Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Rapid adaptation from standing variance and de novo mutation: a general deterministic approximation
Guillaume Martin

Last modified: 2014-06-09


I consider an asexual population undergoing mutation, selection and drift. Theories of adaptation of these systems often rely on stationarity assumptions: stationary variance of a trait distribution in quantitative genetics, stationary regime of xation in stochastic theories of tness dynamics. Yet, these stationary regimes ignore the impact of initial standing variance in fitness, and may not be reached in the early phase of adaptive response to an environmental challenge. They may even not exist in the presence of context-dependent mutation and abrupt changes. I will present an alternative approach to model these dynamics as a stochastic PDE followed by the generating function of the tness distribution. Analytical solutions can be found when drift is neglected (I will discuss when this is reasonable), providing predictions for mutation-selection balance as well as adaptation. I will apply these results to the problem of evolutionary rescue, focusing on the contribution of de novo mutation vs standing variance from a population previously at equilibrium.