title: The May threshold and life-history allometry.
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.
authors.affiliation: Department of Ecology and Evolution, Stony Brook University, NY 11794, USA.
authors.forename: Lev R
authors.initials: LR
authors.lastname: Ginzburg
authors.forename: Oskar
authors.initials: O
authors.lastname: Burger
authors.forename: John
authors.initials: J
authors.lastname: Damuth
mesh_terms: D000818:Animals; D049628:Body Size; D017753:Ecosystem; D005260:Female; D008136:Longevity; D008297:Male; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D012098:Reproduction