A PREDATOR-PREY SYSTEM WITH UNFORTUNATE PARAMETER VALUES

2.8 Easter Island as a Predator-Prey System

As reported in 1998 by Brander and Taylor, the understanding of Easter Island can be greatly advanced by using formal mathematical analysis. The formal description provided here relies on that analysis. One key point is that the Easter Island economy can be viewed as a ‘‘predator-prey’’ system. The forest resource can be considered as the prey and the Easter Islanders as the predators. One important aspect of even relatively simple predator-prey systems is that small to moderate changes in one or more key parameters can give rise to major qualitative changes in the dynamic pattern of population growth and decline. In particular, de­pending on parameter values, it is possible for a given model structure to give rise to smooth, or ‘‘mono­tonic,’’ movement toward a steady state or, alter­natively, to a boom-and-bust cycle. One possible behavior is long-run stability of the type apparently observed in Tahiti. Another possible behavior is the rise and fall that characterizes Easter Island. More broadly, it is quite possible that the same general model might describe a variety of Polynesian societies, with plausible variations in parameter values giving rise to the observed differences in demographic and economic experience.

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