Neighborhood size-effects shape growing population dynamics in evolutionary public goods games

Gregory J Kimmel,Joel S Brown,Philipp M Altrock,Philip Gerlee

doi:10.1038/s42003-019-0299-4

Abstract

An evolutionary game emerges when a subset of individuals incur costs to provide benefits to all individuals. Public goods games (PGG) cover the essence of such dilemmas in which cooperators are prone to exploitation by defectors. We model the population dynamics of a non-linear PGG and consider density-dependence on the global level, while the game occurs within local neighborhoods. At low cooperation, increases in the public good provide increasing returns. At high cooperation, increases provide diminishing returns. This mechanism leads to diverse evolutionarily stable strategies, including monomorphic and polymorphic populations, and neighborhood-size-driven state changes, resulting in hysteresis between equilibria. Stochastic or strategy-dependent variations in neighborhood sizes favor coexistence by destabilizing monomorphic states. We integrate our model with experiments of cancer cell growth and confirm that our framework describes PGG dynamics observed in cellular populations. Our findings advance the understanding of how neighborhood-size effects in PGG shape the dynamics of growing populations.

Highlights

An evolutionary game emerges when a subset of individuals incur costs to provide benefits to all individuals
We revisited recent experimental findings of non-linearities in public goods games played by IGF-II producer and non-producer pancreatic cancer cells in vitro[14], which suggests that our framework can be used to identify critical neighborhood sizes
To investigate the role of nonlinear growth and neighborhood size on the public good game, we considered a population that consists of two sub-populations

Summary

Introduction

An evolutionary game emerges when a subset of individuals incur costs to provide benefits to all individuals. This mechanism leads to diverse evolutionarily stable strategies, including monomorphic and polymorphic populations, and neighborhood-size-driven state changes, resulting in hysteresis between equilibria. It benefits a cancer cell to recruit blood vessels, signal normal cells and defend against the immune system, which benefit neighbors too Such interactions can strongly influence the eco-evolutionary dynamics between cooperators (public good producers) and defectors (free-riders). Benefits that are produced and shared are often only available within a finite neighborhood[21,22] These finite neighborhoods create a form of assortative interaction: an individual always experiences a slightly higher frequency of its own strategy within a neighborhood than present in the entire population. The framework we develop here sheds new light on the conditions needed to maintain cooperative traits that provide public good to the environment

Methods

Results

Conclusion