In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of one species can lead to the extinction of others, and even its own. "Adaptive Dynamics" is the standard framework to describe evolutionary changes to community interactions, and in particular, to predict adaptation driven extinction. Unfortunately, most of the literature in this field is dominated by computer simulations which must make a large number of arbitrary assumptions about a large number of parameters governing interspecies interactions (e.g. random matrices). In this talk, I will present general analytical solutions to Adaptive Dynamics equations and present formulas that govern how equilibrium abundances shift over evolutionary time scales. Our formulas can predict which species will go extinct next and when this will happen. I will then show how to use these results to develop guiding principles to synthetically edit complex ecological communities as to steer them towards a desirable target state.

This is a joint seminar between Applied Math and Biological Physics.