The formal Darwinism project is an ambitious attempt to provide a mathematical population genetic justification for the concept of fitness optimisation, at a very high level of abstraction. As well as advancing the highly technical core of the project, I am also engaged in applications, including (i) inclusive fitness on networks, in relation to altruism and population viscosity (ii) reinterpreting bet-hedging in terms of fitness optimisation (iii) showing that group selection has no similar justification leading to a conclusion of optimisation of group fitness.
This work also has a historical interest. It is essentially capturing Darwin’s central claim in the Origin of Species that the mechanical processes of inheritance and reproduction (now represented by population genetics) give rise to the appearance of design (now represented by optimisation). By incorporating all the advances in evolutionary theory (ESS theory, inclusive fitness, optimality theory), the end result will be a grand overarching theory justifying fitness optimisation as a central concept in biology. It is a mathematical version of the synthesis of theory and its grounding in fundamental concepts to be found in Richard Dawkins’ “The Selfish Gene”. I also engage from time to time in other topics in evolutionary theory and in statistics. In February 2014 I completed "phyreg", an R package, available from CRAN, that implements my 1989 Phylogenetic Regression.
I am the co-author with Rosie Hails of ‘Modern Statistics for the Life Sciences’ (2002, OUP), which introduces undergraduate students (and others!) to the powerful technique of General Linear Modelling. Online supplements show how to do all the exercises in Minitab, SPSS and SAS.