Chaos For the Halibut?

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Abstract
A generalized method for analyzing stability potential in discretetime renewable resource models subject to market-driven harvest is discussed. Two means by which harvest activity can influence dynamical properties of renewable resource models are identified: the "growth factor" and the "market response effect". The growth factor is a systematic influence on stability tied to changes in the position of the bioeconomic equilibrium point along a given open access supply locus. The market response effect involves variation in harvest in response to stock level changes. The analysis is applied to a model of the Pacific Halibut Fishery; a modified discrete-time version of the traditional Schaefer model. In order to investigate potential instability, we vary certain parameters of the model and study the resulting effects on stability. We find that enhancing harvest response by changing the slope of the demand schedule can thrust the model into instability, chaos, and extinction, without changing the bioeconomic equilibrium point for the Pacific Halibut Fishery Model. We also show that enhancing harvest response via slopepreserving increases in market demand can push the model into instability, chaos, and even extinction. Finally, we show that similar adjustments in market demand may be capable of eliminating instability and chaos rooted in powerful intrinsic growth of the stock.

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