A General Framework for Developing Sequential Fisheries Models

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Abstract
A sequential fisheries model relates observed data to the biological dynamics of an underlying stock. Either model component, dynamic or observational, can be subject to statistical variation. Current fisheries literature includes models with (1) variable dynamics and no observation error, (2) deterministic dynamics and observations subject to measurement error, and (3) combined dynamic and measurement variability. This paper presents a general framework for developing sequential fishery models and estimating model parameters from available data. The framework encompasses most traditional stock assessment models and suggests new, potentially useful extensions. It generalizes the conventional definition of state space model to include nonlinear equations with nonnormal error. The paper rigorously compares two paradigms (KF: Kalman filter, EV: errors in variables) used for parameter estimation. Each paradigm is formulated in both frequentist and Bayes contexts, where Bayes is shown to be most appropriate for the EV paradigm. Model design concepts are illustrated with a simple example oriented to catch data and a more complex example with catch-at-age data. Because the framework forces essential questions to be asked about underlying processes, observed data, and sources of variability, it can help delineate the limits of current knowledge and establish rational priorities for future data collection.

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