Inheritance of spatial neighbourhood: A feasible mechanism for evolution and maintenance of cooperation

Cooperative behaviors are widespread in natural world and human societies, yet it can hardly emerge and be maintained in a population of selfish individuals under natural selection unless further mechanisms are introduced. It has recently demonstrated that spatial distribution and interactions of individuals facilitate survival of cooperation through network reciprocity of clustering cooperators. Here, we introduce another attractive profit of spatial distribution of individuals in favoring cooperation: inheritance of geographic advantage. We note that in spatial distributed populations, offspring inherits not only the phenotype but also the spatial neighborhood of its parents, which leads to that in evolutionary process, defectors accumulate from generation to generation and eventually destroy their living environment and then are eliminated, while cooperators prevail. We propose a mathematical model of this evolutionary mechanism. Numerical simulations and approximate analysis of the model confirm our prediction, which shows that high-level cooperation emerges and is maintained for a wide variety of cost-to-benefit ratio, even if mutation happens at some rate in the evolving process.