Abstract
Grasshopper population dynamics are an important part of the North American rangeland ecosystem and an important factor in the economies that derive from the rangeland. Outbreak dynamics have plagued management strategies in the rangeland, and attempts to find simple, linear and mechanistic solutions to both understanding and predicting the dynamics have proved fruitless. These efforts to ground theory in a correspondence with the real world, including whether the population dynamics are ultimately density dependent or density independent, have generated abundant heat but little light. We suggest that a pragmatic approach, in which theories are taken to be rather than competing claims of truth, has greater promise to move ecological research in a constructive direction. Two recent non-linear approaches exploiting the tools of complexity science provide insights relevant to explaining and forecasting population dynamics. Observation and data collection were used to structure models derived from catastrophe theory and self-organized criticality. These models indicate that nonlinear processes are important in the dynamics of the outbreaks. And the conceptual structures of these approaches provide clear, albeit constrained or contingent, implications for pest managers. We show that, although these two frameworks, catastrophe theory and self-organized criticality, are very different, the frequency distributions of time series from both systems result in power law relationships. Further, we show that a simple lattice-based model, similar to SOC but structured on the biology of the grasshoppers gives a spatial time series similar to data over a 50- year span and the frequency distribution is also a power law relationship. This demonstration exemplifies how a both-and rather than an either-or approach to ecological modeling, in which the useful elements of particular theories or conceptual structures are extracted, may provide a way forward in addressing particularly difficult ecological problems.
Highlights
Understanding population ecology and making predictions about population dynamics would be sufficiently challenging based only on the complicating qualities that living entities bring to the problem, but an ecologist must taken into consideration the particularities of a given system
Grasshopper population dynamics are an important part of the North American rangeland ecosystem and an important factor in the economies that derive from the rangeland
The conceptual structures of these approaches provide clear, albeit constrained or contingent, implications for pest managers. These two frameworks, catastrophe theory and self-organized criticality, are very different, the frequency distributions of time series from both systems result in power law relationships
Summary
Understanding population ecology and making predictions about population dynamics would be sufficiently challenging based only on the complicating qualities that living entities bring to the problem (variation and history), but an ecologist must taken into consideration the particularities of a given system. The cusp catastrophe (Fig. 2), which is the stable manifold of a state variable that arises from two driving or control parameters (bimonthly temperature and precipitation in our model), yielded results that were qualitatively and quantitatively consistent with 28 years of grasshopper population dynamics in four ecoregions of Wyoming. We know the size structure (power law distribution) of rangeland grasshopper outbreaks, but we cannot predict the dynamics at a future time This model is valuable for pest managers (and the agencies that fund them) in understanding that the allocation of resources should reflect the underlying pattern of grasshopper population dynamics. Exogenous forces may drive the endogenous dynamics so that it is not the case of either/or but rather of both
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