Maximum Likelihood Estimation of Mixed Stock Fishery Composition

Abstract

In this paper the maximum likelihood method of estimating stock composition is initially presented under the assumption that all of the sampled characteristics are of discrete type (electrophoretic, meristic). The extension to allow continuous data (morphometric) is seen to follow from just a slight change in notation. It is shown that the classification method with error correction is a special case of the maximum likelihood method. Results from finite mixture theory are used to show that, in practice, the method is well defined and that the maximum likelihood estimates of composition are unique and can always be found using the EM (expectation–maximization) algorithm. A comprehensive discussion of the reliability of the estimates is undertaken. An explicit nonparametric (infinitesimal jackknife) estimator of estimate variability is presented. Procedures to reduce variance and bias are discussed. The composition of a test mixed stock fishery is estimated and many of the techniques proposed in the reliability discussion are used.