The replicator dynamics for multilevel selection in evolutionary games.

Area of Science:

• Evolutionary game theory
• Population genetics
• Mathematical biology

Background:

• Group-structured populations evolve through interactions within and between groups.
• The Prisoner's Dilemma and Hawk-Dove game model strategic interactions with varying payoffs.
• Dual-level selection (individual and group) creates complex evolutionary dynamics.

Purpose of the Study:

• To investigate the evolutionary dynamics of cooperation in group-structured populations under dual-level selection.
• To analyze the conditions under which cooperation can persist or be eliminated.
• To mathematically model the population's group composition distribution.

Main Methods:

• Stochastic modeling of group-structured populations.
• Analysis of Prisoner's Dilemma and Hawk-Dove games.
• Derivation and analysis of a non-local partial differential equation (PDE).
• Characterization of long-time behavior and steady states of the PDE.

Main Results:

• A tension exists between individual-level selection favoring defectors and group-level selection favoring cooperators.
• A threshold intensity of between-group selection is necessary for the survival of cooperation.
• Group composition at steady state varies from all-defector to all-cooperator groups depending on selection dominance.
• When optimal groups are mixed, cooperation may not be sustained even with strong group selection.

Conclusions:

• The balance between individual and group selection critically determines the fate of cooperation.
• Cooperation can be sustained when group-level selection is sufficiently strong and aligns with cooperative outcomes.
• In cases of conflicting selection pressures, cooperation may be impossible to maintain, especially when intermediate group compositions are favored.