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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 \u2018small number dynamics\u2019 are then considered. The first is what Mollison calls the \u2018atto-fox\u2019 problem (in a model of fox rabies), referring to the problematic theoretical occurrence of a predicted rabid fox density of<jats:inline-formula><jats:alternatives><jats:tex-math>$$10^{-18}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mn>10<\/mml:mn><mml:mrow><mml:mo>-<\/mml:mo><mml:mn>18<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>(<jats:italic>atto<\/jats:italic>-) 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 \u2018yocto-cell\u2019 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 \u2018refuge\u2019 in predator\u2013prey systems and represents a state for the individuals in which they are immune from destruction. For what I call the \u2018frogspawn\u2019 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.<\/jats:p>","DOI":"10.1007\/s11538-021-00936-x","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T12:02:52Z","timestamp":1630411372000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Atto-Foxes and Other Minutiae"],"prefix":"10.1007","volume":"83","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2062-6372","authenticated-orcid":false,"given":"A. 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