Empirical orthogonal function regression: Linking population biology to spatial varying environmental conditions using climate projections.

Ecologists and oceanographers inform population and ecosystem management by identifying the physical drivers of ecological dynamics. However, different research communities use different analytical tools where, for example, physical oceanographers often apply rank-reduction techniques (a.k.a. empirical orthogonal functions [EOF]) to identify indicators that represent dominant modes of physical variability, whereas population ecologists use dynamical models that incorporate physical indicators as covariates. Simultaneously modeling physical and biological processes would have several benefits, including improved communication across sub-fields; more efficient use of limited data; and the ability to compare importance of physical and biological drivers for population dynamics. Here, we develop a new statistical technique, EOF regression, which jointly models population-scale dynamics and spatially distributed physical dynamics. EOF regression is fitted using maximum-likelihood techniques and applies a generalized EOF analysis to environmental measurements, estimates one or more time series representing modes of environmental variability, and simultaneously estimates the association of this time series with biological measurements. By doing so, it identifies a spatial map of environmental conditions that are best correlated with annual variability in the biological process. We demonstrate this method using a linear (Ricker) model for early-life survival ("recruitment") of three groundfish species in the eastern Bering Sea from 1982 to 2016, combined with measurements and end-of-century projections for bottom and sea surface temperature. Results suggest that (a) we can forecast biological dynamics while applying delta-correction and statistical downscaling to calibrate measurements and projected physical variables, (b) physical drivers are statistically significant for Pacific cod and walleye pollock recruitment, (c) separately analyzing physical and biological variables fails to identify the significant association for walleye pollock, and (d) cod and pollock will likely have reduced recruitment given forecasted temperatures over future decades.