Mapping the abundance of riverine fish populations: integrating hierarchical Bayesian models with a geographic information system (GIS)

A hierarchical Bayesian model is described for mapping the abundance of fish throughout a watershed from single- and multiple-pass removal sampling. A geographic information system (GIS) was used to generate a raster-based model of the river network, which provided three benefits for estimating fish density. Firstly, the horizontal resolution of the raster (50 m) provided an approximation to the statistical sampling frame and allowed correction for the finite number of potential sampling sites in a reach. Secondly, the modelled river network generated explanatory variables for every site in the network, facilitating the mapping of predicted densities and providing the basis for stratified or regression estimators for reach-specific densities. Finally, the spatial autocorrelation of fish densities was modelled in terms of the distance along the river network. A similar Bayesian model was also developed for the wetted width of the river network, and this was combined with the density model to provide estimates of the total stock size. The model was implemented using Markov chain Monte Carlo simulation in the statistical package WinBUGS. Application of the hierarchical model is illustrated with electrofishing data for age-1+ sea trout (Salmo trutta) in a small tributary of the River Conwy, Wales.