ArticleProceedings. Mathematical, physical, and engineering sciences2020
Population dynamics with spatial structure and an Allee effect.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- Diffusion and discrete temporal models of the population growth of domestic cats in urban areas.Scientific reports · 2025Article
- Modeling bacterial growth and Allee effect via Allen-Cahn theoretical framework.Scientific reports · 2025Article
- Demographic effects of aggregation in the presence of a component Allee effect.Journal of the Royal Society, Interface · 2024Article
- Spatial exclusion leads to "tug-of-war" ecological dynamics between competing species within microchannels.PLoS computational biology · 2023Article
- Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Phase transitions in biology: from bird flocks to population dynamics.Proceedings. Biological sciences · 2021Article
Corrections and comments
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Population dynamics including a strong Allee effect describe the situation where long-term population survival or extinction depends on the initial population density. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to extinction, whereas initial densities above the threshold lead to survival. Mean-field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as competition and dispersal. The influence of non-mean-field effects has not been studied in the presence of an Allee effect. To address this, we develop an individual-based model that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure neglected by mean-field models. For example, there are cases where the mean-field model predicts extinction but the population actually survives. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.