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J Theor Biol. 2002 Jul 7;217(1):75-91.

A first formal link between the price equation and an optimization program.

Author information

  • Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, UK. alan.grafen@sjc.ox.ac.uk


The Darwin unification project is pursued. A meta-model encompassing an important class of population genetic models is formed by adding an abstract model of the number of successful gametes to the Price equation under uncertainty. A class of optimization programs are defined to represent the "individual-as-maximizing-agent analogy" in a general way. It is then shown that for each population genetic model there is a corresponding optimization program with which formal links can be established. These links provide a secure logical foundation for the commonplace biological principle that natural selection leads organisms to act as if maximizing their "fitness", provides a definition of "fitness", and clarifies the limitations of that principle. The situations covered do not include frequency dependence or social behaviour, but the approach is capable of extension.

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