Alan Grafen: University of Oxford Department of Zoology

Most fieldworkers and empirical biologists studying whole organisms use as a working hypothesis that organisms have been designed by natural selection to maximise their inclusive fitness. They have used this approach to great effect since the work of Hamilton (1964) became widely known in the 1970s. On the other hand, population geneticists have mostly consistently denied that natural selection causes any quantity to be maximised, and have in general been critical of Hamilton’s work. It is an established part of the Modern Synthesis that the basis for natural selection must be found in population genetics models, which in mathematical terms are expressed in equations of motion. The modern way to represent design, used in economics though little in biology, is through optimisation programs. Recent unpublished work is outlined which, by making formal links between the mathematics of motion and optimisation programs, begins to provide a rigorous justification for the maximisation of inclusive fitness. Previous work relating to non-social behaviour can be found in the following references (available at http://users.ox.ac.uk/~grafen/):