The Changing Physical and Ecological Meanings of North Pacific Ocean Climate Indices

The changing physical and ecological meanings of North Pacific Ocean climate indices

Michael A. Litzowa,1, Mary E. Hunsickerb, Nicholas A. Bondc, Brian J. Burked, Curry J. Cunninghame, Jennifer L. Gosselinf, Emily L. Nortonc, Eric J. Wardd, and Stephani G. Zadorg

aCollege of Fisheries and Ocean Sciences, University of Alaska Fairbanks, Kodiak, AK 99615; bNorthwest Fisheries Science Center, National Marine Fisheries Service, Newport, OR 97365; cJoint Institute for the Study of the Atmosphere and Ocean, University of Washington, Seattle, WA 98105; dNorthwest Fisheries Science Center, National Marine Fisheries Service, Seattle, WA 98112; eCollege of Fisheries and Ocean Sciences, University of Alaska Fairbanks, Juneau, AK 99801; fSchool of Aquatic and Fishery Sciences, University of Washington, Seattle, WA 98105; and gAlaska Fisheries Science Center, National Marine Fisheries Service, Seattle, WA 98115

Edited by Nils Chr. Stenseth, University of Oslo, Oslo, Norway, and approved February 19, 2020 (received for review December 4, 2019) Climate change is likely to change the relationships between (NPGO), have changed over multidecadal time scales. These commonly used climate indices and underlying patterns of climate indices are calculated as the first and second statistical modes variability, but this complexity is rarely considered in studies using (empirical orthogonal function [EOF] axes and corresponding climate indices. Here, we show that the physical and ecological principal component [PC] scores) for North Pacific Ocean sea conditions mapping onto the Pacific Decadal Oscillation (PDO) surface temperature anomaly (SSTa) and sea surface height index and North Pacific Gyre Oscillation (NPGO) index have anomaly fields, respectively (7, 8). The PDO and NPGO patterns changed over multidecadal timescales. These changes apparently are leading modes in global SST variability (9) and play an im- began around a 1988/1989 North Pacific climate shift that was portant role in modulating Pacific (10) and global (11) temper- marked by abrupt northeast Pacific warming, declining temporal ature anomalies. Both indices are defined with EOF/PC analysis variance in the Aleutian Low (a leading atmospheric driver of the for a fixed period of the observational record [1900 to 1993 for the PDO), and increasing correlation between the PDO and NPGO PDO (7), 1950 to 2004 for the NPGO (8)], and subsequent values patterns. Sea level pressure and surface temperature patterns of the index (the PC score) are calculated by “projecting” the associated with each climate index changed after 1988/1989, indi- initial EOF results onto subsequent observations (i.e., the obser-

