The general version of Hamilton's rule

Area of Science:

• Evolutionary biology
• Behavioral ecology
• Mathematical biology

Background:

• The scope and applicability of Hamilton's rule for explaining cooperation are widely debated.
• Existing models often struggle with complex fitness interactions in social behaviors.

Purpose of the Study:

• To construct a generalized version of Hamilton's rule that accommodates varied fitness dependencies.
• To resolve debates regarding the generality of Hamilton's rule in evolutionary theory.

Main Methods:

• Derivation of the Generalized Price equation, linking Price equation to its statistical origins.
• Development of a hierarchy of nested selection rules based on fitness effects.

Main Results:

• A general form of Hamilton's rule is established, applicable to nonlinear and interdependent fitness effects.
• The Generalized Price equation reveals multiple Price-like equations for different models.
• A hierarchy of nested rules for trait selection, including non-social traits, is identified.

Conclusions:

• The generalized Hamilton's rule provides a robust framework for studying the evolution of costly cooperation across diverse scenarios.
• This work clarifies the mathematical underpinnings of evolutionary selection and social behavior analysis.