| Summary: | Exploited marine fish and invertebrate stocks fluctuate in a myriad of complex patterns, reflecting variability on interannual, decadal, and longer time-scales. The specific mechanisms producing such fluctuations generally remain unknown, but likely involve some complex interrelation of (1) the effect of harvesting on a stock-recruitment relationship, (2) inter- and intra-specific biotic interactions (predation, competition), and (3) environmental variability. In this dissertation, I describe patterns of variability observed in exploited fish and invertebrate stocks and explore the dynamics of single- and two-species population models incorporating the three general mechanisms mentioned above. Hierarchical cluster analysis was used to classify the abundance fluctuations of 30 stocks into six identifiable groups: steady state; low variation, low frequency; cyclic; irregular; high variation, high frequency; and spasmodic. Each of the six general patterns of variability can be produced from a simple multiple-equilibrium population model (referred to as the Steele and Henderson model) by varying the intrinsic rate of growth, and the time-scale and amplitude of environmental variability. Optimal harvesting policies were obtained for the Steele and Henderson model, and the model was fit to the Georges Bank haddock (Melanogrammus aeglefinus) data to evaluate various rebuilding strategies. In the presence of autocorrelated environmental variability, an optimal policy requires consideration of the current stock size and the effect of recent environmental conditions on stock productivity. The Steele and Henderson model provided plausible parameter estimates for the entire haddock data set (1931-1993), whereas the more traditional, single-equilibrium Schaefer model provided plausible parameter estimates only for the recent years of low productivity (1976-1993). The low production in recent years provides impetus for managers to consider a variety of plausible stock production models, and the uncertainty of production dynamics, in choosing rebuilding strategies. Finally, a two-species extension of Steele and Henderson's model was developed in which the predator is partially coupled to the prey. Predator abundance can increase when the modeled prey abundance is low, due to consumption of alternate prey, consistent with the pattern observed in the spiny dogfish (Squalus acanthias)-haddock abundances.
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