Modelling the otolith shape as an ellipse: An attempt for back-calculation purposes

Abstract

Back-calculation formulae (BCF) frequently used for deriving fish growth can only be applied when considering a predefined reference axis to measure growth rings and daily growth increments on otoliths. Many otoliths are difficult to interpret and it is often not possible to age fish along the predefined axis. A back-calculation model which avoids this constraint of standardization is presented. This method is based on the elliptical modelling of a quadrant of the otolith’s transverse section plane, using data recorded with an image analysis system. Considering the nucleus as the ellipse center, the two parameters “a” and “b”, the large and small axes of the ellipse, respectively, are estimated. When the longitudinal axis of the section and the otolith nucleus are taken as references, a point from the otolith edge or from one ring can be defined by its polar co-ordinates: α = angle between the interpreted axis and the longitudinal axis, r = distance from the nucleus to the intersection between the interpreted axis and the margin or a particular zone of reading (annulus or daily growth increments zone). We use these co-ordinates and replace a and b by their expression as a function of the fish length (L) in the ellipse analytical formulation. The BCF obtained is therefore of the type L = f(L, r, α), (f is a function describing the relationship between L, r, α) and affords, knowing that r and α characterize a ring, the recognition of Lf.α by successive iterations. © 1993 Conseil International pour l’Exploration de la Mer.