cating that identical index values reflect different states of basin- ENVIRONMENTAL SCIENCES vations are multiplied by the EOF loadings to generate a new scale climate over time. The PDO and NPGO also show time- dependent skill as indices of regional northeast Pacific ecosystem index value). This commonly employed approach assumes a sta- variability. Since the late 1980s, both indices have become less tionary relationship between evolving patterns of ocean climate relevant to physical–ecological variability in regional ecosystems variability and the patterns identified by the original statistical from the Bering Sea to the southern California Current. Users of definitions. However, there are reasons to expect nonstationary these climate indices should be aware of nonstationary relation- relationships between the PDO and NPGO indices and underlying ships with underlying climate variability within the historical record, and the potential for further nonstationarity with ongoing Significance climate change. The PDO and NPGO indices are important tools for summariz- climate change | climate index | nonstationary relationship | North Pacific ing and understanding climate variability. As with other cli- Gyre Oscillation | Pacific Decadal Oscillation mate indices, the PDO and NPGO are assumed to have stable relationships with the climate variables they synthesize. We limate indices reduce complex patterns of internal climate found that a late-1980s North Pacific climate shift resulted in Cvariability into single variables (1). The most commonly used changing correlations between large-scale climate patterns and indices, such as the North Atlantic Oscillation and Multivariate the PDO and NPGO, and widespread weakening in relation- El Niño–Southern Oscillation indices, represent coupled atmo- ships between the PDO/NPGO and regional physical and ecosphere–ocean processes that are important drivers of climate logical processes. These findings suggest that understanding variability (2). By summarizing multiple correlated climate var- based on observed correlations with PDO/NPGO variability iables, these indices often explain a higher proportion of eco- may have limited utility when applied to different time pe- logical variance than do individual local climate variables (3). riods. Time dependence in correlations with these static cli- However, the future climate will likely be characterized by novel mate indices may accelerate in the future, as climate change patterns of covariance among physical variables (4), and this may is expected to further shuffle relationships among climate be particularly true for the internal modes of atmosphere–ocean variables. variability that are commonly tracked by climate indices (2). These changes imply that the sets of correlated variables map- Author contributions: M.A.L., M.E.H., N.A.B., B.J.B., C.J.C., J.L.G., E.L.N., E.J.W., and S.G.Z. designed research; M.A.L., M.E.H., N.A.B., B.J.B., C.J.C., J.L.G., E.L.N., and E.J.W. performed ping onto climate indices are likely to change over time, so that research; C.J.C. and E.J.W. contributed new reagents/analytic tools; M.A.L., M.E.H., N.A.B., the physical and ecological implications of an index value may be B.J.B., C.J.C., J.L.G., E.L.N., and E.J.W. analyzed data; M.A.L. wrote the paper; and M.E.H., nonstationary (time dependent). Climate indices have been foun- N.A.B., B.J.B., C.J.C., J.L.G., E.L.N., E.J.W., and S.G.Z. edited drafts. dational to our understanding of the role that climate variability The authors declare no competing interest. plays in physical, ecological, and social systems; nonstationary re- This article is a PNAS Direct Submission. lationships between indices and underlying conditions raise the Published under the PNAS license. possibility that this understanding may fail when deployed for out- Data deposition: Data and code for reproducing all results are publicly available on the of-sample prediction (1, 5). This potential for time dependence in changing-pdo-npgo repository (https://github.com/mikelitzow/changing-pdo-npgo; DOI: the physical and ecological meanings of climate indices is an un- 10.5281/zenodo.3635046). derappreciated potential consequence of climate change (5, 6). 1To whom correspondence may be addressed. Email: [email protected]. Here, we show how physical and ecological variables mapping This article contains supporting information online at https://www.pnas.org/lookup/suppl/ onto two leading Pacific Ocean climate indices, the Pacific De- doi:10.1073/pnas.1921266117/-/DCSupplemental. cadal Oscillation (PDO) and North Pacific Gyre Oscillation

www.pnas.org/cgi/doi/10.1073/pnas.1921266117 PNAS Latest Articles | 1of7 Downloaded by guest on September 30, 2021 physical and ecological conditions. Both indices track statistical Winter SST patterns that result from multiple physical processes. For instance, A the PDO is driven primarily by the Aleutian Low, teleconnections 0.9 from the tropics, and midlatitude ocean dynamics, with a range of individual driving processes within these larger categories (12). 0.6 Because the individual generative processes operate on different timescales, a one-to-one correspondence between the index value and conditions mapping onto the index is not expected over time 0.3 (12). Several lines of evidence, including increasing association between the NPGO and the first, rather than second, mode of 0.0

North Pacific climate (13, 14), and changing associations between Anomaly (ºC) the PDO/NPGO and ecological variability (14–19), suggest that this assumption of stationarity may be increasingly invalid. How- −0.3 ever, no comprehensive investigation of nonstationary relation- 1960 1980 2000 2020 ships with the PDO and NPGO has been conducted. We focus on changing relationships between the PDO/NPGO indices and regional physical and ecological conditions after a 1988/1989 climate B Aleutian Low variability shift in the North Pacific (13, 20). Examples of changing associations with the PDO/NPGO have been noted following this shift 550 (14, 15, 17, 18), which appeared to involve a transition to novel 500 patterns of extratropical atmospheric variability associated with the increased incidence of Central Pacific El Niño events (16, 21). 450 Results and Discussion 400 We begin our analysis by examining post-1988/1989 changes in basin-scale atmosphere–ocean processes reflected in the PDO 350 and NPGO indices (7, 8, 12). This 1988/1989 shift involves si- 300 multaneous climate change in the ocean (a ∼0.3 °C step increase

