Research

Research Interests

Mathematical population genetics: probability distributions of gene frequencies in populations modeled by diffusion processes; probability distributions of genealogical processes; probability distributions of gene phylogenies which can be deduced from mutation patterns on DNA sequences; measure-valued diffusion process; models in the evolution of gene frequencies and phylogenies; and computational algorithms for ancestral inference, such as algorithms to estimate mutation, recombination, migration and selection rates, the time to the most recent common ancestor of sequences, and ages of mutations. Stochastic processes in Mathematical Genetics. Combinatorial structure of stochastic processes involving random partitions. Multivariate orthogonal polynomials. Eigenfunctions and spectral expansions of stochastic process transition functions.

Software

GENETREE software for the estimation of mutation and population growth rates and for ancestral inference on the ages of mutations and time to the most recent common ancestor from samples of DNA sequences is available to researchers .

Research Grants

  • 2005-2008 EPSRC grant, Combinatorial structure of stochastic models in Population Genetics, £178,882;
  • 2001-2004 EPSRC grant, Computationally intensive methods for inference about selection in DNA sequences, £50,000;
  • 2001-2004 BBSRC/EPSRC Biomathematics grant, Demographic and ancestral inference from DNA sequences, £117,240;
  • 1998 Australian Research Council (ARC) small grant, Ancestral inference from DNA sequences under selection, $14,744;
  • 1996-1998 ARC large grant, Statistical analysis and ancestral inference from DNA sequences in a subdivided population, $160,000
  • 1994 ARC small grant, Ancestral inference from DNA sequences under selection, $8,900.
  • 1992-1994 ARC large grant, Mathematical models and analysis of genetical data: DNA sequences and diseases, $162,000 (with Professor W.J. Ewens and Dr G.A. Watterson)

Postdoctoral Research Fellows & Assistants:

  • 1992–1994 Dr P. Marjoram,
  • 1996–1998 Dr M. Bahlo,
  • 2001–2003 Dr M. De Iorio,
  • 2003–2008 Dr D. Spano.