Population coherence and environmental impacts across spatial scales: a case study of Chinook salmon

. A central problem in understanding how species respond to global change is in parsing the effects of local drivers of population dynamics from regional and global drivers that are shared among populations. Management and conservation efforts that typically focus on a particular population would benefit greatly from being able to separate the effects of environmental processes at local, regional, and global scales. One way of addressing this challenge is to integrate data across multiple populations and use multivariate time series approaches to estimate shared and independent components of dynamics among neighboring populations. Here, we use a data set of 15 populations of Chinook salmon ( Oncorhynchus tshawytscha ) covering a broad geographical range in the eastern North Pacific Ocean to show how Dynamic Factor Analysis (DFA) can be used to estimate temporal coherence in population dynamics and to detect environmental drivers across spatial scales. Our results show that productivity dynamics of Chinook salmon populations strongly covary at the regional scale, but to a lesser degree at larger spatial scales. The timing of river ice break- up in spring was identified as an important driver of regional produc tivity dynamics. In addition, broad- scale variability in population productivity was linked to the North Pacific Gyre Oscillation, a dominant pattern of sea surface height variability. These broad- scale patterns in productivity dynamics may be associated with recent regime shifts in the Northeast Pacific Ocean. Howev er, our results also demonstrate that populations within regions do not always respond consistently to the same environmental drivers, thus suggesting location- specific impacts. Overall, this study illustrates the use of DFA for quantifying the spatial and temporal complexity of multiple population responses to envi ronmental change, thereby providing insights to processes that affect populations across large geographic areas, but that might be filtered by local habitat conditions.

v www.esajournals.org OHLBERGER ET AL. dynamics from those occurring at regional and global scales.
Population-level responses to environmental variation are integrated over space and time because the conditions experienced by an organism change due to ontogenetic development and shifts in habitat use. Migratory organisms are particularly prone to these effects (Jenni andKery 2003, Runge et al. 2014). For instance, in anadromous fishes, eggs and juveniles experience freshwater conditions specific to their natal stream, whereas adults are exposed to large-scale climate conditions in the ocean (Quinn 2005). In addition, life history, habitat variation, and limitations to dispersal interact to create spatial structure within species and populations (Levin 1992). Multiple populations of the same species thus experience environmental conditions that may or may not be shared, and may therefore respond differently to environmental change (Hilborn et al. 2003). Inferring environmental impacts and coherence in population responses from multiple population time series thus poses the challenge of accounting for the complex spatial, temporal, and organizational dependencies associated with ecological data, particularly when addressing issues related to climate change, harvesting, or species conservation.
One way of addressing this challenge is to use multivariate methods that reduce the dimensionality of the data set under consideration to quantify dynamics that are shared among related time series. Although multivariate time series approaches have been widely used in finance for decades (Harvey 1989, Zuur et al. 2003a, their application to ecological time series is rare. Dynamic factor analysis (DFA) is a dimension reduction technique designed for multivariate time series analysis that has several advantages compared to ordination techniques such as Principal Component or Correspondence Analysis (Zuur et al. 2003a). DFA uses smooth trends, which are modeled as random walks and are shared among multiple observation time series, in order to detect spatial coherence between distinct populations or species. Furthermore, covariates can easily be incorporated into the analysis, which allows characterizing the link between the populations and environmental factors as well as trends that are shared among populations but are not linked to known covariates. Finally, this framework can handle time series that vary in length or contain missing values, a challenge that ecologists commonly face when analyzing data that have been collected intermittently or by different research groups or management bodies.
