On the Dynamic Persistence of Cooperation: How Lower Fitness Induces Higher Survivability

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Abstract
Sub-populations of cooperators and defectors inhabit sites on a lattice. The interactions among the individuals at a site, in the form of a prisoners-dilemma (PD) game, determine their fitnesses. The PD pay-off parameters are chosen so that cooperators are able to maintain a homogeneous population, while defectors are not. Individuals mutate to become the other type and migrate to a neighboring site with low probabilities. Both density dependent and density independent versions of the model are studied. The dynamics of the model can be understood by considering the life-cycle of a population at a site. This life-cycle starts with one cooperator establishing a population. During this life-cycle new cooperator populations are founded by single cooperators that migrate out to empty neighboring sites. The system can reach a steady state where cooperation prevails if the global ``birth'' rate of populations is equal to the rate of their ``death.'' This steady state is dynamic in nature---cooperation persists although every single population of cooperators dies out. These dynamics enable the persistence of cooperation in a large section of the model's parameter space. Submitted to Journal of Theoretical Biology
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