Hamilton’s Rule and Inclusive Fitness, Part I: What Did Hamilton (1964) Actually Define?

Keywords

Inclusive fitness, Hamilton’s rule, kin selection, altruism, social evolution, population genetics, gene substitution, Fisher’s average effect, relatedness, evolution of cooperation, greenbeard effect, dominance, allele frequency change, mathematical modeling, empirical research

Summary

In this episode of the Natural Reward podcast, brothers Owen and Jon Gilbert revisit Hamilton’s original papers on inclusive fitness and the evolution of altruism. They discuss how Hamilton’s rule (rb – c > 0) emerged as a condition for the spread of social alleles, and how Hamilton’s original formulation of inclusive fitness involved subtracting the “dilution effect” of uncorrelated interactions from total fitness.

The conversation explores longstanding ambiguities in the 1963–64 papers, including whether inclusive fitness applies to alleles, genotypes, or individuals, and how assumptions such as haploidy or additive gene action affect the interpretation of Hamilton’s rule. Owen outlines how the quantity rb – c corresponds to Fisher’s average effect of a gene substitution under certain conditions, while becoming frequency dependent under dominance or decoupled from relatedness in greenbeard scenarios.

These distinctions have important implications for empirical work: subsequent theoretical generalizations often redefine r, b, and c so that rb – c tracks allele-frequency change, making it difficult to determine when Hamilton’s original rule has actually been tested. The episode concludes by emphasizing the need for clearer theoretical guidance in designing experiments capable of rigorously evaluating Hamilton’s rule in natural populations.

Takeaways

• Hamilton (1964) defined inclusive fitness by subtracting the dilution effect from total fitness.
• It is not always clear in Hamilton’s early papers whether inclusive fitness applies to alleles, genotypes, or individuals.
• Under haploidy or additive gene action, rb – c corresponds to Fisher’s average effect of a gene substitution.
• With dominance, the average effect becomes frequency dependent.
• In greenbeard scenarios, altruistic alleles can be favored even when rb – c < 0.
• Later theoretical work often defines r, b, and c so that rb – c is proportional to allele-frequency change.
• Empirical researchers typically measure genealogical relatedness and phenotypic costs and benefits.
• Applying Hamilton’s rule outside of strictly altruistic contexts can make b and c difficult to interpret.
• A central challenge is determining how to test Hamilton’s rule in real populations with measurable parameters.

Chapters

00:00 Introduction to Inclusive Fitness and Hamilton's Rule01:16 Exploring Hamilton's Original Work03:27 Clarifying Inclusive Fitness Definitions05:08 Mathematical Clarity in Inclusive Fitness07:18 The Concept of Exclusive Fitness10:39 Dominance and Its Implications12:55 Average Effect of Gene Substitution15:35 Challenges in Empirical Applications of Hamilton's Rule