There is no best method for constructing size-transition matrices for size-structured stock assessments

Stock assessment methods for many invertebrate stocks, including crab stocks in the Bering Sea of Alaska, rely on size-structured population dynamics models. A key component of these models is the size-transition matrix, which specifies the probability of growing from one size-class to another after a certain period of time. Size-transition matrices can be defined using three parameters, the growth rate (k), asymptotic size (L∞), and variability in the size increment. Most assessments use mark-recapture data to estimate these parameters and assume that all individuals follow the same growth curve, but this can lead to biased estimates of growth parameters. We compared three approaches: the traditional approach, the platoon method, and a numerical integration method that allows k, L∞, or both to vary among individuals, under a variety of scenarios using simulated data based on golden king crabs (Lithodes aequispinus) in the Aleutian Islands region of Alaska. No estimation method performed best for all scenarios. The number of size-classes in the size-transition matrix and how the data are generated heavily dictate performance. However, we recommend the numerical integration method that allows L∞ to vary among individuals and smaller size-class widths.