A new method for estimating the morphometric size at maturity of crabs
Existing techniques for estimating the morphometric size at maturity of crabs are based on assumptions that may be unnecessary. Here we demonstrate a new method of detecting changes in relative growth (or allometric) relationships and estimating morphometric size at maturity. This method involves fitting several smoothing splines to relationships between body size and claw size, selecting the "best" spline, and finding this spline's maximum second derivative. The body size where the second derivative of the best spline is maximized estimates the morphometric size at maturity. Monte Carlo simulations suggest that uncertainty and bias in the estimate of morphometric size at maturity can be decreased by measuring a large number of crabs from a wide range of body sizes. Our spline method does not require a priori assumptions about the shape of the relative growth relationship; it can detect multiple changes in the relative growth rate; and it is robust to outliers. The modeling technique may also be used to identify regions of allometric change in other types of relationships. We demonstrate the new technique by estimating the morphometric size at sexual maturity for males of both brachyuran (Chionoecetes tanneri) and anomuran (Paralomis spinosissima and P. formosa) crabs.