Emergence of parochial altruism in well-mixed populations of multiple groups

• Conditions for the emergence of parochial altruism are specified subject to mutation.
• Parochial altruism is facilitated by assortment as well as by intergroup punishment.
• Effect of affiliation on parochial altruism critically depends on mutation rates.
• Parochial altruists belonging to more groups are less abundant for low mutation.
• However, they are more favored by nature selection for a higher mutation rate.

Understanding the evolution of parochial altruism is of great importance. We here institute an analytical model to study the emergence of parochial altruism in group-structured populations. Individuals' strategy is contingent on interacting partners' group property. Only when sharing common tag(s), they play the prisoner's dilemma game; otherwise they play the punishment game. The conditions for the emergence of parochial altruism are specified for weak selection. Emergence of parochial altruism is promoted by assortment as well as by intergroup punishment. Furthermore, the affiliation plays a negative (positive) role in the emergence of parochial altruism for low (high) mutation.