Mobility, fitness collection, and the breakdown of cooperation

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 noncooperating individuals, who 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 noncooperative 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 noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions.

The evolution of cooperation is affected by the persistence of fitness effects, the neighborhood size and their interaction

“…This effect benefits the defectors and hurts the cooperators at the boundaries, allowing the defectors to break down the initially small cooperative cluster. This effect impacts the simulation less with physically larger neighborhood sizes and thus a positive relation between persistence and cooperator evolution is observed, as in other studies (Alonso-Sanz, 2009b; Gelimson et al, 2013). …”

“…This critical initiation phase in our model may explain why our results on fitness persistence in a Moore Neighborhood impeded the evolution of cooperation in contrast to a previous study Gelimson et al (2013). A similar result is mentioned briey in (Alonso-Sanz, 2009a, Fig.…”

“…In a one-dimensional spatial structure, persistence is actually necessary to sustain cooperation (Gelimson et al, 2013). Furthermore, in ordered lattice spatial structures, persistence hinders the spread of defectors along the lattice, promoting cooperation in an iterated PD model (Alonso-Sanz, 2009a,b).…”

“…Our model allows both current and past interactions to determine the current reproductive fitness of an individual, and we can vary the degree of influence of past interactions. Fitness effects accrue incrementally throughout an individual’s entire life but the persistence of past interaction effects varies (Gelimson et al, 2013). …”

Percolation and cooperation with mobile agents: Geometric and strategy clusters

“…Some level of information processing capability is required, for example, when the movement is strategy dependent [28,29] or driven by payoff [30][31][32][33], success [34][35][36][37] or the neighborhood composition [38][39][40][41][42][43][44][45]. However, the simplest scenario is when mobility is diffusive [29,[46][47][48][49][50][51][52][53]. Indeed, as hypothesized in Ref.…”