The Effect of Parameter Uncertainties in an Age–Length Relationship upon Estimating the Age Composition of Catches

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Abstract
A simple, but frequently applied, procedure for decomposing fish length frequencies into age-classes is considered. This decomposition consists of converting fish lengths into ages using an age–length relationship. A method for assessing the effect of parameter uncertainties in this relationship upon estimates of the age composition of catches is presented. It is assumed that the parameter uncertainties can be described by probability distributions. Our aim is to determine probability distributions of age composition estimates resulting from these uncertainties. This is done using a stochastic sensitivity analysis technique involving Monte Carlo simulations and/or a first-order theory if such a theory is valid in the case under consideration. The method is illustrated by its application to data from the southern bluefin tuna (Thunnus maccoyii) fishery. It is found that simulated (Monte Carlo) catch estimates for age-classes 3 (fish at age 2–3 yr) to 13 (fish at age 12–13 yr) are normally distributed. The coefficients of variation of these estimates are less than 12%. Simulated catch estimates for age-classes 1, 2, and 14–20 deviate considerably from normality and their ranges bounded by the 2.5 and 97.5 percentiles are extremely wide; they include values different by up to 810% from the best deterministic catch estimates.Key words: catch, age composition, uncertainties, sensitivity analysis, Monte Carlo simulations, southern bluefin tuna

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