Fixation and extinction in time-fluctuating spatially structured metapopulations

Abstract

Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations and environmental variability therefore have a significant impact on the evolution of microbial populations. Here, we consider a class of spatially explicit metapopulation models arranged as regular (circulation) graphs where wild-type and mutant cells compete in a time-fluctuating environment in which demes (subpopulations) are connected by slow cell migration. The carrying capacity is the same at each deme and endlessly switches between two values associated to harsh and mild environmental conditions. Environmental variability can lead to population bottlenecks, following which the population is prone to fluctuation-induced extinction. Here, we analyse how slow migration, spatial structure, and fluctuations affect the phenomena of fixation and extinction on clique, cycle, and square lattice metapopulations. When the carrying capacity remains large, bottlenecks are weak and deme extinction can be ignored. The dynamics is thus captured by a coarse-grained description within which the probability and mean time of fixation are obtained analytically. This allows us to show that, in contrast to static environments, the mutant fixation probability depends on the rate of migration. We also show that the fixation probability and mean fixation time can exhibit a non-monotonic dependence on the switching rate. When the carrying capacity is small under harsh conditions, bottlenecks are strong, and the metapopulation evolution is shaped by the coupling of deme extinction and strain competition. This yields rich dynamical scenarios, among which we identify the best conditions to eradicate mutants without dooming the metapopulation to extinction. We offer an interpretation of these findings in the context of an idealised treatment strategy and discuss possible generalisations of our models.

16+15 pages, 6+7 figures, 2 tables. Simulation data and codes for figures are electronically available from the University of Leeds Data Repository, DOI: https://doi.org/10.5518/1660

References in corpus (27)

• Evolutionary dynamics on any population structure
• Fixation of strategies for an evolutionary game in finite populations
• Stochastic Models of Evolution in Genetics, Ecology and Linguistics
• Robust ecological pattern formation induced by demographic noise
• Stochastic population dynamics in spatially extended predator-prey systems
• Growth dynamics and the evolution of cooperation in microbial populations
• Evolutionary game theory in growing populations
• Quasi-cycles in a spatial predator-prey model
• Intrinsic noise in systems with switching environments
• Evolution of a Fluctuating Population in a Randomly Switching Environment
• Characterization of spiraling patterns in spatial rock-paper-scissors games
• Evolutionary and Population Dynamics: A Coupled Approach
• Population Dynamics in a Changing Environment: Random versus Periodic Switching
• Eco-Evolutionary Dynamics of a Population with Randomly Switching Carrying Capacity
• Dynamics of bacterial populations under the feast-famine cycles
• Fixation properties of rock-paper-scissors games in fluctuating populations
• The Emergence of Cooperation from a Single Mutant during Microbial Life-Cycles
• Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance
• Exclusion of the fittest predicts microbial community diversity in fluctuating environments
• Frequent asymmetric migrations suppress natural selection in spatially structured populations
• Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise
• Mutant fate in spatially structured populations on graphs: connecting models to experiments
• Evolution of cooperation in deme-structured populations on graphs
• Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations
• Spatial patterns emerging from a stochastic process near criticality
• Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and size
• Slow spatial migration can help eradicate cooperative antimicrobial resistance in time-varying environments