A first formal link between the price equation and an optimization program.
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.
Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, UK. alan.grafen@sjc.ox.ac.uk
Alan
A
Grafen
D000220:Adaptation, Biological; D000818:Animals; D005075:Biological Evolution; D005828:Genetics, Population; D008957:Models, Genetic