Modeling spatiotemporal trends in the productivity of North Pacific Salmon


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Jiguo Cao, Department of Statistical and Actuarial Sciences, University of Western Ontario, Canada. E-mail:


Fisheries management of North Pacific salmon stocks greatly relies on the understanding of changes in spawning and survival over time and across habitats. Underlying the yearly observed number of surviving salmon is a productivity parameter that cannot be directly measured and, moreover, is masked by short-term changes in the observed population. We model the unobserved productivity of chum, sockeye, and two broodlines of pink salmon along the Pacific Coast of North America as a smoothly varying function of time and spatial location based on the Ricker spawner–recruit model of salmon reproduction. The candidate models belong to the class of Gaussian additive models and require the selection of smoothing parameters that control the trade-off between fit to the data and smoothness of the estimated functions. We select the smoothing parameters by optimizing the pseudo Bayes information criterion, which incorporates prior knowledge about the degree of smoothness of the estimated functions and is well suited for detecting low-frequency oscillations in the data, such as those due to long-term climate effects. Comparing the candidate models based on fit and model parsimony via the Akaike information criterion, we find that the productivity components of time and spatial location may be related nonlinearly. We find evidence of an increase in productivity in the mid-1970s for chum and sockeye populations and a north–south inverse relationship in productivity among sockeye and odd-year pink salmon stocks. Copyright © 2012 John Wiley & Sons, Ltd.