In his classic work, Pigs for the Ancestors, Roy Rappaport proposed that the ritual cycle of the Tsembaga was a mechanism to regulate human population growth and prevent the degradation of the Tsembaga ecosystem. Rappaport provided detailed ethnographic and ecological information to support his claim, but many aspects of Rappaport's model were subsequently criticised. Several simulation models of the Tsembaga ecosystem were constructed to test Rappaport's hypothesis and evaluate possible alternatives. The basic conclusions were that it was possible to develop models supporting Rappaport's hypothesis but they were extremely sensitive to parameter choices, and other simpler population control mechanisms might be more likely. In this paper, a much simpler dynamical system model for a slash-and-burn agricultural system is developed and applied to the Tsembaga system. By analysing the structure of the model for different physical and socioeconomic conditions, sources of instability and possible stabilising mechanisms are identified. The model indicates that behavioral plasticity (ability to modify behavior over a wide range of behavioral options, quickly and easily) is a fundamental source of instability which is strong enough to nullify more direct stabilising influences such as malnutrition and disease. This suggests that the only possible mechanism to counter to this fundamentally destabilising force may be cultural, i.e. the ritual cycle. Finally, a condition is outlined for which the ritual cycle will produce (local) stability.
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