In this study, we analyzed a data set of 15 populations of Chinook salmon (Oncorhynchus tshawytscha) whose spawning locations span nearly one million square kilometers across Alaska (USA) and the Yukon Territory (Canada). Chinook salmon is a highly valued species of Pacific salmon, and is important to commercial, recreational and subsistence fisheries throughout the North Pacific (Heard et al. 2007). In Alaska, many of the geographically distinct populations have experienced declines in productivity over the most recent decade (ADFG 2012(ADFG , 2013, whereas other species of Pacific salmon in the region have not followed this trend (Ruggerone et al. 2010). In Western Alaska, recent declines in run abundance have resulted in closures of commercial fisheries and restrictions in subsistence harvests (JTC 2013, Schindler et al. 2013). This broad-scale pattern of declines in abundance suggests common causality, for example, due to large-scale climate variability. Here, we used DFA to characterize temporal and spatial patterns in the productivity of Chinook salmon populations across Alaskan rivers while controlling for impacts of freshwater and ocean conditions for which time series data exist. We subsequently examine the ability of the models to predict population productivity of Chinook salmon in these systems.

Time series data
Chinook salmon is an anadromous fish inhabiting the Subarctic North Pacific Ocean and adjacent freshwater habitats. Adults return to fresh water in summer and fall to breed in their natal streams and rivers; they die shortly after spawning. Their eggs incubate overwinter and juveniles emerge in spring. Most Alaskan populations have a "stream-type" life history and typically spend at least a full year feeding in freshwater before migrating out to sea where they remain for 1-6 yr before returning to spawn (Gilbert 1912, ADFG 2013. Chinook salmon are targeted by commercial, recreational and subsistence fisheries, and are caught as bycatch in other commercial fisheries (Stram and Ianelli 2014). We used estimates of spawning escapement and subsequent recruits (catch + escapement) for 15 Chinook salmon populations with ocean entry locations throughout Alaska (Fig. 1, Table 1), and calculated the natural logarithm of recruits per spawner as our index of population productivity (results when using residuals from a Ricker stock-recruitment fit as alternative productivity index are presented in Appendix S1). The escapement and recruitment estimates derive from recent run reconstruction models (see Fleischman et al. 2011Fleischman et al. , 2013, which were fit using a Bayesian state-space approach that simultaneously accounts for observation error and process noise. These models were fit as follows: (1) recruitment is multiplied by estimated age-at-maturity parameters to predict age-specific abundances, which are fit to age composition data from the catch and escapement, (2) exploitation rates are estimated (e.g., based on mark-recapture data) to predict total harvest, which is then fit to observed harvest data (based on fishery trip reports and postseason surveys), and (3) escapement is predicted based on harvest and total abundance and fit to in-river abundance indices from air surveys or direct weir/tower counts.

Environmental indicators
We used a variety of indicators for environmental conditions experienced by Chinook salmon during the freshwater, estuarine and marine phases of their life cycle. Variables were lagged to correspond to the time period relative to the brood year when the environmental conditions that these indicators reflect were hypothesized to affect Chinook salmon survival. By using fixed lags, we assume that the life history of the populations is characterized by a fixed age-structure and that most individuals smolt at age 1 (e.g., a covariate with a time lag of 2 yr is assumed to affect survival during the first year in the ocean). Because the model cannot handle missing data in the covariate time series (as opposed to missing data in the productivity time series data), we had to restrict our analysis to certain indicators, that is, we eliminated some of the indicators that may be hypothesized to affect Chinook salmon productivity but had incomplete data. Data sources and lags considered for each indicator are provided in Table 2.
Environmental conditions considered for the freshwater phase were river ice break-up dates in spring (ICE), which has been linked to smolt migration timing (e.g., sockeye salmon, Hartman et al. 1967), and summer air temperature (TEMP) as a proxy for river temperature, which is known to influence the growth and survival of Chinook salmon fry in fresh water (McCullough 1999, Crozier et al. 2010. A complete time series of ice break-up dates covering the entire study period was taken at Dawson on the upper Yukon River. This time series was used as a regional proxy for ice break-up dates in other rivers, which tend to be strongly correlated even over large distances (Jensen et al. 2007). For instance, ice break-up dates at Dawson and Bethel on the lower Kuskokwim River, which are about 1200 km apart, have a Pearson correlation of >0.7 (Bieniek et al. 2011). Regional time series of air temperature were taken at Faro, Yukon Territory (WAK), Anchorage (SCA), and Juneau (SEA). We used indicators for which long-term time series exist as our proxy for freshwater conditions across multiple populations. Covariates are treated the same across populations for which shared trends are estimated, but the effect sizes of the covariates are population-specific.
