Stochastic population dynamics in switching environments

Modelling the dynamics of finite populations involves intrinsic demographic noise. This is particularly important when the population is small, as it is frequently the case in biological applications, such as gene circuits. At the same time populations can be subject to switching or changing environments; for example promotors may bind or unbind, or bacteria can be exposed to changing concentrations of antibiotics. How does one integrate intrinsic and extrinsic into models of population dynamics, and how does one derive coarse grained descriptions? How can simulations best be performed efficiently? In this talk I will address some of these questions. Theoretical aspects include systematic expansions in the strength of each type of noise to derive reduced models such as stochastic differential equations, or piecewise deterministic Markov processes. I will show how this can lead to peculiar features including master equations with negative “rates”. I will also discuss a number of applications, in particular in game theory, and so-called phenotype switching, a strategy used by bacteria to hedge their bets in switching external conditions.