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Atto-Foxes and other minutiae

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dc.contributor.author Fowler, Andrew C.
dc.date.accessioned 2021-09-08T08:51:35Z
dc.date.available 2021-09-08T08:51:35Z
dc.date.issued 2021
dc.identifier.uri http://hdl.handle.net/10344/10549
dc.description peer-reviewed en_US
dc.description.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 10−18 (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. en_US
dc.language.iso eng en_US
dc.publisher Springer en_US
dc.relation.ispartofseries Bulletin of Mathematical Biology;83, 104
dc.subject Atto-foxes en_US
dc.subject Boom-and-bust en_US
dc.subject Extinction en_US
dc.title Atto-Foxes and other minutiae en_US
dc.type info:eu-repo/semantics/article en_US
dc.type.supercollection all_ul_research en_US
dc.type.supercollection ul_published_reviewed en_US
dc.identifier.doi 10.1007/s11538-021-00936-x
dc.contributor.sponsor SFI en_US
dc.relation.projectid SFI/13/IA/1923 en_US
dc.rights.accessrights info:eu-repo/semantics/openAccess en_US


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