Our ocean climate conditions were sea surface temperature (SST, winter/spring), sea level pressure (SLP, winter/spring), and a strong winds index (SWI) in the Bering Sea. Ocean climate conditions may be especially important during the early marine phase of the salmon, that is, during their first year at sea (Beamish and Mahnken 2001, Wells et al. 2008, Scheuerell et al. 2009, Burke et al. 2013. Accordingly, SSTs for the three regions were calculated by averaging temperatures within the areas bounded by 57-64° N and 157-169° W for WAK, 56-61° N and 146-157° W for SCA, and 54-60° N and 130-140° W for SEA, which were chosen to represent thermal conditions close to the stocks ocean entry locations. We included several indices that characterize climatic conditions across large spatial scales in the North Pacific and may thus integrate fish population responses across a wide geographical range. We used annual and winter indices of the Pacific Decadal Oscillation (PDO), a dominant pattern of temperature variability that has been linked to variability in Pacific salmon abundance (Mantua and Hare 2002), and the North Pacific Gyre Oscillation (NPGO), a dominant pattern of sea surface height variability (Di Lorenzo et al. 2008). We also used the North Pacific Index (NPI) and the Arctic Oscillation (AO), which describe broad-scale patterns of sea level pressure variation.
We considered biotic indices of prey availability and competition, which also can be particularly important for salmon survival at sea (Beamish and Mahnken 2001). Specifically, we considered Kamchatka pink salmon (KAM) and walleye pollock biomass from the Bogoslof region in the Eastern Bering Sea (BOG). Older age-classes of Asian and North American salmon populations have overlapping distributions at sea and may compete for limited resources (Ruggerone et al. 2003), and Chinook salmon may prey upon or compete with walleye pollock (Davis et al. 2009). Finally, we used data on Russian Chinook catches (RUS) and the Bering Sea and Aleutian Islands (BSAI) Chinook bycatch, as these indices may reflect broad-scale changes in ecosystem dynamics that affect salmon survival. Changes in Russian catches may indicate similar or inverse production dynamics of western and eastern Chinook populations in the North Pacific Ocean, whereas Chinook bycatch could either reflect changes in productivity, or negatively affect productivity by decreasing ocean survival in these populations.

Data analysis
Dynamic Factor Analysis is a dimension reduction technique designed for multivariate time series analysis (Zuur et al. 2003a). The time series (y) are modeled as a linear combination of shared hidden trends (x), potential explanatory variables (d), and observation errors (v): Here, Z is a matrix of factor loadings on the hidden trends, and D is a matrix containing regression coefficients of the covariate effects. This formulation of the observation equation assumes that the time series have a mean of zero (otherwise a level parameter is required), and that the errors are normally distributed (MVN: multivariate normal) with mean zero and variance-covariance matrix R. The hidden trends (x) are modeled as random walk processes with a noise component (w): The process noise is assumed to be normally distributed with mean zero and variance-covariance matrix I, which is the identity matrix, that is, the hidden trends are assumed to have a variance of 1 and no covariance structure. These trends are the information shared by the response variables that are not explained by the covariates. The initial state vector is set to a mean of zero and a diagonal variance-covariance matrix (Λ) with large variances: Model parameters and states were estimated using the MARSS package (Holmes et al. 2012) in the programming environment R (R Development Core Team 2014).
