Effect of group selection on the evolution of altruistic behavior

By using a Monte Carlo simulation, we studied the effect of group selection on the altruistic trait that is controlled by a single locus. The altruistic trait is disadvantageous to the bearer but advantageous to the others. Group selection is defined as the differential reproductive rate among demes caused by genotypic difference among demes. We found that the simulation reproduced many results of former studies. Additionally, when the mutation rate and the migration rate are small enough, we observed two new phenomena: (1) When the effect of the group selection is as large as that of the individual selection, the gene frequency is quite unstable. We found two local stable states, the A- and the S-state. When the metapopulation is in the A-state, altruists are nearly fixed. When in the S-state, on the contrary, altruists are almost lost. The metapopulation shifted quickly from one state to another. We call this phenomenon as the S-A transition. (2) When the mutation rate and migration rate are small enough we found an extremely strong mechanism to stop the non-altruists from expanding no matter how strong the individual selection coefficient is. This is caused by a phenomenon, which we call SA splitting, in which most demes are fixed either by altruists or non-altruists; thus, the relatedness of the metapopulation becomes nearly equal to one. We show SA splitting plays an important role in S-A transition. We define a parameter d to see the degree of SA splitting. We found that d is roughly proportional to mutation rate and deme size.