A review is made of the literature on the back-calculation of fish body length from marks on scales or other hard parts (otoliths, vertebrae, fin rays, etc.). Though the technique is widely used it does not appear to be well understood. Regression methods are commonly used, apparently in ignorance of the more realistic proportional methods. It is not generally recognized that there are two equally plausible back-calculation hypotheses which can lead to significantly different back-calculated lengths. The Fraser-Lee equation, the most commonly used back-calculated formula, follows neither of these hypotheses but is based on a misuse of linear regression. It is recommended that back-calculation be restricted to procedures following one of the proportional hypotheses; that the difference between lengths calculated using the two hypotheses is a useful measure of the minimum uncertainty in back-calculation lengths; and that more attention be paid to validating back-calculation hypotheses by comparing observed and back-calculated lengths for individual fish. The pattern of heteroscedasticity in body length-scale radius plots is noted as a useful diagnostic in evaluating back-calculation hypothesis.

A maximum likelihood approach is described for the analysis of growth increment data derived from tagging experiments. As well as describing mean growth this approach allows the separate estimation of measurement error and growth variability, and uses mixture theory to provide an objective way of dealing with outliers. The method is illustrated using data for Pacific bonito (Sarda chiliensis) and the growth variability model is compared to other published models. The difference between growth curves derived from tagging and age-length data is emphasised and new parameters are given for the von Bertalanffy curve that have better statistical properties, and represent better the growth information in tagging data, than do the conventional parameters.

The two most common ways of estimating fish growth use age–length data and tagging data. It is shown that growth parameters estimated from these two types of data have different meanings and thus are not directly comparable. In particular, the von Bertalanffy parameter l∞ means asymptotic mean length at age for age–length data, and maximum length for tagging data, when estimated by conventional methods. New parameterizations are given for the von Bertalanffy equation which avoid this ambiguity and better represent the growth information in the two types of data. The comparison between growth estimates from these data sets is shown to be equivalent to comparing the mean growth rate of fish of a given age with that of fish of length equal to the mean length at that age. How much these growth rates may differ in real populations remains unresolved: estimates for two species of fish produced markedly different results, neither of which could be reproduced using growth models. Existing growth models are shown to be inadequate to answer this question.

``Risk'' has appeared more frequently in the fisheries management literature in recent years. The reasons for this are partly internal (scientists seeking better ways to advise fishery managers) and partly external (e.g., adoption of the precautionary approach). Though terminology varies, there is consensus that there are two stages in dealing with risk. The first (here called risk assessment) is the formulation of advice for fisheries managers in a way that conveys the possible consequences of uncertainty. This advice is in the form of an evaluation of the expected effects of alternative management options, rather than recommendations. Risk assessment has been undertaken in many fisheries, and there is general agreement as to how it should be done (although technical details differ). The second stage (risk management) is the way fishery managers take uncertainty into account in making decisions. Much fisheries risk management is informal, i.e., nonquantitative, undocumented, and loosely linked (if at all) with a risk assessment. The major reason for this is that the objectives of fisheries management are often conflicting and are rarely stated in a way that provides explicit direction to managers or scientists.

Risk analysis can enhance the value of scientific advice to fishery managers by expressing the uncertainty inherent in stock assessments in terms of biological risk. I present a case study involving an overexploited population of orange roughy (Hoplostethus atlanticus) on the Chatham Rise, New Zealand. This analysis quantifies the risk to the fishery and shows how this decreases as the rate of reduction in total allowble catch increases. The technique helps fishery managers balance biological risk against economic risk. Ways of generalizing the technique are discussed.