Multiple scales in metapopulations can give rise to paradoxical behavior: in a conceptual model for a public goods game, the species associated with a fitness cost due to the public good production can be stabilized in the well-mixed limit due to the mere existence of these scales. The scales in this model involve a length scale corresponding to separate patches, coupled by mobility, and separate time scales for reproduction and interaction with a local environment. Contrary to the well-mixed high mobility limit, we find that for low mobilities, the interaction rate progressively stabilizes this species due to stochastic effects, and that the formation of spatial patterns is not crucial for this stabilization.@en

How does delayed fitnesses adaptation after local habitat changes affect survival of species metapopulation? We study this question in a two-species model system, where the species composition of a local patch determines the reference fitness of all its individuals. When individuals move, this local species composition changes. As the local environment on the patch might adapt slowly to this change, we assume that individuals in turn adapt their fitness with a stochastic delay. We show that the combination of delay and spatial substructure can yield significantly different phase diagrams for the survival of these species with respect to models with immediate response. We investigate this exemplarily for the case where the two species interact via an exoproduct: thus, our population consists of a slow-growing producer species and a fast-growing dominant species. We provide a conceptual understanding of the role of delay by presenting analytic results in the well-mixed and low-mobility limit. By studying intermediate mobilities numerically, we ensure that our results are robust, and may be relevant to different ecological situations as well as microbial metapopulation experiments.@en

A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the population and is progressively degraded. Different treatment regimes, involving single or periodical doses, are evaluated in terms of the minimal population size (a measure of the extinction probability), and the population composition (a measure of the selection pressure for resistance or tolerance during the treatment). We show that there exist timescales over which the low-stress regime is as effective as the high-stress regime, due to the competition between the two species. For multiple periodic treatments, competition can ensure that the minimal population size is attained during the first pulse when the high-stress regime is short, which implies that a single short pulse can be more effective than a more protracted regime. Our results suggest that when the duration of the high-stress environment is restricted, a treatment with one or multiple shorter pulses can produce better outcomes than a single long treatment. If ecological competition is to be exploited for treatments, it is crucial to determine these timescales, and estimate for the minimal population threshold that suffices for extinction. These parameters can be quantified by experiment.@en

Organisms that exploit different environments may experience a stochastic delay in adjusting their fitness when they switch habitats. We study two such organisms whose fitness is determined by the species composition of the local environment, as they interact through a public good. We show that a delay in the fitness adjustment can lead to the coexistence of the two species in a metapopulation, although the faster-growing species always wins in well-mixed competition experiments. Coexistence is favored over wide parameter ranges and is independent of spatial clustering. It arises when species are heterogeneous in their fitness and can keep each other balanced.@en