in mean winter SST; Fig. 1A) and atmosphere [a ∼33% decline (pa) Standard deviation in low-frequency temporal variability of the Aleutian Low (14); 1960 1980 2000 2020 Fig. 1B]. A trend of strengthening negative correlation between the PDO and NPGO indices also commences shortly after 1988/1989 (Fig. 1C). This decay in independence con- C PDO−NPGO correlation trasts with the orthogonal identity of the PDO and NPGO patterns under the EOF/PC methods used in their definition, 0.25 and suggests that distinguishing the causative role of the two patterns as agents of regional physical–ecological change is 0.00 increasingly problematic (22). These changes in the nature of basin-scale climate variability −0.25 motivate us to examine changes in atmospheric patterns related to PDO and NPGO variability after 1988/1989. While several atmospheric processes are involved in producing the PDO and −0.50 NPGO patterns (12), variability in sea level pressure (SLP) fields

produces wind stress that drives heat fluxes, wind mixing, and correlation Pearson's −0.75 Ekman transport, which are primary drivers of PDO/NPGO variability (7, 8, 12). Therefore, a common approach for identi- 1960 1980 2000 2020 fying atmospheric patterns that act as proximate drivers involves regressing SLP fields onto the index in question (7, 8, 12). This Fig. 1. Changes in North Pacific atmosphere and ocean climate after 1988/ 1989. (A) Increasing winter SST anomalies. (B) Decreasing temporal variance approach identifies changes in the atmospheric drivers of both (SD over 11-y rolling windows) in winter Aleutian Low SLPa values. (C) patterns after 1988/1989; the center of SLP variability associated Increasing correlation between PDO and NPGO indices (correlation over with the PDO shifts southeastward and intensifies (Fig. 2 A–C), 11-y or 132-mo rolling windows). The vertical dashed lines indicate 1988/ while SLP–NPGO regression coefficients decrease ∼70% (Fig. 2 1989; trend lines are best stepwise linear (A) or nonparametric (B and C) D–F). Changing relationships between SLP fields and the PDO/ regressions. NPGO indices imply changes in relationships with dependent wind stress fields that may change the ocean environmental variables that map onto the indices (14). This possibility is sup- area of positive temperature anomalies, shifted offshore in the ported by self-organizing map (SOM) analysis that identifies northern North Pacific into a more NPGO-like pattern (node 4), leading patterns of winter SSTa fields associated with the indices while negative PDO values are increasingly associated with di- over time (details in Methods). This analysis invokes six leading minished negative coastal anomalies, and a much larger area of SSTa patterns, or nodes (Fig. 3). These nodes have a time- positive anomalies in the central and western basin (node 5). dependent distribution (Fig. 4). Nodes 1 and 2 reflect the spa- Similar temporal changes are seen for the expression of the tial oscillation between coastal and central North Pacific tem- NPGO, especially the increasing association of positive (nega- perature anomalies associated with the PDO pattern, while node tive) index values with node 3 (node 4). An important result of 6 reflects the north–south dipole pattern of the NPGO. These this analysis is the very recent incidence of node 4, with four of three nodes invoking the canonical PDO/NPGO patterns occur the eight occurrences observed after 2014 (Fig. 4), suggesting predominantly prior to 1988/1989, and three other nodes (3–5) further changes to spatial patterns associated with the strong occur exclusively after 1988/1989 (Fig. 4). These results suggest PDO/NPGO values observed since the onset of persistent heat- that positive PDO values are increasingly associated with a larger wave conditions in the North Pacific (10, 23). This SOM analysis

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Fig. 2. Differences in atmospheric forcing of the PDO and NPGO indices before and after 1988/1989. Coefficients (Pa) for regression of SLP (November to January) onto PDO (February to April) index (A) 1950 to 1988, (B) 1989 to 2012, and (C) Difference in era coefficients (1989 to 2012) − (1950 to 1988). (D–F) The same regressions for the NPGO index.

