The simplest mathematical models of predator-prey interactions produce coupled oscillations that are highly unstable. However, by adding various elements of realism to these models it is possible to reveal the features of real predator-prey relationships that are likely to contribute to their stability. A further insight provided by models is that predator-prey systems may exist in more than one stable state. We have seen that a variety of patterns in the abundance of predators and prey, both in nature and in the laboratory, are consistent with the conclusions derived from models. Unfortunately, we are rarely in a position to apply specific explanations to particular sets of data, because the critical experiments and observations to test the models have rarely been made. Natural populations are affected not just by their predators or their prey, but also by many other environmental factors that serve to 'muddy the waters' when direct comparisons are made with simple models.
Moreover, the attention of both modelers and data gatherers (not that the two need be different) is increasingly being directed away from single- or two-species systems, towards those in which three species interact. For example, a pathogen attacking a predator that attacks a prey, or a parasitoid and a pathogen both attacking a prey/host. Interestingly, in several of these systems, unexpected dynamical properties emerge that are not just the expected blend of the component two-species interactions (Begon et al., 1996; Holt, 1997). We return to the problems of 'abundance' in a broader context in Chapter 14.
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