We performed DFA analyses for Chinook salmon from the three regions: Western Alaska (6 populations), Southcentral Alaska (5 populations), and Southeast Alaska (4 populations). Populations within each region have ocean entry points in close geographic proximity (Fig. 1). In addition to the three regional models, we selected the most parsimonious model that included all 15 Alaskan Chinook salmon populations (indicators specific to the Bering Sea were not included). A maximum number of three shared trends was tested. We further allowed a maximum of three covariates in any single model to reduce the total number of models to be fit (i.e., we tested models without covariates and models with one, two, and three covariates). We tested the following error structures (R matrix): different variances and no covariance (diagonal and unequal), shared variance but no covariance (diago-nal and equal), or shared variance and covariance (equalvarcov) between stocks. For the statewide model, we also tested error structures with either shared variances and covariances by region, or shared variances but not covariances by region. Using the 1976-2005 brood years for our statewide and SCA analyses and the 1981-2005 brood years for our WAK and SEA analyses ensured that in any given year the model included data for at least three populations. However, we were able to include all data sets in the analysis, because the modeling approach smoothly handles missing data. We used standard model selection based on the AICc to identify the explanatory model that contained the lowest number of common trends without suffering from much information loss, included the most relevant explanatory variables, and used the most parsimonious form of the variance-covariance matrix. The model with the lowest AICc value was selected as the best model, and models with a ∆AICc of less than 2 were considered competitive models with similar support (Burnham and Anderson 2002). We subsequently performed a retrospective analysis to evaluate the ability of the selected model to accurately forecast Chinook salmon population productivity in each of the three regions. To accomplish this, we computed one-stepahead forecasts from the DFA model and used the predictions for each year to calculate an overall forecast error, which was defined as the square root of the mean squared prediction error (RMSE). Using this metric of predictive ability, we compared the selected models including covariates, that is, the model with the greatest support according to the AICc model selection, to (1) trend-only DFA models without covariates, (2) models that in any given year use the previous observation as predicted value, and (3) models that produce predictions by randomly drawing from a normal distribution with a mean and variance derived from the respective time series.

results
The statewide model with the greatest data support estimated two common trends in recruitment dynamics among the 15 Chinook populations (Fig. 2). The first trend was characterized by a period of above-average productivity around 1981-1992 and a moderate decline towards the end of the time series. A steep drop in productivity during the early 2000s dominated the second trend. Overall these trends combined to produce particularly low productivity during the most recent decade. The population loadings on these trends tended to be clustered by region: WAK populations showed mostly positive loadings on the first trend and SCA populations showed strong positive loadings on the second trend, whereas SEA populations were associated with both trends. The best model included the winter NPGO as a global environmental indicator of Chinook salmon productivity across Alaska that explained additional variation beyond the two trends described above. The NPGO in year 2, that is, 2 yr after the brood year, showed mostly positive and some negative associations with population productivity, and the effect was significant for some of the stocks (Fig. 3). In particular, Chinook salmon returning to the Kuskokwim, Yukon, Anchor, Stikine, and Taku rivers were all positively correlated with the NPGO. The best model included an error structure of variances and covariances that were identical within regions but different between regions. The second and third most parsimonious model included three common trends. However, all alternative models tested in the statewide analysis had a ∆AICc > 2 (Appendix S1: Table S1).
The regional models with the greatest data support had only a single common trend within each region (Fig. 4). Populations consistently showed positive loadings on the detected trends,  Shown are maximum likelihood estimates and 95% confidence intervals for the NPGO effect, which was the only indicator that was included into the most parsimonious model. CIs were calculated based on the hessian approach by re-fitting the DFA using the maximum likelihood estimates produced by the original model that allowed for an error structure of different variances and covariances by region.
v www.esajournals.org OHLBERGER ET AL. suggesting that population productivity followed similar temporal dynamics within regions. In line with the statewide model, these models suggest declining productivity towards the end of the time series, beginning with the 2000 brood year, approximately. Both the shared trends and selected indicators differed by region, suggesting less coherent dynamics among regions (Figs. 4 and 5).
