Refuge I: Stabilization of Cooperation in Boundary Region

Agent-Patch Simulation time series: MORTALITY RISK GRADIENT/MIXED INITIAL POPULATION (Maximum Risk 2.5%/Cycle) Defector: Yellow Cooperator: Light Blue			Back to Start EAME Home e-mail Programmer

Frame 1: Cycle 0 Cooperators: 40 Defectors: 40	Frame 2: Cycle 875 Cooperators: 416 Defectors: 323	Frame 3: Cycle 3,000 Cooperators: 591 Defectors: 445	Frame 4: Cycle 7,000 Cooperators: 1246 Defectors: 545

Frame 5: Cycle 15,000 Cooperators: 816 Defectors: 492	Frame 6: Cycle 30,000 Cooperators: 990 Defectors: 498	Frame 7: Cycle 75,000 Cooperators: 937 Defectors: 487	Frame 8: Cycle 1,138,920 Get the Picture? It stays like this.

Typical configuration when Cooperators fail to break out. (Cf. Frame 2.) Cycle 5,000; Defectors: 217	Population Sizes Over Time.

We run the same configuration as in Step one, with the sole difference that as the agents move out from the area of origin, they experience increased mortality risks. To be precise, each move away from the origin increases the risk of some fatal accident happening by .1% for each cycle. Only in the most upper left patch is there no risk of accidental mortality. Along the right and bottom edges, the chance of dying by accident is 2.5% each cycle. Compare this to a nominal reproductive time of 50 cycles. Neither cooperator nor defector communities can survive long in this region. But in the "boundary region" between the area where defectors alone prosper (see the lower left hand frame) and the outer regions where no one survives, cooperators seem to be able to carve out a stable existence. Why?

Part of the answer we saw in the Step 1. Cooperators maintain higher reproductive rates than defectors, and can thus afford higher mortality risks. They can survive in regions where communities of defectors cannot. But this isn't the whole story, since a glance at the image series shows that cooperators are not isolated from defectors. Defectors frequently wander out and prey on cooperator communities, but those communities quickly die, and then so do the defectors that killed them. Meanwhile, uninvaded cooperator communities are proliferating and being established by individual migrants into previously vacated patches. Cooperators can take the risk. They also run faster, at least collectively. Finally, the very randomness of the way in the mortality risk operates creates gaps, "firebreaks" in the distribution of cooperators. Simulations verify that if mortality risk is low enough to allow cooperators to maintain populations in most patches, then they are not stable in the long term.

So, hostile environments are good for cooperation. It appears that this pattern is also stable when it is whole patches, rather than individuals that are randomly extinguished. Gradients of increasing metabolic cost can have the same effect as well. It seems that any pattern of increasing costs that results in fragmentation of the cooperator community at the outer boundary can create long term stability for cooperation, even in the absence of any discrimination on the part of agents in their behavior.