A Hypothesis Regarding the Abruptness of Density Dependence and the Growth Rate of Populations

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Abstract
Most population models incorporate density dependence in a manner that implies the effects of density set in at increasingly higher rates as population densities decrease to zero. For many populations, it may be more plausible to assume that the effects of density set in at a maximum rate around some characteristic density K > 0: that is, the per capita rate of increase of the population has an inverted sigmoidal form as a function of population density. In the model discussed here, the rate at which density dependence sets in around K is governed by a parameter γ, which I refer to as the "abruptness" parameter: the larger the parameter γ, the weaker the effects of density dependence are for population densities below K, the more rapidly density dependence sets in around K, and the more severe the effects of density dependence are beyond K. Results obtained from an Evolutionary Stable Strategy (ESS) analysis of the abruptness parameter γ suggest the hypothesis that populations with a density‐independent growth rate of <100% from one generation to the next (i.e., a reproductive value of 100%. Further, if true, this hypothesis suggests that females with high reproductive rates who deposit young on resources and provide no further maternal care should clump their young to reduce the level of abruptness in density dependence. Also, this hypothesis, together with the fact that high levels of abruptness promote oscillations in populations, implies that we are more likely to observe cyclic and chaotic behavior in relatively slower growing populations than previously thought.

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