Pitfalls in stock discrimination by shape analysis of otolith contours

Abstract

Abstract This paper focuses on artefacts that may corrupt stock discrimination by shape analysis of otolith contours, how one can examine if such artefacts are important, and how they can be avoided. The scope focuses on Fourier transforms of contour points, the linear Fisher discrimination technique, and success rates based on cross validation by the “leave one out at a time” technique. The “zero-score” technique is introduced as a tool to examine the importance of a possible artefact, based on the theoretical result that the probability of correct classification of any otolith from either of two identical groups is zero. If one of the identical groups is exposed to a possible influential factor, e.g. a different smoothing, a high classification rate will reveal that this factor is an important artefact. The concept of a “lasso contour” is introduced that drastically reduces the impact of smoothing and provides a non-concave shape that enables a one-dimensional representation of the contour without ambiguities. Results are illustrated by comparison between Greenland halibut (Reinhardtius hippoglossoides) otolith contours from southern Greenland and Northeast Arctic waters. The conclusion is that the probability of correct classification of locality based on the original contours is too optimistic (77–79%), while the scores based on lasso contours are insensitive to smoothing and still optimistically high (68–70%).