Integrated stock mixture analysis for continous and categorical data, with application to genetic–otolith combinations

Fish populations or stocks often intermix on fishing grounds, thus posing problems for stock assessors or managers attempting to optimize yields and minimize overexploitation of individual stocks. A Bayesian framework is developed here to simultaneously analyse many of the different data types (e.g., otolith elemental composition, nuclear and mitochondrial DNA) that have been used to identify stock origins of fish in mixed groups and thus take maximal advantage of the available information. Elements of this framework include the capability to analyse each data type either separately or in combination for any number of mixed-group samples, Bayesian credible intervals to evaluate the uncertainty associated with the estimated proportion of the original stocks in the mixed groups, and posterior predictive diagnostics to evaluate the assumptions of the underlying models. The framework was used to re-analyse a subset of otolith elemental composition and microsatellite allele frequency data obtained from the same fish from Atlantic cod ( Gadus morhua ) stocks in the Gulf of St. Lawrence, Canada.