Group size determined by fusion and fission: A mathematical modelling with inclusive fitness

We consider a mathematical model for the group size determination by the intra-reactions, self-growth, ostracism and fission within a group, and by the inter-reactions, immigration and fusion between two groups. In some group reactions, a conflict between two groups occurs about the reaction to change the group size. We construct a mathematical model to consider such conflict, taking into account the inclusive fitness of members in each group. In the conflict about the fusion between two groups, our analysis shows that the smaller group wants to fuse, while the larger does not. Also the criterion to resolve the conflict is discussed, and some numerical examples are given, too. It is concluded that, depending on the deviation in the total cost paid for the conflict by counterparts, the group reactions could result in a terminal group size different from that reached only by a sequence of outsider's immigrations into a group.