A generalized stock production model

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Using an inverse-logistic model to describe growth increments of blacklip abalone (Haliotis rubra) in Tasmania

A new description of growth in blacklip abalone (Haliotis rubra) with the use of an inverse-logistic model is introduced. The inverse-logistic model avoids the disadvantageous assumptions of either rapid or slow growth for small and juvenile individuals implied by the von Bertalanffy and Gompertz growth models, respectively, and allows for indeterminate growth where necessary. An inverse-logistic model was used to estimate the expected mean growth increment for different black-lip abalone populations around southern Tasmania, Australia. Estimates of the time needed for abalone to grow from settlement until recruitment (at 138 mm shell length) into the fishery varied from eight to nine years. The variability of the residuals about the predicted mean growth increments was described with either a second inverse-logistic relationship (standard deviation vs. initial length) or by a power relationship (standard deviation vs. predicted growth increment). The inverse-logistic model can describe linear growth of small and juvenile abalone (as observed in Tasmania), as well as a spectrum of growth possibilities, from determinate to indeterminate growth (a spectrum that would lead to a spread of maximum lengths).

Food conversion efficiency and the von Bertalanffy growth function. Part II and conclusion: Extension of the new model to the generalized von Bertalanffy growth function

The simple model relating food conversion efficiency (K sub(1)) to body weight derived from the theoretical concepts behind von Bertalanffy's growth model, is extended here in the context of Pauly's generalization of that model. The exponent, which was fixed to 1/3 in the simple model, is in the extended model equivalent to 1-d, with d being the weight exponent of the anabolism term in Pauly's growth model. This makes the model applicable to fish for which the assumptions of the original (special) version of von Bertalanffy's growth model are violated.