is conducted with SSTa data that have not been detrended and of the relationship between each raw variable and the response so is able to capture the changing association between the PDO/ (PDO, NPGO) to differ between the two eras (before and after NPGO indices and SSTa fields as the North Pacific warms (24). 1988/1989). Changes in relationships were examined with the These results show that basin-scale atmosphere and surface ratio of the two slopes (slope after 1988/1989:slope before 1988/ ocean variability associated with the PDO and NPGO changed 1989; details in Methods). In this framework, a ratio near 1 in- after 1988/1989; we next ask whether similar nonstationary re- dicates a relationship with the PDO or NPGO that is nearly lationships are seen for regional-scale processes. While progress constant between eras. A negative ratio indicates that the sign of has been made in establishing mechanistic understanding of the relationship has changed (for example, a positive correlation statistical relationships between climate indices and regional becomes negative). The magnitude of the ratio can be used to – physical ecological variability (25), such mechanistic under- indicate whether the strength of the relationship has weak- standing is contingent on regional details and thus impractical to ened (values between −1 and 1) or become stronger (values less invoke for multiple systems. This consideration is particularly than −1or>1). relevant to the mechanistic understanding of linkages between These model results show evidence of widespread time- nonstationary basin-scale processes and nonstationary PDO/ dependent physical and ecological meanings of the two indices NPGO effects in regional ecosystems, which have to date been (Fig. 5 B–D). Regional physical (environmental) variables map- investigated only in the Gulf of Alaska (14, 17, 26). We therefore ping onto the PDO in the Bering Sea and Gulf of Alaska show take a statistical modeling approach to answer the question of declining associations after 1988/1989, while weaker evidence for whether PDO/NPGO effects have changed at a regional scale. changing PDO expression was observed in the California Cur- We use hierarchical Bayesian linear regression models to test the B hypothesis that the ability to predict large-scale patterns (the rent (Fig. 5 ). Physical variables mapping onto the NPGO show PDO and NPGO) based on observed values of regional physical consistent indications of weakening relationships since 1988/ and biological variables changed between the two eras, as in- 1989. Most estimated ratios for salmon population data show dicated by slopes of the relationships that changed either in di- weaker relationships with the PDO/NPGO after 1988/1989, with rection or magnitude (see Methods for details). This analysis uses some evidence of changing signs of relationships in the northern a set of long-term environmental and biological time series from California Current (Fig. 5C). Relationships with other biological the Bering Sea, Gulf of Alaska, and northern, central, and variables were also shifted toward zero (indicating weakening southern California Current ecosystems (Fig. 5A and details in SI relationships), with the degree of change between eras varying by Appendix, Tables S1–S3). Time series were aggregated into region (Fig. 5D). Thirty-seven of the 38 individual tests for groups representing environmental variables, salmon population changing relationships returned a median posterior less than 1, data, and nonsalmon biological data, and separate hierarchical suggesting that weakening PDO/NPGO relationships were nearly models were fit to data from each group. We allowed the slope ubiquitous after 1988/1989 (SI Appendix, Table S4).

Litzow et al. PNAS Latest Articles | 3of7 Downloaded by guest on September 30, 2021 Fig. 3. Dominant spatial patterns in winter (November to March) North Pacific SST anomalies, 1951 to 2018. Six leading patterns (nodes) from self-organizing map (SOM) analysis. (A and B) Nodes 1 and 2 are PDO-like patterns occurring primarily before 1988/1989, (C–E) nodes 3–5 occur only after 1988/1989, and (F) node 6 is a NPGO-like pattern occurring almost exclusively before 1988/1989.

The Gulf of Alaska results are consistent with a previously observational record, the complexity of multivariate physical and advanced hypothesis positing that declining variance in the ecological variability, and the inability to satisfactorily model Aleutian Low after 1988/1989 weakened atmosphere and ocean these complex interactions, mechanistic understanding of ecological circulation that had previously driven correlated variability in regional environmental processes. Absent a strong signal of shared variability among regional climate variables that had previously responded in unison to Aleutian Low variability, the PDO NPGO 2015 2001 shared statistical response to PDO variability was also lost, ap- 2 – – 20031987 parently resulting in PDO environment and PDO biology rela- 2 2002 tionships that weakened (shifted toward zero) (14, 17, 26). 1984 2016 2003 197719981988 1977 2000 2010 2017 1999 Similar mechanistic investigations are needed to better un- 1 19861994 19761961 198319701985 20131954 derstand nonstationary expression of PDO/NPGO variability in 1981 1 1978 1989 198219801993 19962004 1988 2008 2009 a 1951−1988 199219781960 2018200520101961 1998 20111953 other regions. We note that the strength of correlation between 200120141997 1960 201219641975 0 19591958 2006 the indices (Fig. 1C) has reached a level that will make in- 2007 1985 2004 a 1989−2013 1973 19871984 1955 19791968 1975 19701983 1990 196619631999 1990201319531955 0 198219711962 a 2014−2018 dependent interpretation of PDO or NPGO effects in this con- 19672002 19951989 1956 1954 1992197219741963 Index value Index 2008 2016 1965 201119691964 195919732017 20071951 text difficult (22). Until better mechanistic understanding is −1 1952 197919811968 1996 1957 19581965 20142015 19742000 1967 available, our results indicate the need to take care when making 1971 2009 1966 1991 1991201219511976 −1 1969 1962 198019571952 19972006 the assumption that the PDO and NPGO show stationary rela- 1972 1986 2005 tionships with physical and biological variability around the −2 1995

