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An assorted range of approaches have contributed to our understanding of the oscillatory behavior of population sizes in predation models. Among these are Mathematical Biology, Statistics and Artificial Life (ALife). In this paper, I will give a review of these different approaches. In addition, another approach, based on EvolutioHary Game Theory, is proposed and discussed. This paper also suggests that a complementary study of both the Mathematical, Artificial Life and Game Theory approach is needed to explain some of the mysticism surrounding the global emergent behavior of local predator-prey relationships.