Mitochondrial inheritance and the evolution of sexes and germ line

      Illegal harvesting and corruption are major obstacles for common resource management. In a previous paper we developed a game model for harvesters who may choose between cooperation (sustainable resource use) and defection (resource overuse). To maintain cooperation, harvesters may hire a rule-enforcer who checks harvesters and detects defection. However some enforcers are corrupt and receive bribe from a defective harvester who can then escape punishment. In this paper, we extended the model by incorporating the resource dynamics, and by studying the case in which the number of players N is more than two. Evolutionary dynamics of harvesters and enforcers are bistable: depending on initial composition, the system evolved either to cooperative equilibria or to defective equilibria. We denoted the size of the domain of attraction for cooperative outcomes by IC, named an index for cooperation evolution. The index IC decreases with N. However even for a mildly large N (about 10), the cooperation can evolve. The index decreased with the rate of resource recovery (or growth), and increased with the speed of resource dynamics. This suggests that open resource management by delegated enforcement system is more difficult when the number of players is large, when the growth rate is fast, and when the response of the resource depletion due to overexploitation is slow. We discuss the implication of these results in the context of natural resource management.