Defining indices of ecosystem variability using biological samples of fish communities: A generalization of empirical orthogonal functions

Multivariate data reduction techniques are widely used to describe modes of variability in atmospheric and oceanographic conditions for the world's oceans. Dominant modes of variability such as the Pacific Decadal Oscillation (PDO) are typically defined as a statistical summary of physical measurements, and include both principle components representing modes of variability over time, and an empirical orthogonal function (EOF) giving the spatial pattern associated with a positive or negative phase for each mode. Typically, these indices are compared with biological conditions to describe or predict physical drivers of ecological dynamics. In some circumstances, however, it may instead be useful to apply EOF analysis directly to biological measurements, estimating indices of biological variability as well as maps of biological response associated with each index. We therefore develop a generalization of EOF analysis that can be applied directly to multispecies biological samples using a multivariate spatio-temporal model. These biologically derived indices can then be compared with relevant indices derived from physical data, or used as covariates in spatially-varying coefficient models. We first show that a spatio-temporal model can replicate previous EOF estimates of the PDO and North Pacific Gyre Oscillation. We then identify three axes of variability in the eastern Bering Sea using biomass-sampling data for fourteen bottom-associated fishes and decapod crustaceans from 1982 to 2017. The first axis represents habitat preferences that are stable over time, and the second represents a multi-decadal trend in distribution for most species; for example, showing an increasing density for Alaska skate and arrowtooth flounder in the middle and inner domain. Finally, the third axis shows high interannual variability from 1982 to 1998 switching to multiyear stanzas from 1999 to 2017 and is highly correlated (0.87) with the extent of the cold bottom temperatures in this region and associated impacts on Alaska pollock and Pacific cod. These axes represent ecological dynamics for adult fishes and therefore integrate the impact of bottom-up and top-down processes, and they also confirm the importance of cold-pool extent for fish distribution in the Bering Sea while visualizing its varied impact on individual species. Moreover, this spatio-temporal approach allows oceanographers to define annual indices representing modes of variability in diverse biological communities from widely available field-sampling data.