northeast Pacific over multidecadal timescales. These findings −2 1993 underscore the importance of distinguishing phenomena that are 1956 1994 2018 correlated with climate indices from those that are predicted by 123456 123456 climate indices; the former relationships are prone to non- Node stationarity, the latter less so (12). The importance of improved Fig. 4. Changing incidence of spatial patterns associated with the PDO and mechanistic understanding of correlative relationships with cli- NPGO indices. Years of occurrence for the six nodes from SOM analysis (Fig. 3) mate indices has long been recognized. However, given the short plotted against corresponding winter (November to March) PDO–NPGO values.

4of7 | www.pnas.org/cgi/doi/10.1073/pnas.1921266117 Litzow et al. Downloaded by guest on September 30, 2021 A B with novel patterns in SLP fields, leading to unusual Ekman transport, wind mixing, and heat fluxes (23). These same mecha- Bering Sea Wind direction (4) nisms are primary drivers of the PDO and NPGO patterns (7, 8, Ice cover (3), SST (2) 12), so these previously unobserved combinations of atmo- Groundfish (4) Salmon (18) spheric forcing and ocean responses suggest the potential for

Gulf of Alaska Northern California further nonstationarity in relationships between the PDO/ SLP, SST, SSH, Current Downwelling, SST (2), Bifurcation NPGO indices and underlying conditions, beyond the post-1988/ Wind stress, index, Upwelling (4), Freshwater Spring transition 1989 changes documented here. Groundfish (5), Salmon (25), Oysters Salmon (41) Forage fish (2), Central California Current Materials and Methods Crustaceans (3) SST (2), SSH (2), Upwelling (2), Seabirds (7) Basin-Scale Atmosphere and Ocean Patterns. Trends in winter SST (Fig. 1A) Environment Southern California Current were calculated from ERSSTv5 (46) data for the area 30° to 66°N, 150°E to Temperature, Oxygen, Salinity, Biology Ichthyoplankton (12) 110°W. We removed the monthly mean for the period 1951 to 1981 from each cell, and then calculated area-wide average winter (November to C D March) anomalies for each year. Temporal variation in the Aleutian Low (Fig. 1B) was calculated as the SD over 11-y rolling windows for November to March SLPa values (monthly mean removed) from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis (47) averaged over cells with centers at 45° to 55°N, 152.5° to 167.5°W. Regression of SLP data onto the PDO/NPGO indices (Fig. 2) used SLP data from the NCEP/NCAR reanalysis for the area 20° to 67.5°N, 132.5°E to 110°W. For each cell, SLP values were averaged over the period November to January and then regressed on February to April PDO/NPGO index values, matching the time lag of the Aleutian Low–PDO relationship (12)

