Stochastic population dynamics of spatially extended systems

Abstract

Natural populations are exposed to various sources of internal and external noise that govern their dynamics, longtime behavior, and give rise to extraordinary macroscopic properties. These sources of noise can induce pattern formation and cause fixation or extinction events, thus having considerable impact on the population's survival. This work explores the importance of stochasticity and space by elucidating the shortcomings of traditional deterministic modeling through spatial extensions of two general themes: the Lotka-Volterra predator-prey model, and a game theoretic model of cooperative antimicrobial resistance. The effects of environmental variability on biodiverse ecosystems are of growing interest due to their potential applications in protecting endangered species or eradicating harmful organisms. All finite stochastic system will eventually reach its final absorbing state (typically total extinction), but on a characteristic time that usually grows exponentially with its system size, thus often rendering itself effectively stable for experimentally reasonable timescales. However, tuning system parameters can reduce the characteristic extinction time and induce stochastic extinction events. Through agent-based Monte Carlo simulations, this work investigates the Lotka-Volterra predator-prey model on a two-dimensional lattice subjected to a spatially varying carrying capacity resulting in two distinct diffusively-coupled environments. One subsystem experiences stable predator-prey coexistence, whereas its neighbor is a vulnerable, extinction-prone region. Upon placing the two environments in diffusive contact, wave fronts emerging from the coexisting system into the vulnerable region excite and revive the predator and prey populations. The robustness of this stabilization of finite-size, excitable systems is discussed in the context of this model and related systems. Antimicrobial resistance is a global threat and combating its spread is of paramount importance. Antimicrobial resistance often results from a cooperative behavior with shared drug protection. Microbial communities generally evolve in volatile, spatially structured settings. Migration, space, fluctuations, and environmental variability all have a significant impact on the development and proliferation of antimicrobial resistance. While drug resistance is enhanced by migration in static conditions, this changes in time-fluctuating spatially structured environments. Here, we consider a two-dimensional metapopulation consisting of demes in which drug-resistant and sensitive cells evolve and migrate in a time-varying environment. This contains a toxin against which protection can be shared (cooperative antimicrobial resistance). When the environment and the deme composition vary on the same timescale, strong population bottlenecks cause fluctuation-driven extinction events, countered by migration. We investigate the influence of migration and environmental variability on the eco-evolutionary dynamics by asking at what migration rate fluctuations can help clear resistance and what are the near-optimal environmental conditions ensuring the quasi-certain eradication of resistance in the shortest possible time. By combining analytical and computational tools, we answer these questions by determining when the resistant strain goes extinct across the entire metapopulation. While dispersal generally promotes strain coexistence, here we show that slow-but-nonzero migration can speed up and enhance resistance clearance, and determine the near-optimal conditions for this phenomenon. We discuss the impact of our findings on laboratory-controlled experiments and outline their generalization to lattices of any spatial dimension.