Mobility, fitness collection, and the breakdown of cooperation

TL;DR

This paper investigates how mobility affects cooperation in spatial prisoner's dilemma models, revealing that even small mobility can undermine cooperation and that additional mechanisms are needed for stable cooperation.

Contribution

It explicitly incorporates the separation of fitness collection and selection processes and analyzes the impact of mobility on cooperation in one and two dimensions.

Findings

Small diffusive mobility restricts cooperation.

A phase transition exists controlled by mobility and costs.

In 2D, the model belongs to the Directed Percolation universality class.

Abstract

The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables non-cooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and non-cooperative absorbing states. While in one dimension the model is in the class of the Voter Model, it belongs to the Directed Percolation (DP) universality class in two dimensions.