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On Hamilton’s Rule and Inclusive Fitness Theory with Nonadditive Payoffs

Published online by Cambridge University Press:  01 January 2022

Abstract

Hamilton’s theory of inclusive fitness is a widely used framework for studying the evolution of social behavior, but controversy surrounds its status. Hamilton originally derived his famous rb > c rule for the spread of a social gene by assuming additivity of costs and benefits. However, it has recently been argued that the additivity assumption can be dispensed with, so long as the −c and b terms are suitably defined, as partial regression coefficients. I argue that this way of generalizing Hamilton’s rule to the nonadditive case, while formally correct, faces conceptual problems.

Type
50 Years of Inclusive Fitness
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

Thanks to Johannes Martens, Jonathan Birch, Andy Gardner, James Marshall, and Alan Grafen for comments and discussion. This work was supported by the European Research Council Seventh Framework Program (FP7/20072013), ERC grant agreement 295449.

References

Allen, Benjamin, Nowak, Martin A., and Wilson, Edward O.. 2013. “Limitations of Inclusive Fitness.” Proceedings of the National Academy of Sciences USA 110:21035–39.CrossRefGoogle ScholarPubMed
Birch, Jonathan. 2014. “Hamilton’s Rule and Its Discontents.” British Journal for the Philosophy of Science 65:381411.CrossRefGoogle Scholar
Birch, Jonathan, and Okasha, Samir. 2015. “Kin Selection and Its Critics.” Bioscience 65:2232.CrossRefGoogle Scholar
Bourke, Andrew F. G. 2011. Principles of Social Evolution. Oxford: Oxford University Press.CrossRefGoogle Scholar
Falconer, Douglas S. 1995. Introduction to Quantitative Genetics. 4th ed. London: Longman.Google Scholar
Fisher, Ronald A. 1941. “Average Effect and Average Excess of a Gene Substitution.” Annals of Human Genetics 11:5363.Google Scholar
Frank, Steven A. 1997. “The Price Equation, Fisher’s Fundamental Theorem, Kin Selection, and Causal Analysis.” Evolution 51:1712–29.CrossRefGoogle ScholarPubMed
Frank, Steven A. 1998. Foundations of Social Evolution. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Gardner, Andy, West, Stuart A., and Wild, Geoff. 2011. “The Genetical Theory of Kin Selection.” Journal of Evolutionary Biology 24:1020–43.CrossRefGoogle ScholarPubMed
Gelman, Andrew, and Hill, Jennifer. 2007. Data Analysis Using Regression and Multi-level/Hierarchical Models. Cambridge: Cambridge University Press.Google Scholar
Grafen, Alan. 1985. “A Geometric View of Relatedness.” Oxford Surveys in Evolutionary Biology 2:2889.Google Scholar
Grafen, Alan 2002. “A First Formal Link between the Price Equation and an Optimization Program.” Journal of Theoretical Biology 217:7591.CrossRefGoogle Scholar
Grafen, Alan 2006. “Optimization of Inclusive Fitness.” Journal of Theoretical Biology 238:541–63.CrossRefGoogle ScholarPubMed
Grafen, Alan 2009. “Formalizing Darwinism and Inclusive Fitness Theory.” Philosophical Transactions of the Royal Society B 364:3135–41.CrossRefGoogle ScholarPubMed
Hamilton, William D. 1964. “The Genetical Evolution of Social Behaviour.” Pts. 1 and 2. Journal of Theoretical Biology 7:152.CrossRefGoogle Scholar
Hamilton, William D. 1970. “Selfish and Spiteful Behaviour in an Evolutionary Model.” Nature 228:1218–20.CrossRefGoogle Scholar
Hamilton, William D. 1996. Narrow Roads of Gene Land. Vol. 1. New York: Freeman.Google Scholar
Marshall, James A. R. 2011. “Group Selection and Kin Selection: Formally Equivalent Approaches.” Trends in Ecology and Evolution 26:325–32.CrossRefGoogle ScholarPubMed
Marshall, James A. R. 2015. Social Evolution and Inclusive Fitness Theory. Princeton, NJ: Princeton University Press.Google Scholar
Nowak, Martin A., Tarnita, Corina E., and Wilson, Edward O.. 2010. “The Evolution of Eusociality.” Nature 466:1057–62.CrossRefGoogle ScholarPubMed
Tarnita, Corina E., and Wilson, Edward O. 2011. “Nowak et al. Reply.” Nature 471:E0E10.Google Scholar
Okasha, Samir, and Martens, Johannes. 2016a. “The Causal Meaning of Hamilton’s Rule.” Royal Society Open Science. doi:10.1098/rsos.160037.CrossRefGoogle Scholar
Okasha, Samir, and Martens, Johannes 2016b. “Hamilton’s Rule, Inclusive Fitness Maximization, and the Goal of Individual Behaviour in Symmetric Two-Player Games.” Journal of Evolutionary Biology 29:473–82.CrossRefGoogle Scholar
Price, George R. 1970. “Selection and Covariance.” Nature 227:520–21.CrossRefGoogle ScholarPubMed
Queller, David C. 1992a. “A General Model for Kin Selection.” Evolution 46:376–80.CrossRefGoogle Scholar
Queller, David C. 1992b. “Quantitative Genetics, Inclusive Fitness and Group Selection.” American Naturalist 139:540–58.CrossRefGoogle Scholar
Queller, David C. 2011. “Expanded Social Fitness and Hamilton’s Rule for Kin, Kith and Kind.” Proceedings of the National Academy of Sciences USA 108:10792–99.CrossRefGoogle ScholarPubMed
van Veelen, Matthias. 2009. “Group Selection, Kin Selection, Altruism and Cooperation: When Inclusive Fitness Is Right and When It Can Be Wrong.” Journal of Theoretical Biology 259:589600.CrossRefGoogle ScholarPubMed