Multiplicative modelling of catch-at-age data, and its application to catch forecasts

Abstract

A natural interpretation of fish catch-at-age data leads to an approximate multiplicative model with three factors: year, age, and year class. These factors are however, interrelated (year class = year - age) and estimates of the parameters of such a model are not unique. Specific solutions may be obtained by imposing biologically meaningful constraints on the parameters: for example, by specifying the trend in the year effect. The choice of error distribution and its parameters is also important in fitting such models. Examination of the sampling procedures used in data collection suggests a simple approximate formulation for the error variance of the log-transformed data. The model may be fitted by standard least-squares methods, or by a simpler calculation based on log-catch ratios. The model may be applied to any coherent set of catch-at-age data, representing the total international catch, that of a single fleet, or a research survey. The method is independent of VPA, but conceptually closely related to separable VPA. It may be used to estimate the steadystate age composition (i.e. a corrected catch curve), which is a required starting point for some assessment procedures, and also to estimate relative year-class strength for all year classes represented in the data, even those only present as older ages in early years. The fitted parameters may also be used as the basis of a simple forecast of catch-at-age for the data set to which it has been fitted.