Additional file 1 of The evolutionary and coevolutionary consequences of defensive microbes for host-parasite interactions

Appendix A. In this supplementary material we present the mathematical details for the evolutionary investment in defensive microbe or immune based systems. Together with the details of the invasion analysis mediated by intense shared parasitism, these results on the evolution of a defensive microbe system are corroborated with numerical simulations and an individual-based approach. (PDF 3130 kb)