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Published on: November 15, 2013

The general version of Hamilton's rule.

Matthijs van Veelen¹

¹Department of Economics, Universiteit van Amsterdam, Amsterdam, Netherlands.

|September 12, 2025

Summary

This summary is machine-generated.

This study resolves debates on Hamilton's rule by creating a general version applicable to diverse social behaviors and fitness dependencies. It reveals a hierarchy of selection rules, offering a constructive solution for understanding costly cooperation.

Keywords:

Hamilton's rule Price equation Queller's rule evolutionary biology kin selection none population genetics relatedness

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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.