Demographic Stochasticity in Evolutionary Biology.

Abstract

Demographic stochasticity, the random fluctuations arising from the intrinsic discreteness of populations and the uncertainty of individual birth and death events, is an essential feature of population dynamics. Nevertheless theoretical investigations often neglect this naturally occurring noise due to the mathematical complexity of stochastic models. This dissertation reports the results of analytical and computational investigations of models of competitive population dynamics, specifically the competition between species in homogeneous or heterogeneous environments with different phenotypes of longevity or dispersal, fully accounting for demographic stochasticity. A novel asymptotic approximation is introduced and applied to derive remarkably simple analytical forms for key statistical quantities describing the populations' dynamical evolution. These formulas characterize the selection processes that determine which (if either) competitor has an evolutionary advantage. The theory is verified by conventional asymptotic analysis and large-scale numerical simulations.

After introducing demographic stochasticity into the deterministic models and motivating our mathematical approach to the analysis, we discover that the fluctuations can (1) break dynamical degeneracies, (2) support polymorphism that does not exist in deterministic models, (3) reverse the direction of the weak selection and cause shifts in selection regimes, and (4) allow for the emergence of evolutionarily stable dispersal rates. Both dynamical mechanisms and time scales of the fluctuation-induced phenomena are identified within the theoretical approach. The analysis highlights the fundamental physical effect of the fluctuations and provides an intuitive interpretation of the complex dynamics. An interaction between stochasticity and nonlinearity is the foundation of noise-driven dynamical selection.