Consolidating birth-death and death-birth processes in structured populations

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Population Dynamics

Background:

• Network models are crucial for understanding cooperation evolution in structured populations.
• Existing models like Death-Birth (DB) and Birth-Death (BD) show sensitivity to architectural details, impacting cooperation outcomes.
• Biological populations lack strict, synchronized birth and death events, necessitating more flexible models.

Purpose of the Study:

• To investigate the impact of different update rules on cooperation evolution in structured populations.
• To introduce and analyze a mixed Death-Birth/Birth-Death (DB/BD) rule for modeling evolution in finite populations.
• To determine conditions under which population structure promotes or inhibits cooperation.

Main Methods:

• Analysis of two biologically motivated models: Death-Birth (DB) and Birth-Death (BD) processes.
• Derivation of conditions for selection favoring cooperation under a mixed DB-BD update rule (probability δ).
• Examination of social dilemmas, including the Snowdrift Game, under weak selection.

Main Results:

• The strict Birth-Death (BD) model uniquely shows kin competition counterbalancing kin selection.
• A mixed DB-BD rule (for any δ) demonstrates that population structure generally does not inhibit cooperation.
• Cooperation is never inhibited by population structure under any mixed DB-BD update rule and weak selection.

Conclusions:

• The order of birth and death events significantly influences cooperation evolution in network models.
• A mixed DB-BD update rule provides a more robust framework, suggesting structure typically supports cooperation.
• Findings challenge the notion that simplifying assumptions in network models can fundamentally alter conclusions about cooperation.