Mathematical eco-epidemiology and the dilution effect. Professor Mick Roberts, Massey University, Albany, New Zealand

Mathematical models are used to describe the interactions between species in an ecosystem and the dynamics of their infectious diseases. Two specific examples set the scene: the competition between red and grey squirrels and squirrel pox virus in the UK; and the response of the Serengeti ecosystem to the eradication of rinderpest. A more generic example illustrates how a pathogen could regulate a predator-prey interaction, keeping the predator population at a density that allows the prey population to persist. Even more generic is the notion of a dilution effect - the idea that reduced biodiversity increases the risk of transmission of an infectious disease. A mathematical framework suggests that the effect is not ubiquitous, but depends on the nature of the interactions between ecosystem species and on the criteria used to define risk of transmission.