Mathematical biosciences
-
We investigate how the loss of previously evolved diversity in host resistance to disease is dependent on the complexity of the underlying evolutionary trade-off. Working within the adaptive dynamics framework, using graphical tools (pairwise invasion plots, PIPs; trait evolution plots, TEPs) and algebraic analysis we consider polynomial trade-offs of increasing degree. Our focus is on the evolutionary trajectory of the dimorphic population after it has been attracted to an evolutionary branching point. ⋯ In particular, the loss of diversity in this model always occurs in such a way that the remaining strain is not attracted back to the branching point but to an extreme of the trade-off, meaning the diversity is lost forever. We also show similar results for a non-polynomial but complex trade-off, and for a different eco-evolutionary model. Our work further highlights the importance of trade-offs to evolutionary behaviour.