title: Fixation in finite populations evolving in fluctuating environments.
abstract: The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death events. The rates of these events may vary in time depending on the state of the environment, which follows an independent Markov process. We develop a general theory for the fixation probability of a mutant in a population of wild-types, and for mean unconditional and conditional fixation times. We apply our theory to evolutionary games for which the payoff structure varies in time. The mutant can exploit the environmental noise; a dynamic environment that switches between two states can lead to a probability of fixation that is higher than in any of the individual environmental states. We provide an intuitive interpretation of this surprising effect. We also investigate stationary distributions when mutations are present in the dynamics. In this regime, we find two approximations of the stationary measure. One works well for rapid switching, the other for slowly fluctuating environments.
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK.
authors.forename: Peter
authors.initials: P
authors.lastname: Ashcroft
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA Harvard School of Public Health, Boston, MA 02115, USA Dana-Farber Cancer Institute, Boston, MA 02215, USA.
authors.forename: Philipp M
authors.initials: PM
authors.lastname: Altrock
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK tobias.galla@manchester.ac.uk.
authors.forename: Tobias
authors.initials: T
authors.lastname: Galla
mesh_terms: D008962:Models, Theoretical
keywords: evolutionary dynamics; fluctuating environments; stochastic processes