Estimation of Size-Specific Molting Probabilities in Adult Decapod Crustaceans Based on Postmolt Indicator Data

Abstract

For crustaceans that exhibit a well-defined molting season, postmolt indicator methods may be used to classify a sample of animals collected after the molting season into those that have molted and those that have failed to molt. This binary classification of a sample may be used to estimate size-specific molting probabilities. We derive maximum likelihood estimators for these molting probabilities, and for the variances of estimated molting probabilities, based on such postmolt indicator data. Estimators assume that the premolt–postmolt relation is linear with an additive and normally distributed error term of constant variance and, in their simplest form, assume that the ratio (Ri) of size-specific survival probabilities through the molting season for molting as compared with nonmolting individuals is known. For the more likely situation in which only a plausible range for Ri is specifiable, an estimation procedure is proposed which minimizes the maximum possible error (mean square error) of the molting probability estimator over this range. We illustrate application of estimators using shell condition data collected from the northern California population of adult female Dungeness crabs (Cancer magister). Estimated annual molting probabilities for adult female Dungeness crabs were greater than 0.90 for crabs less than 135 mm carapace width, but then declined rapidly until they were near zero for crabs exceeding 160 mm carapace width. This conclusion was not substantively affected by choices of a survival ratio ranging from 0.4 to 1.0.