Biology & Philosophy

, Volume 29, Issue 2, pp 181–195 | Cite as

Fitness, inclusive fitness, and optimization

  • Laurent LehmannEmail author
  • François Rousset


Individual-as-maximizing agent analogies result in a simple understanding of the functioning of the biological world. Identifying the conditions under which individuals can be regarded as fitness maximizing agents is thus of considerable interest to biologists. Here, we compare different concepts of fitness maximization, and discuss within a single framework the relationship between Hamilton’s (J Theor Biol 7:1–16, 1964) model of social interactions, Grafen’s (J Evol Biol 20:1243–1254, 2007a) formal Darwinism project, and the idea of evolutionary stable strategies. We distinguish cases where phenotypic effects are additive separable or not, the latter not being covered by Grafen’s analysis. In both cases it is possible to define a maximand, in the form of an objective function ϕ(z), whose argument is the phenotype of an individual and whose derivative is proportional to Hamilton’s inclusive fitness effect. However, this maximand can be identified with the expression for fecundity or fitness only in the case of additive separable phenotypic effects, making individual-as-maximizing agent analogies unattractive (although formally correct) under general situations of social interactions. We also feel that there is an inconsistency in Grafen’s characterization of the solution of his maximization program by use of inclusive fitness arguments. His results are in conflict with those on evolutionary stable strategies obtained by applying inclusive fitness theory, and can be repaired only by changing the definition of the problem.


Fitness Inclusive fitness Maximization Optimization program Game theory Dynamic sufficiency 



This work was partly funded by Swiss NSF Grant PP00P3-123344. We thank Christine Clavien, Alan Grafen, Charles Mullon, and Samir Okasha for useful comments on various drafts.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Ecology and EvolutionUniversity of LausanneLausanneSwitzerland
  2. 2.CNRS, Institut des Sciences de l’évolutionUniversité Montpellier IIParisFrance

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