Quantifying acoustic survey uncertainty using Bayesian hierarchical modeling with an application to assessing Mysis relicta population densities in Lake Ontario

A Bayesian hierarchical model was applied to acoustic backscattering data collected on Mysis relicta (opossum shrimp) populations in Lake Ontario in 2005 to estimate the combined uncertainty in mean density estimates as well as the individual contributions to that uncertainty from the various information sources involved in the calculation including calibration, target strength determination, threshold specification and survey sampling design. Traditional estimation approaches often only take into account the variability associated with the survey design, while assuming that all other intermediate parameter estimates used in the calculations are fixed and known. Unfortunately, unaccounted for variation in the steps leading up to the global density estimate may make significant contributions to the uncertainty of density estimates. While other studies have used sensitivity analyses to demonstrate the degree to which uncertainty in the various input parameters can influence estimates, including the uncertainty directly as demonstrated here using a Bayesian hierarchical approach allows for a more transparent representation of the true uncertainty and the mechanisms needed for its reduction. A Bayesian analysis of the mysid data examined here indicates that increasing the sample size of biological collections used in the target strength regression prove to be a more direct and practical way of reducing the overall variation in mean density estimates than similar steps employed to increase the number of transects surveyed. A doubling of target strength net tow samples resulted in a 23% reduction in variance relative to an 11% reduction that resulted from doubling the number of survey transects. This is an important difference as doubling the number of survey transects would add 5 days to the survey whereas doubling the number of net tows would add only one day. Although these results are specific to this particular data set, the method described is general.