ArticleBulletin of mathematical biology2021
Atto-Foxes and Other Minutiae.
Article in Bulletin of mathematical biology, 2021. 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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6 citing papers in PubMed.
- Multiscale modelling of birth-death processes.Journal of mathematical biology · 2026Article
- Towards modeling phage therapy.PLoS computational biology · 2026Article
- A hybrid framework for compartmental models enabling simulation-based inference.Journal of mathematical biology · 2026Article
- Pattern Formation as a Resilience Mechanism in Cancer Immunotherapy.Bulletin of mathematical biology · 2025Article
- Reversible, tunable epigenetic silencing of TCF1 generates flexibility in the T cell memory decision.Immunity · 2024Article
- Permanence via invasion graphs: incorporating community assembly into modern coexistence theory.Journal of mathematical biology · 2022Article
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Abstract
This paper addresses the problem of extinction in continuous models of population dynamics associated with small numbers of individuals. We begin with an extended discussion of extinction in the particular case of a stochastic logistic model, and how it relates to the corresponding continuous model. Two examples of 'small number dynamics' are then considered. The first is what Mollison calls the 'atto-fox' problem (in a model of fox rabies), referring to the problematic theoretical occurrence of a predicted rabid fox density of [Formula: see text] (atto-) per square kilometre. The second is how the production of large numbers of eggs by an individual can reliably lead to the eventual survival of a handful of adults, as it would seem that extinction then becomes a likely possibility. We describe the occurrence of the atto-fox problem in other contexts, such as the microbial 'yocto-cell' problem, and we suggest that the modelling resolution is to allow for the existence of a reservoir for the extinctively challenged individuals. This is functionally similar to the concept of a 'refuge' in predator-prey systems and represents a state for the individuals in which they are immune from destruction. For what I call the 'frogspawn' problem, where only a few individuals survive to adulthood from a large number of eggs, we provide a simple explanation based on a Holling type 3 response and elaborate it by means of a suitable nonlinear age-structured model.
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