Estimation of size–transition matrices with and without molt probability for Alaska golden king crab using tag–recapture data

• Crab growth was modeled with and without the molt probability sub-model in the size transition model.
• The estimates of the size–transition matrices differed among approaches.
• Overall, the fit of the integrated model that included the molt probability sub-model was better than that did not include this sub-model.
• Key stock assessment outputs did not differ markedly between approaches for modeling growth.

Size-structured population dynamics models are used for stock assessments of hard to age invertebrate species, such as crabs, and size–transition matrices play an important role in modeling growth in those models. Crabs grow by molting and then incrementing in size. Therefore, the size–transition matrix should ideally contain sub-models for the probability of molt and the growth increment. Size–transition matrices were estimated in an integrated model setting, which included tagging data. Various models, including those that explicitly model molt probability and that include the molt implicitly in the size–transition model, were applied to data for golden king crab (Lithodes aequispinus) in the eastern Aleutian Islands region. Several diagnostic statistics (e.g., covariance matrix, likelihood, AIC, mean growth increment metric, sensitivity of estimates of mature male biomass, and the fits to the tag recapture, catch-per-unit effort, and length frequency data) were used to investigate the implications of the way growth was modeled. Overall, the fit of the integrated model that included the molt probability sub-model was better than that of the model that did not include this sub-model. However, the trends in key stock assessment outputs did not differ markedly between approaches for modeling growth even though the estimates of the size–transition matrices differed.