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Mathematical biology: ecology and evolution

My research interests are in Mathematical Biology, the mathematical modelling and analysis of biological systems. Looking at my research from the biological point of view, I am interested in the effects of change on ecological communities, which often involve evolutionary effects. From the mathematical point of view, I am interested in dynamical systems, both deterministic and stochastic, and the connections between the two. The effect of spatial variation on the dynamics is often crucial and its inclusion can provide insight unobtainable from spatially uniform models. The mathematics involved is usually nonlinear ordinary, partial or integro-differential equations, or their analogues in discrete time, often backed up by computer simulation. Topics of current interest include Habitat Loss and Habitat Fragmentation, Evolution of Sex in Plants, and Bacterial Evolution. I believe strongly in interdisciplinary research, and almost all my work is now in collaboration with biologists.

The effects of habitat loss and habitat fragmentation on ecological communities

Habitat loss and habitat fragmentation are major causes of the current extinction crisis.

• Habitat loss. A patchy environment consists of discrete patches of potential habitat, and we are interested in the effect of erosion and particularly removal of some of the patches. Recent results show that the simplest models give misleading results. It is very difficult to predict
  • which species in a community is most at risk of extinction, and
  • when a given habitat is close to a point at which mass extinctions will occur.
  In particular, the biodiversity in a habitat is not necessarily a good indicator of the robustness of the habitat in terms of maintaining that biodiversity under the pressure of habitat loss. It will be necessary to extend and refine the current models to give a realistic picture of the phenomena involved.
• Habitat fragmentation. Here we are interested in cases where habitat removal results in the habitat becoming more fragmented with time. This fragmentation process may occur very suddenly, even if the removal process is occurring gradually. But, even before complete fragmentation, computer simulations show that the habitat may become much poorer at supporting biodiversity, as individuals or groups get partially trapped in smaller and smaller areas. A theory of how the quality of the habitat depends on the removal process is required, and may be important for the management of reserves. A full treatment of this problem will require some simulation and some analysis of stochastic processes and percolation.

Asexual and sexual reproduction in plants

The question of why sexual reproduction occurs at all is an old and vexed one. A rare mutant gene that suppresses meiosis in a lizard, for example, leading to parthenogenetic production of offspring, doubles its representation in the population at each generation. A rare mutant gene in a hermaphrodite plant (where the same flower produces both seeds and pollen) that suppresses meiosis in its seeds but not its pollen, increases its representation by half. Theories for the persistence of sex despite this cost of meiosis are of two kinds,

• that parthenogenetic varieties evolve more slowly, or
• that they accumulate deleterious mutations.

There are many mathematical models testing such theories in animals, but the situation in plants is fundamentally different, because a plant that produces genetically identical offspring from its unfertilised seed may nevertheless produce genetically diverse offspring as well by fertilising the seeds of a sexual plant with its pollen. Many mathematical models of the situation in animals have been analysed, but the situation in plants has been far less well explored, although some work has been done here in Bath by Nick Britton, Mike Mogie of the Department of Biology and Biochemistry, and Claudia Carrillo, a PhD student. The advantage of being asexual depends on the fraction of neighbouring plants that are sexual, because

• sexuals allow genetically diverse offspring, but
• not all sexually produced offspring carry the gene for asexuality.

This is an example of frequency-dependent selection, and suggests that the spatial distribution of reproductive mode is important. Computer simulations, mean-field and improved approximations, and new techniques for the analysis of spatial processes that are now becoming available, might be used to analyse such a situation.

Evolution of antibiotic resistance in bacteria

Bacteria reproduce asexually by fission, splitting to produce two offspring genetically identical to the parent, but they can also exchange genetic material with other bacteria of the same or different species in a process of recombination. It was thought that bacteria could evolve antibiotic resistance so quickly because their speed of reproduction allowed them to do so through genetic mutation, but it now seems that more often they acquire it through recombination. The genetic structure of a population where such processes are taking place is very complex, containing many clones, each of which has a cloud of mutated relatives around it in gene space, but some (at least) of which were produced originally at an isolated point in gene space by recombination. There are data available on this structure for certain bacteria, and Ed Feil in the Department of Biology and Biochemistry is an expert on these systems. Evolution in such a population has not been studied mathematically, and presents a challenging and potentially very important problem.

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Department of Mathematical Sciences, University of Bath, Bath BA2 7AY
Tel: +44 (0) 1225 386005 · Fax: +44 (0) 1225 386492
This page maintained by n.f.britton@bath.ac.uk. Last updated: 1 June 2002

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