Theoretical models for the evolution and ecological dynamics of host-parasite systems.

Natural organisms are infected by many different parasites, and as a consequence, hosts have evolved a wide range of defences to cope with them. Resistance may be conferred through mechanisms that reduce susceptibility to infection ('avoidance') or increase the rate of clearance ('recovery'). Other forms of resistance reduce the deleterious effects of infection ('tolerance'), or inhibit the parasite's growth ('control'). In addition to these innate forms, hosts may also benefit from immunological memory ('acquired immunity'). The evolution of resistance is expected to be costly in terms of other life history traits. In the presence of such 'trade-offs', the host population may evolve towards an evolutionarily stable strategy (ESS) that balances the costs and benefits of resistance. Another possibility is that a process of evolutionary branching occurs, leading to polymorphism of distinct strategies. Parasites also show adaptation to their hosts and have generally not evolved to be avirulent. Again, this is the result of trade-offs between virulence and other aspects of life history. Often, a higher transmission rate is attained at the cost of increased virulence. This thesis uses a mathematical modelling approach to examine hostparasite interactions. The first part considers the evolutionary dynamics of quantitative host resistance and parasite traits, employing fitness expressions constructed using the techniques of adaptive dynamics. The second part examines the population dynamics of host-parasite interactions; in particular, how different assumptions about the nature of the transmission process may affect the dynamics