Talk abstract:

Virulence Evolution in Macro-parasites

Andrea Pugliese
Dipartimento di Matematica
Universitá di Trento
Via Sommarive 14
38050 Povo (TN), Italy
pugliese@science.unitn.it

There exists a large body on theory of virulence in micro-parasites; it is now widely accepted that parasite virulence may be adaptive, if it increases the transmission of parasites to new hosts. Most models show that, under reasonable assumptions, an intermediate level of virulence should be sustained. On the other hand, evolutionary models for macro-parasites are, to a large degree, missing, possibly because of the complexity of the equations describing their dynamics. In this talk I analyse the subject of virulence evolution for macro-parasites; such a study may provide the opportunity, at least in future, of addressing multiple trade-offs (reproductive rate vs. virulence vs. competitivity ability) when direct competition operates among parasites within the same host. In the models considered, parasites interact only by causing the death of the host. These models have been generally been studied through approximations that do not lend themselves to evolutionary interpretation. On the other hand, I could compute analytically the conditions for invasion of a new strain in the exact infinite model. Using these conditions, one finds a unique evolutionary stable strategy of intermediate virulence. In reasonable numerical example, it appears that the virulence at the evolutionary stable strategy, though intermediate relative to feasible strategies, is rather high compared with hosts' natural death rate and optimal strategies for micro-parasites. In corresponding stochastic simulations of small hosts populations (in the hundreds of individuals) `optimal' parasites went often extinct, sometimes causing at the same time extinction of the host population; while more benign parasites coexisted easily with the hosts. Extensions of this findings to situations where hosts are structured in small populations loosely connected will be explored through verbal scenarios and preliminary simulations. Some of these scenarios may be of interest in understanding changes of virulence in established diseases.

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1998-1999 Mathematics in Biology