SOM Modeling. SOMs are a type of neural network being increasingly employed for meteorological and oceanographic applications (48). Here, they are used to describe the shift that occurred in 1988/1989 in the char- Fig. 5. Changes in physical and ecological conditions mapping onto the acteristics of the winter mean patterns in North Pacific surface temperatures, PDO and NPGO indices. (A) Location of physical (environmental) and bi- and to determine how these patterns relate to the PDO and NPGO. The first ological time series used in analysis. Numbers in parentheses indicate the data layer consists of gridded mean surface temperatures during winters ENVIRONMENTAL SCIENCES number of individual time series in each group, spread over season, space, or (November to March) 1951 to 2018 (winter year corresponding to January) species. (B–D) Bayesian linear regression results for changes in relationships over the area 20° to 65°N, 120°E to 115°W. We used SST from the NCEP/ between regional variables and the PDO and NPGO indices after 1988/1989: NCAR Reanalysis, which itself is based on the product of Reynolds and Smith posterior distributions of the ratios of slope in era 2 (after 1988/1989) to (49). These temperatures have not been detrended. We posit that the use of slope in era 1 (before 1988/1989). Values between −1 and 1 indicate a slope “raw” data without detrending is appropriate in our examination of po- that has become weaker or smaller in magnitude after 1989, values <0in- tential shifts in physical conditions that are relevant to the ecosystem. The dicate a switch in the sign of the relationship between eras, and values less second and third data layers consisted of winter mean (November to March) than −1or>1 indicate a stronger association (greater slope) in era 2. Sep- values of the PDO and NPGO. The surface temperature data layer was arate models were fit to environmental variables (B), productivity for three weighted a factor of 1,000 times greater than the PDO and NPGO data salmon species (C), and other biology time series (D). The dots indicate layers, which made the sorting of the years completely dependent on the posterior medians, light (heavy) horizontal lines indicate 90% (50%) range surface temperature distributions. We constructed SOMs with a variety of of distributions, and vertical line indicates ratio of 1, or no change in slope configurations, and subjectively settled on a 3 × 2 matrix (6 patterns). Each between eras. pattern is not independent in that the learning procedure leads to an or- dered mapping of the input data, such that neighboring patterns (or nodes) are similar to one another and ones located far apart are more dissimilar. correlations with climate indices remains poor. As a result, the PDO We carried out multiple SOM runs with different seed values. These repli- and NPGO indices are commonly employed as covariates in cor- cates yielded similar if not identical groupings of years. relative studies that fit statistical models to estimate the effects of climate variability for fisheries management (25, 27, 28), hydrology Modeling Time-Varying Relationships. To model changing associations be- (29–31), agriculture (32–34), and economic planning (35, 36). Sta- tween climate indices (November to March PDO, NPGO) and individual tistical approaches commonly used in these correlative studies may predictor variables (environmental or biological), we used a hierarchical regression model that allowed for comparisons across regions, response produce era-dependent errors in inference when confronted with variables, and predictors. Because we are working with anomalies, the av- nonstationary relationships of the kind we document here (14, 26, erage of these winter PDO/NPGO time series across years is approximately 37, 38). Unfortunately, the vulnerability of correlative studies to zero. For all models evaluating time-dependent relationships with biological violations of the assumption that underlying processes are stationary time series, winter PDO/NPGO values were smoothed with 2-y running means in time is rarely evaluated (6). In addition, observed PDO/NPGO (values from the year before and year of interest) in order to account for relationships are often used to project relationships into the future lagged effects. For the predictor variables, we utilized data from five dif- (32–35), but nonstationarity in the physical and ecological variables ferent regions in the northeast Pacific Ocean (EBS, eastern Bering Sea; GOA, Gulf of Alaska; NCC, northern California Current; CCC, central California mapping onto the PDO/NPGO would dramatically reduce out-of- Current; SCC, southern California Current). From each region, we collated sample predictive skill for these uses (1, 5, 6). This problem of the data on environmental variables and biological variables that have been loss of predictive skill when relationships among physical covariates linked to climate indices, or used as ecosystem indicators themselves. To allow change has long been recognized in paleoecology (39) and global for comparisons within and across regions, each of the environmental and change ecology (40). In this context, we note that anthropogenic biological variables was standardized. Tables describing the variables and climate change is beginning to emerge from the envelope of natural mapping them to regions are provided in SI Appendix, Tables S1–S3. variability in many ecosystems globally and involves rates of change After standardization, predictor variables from each region were included – in a hierarchical linear model that allowed for relationships to change after that differ across different climate variables (41 43), implying a ^ = · ð · Þ 1988/1989. The general form of the model used is yt,i xt,i bi zt,i ri , where growing potential for changing relationships to climate indices with x denotes the value of the independent variable at time t for time series i, fixed statistical definitions. Recent extreme temperature anomalies t,i bi is the estimated coefficient for time series i, zt,i is an indicator designating over much of the northeast Pacific that have been attributed to whether the data point corresponds to the first or second era (0 if 1988 and anthropogenic radiative forcing (44, 45) have also been associated before, 1 if 1989 and after), and ri is the estimated ratio of the slopes in era 2

