Can Economic Forces Cause Ecological Chaos? The Case of the Northern California Dungeness Crab Fishery

Unpredictable, deviation amplifying dynamics known as chaos emerge from simple models of biological populations as certain parameters reach critical values (May 1974). Although all ecological systems contain the necessary ingredients for chaotic dynamics positive feedback self-replication and inertia in their negative feedback (control) processes they rarely seem to exhibit chaotic behavior (Hassell et al. 1976, Thomas et al. 1980, Berryman and Millstein 1989, Turchin 1991, Berryman unpubl.). It is possible to precipitate chaos in natural populations, however, by increasing the reproductive rates of the organisms or the inertia of negative feedback processes (Berryman and Millstein 1989). Chaotic dynamics emerge from models of biological populations through a cascade of bifurcations; from stable fixed points, through periodic cycles of increasing amplitude and complexity, to aperiodic chaotic orbits (May 1974). Regular periodic cycles, therefore, can be considered as harbingers of chaos. Cyclical dynamics have been observed in catch records of Dungeness crab, Cancer magister, from the northern Californian fishery (Fig. 1). Several hypotheses have been proposed to explain these cycles, including external forces such as wind stress (Johnson et al. 1986), upwellings, sunspot activity, and water temperature, and internal feedback responses such as density-dependent egg and larval predation and cannibalism of young (reviewed by Hankin 1985). However, an alternative hypothesis is that the cycles were induced by the interaction of the crab population with the economics of the fishery. This hypothesis arose from a preliminary inductive or diagnostic examination of the crab harvest trajectory (Fig. 1). First observe that the partial autocorrelation function (Fig. 1, insert) has significant peaks at lags 1 and 2, suggesting that the system may be influenced by fast acting (lag 1) and delayed (lag 2) feedback. The effects of these two feedbacks can be discerned in the timetrajectory (Fig. 1), where we see; (1) a pattern of highfrequency, low-amplitude oscillation over the first 9 yr (1945-1953) and the 22nd to 26th yr (1966-1970), which seemed to fluctuate around a common mean of about 72x 105 kg (broken line K in Fig. 1), and (2) a pattern of low-frequency, high-amplitude oscillations, or cycles, over the 11th to 22nd (1955-1966) and 27th to 34th yr (1971-1978), which seemed to become more pronounced and to increase in amplitude with time. These patterns are even more obvious on the reproduction phase portrait (Fig. 2): Notice the tightly bounded oscillations around the equilibrium (R = 0) line near the