Movement patterns, social dynamics, and the evolution of cooperation

Abstract

The structure of social interactions influences many aspects of social life, including the spread of information and behavior, and the evolution of social phenotypes. After dispersal, organisms move around throughout their lives, and the patterns of their movement influence their social encounters over the course of their lifespan. Though both space and mobility are known to influence social evolution, there is little analysis of the influence of specific movement patterns on evolutionary dynamics. We explored the effects of random movement strategies on the evolution of cooperation using an agent-based prisoner's dilemma model with mobile agents. This is the first systematic analysis of a model in which cooperators and defectors can use different random movement strategies, which we chose to fall on a spectrum between highly exploratory and highly restricted in their search tendencies. Because limited dispersal and restrictions to local neighborhood size are known to influence the ability of cooperators to effectively assort, we also assessed the robustness of our findings with respect to dispersal and local capacity constraints. We show that differences in patterns of movement can dramatically influence the likelihood of cooperator success, and that the effects of different movement patterns are sensitive to environmental assumptions about offspring dispersal and local space constraints. Since local interactions implicitly generate dynamic social interaction networks, we also measured the average number of unique and total interactions over a lifetime and considered how these emergent network dynamics helped explain the results. This work extends what is known about mobility and the evolution of cooperation, and also has general implications for social models with randomly moving agents.

Figure 1

Flowchart depicting an agent’s activity cycle. The first action is to check whether the agent has enough energy to continue living, indicated in double-line outline.

Figure 2

Example path trajectories from random movement strategies (Table 1) at t = 10,000. The random walks are represented to scale in relation to the three large squares, each 500 × 500 cells.

Figure 3

Mean number of unique cells visited by a solitary agent at t = 100 using each movement strategy plotted against the percentage of simulations won (or not lost by t = 200,000) by cooperators when all agents employed the given movement strategy.

Figure 4

Proportion of runs ending with cooperator success when cooperators and defectors use different random movement strategies. More restricted movement on the part of both types of agents contributed to more cooperator success. More exploratory random movement strategies tended to contributed to more defector success.

Figure 5

Screen shots of a representative simulation that did not end in a victory for either defectors or cooperators. Cooperators (black) used TC, defectors (gray) used SP. Scenarios like this occurred only when defectors used the most exploratory walks, SP or ZZ.

Figure 6

Proportion of runs that timed out after 200,000 time steps when defectors used the SP or ZZ walks under limited dispersal and finite local capacity.

Figure 7

Proportion of runs ending with a cooperator victory under unlimited local capacity. Results differed depending on whether dispersal was limited (A) or random (B).

Figure 8

The average interaction rate for cooperators (black) and defectors (grey) for all simulation conditions. An agent’s interaction rate is the proportion of time steps in the agent’s life in which a game interaction occurred. For each capacity/dispersal condition, 81 trials occurred in nine blocks of nine trials, with each trial consisting of 200 runs. Blocks were run in order of increasingly restricted defector movement strategies (indicated by the movement strategies’ abbreviations). Within each block all nine cooperator movement strategies were tested, in the same order of increasing restrictedness.

Figure 9

The average number of unique interactions for cooperators (black) and defectors (grey) for all simulation conditions. The number of unique interactions for an agent is the number of unique individuals with whom the agent played the PD game throughout the agent’s lifespan. For each capacity/dispersal condition, 81 trials occurred in nine blocks of nine trials, with each trial consisting of 200 runs. Blocks were run in order of increasingly restricted defector movement strategies (indicated by the movement strategies’ abbreviations). Within each block all nine cooperator movement strategies were tested, in the same order of increasing restrictedness.