Extinction in complex communities as driven by adaptive dynamics. (2nd July 2021) - Nguyen, Vu A. T.; Vural, Dervis Can
Abstract: 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. Abstract : Here we analytically solve canonical adaptive dynamics equations (yellow), which govern how interspecies interactions evolve. We assume that a Lotka‐Volterra‐type interaction defines the fitness landscape, and take the trait dependence of interspecies interactions as given (red). From here we calculate (green), (1) the evolution of interaction mediating traits (2) how equilibrium abundances of species shift as they coevolve (3) time to first extinction as caused by coadaptation, and (4) the number of extant species as a function of time, as many such adaptation driven extinctions accumulate.