To be Rare is to be Chaotic

Abstract

Rare species far outnumber common species. The demographic causes of rarity are thought to be first, a low carrying capacity and second, an effective community of associated predators, parasites, and/or competitors keeping the population well below its carrying capacity. To my knowledge these two conceptions encompass all proposed demographic explanations of rarity. It is the purpose of this note to suggest that a third possibility exists, that of chaos. Briefly, any population that can be modeled with a discrete formulation (e.g., populations with nonoverlapping generations) and which exhibits strong density-dependent feedback is likely to exhibit chaotic behavior over time (May 1975, 1976, Gukenheimer et al. 1977). Extremely chaotic behavior includes as a necessary attribute the existence of long periods of rarity followed by population flushes; the stronger the chaos, the longer the period of rarity (May 1975, Vandermeer 1982). Such an origin of rarity is quite different from a low carrying capacity or a depression of numbers resulting from pressure from predators or competitors. In practice, of course, its recognition could be quite difficult. The model of concern is,