RAPID COMMUNICATION The determination of maturity stages in male elasmobranchs (Chondrichthyes) using a segmented regression of clasper length on total length

A novel statistical method for estimating the stages of maturity in male sharks and skates based on a segmented regression (SRM) is proposed. We hypothesize that this method is able to find the transition points in the three-phase relation- ship between total length (TL) and clasper length (CL). We applied an SRM to TL-CL data of nine species, from large pelagic sharks (e.g., Carcharhinus falciformis) to small coastal skates (e.g., Rioraja agassizi), captured in the southwestern Atlantic and northeastern Pacific. As expected, SRM detected two breakpoints, defining three maturity stages (immature, maturing, and mature), in six out of nine species. For three species, it was not possible to find two breakpoints because of incomplete sampling of TL. This novel method is noninvasive, it is applicable to previously collected data, is easy to use, and provides a reliable tool for increasing our understanding of elasmobranch reproductive strategies. Resume : Une nouvelle methode statistique pour estimer les stades de maturite des requins et raies mâles reposant sur une regression segmentee (SRM) est proposee. Nous postulons que cette methode permet de trouver les points de transition dans la relation atrois phases entre la longueur totale (TL) et la longueur du pterygopode (CL). Nous avons applique une SRM aux donnees de TL-CL de neuf especes allant de grands requins pelagiques (p. ex. Carcharhinus falciformis )ade petites raies cotieres (p. ex. Rioraja agassizi) captures dans le sud-ouest de l'Atlantique et le nord-est du Pacifique. Comme prevu, la SRM a fait ressortir deux points de rupture qui definissent trois stades de maturite (immature, en cours de maturation et mature) dans six des neuf especes. Pour trois especes, il n'a pas ete possible de trouver deux points de rupture en raison de l'echantillonnage incomplet de la TL. Cette nouvelle methode n'est pas invasive, peut s'appliquer ades donnees dejarecueillies, est d'utilisation facile et constitue un outil fiable permettant d'accroitre la comprehension des strategies de reproduction des elasmobranches. (Traduit par la Redaction) In this study, we propose and evaluate the use of a novel statis- tical method, based on a segmented regression model (SRM; Muggeo 2003), to estimate the breakpoints and slopes in the total length (TL)-CL relationship of male elasmobranchs. We hypothe- size that the TL-CL relationship presents three linear phases, with each step representing successive maturity stages that can be effectively modelled by SRM: (i) immature, (ii) maturing, and (iii) mature organisms. We evaluated the performance of the SRM in the estimation of maturity stages in the males of nine elasmo- branch species, including sharks (pelagic and demersal), guitar- fish, and skates. We discuss the applicability of the method by comparing our results with previous maturity estimates.