Mathematical models of evolution with trade-offs in host-parasite systems.

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This proposal presents a new methodology for studying evolution in host-parasite systems, combining evolutionary and ecological dynamics into a mathematical framework. The proposed models are mathematically tractable using results from bifurcation and dynamical systems theory and include many evolutionary aspects that modern mathematical models have not been able to capture. This study aims to explore the role of cost-benefit trade-offs in the evolution of host and parasite populations with both continuous and discrete generations. In particular the conditions leading to evolutionary branching of are going to be studied.