interior fixed points situation discussed in previous models [40,41]. Moreover, the equilibrium curve of unstable manifold situations in our model (see Fig.…”

Section: Iii1 Emergence Of Multiple Segments Of Stable and Unstablecontrasting

confidence: 85%

“…In addition, f (x, r c ) is a control function that describes the asymmetrical feedback mechanisms in our model. While f actually characterizes the current impact of population strategies on environment, previous works exclusively focus on linear selection gradient feedback laws, such as f = θx − (1 − x) in [40] and f = e L x + e H (1 − x) in [41]. Here, we stress our effects on generality of nonlinearity in feedback control laws, the general form of which is:…”

Section: Modeling Frameworkmentioning

confidence: 99%

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Steering eco-evolutionary game dynamics with manifold control

Wang

Zheng

2020

Proc. R. Soc. A.

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Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature, and have shown profound effects on the resulting eco-evolutionary dynamics. Incorporating linear environmental feedback law into replicator dynamics of two-player games, recent theoretical studies shed light on understanding the oscillating dynamics of social dilemma. However, detailed effects of more general nonlinear feedback loops in multi-player games, which is more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centered on cooperators not only accelerates the convergence of stable manifolds, but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population states. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments. POPULAR SUMMARYChanges in environment where individuals interact and compete can drastically impact evolutionary course and outcome in a wide variety of population systems, ranging from microbial cooperation to antibiotic resistance evolution. Such environmental changes are often unprecedented in the nature or simply the result of manual interventions using control devices like chemostat. There has been growing interest in incorporating environmental feedbacks into eco-evolutionary dynamics, yet it remains largely unknown if it is possible (and how) to steer ecoevolutionary dynamics with external switching feedback control laws that adjust selection gradient in the population systems. To fill this theoretical gap, we study eco-evolutionary dynamics of group cooperation with environmental feedbacks that modulate multi-person public goods game interactions. We find the existence of stable equilibrium manifold where the population can settle on and derive potential external control inputs that can steer the population to any desired states.In this work, we extend the mathematical framework of eco-evolutionary game dynamics to incorporate realistic asymmetrical environmental feedbacks, for game interactions organized by focal cooperators may have a different efficiency than the ones by defectors. Because of such complex interactions, multiple segments of stable and unstable manifolds can emerge from the population dynamical systems. Our work is in line with previous experimental work demonstrating the existence of (unstable) manifold ('separatrix') in population systems. Ou...

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Section: Iii1 Emergence Of Multiple Segments Of Stable and Unstablecontrasting

confidence: 85%

Section: Modeling Frameworkmentioning

confidence: 99%

Steering eco-evolutionary game dynamics with manifold control

Wang

Zheng

2020

Proc. R. Soc. A.

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“…The cell population size thus changes at a rate equal to the the average payoff times the resource density. Corresponding to these payoffs, the frequencies of cells with the two motility traits change in time according to a replicator equation for the fraction x of fast cells [ 30 , 31 ]. The time variation of the resource density, total cell population size and fraction of fast cells is thus described by the following set of ordinary differential equations: where r and K are the maximum growth rate and the carrying capacity of the resource, respectively (rescaled so that the probability of encounter between the resource and the cells is 1 in a time interval), and d is the mortality rate of cells (assumed to be identical for every cell type).…”

Section: Models and Methodsmentioning

confidence: 99%

“…We show that the picture changes when feedbacks between cell behaviour and their environment are also taken into account [ 27 – 30 ]. In our case, this requires considering possible advantages that motility confers to cells both in isolation and as a consequence of collective displacement.…”

Section: Introductionmentioning

confidence: 99%

Aggregative cycles evolve as a solution to conflicts in social investment

Miele

Monte

2021

PLoS Comput Biol

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Multicellular organization is particularly vulnerable to conflicts between different cell types when the body forms from initially isolated cells, as in aggregative multicellular microbes. Like other functions of the multicellular phase, coordinated collective movement can be undermined by conflicts between cells that spend energy in fuelling motion and ‘cheaters’ that get carried along. The evolutionary stability of collective behaviours against such conflicts is typically addressed in populations that undergo extrinsically imposed phases of aggregation and dispersal. Here, via a shift in perspective, we propose that aggregative multicellular cycles may have emerged as a way to temporally compartmentalize social conflicts. Through an eco-evolutionary mathematical model that accounts for individual and collective strategies of resource acquisition, we address regimes where different motility types coexist. Particularly interesting is the oscillatory regime that, similarly to life cycles of aggregative multicellular organisms, alternates on the timescale of several cell generations phases of prevalent solitary living and starvation-triggered aggregation. Crucially, such self-organized oscillations emerge as a result of evolution of cell traits associated to conflict escalation within multicellular aggregates.

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“…the environmental state) will conversely affect individual behaviours. To characterize this feedback relation, we here adopt the difference form of the replicator dynamics with environmental feedbacks [20,23] to describe the evolution of the average time proportion of state s 1 :…”

Section: Non-stationary Environmental State Distributionmentioning

confidence: 99%

Learning enables adaptation in cooperation for multi-player stochastic games

Huang

Cao

Wang

2020

J. R. Soc. Interface.

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Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g. the ‘tragedy of the commons’), modulate their behaviours to adapt to the fluctuation of the environment has not yet been addressed satisfactorily. Using evolutionary game theory, we develop a framework of stochastic games that incorporates the adaptive mechanism of reinforcement learning to investigate whether cooperative behaviours can evolve in the ever-changing group interaction environment. When the action choices of players are just slightly influenced by past reinforcements, we construct an analytical condition to determine whether cooperation can be favoured over defection. Intuitively, this condition reveals why and how the environment can mediate cooperative dilemmas. Under our model architecture, we also compare this learning mechanism with two non-learning decision rules, and we find that learning significantly improves the propensity for cooperation in weak social dilemmas, and, in sharp contrast, hinders cooperation in strong social dilemmas. Our results suggest that in complex social–ecological dilemmas, learning enables the adaptation of individuals to varying environments.

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Evolutionary games with environmental feedbacks

Cited by 172 publications

References 53 publications

Steering eco-evolutionary game dynamics with manifold control

Steering eco-evolutionary game dynamics with manifold control

Aggregative cycles evolve as a solution to conflicts in social investment

Learning enables adaptation in cooperation for multi-player stochastic games

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