Delayed adaptation in stochastic metapopulation models

Marianne Bauer, Erwin Frey

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Article number68002
Issue number6
Publication statusPublished - 2018
Externally publishedYes


We acknowledge funding from the EUs Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 660363 and an LMU Research Fellowship (MB), and the German Excellence Initiative via the programme “Nanosystems Initiative Munich”. Part of this work was performed at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611 (EF).


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