ST JOHN’S COLLEGE, UNIVERSITY OF OXFORD
The Deep Mathematical Theory of Selfish Genes
FURTHER PARTICULARS
The College intends to appoint two two-year Fixed-term Research Associates to work in its Research Centre. The college will host a further two years of the project and provide matching funding, if external funding can be obtained. The successful applicants will work with Professors Alan Grafen and Charles Batty on an abstract mathematical project that underpins and develops modern Darwinian theory.
About the project
Alan Grafen has been publishing papers on ‘formal Darwinism’ since 1999. The quickest way to appreciate the project to date is to consult
1) a simple verbal account of the work to date (A. Grafen 2007. The formal Darwinism
project: a mid-term report. Journal of evolutionary Biology 20, 1243-1254.
doi:10.1111/j.1420-9101.2007.01321.x), available at
2) an elementary mathematical introduction (A. Grafen 2008. The simplest formal argument for fitness optimisation. Journal of Genetics, 87, 421-433. doi:
10.1007/s12041-008-0064-9 ) available at
3) a reasonably complete form of the argument but using finite mathematics for ‘inclusive fitness’ (A Grafen 2006 Optimization of inclusive fitness. Journal of theoretical Biology 238, 541-563), available at
and
4) a paper using the heavier mathematical tools likely to be required for future work, applied to the problem of allowing the existence of different classes of individual (A. Grafen 2006. A theory of Fisher’s reproductive value. Journal of mathematical Biology 534, 15-60.), available at
The work now requires collaboration with mathematicians, in order to tackle more abstract problems, to solve them more efficiently, and to publish the results in a mathematically acceptable way. This has brought about the involvement of co-applicant Charles Batty, a pure mathematician, and this advertisement for two research associates.
The postholders will be involved in linking the mathematics of motion with the
mathematics of optimisation at an abstract level. The tools will include measure theory and Markov processes over compact Hausdorff spaces. The goals of the project are to unify, formalise and extend existing results into a rigorous and general statement about the connections between natural selection, on the one hand, and optimality in the design of organisms, including a precise definition of ‘optimal’, on the other.
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