A hierarchical Bayesian approach for estimating freshwater mussel growth based on tag-recapture data

•We designed a mark-recapture survey for two example freshwater mussel species by using a passive integrated transponder technique.•We developed four models to investigate the existence of individual and sex variability in growth of freshwater mussels.•Female oyster mussel tended to have higher means of asymptotic length and growth rate than males.•The model incorporating individual variability provided the best fit to the mark recapture data for both example species. In fisheries stock assessment and management, the von Bertalanffy growth model is commonly used to describe individual growth of many species by fitting age-at-length data. However, it is difficult or impossible to determine accurate individual ages in some cases. Mark-recapture survey becomes an alternative choice to collect individual growth information. In mark-recapture studies, some tagged animals can be recaptured more than one time and ignorance of the autocorrelations for each individual may result in substantial biases in estimations of growth parameters. To investigate the existence of individual and sex variability in growth, we designed an experiment to collect mark-recapture data for one endangered freshwater mussel species (Epioblasma capsaeformis) and one common, non-imperiled species (Actinonaias pectorosa) by using a passive integrated transponder (PIT) technique. Models with individual and sex variability (M1), sex-related differences (M2), individual variability (M3) and nonhierarchy (M4) were developed to estimate growth of E. capsaeformis and A. pectorosa. Deviance information criterion (DIC) was used to measure the performance of these models. For E. capsaeformis, female mussels tended to have higher means of asymptotic length (44.96mm) and growth rate coefficient (0.283/year) than males (42.18mm and 0.213/year). The model M3 yielded the lowest DIC value for both species, indicating individual differences should be considered in parameter estimation. Thus, we suggest that a hierarchical approach be used to consider individual variability for modeling growth of mussels with mark-recapture data, especially when there is a high percentage of multiple recaptures.