  In a complex community, species continuously adapt to each other. On rare
occasions, the adaptation of a species can lead to the extinction of others,
and even its own. "Adaptive dynamics" is the standard mathematical framework to
describe evolutionary changes in community interactions, and in particular,
predict adaptation driven extinction. Unfortunately, most authors implement the
equations of adaptive dynamics through computer simulations, that require
assuming a large number of questionable parameters and fitness functions. In
this study we present analytical solutions to adaptive dynamics equations,
thereby clarifying how outcomes depend on any computational input. We develop
general formulas that predict equilibrium abundances over evolutionary time
scales. Additionally, we predict which species will go extinct next, and when
this will happen.
