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Steering eco-evolutionary game dynamics with manifold control.

ABSTRACT: 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. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a 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 centred 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 state. 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.

SUBMITTER: Wang X

PROVIDER: S-EPMC7016546 | biostudies-literature | 2020 Jan

REPOSITORIES: biostudies-literature

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Steering eco-evolutionary game dynamics with manifold control.

Wang Xin X Zheng Zhiming Z Fu Feng F

Proceedings. Mathematical, physical, and engineering sciences 20200108 2233

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. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general <i>nonlinear</i> feedback loops in multi-play ...[more]

PMID: 32082066

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Project description:Heritable trait variation is a central and necessary ingredient of evolution. Trait variation also directly affects ecological processes, generating a clear link between evolutionary and ecological dynamics. Despite the changes in variation that occur through selection, drift, mutation, and recombination, current eco-evolutionary models usually fail to track how variation changes through time. Moreover, eco-evolutionary models assume fitness functions for each trait and each ecological context, which often do not have empirical validation. We introduce a new type of model, Gillespie eco-evolutionary models (GEMs), that resolves these concerns by tracking distributions of traits through time as eco-evolutionary dynamics progress. This is done by allowing change to be driven by the direct fitness consequences of model parameters within the context of the underlying ecological model, without having to assume a particular fitness function. GEMs work by adding a trait distribution component to the standard Gillespie algorithm - an approach that models stochastic systems in nature that are typically approximated through ordinary differential equations. We illustrate GEMs with the Rosenzweig-MacArthur consumer-resource model. We show not only how heritable trait variation fuels trait evolution and influences eco-evolutionary dynamics, but also how the erosion of variation through time may hinder eco-evolutionary dynamics in the long run. GEMs can be developed for any parameter in any ordinary differential equation model and, furthermore, can enable modeling of multiple interacting traits at the same time. We expect GEMs will open the door to a new direction in eco-evolutionary and evolutionary modeling by removing long-standing modeling barriers, simplifying the link between traits, fitness, and dynamics, and expanding eco-evolutionary treatment of a greater diversity of ecological interactions. These factors make GEMs much more than a modeling advance, but an important conceptual advance that bridges ecology and evolution through the central concept of heritable trait variation.

Dataset Information

Steering eco-evolutionary game dynamics with manifold control.

Publications

Steering eco-evolutionary game dynamics with manifold control.

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