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Partial derivatives of the negative exponential, monomolecular, Mitcherlich, Gompertz, logistic, Chapman-Richards, von Bertalanffy, Weibull and the Richard's nonlinear growth models are presented. The application of these partial derivatives in estimating the model parameters is illustrated. The parameters are estimated using the Marquardt iterative method of nonlinear regression relating top height to age of Norway spruce (Picea abies L.) from the Bowmont Norway Spruce Thinning Experiment. Formulas that provide good initial values of the parameters are specified. Clear definitions of the parameters of the nonlinear models in the context of the system being modelled are found to be critically important in the process of parameter estimation.

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Sablefish (Anoplopoma fimbria) supports substantial fisheries in both the eastern and western Pacific Oceans. Juvenile recruitment along the west coast of the continental United States has been highly variable over the past three decades. Using a generalized additive model, we demonstrate that physical oceanographic variables within the California Current System have significant effects on sablefish recruitment. Significant relationships were found between juvenile recruitment and northward Ekman transport, eastward Ekman transport, and sea level during key times and at key locations within the habitat of this species. The model explains nearly 70% of the variability in sablefish recruitment between the years 1974 and 2000. The predictive power of the model was demonstrated by refitting without the last 5 yr of data and subsequent prediction of those years. Bootstrap assessments of bias associated with parameter estimates and jackknife-after-bootstrap assessments of the influence of individual data on parameter estimates are presented and discussed. Using this model, it is possible to draw preliminary conclusions concerning yearclass strength of cohorts not yet available to the survey gear as well as historic year-class strengths. We discuss changes in zooplankton abundance and shifts in species of copepods associated with fluctuations in the physical variables that appear to have a major influence on sablefish recruitment.