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Updated: Jun 11, 2026

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Published on: July 30, 2019
The May threshold and life-history allometry
Lev R Ginzburg1, Oskar Burger, John Damuth
1Department of Ecology and Evolution, Stony Brook University, NY 11794, USA.
Abstract:
One of Robert May's classic results was finding that population dynamics become chaotic when the average lifetime rate of reproduction exceeds a certain value. Populations whose reproductive rates exceed this May threshold probably become extinct. The May threshold in each case depends upon the shape of the density-dependence curve, which differs among models of population growth. However, species of different sizes and generation times that share a roughly similar density-dependence curve will also share a similar May threshold. Here, we argue that this fact predicts a striking allometric regularity among animal taxa: lifetime reproductive rate should be roughly independent of body size. Such independence has been observed in diverse taxa, but has usually been ascribed to a fortuitous combination of physiologically based life-history allometries. We suggest, instead, that the ecological elimination of unstable populations within groups that share a value of the May threshold is a likely cause of this allometry.
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