Moderate death rates can be beneficial for the evolution of cooperation

TL;DR

This paper explores how moderate death rates influence the evolution of cooperation, revealing that cooperation is maximized at intermediate mortality levels due to spatial and density effects.

Contribution

It introduces a density-dependent birth rate into the spatial evolutionary game model, highlighting the beneficial role of moderate death rates for cooperation evolution.

Findings

Cooperation peaks at moderate death rates.

Defectors go extinct at lower death rates than cooperators.

Moderate mortality enhances cooperative cluster formation.

Abstract

Spatial structure is one of the simplest and most studied ecological factors that affect the evolution of cooperation. It has been shown that spatial reciprocity promotes cooperation due to the formation of cooperative clusters, which provide mutual support against defectors. The usual assumption is that of constant population size, where no density-related effect is possible. Here, we extend the investigation of density-related effects on the evolution of cooperation. We integrate evolutionary game theory to the Lattice Lotka-Volterra Model. In our model, the birth rate depends on the local density and on the payoff accumulated in the interactions. We characterize the evolution of cooperation in terms of the coexistence and the extinction of the types. The main result is that cooperation is most favoured at moderate levels of the death rate. Interestingly, defectors are extinct at values of the death rate that are lower than that at which cooperators are extinct. When death knocks the door, defectors are the first to perish, whereas cooperators stand longer due to mutual support.