Population Extinction on a Random Fitness Seascape

Abstract

Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed population with logistic growth at each location, subject to "seascape" noise, wherein the population's fitness randomly varies with {\it location and time}. Despite its simplicity, the model actually incorporates variants of directed percolation, and directed polymers in random media, within a mean-field perspective. Probability distributions of the population can be computed self-consistently; and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes. The results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction.

References in corpus (6)

• The one-dimensional KPZ equation and its universality class
• Demographic noise can reverse the direction of deterministic selection
• Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
• Mean Field Limits for Interacting Diffusions in a Two-Scale Potential
• Bacterial range expansions on a growing front: Roughness, Fixation, and Directed Percolation
• Traveling wave solution of the Reggeon Field Theory

Cited by in corpus (5)

• Dynamical mean-field theory: from ecosystems to reaction networks
• Extinctions of coupled populations, and rare-event dynamics under non-Gaussian noise
• A Seascape Origin of Richards Growth
• Classification of diffusion processes in dimension $d$ via the Carleman approach with applications to models involving additive, multiplicative or square-root noises
• Neutral theory of cooperative dynamics