James T. Thorson¹, Andrew O. Shelton¹, Eric J. Ward¹, and Hans Skaug<sup>2

1</sup>Northwest Fisheries Science Center and ²University of Bergen
October 14, 2014

Indices of abundance are the bedrock for stock assessments or empirical management procedures used to manage fishery catches for fish populations worldwide, and are generally obtained by processing catch-rate data. Recent research suggests that geostatistical models can explain a substantial portion of variability in catch rates via the location of samples (i.e., whether located in high- or low-density habitats), and thus use available catch-rate data more efficiently than conventional “design-based” or stratified estimators. However, the generality of this conclusion is currently unknown because geostatistical models are computationally challenging to simulation-test and have not previously been evaluated using multiple species. We develop a new maximum likelihood estimator for geostatistical index standardization, which uses recent improvements in estimation for random fields. We apply the model to data for 28 groundfish species off the U.S. West Coast and compare results to a previous “stratified” index standardization model, which accounts for spatial variation using post-stratification of available data. This demonstrates that the stratified model generates a relative index with 60% larger estimation intervals than the geostatistical model. We also apply both models to simulated data and demonstrate (1) that the geostatistical model has well-calibrated confidence intervals (they include the “true” value at approximately the nominal rate), (2) that neither model on average under- or overestimates changes in abundance, and (3) that the geostatistical model has on average 20% lower estimation errors than a stratified model. We therefore conclude that the geostatistical model uses survey data more efficiently than the stratified model, and therefore provides a more cost-efficient treatment for historical and ongoing fish sampling data.