Age at maturation predicted from routine scale measurements in Norwegian spring-spawning herring (Clupea harengus) using discriminant and neural network analyses

We evaluate two methods allowing the prediction of age at maturation from the widths of the annual growth layers in scales (or otoliths) in a case study on Norwegian springspawning herring. For this stock, scale measurements have been made routinely for many decades. We compare the performance in classifying age at maturation (at 3, 4, . . . , 9 years) between conventional discriminant analysis (DA) and the new methodology of artificial neural networks (NN) trained by back-propagation against a control of historical estimates of age at maturation obtained by visual examination of scales. Both methods show encouraging, and about equally high, classification success. The marginal differences in performance are in favour of DA, if the proportion of correctly classified cases is used as criterion (DA 68.0%, NN 66.6%), but in favour of NN if other criteria are used, including prediction error (error >1 year: DA 5.2%, NN 2.9%), and the average degree of underor overestimation (underestimation 1.1% of mean with DA; overestimation 0.2% of mean with NN). Evidence is provided that both methods approach the a priori limits to maximal classification success, limits set by overlapping combinations of predictor variables between maturation groups. The methods allow studies on age at maturation in this stock over a very long timespan, including periods well before, during, and after its collapse to commercial extinction. Similar techniques might well be applicable to any other fish stock with long-term data on scale or otolith growth layers.