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This work generalizes Matsumoto et al.'s dynamic model of population and renewable resources by substituting a distributed delay for the time delay. It is proved that the equilibrium point may lose or gain local stability, allowing for the observation of alternating stability/instability areas if some conditions hold. [ABSTRACT FROM AUTHOR]

In this paper we develop an invasive species differential equations model for the population collapse on Easter Island. This model, motivated by recent archaeological results of T. Hunt, allows us to examine the role of rats in the collapse. In Hunt's theory, the decline of resources was accelerated by Polynesian rats and not merely the result of the overuse by the island's human population. Hunt uses archaeological data which suggests a different timeline for the settlement and the long term population dynamics of Easter Island. Our goal is to estimate the plausibility of Hunt's hypothesis. [ABSTRACT FROM AUTHOR]