Measuring the impact of oceanographic indices on species distribution shifts: The spatially varying effect of cold-pool extent in the eastern Bering Sea

Oceanographers have spent decades developing annual indices that summarize physical conditions in marine ecosystems. Examples include the Pacific Decadal Oscillation, summarizing annual variation in the location of warm waters in the North Pacific, and cold-pool extent (CPE), summarizing the area with cold near-bottom waters in the eastern Bering Sea. However, these indices are rarely included in the species distribution models that are used to identify and forecast distribution shifts under future climate scenarios. I therefore review three interpretations of spatially varying coefficient models, explain how they can be used to estimate spatial patterns of population density associated with oceanographic indices, and add this option to the multivariate spatiotemporal model VAST. I then use a case study involving bottom trawl data for 17 fish and decapod species in the eastern Bering Sea 1982-2017 to answer: does a spatially varying coefficient model for CPE explain variation in spatial distribution for species in this region? And (2) does a spatially varying effect of CPE remain substantial even when local temperature is also included as a covariate? Results show that CPE and local bottom temperature are both identified as parsimonious by Akaike Information Criterion for 13 of 17 species, jointly explain nearly 9%-14% of spatiotemporal variation on average, and CPE does explain variation in excess of local temperature alone. I therefore conclude that spatially varying coefficient models are a useful way to assimilate oceanographic indices within species distribution models, and hypothesize that these will be useful to account for decadal-scale variability within multidecadal forecasts of distribution shift.