Litzow et al. PNAS Latest Articles | 5of7 Downloaded by guest on September 30, 2021 to era 1. For all models, we assumed the residuals were Gaussian, between salmon population productivity and climate indices (i.e., PDO and ∼ ð^ σ Þ yt,i N yt,i , resid , and did not include an intercept because the response NPGO) had changed before and after 1988/1989 with a multiplicative ef-

variables (PDO/NPGO anomalies) are centered on 0. Within the same region fect of era (rj): and response variable (PDO or NPGO), we allowed the slope for each pre- ∼ ðμ σ Þ δ = ≤ dictor variable to vary hierarchically so that bi N b, b , where each vari- i,t bi t 1988, μ σ δ = ≥ able is indexed by i, and b and b are hyperparameters describing the i,t bi rj t 1989. population of estimated slopes across variables. The ratio ri allowed the percent change in slope to be different by variable (i) but was also estimated Era effects were estimated separately for each region j, such that the ap- ∼ ðμ σ Þ − propriate region-specific parameter rj was correctly indexed to each stock i. hierarchically, ri N r , r . Values of ri greater than 1 and less than 1 indicate a slope that has become weaker or smaller in magnitude after 1989, Process errors in stock–recruitment relationships, «i,t, were assumed to be < « = ϕ « + e ϕ ri 0 indicates a switch in the direction of association with the predictor autocorrelated such that i,t i i,t−1 i,t, where i is the lag-1 correlation − > variable, and ri less than 1orri 1 indicates a stronger association (greater coefficient and ei,t are the uncorrelated errors which are normally distrib- slope) in era 2. 2 uted ei,t ∼ Nð0, σe Þ. Separate models for each of the indices (PDO and NPGO) We conducted estimation separately by region (EBS, GOA, NCC, CCC, SCC), were fit to data from each salmon species separately. Within species-specific response variable (PDO, NPGO), and variable type (environmental, biologi- models, Ricker α parameters were structured hierarchically such that cal). Estimation was performed in a Bayesian framework using R (50) and Stan i α ∼ ðμ σ2Þ μ σ2 (51). For each model, we ran three parallel Markov chain Monte Carlo chains i N α, α , where α and α are hyperparameters describing the mean and for 6,000 iterations, discarding the first 3,000 samples. The R-hat statistic was variance in stock-specific parameters. Prior probability distributions for 2 2 2 used to assess convergence, with a threshold of 1.05 or below (52). Posterior model parameters were mildly informative: μα ∼ Nð0, 5 Þ, σα ∼ Nð0, 5 Þ½0, , summaries (medians, quantiles) were then generated to allow comparison β ∼ ð 2Þ σ2 ∼ ð 2Þ ∼ ð 2Þ ∼ ð 2Þ ϕ^ ∼ ð 2Þ i N 0, 0.001 , e N 0, 1 , bi N 0, 1 , rj N 1, 1 , and i N 0, 2 , across variables and regions. where the model correlation coefficient was smoothly transformed onto the Time-varying models for salmon stock-recruitment dynamics were struc- ϕ^ ϕ^ scale −1asϕ = ð2e i =1 + e i Þ − 1. tured in a similar fashion to those for other biological time series (described i above), save for the addition of parameters representing density-dependent compensation and accounting for lag-1 autocorrelation in the residual error Data Availability. Data and code for reproducing all results are publicly structure. Models for salmon data were based around a linearized version of available on the changing-pdo-npgo repository (https://github.com/mikelitzow/ ð = Þ = α − β + δ + « the Ricker model (53), ln Ri,t Si,t i iSi,t i,t xt,i i,t, where Ri,t is the changing-pdo-npgo; DOI: 10.5281/zenodo.3635046). Data for reproducing – recruitment of stock i from the spawning abundance Si,t in brood year t, αi is Fig. 5 are also available in Datasets S1 S4. β the density-independent Ricker productivity parameter for stock i, i de- scribes the strength of density-dependent compensation or the rate at which ACKNOWLEDGMENTS. Funding was provided by the Fisheries and the population productivity declines with increasing stock size, and δi,t de- Environment Program, National Oceanic and Atmospheric Administration. scribes the effect of a covariate (xt,i)inyeart on stock i. Similar to the We thank L. Botsford and an anonymous reviewer for helpful feedback on model structure described above, we quantified whether the relationship the paper.

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