Under multilevel selection: “When shall you be neither spiteful nor envious?”

• We study the egalitarianism-game in multilevel selection situation.
• Egalitarianism-game determines the number of juveniles and their survival depends on the size of their group.
• We apply the standard definition of ESS to a structured population.
• When the survival has a massive effect on the fitness, then donator has evolutionary advantage over envious and spiteful.

In this paper, we study the egalitarianism-game in multilevel selection situation. The individuals form reproductive groups. In each group, an egalitarianism-game determines the number of juveniles of different phenotypes (spiteful, envious, neutral and donator). Before the juveniles form the next reproductive group, they have to survive either predators' attacks or a fight between two groups. We adopt the ESS definition of Maynard Smith to multilevel selection. Based on the “group size advantage” assumption (which claims that each juvenile's survival rate depends on the size of his own group, supposing that either the survival rate under predators' attacks is higher in larger groups, or in inter-group aggression usually the larger group wins) we found that when the survival probability has a massive effect on the average fitness, then “group fitness maximizing behavior” (in our case, either neutral or donator) has evolutionary advantage over “competitive behavior” (in our case, either spiteful or envious).