Higher productivity in WAK populations was associated with earlier ice break-up in year 2, lower Russian Chinook catches in year 3, and a positive winter NPGO index in year 2. The SCA model included BSAI Chinook bycatch and BOG pollock biomass in year 2, and Russian Chinook catches in year 3, however, these indicators showed inconsistent associations with Chinook population productivity in the SCA region. Higher productivity of SEA populations was weakly associated with increased Russian Chinook catches in year 3, and showed weak associations to the timing of ice break-up in year 1. In the case of WAK and SEA several alternative models had a ∆AICc < 2, suggesting that other indicators such as the PDO are linked to population productivity in these regions (Appendix S1: Tables S2-S4). The observation error structure indicated that populations share the same variance by region and that models with or without a uniform covariance structure perform similarly well. Overall, model fits captured both the long-term trends and interannual variability in the data (Fig. 6, see also Appendix S1: Fig. S1).
Using a different regional clustering with the Nelson River population as part of a larger Western Alaska region produced slightly different results. This alternative DFA selected the same covariates for the most parsimonious WAK models, but instead estimated two shared trends, which suggested less coherent dynamics among WAK populations when Nelson was included in the region. The SCA model without Nelson estimated one shared trend and selected similar covariates (Appendix S1: Tables S5 and S6).
Compared to models without covariates, the selected regional models had higher predictive power when performing 1-yr ahead forecasts of population productivity. The covariate models Fig. 4. Trends and loadings of the regional models. Shown are common trends and population-specific loadings on these trends for each of the regions: WAK (top/blue), SCA (center/green), and SEA (bottom/purple).
had the lowest forecast errors, followed by trendonly models without covariates and models that used the previous observation as predicted value (Fig. 7). However, the relative performance of the different models varied by population and region. As expected, models using the previous observation as predicted value produced weak forecasts in populations with volatile productivity dynamics, but performed reasonably well in populations characterized by strong autocorrelation in the time series. Including covariates into the regional models reduced population-specific forecast errors by an average of 19% across all 15 populations. The strongest effect was found for Western Alaska populations with an average reduction in forecast error of 29% across populations.

dIscussIon
We found strong support for temporal synchrony in Chinook salmon productivity dynamics within regions and some support for synchronous dynamics at larger spatial scales across Alaska (i.e., among regions, Fig. 1). The regional models had only one common trend in each of the three regions (Fig. 4), and populations showed regional clustering in the statewide analysis (Fig. 2). The estimated trends demonstrate that productivity of Alaskan Chinook salmon has generally declined during the most recent decade, starting around 2000. Our results further suggest that the timing of river ice break-up (an indicator of regional spring warming) is a potentially important factor determining population productivity in Western Alaska, and that productivity dynamics of Chinook salmon across Alaska are linked to the NPGO index. However, the results also show that populations within regions do not respond consistently to the same environmental drivers, suggesting that environmental effects on recruitment are regulated at local scales. Our findings further indicate that broad-scale changes in Chinook salmon productivity may be linked to recent regime shifts in the North Pacific Ocean. The climate of the North Pacific experienced regime shifts in 1977 and 1989 (Hare and Mantua 2000). The statewide model trends show increased productivity to above-average levels shortly after 1977 and a decline shortly after 1989 (Fig. 2). Declines in productivity in Western Alaskan Chinook salmon appeared to be especially linked to the 1989 regime shift (Fig. 4).
The finding that Chinook salmon productivity dynamics covary at the regional scale is consistent with previous studies on other species of Pacific salmon showing that correlations in survival indices of pink (Oncorhynchus gorbuscha), chum (Oncorhynchus keta), and sockeye (Oncorhynchus nerka) salmon tend to be higher at smaller distances (Peterman et al. 1998, Pyper et al. 2001, Mueter et al. 2002, Sharma et al. 2013, Stachura et al. 2014. For instance, Peterman and Dorner (2012) showed that productivity of sockeye salmon from Washington to Southeast Alaska has declined markedly since the late 1990s, while productivity of central and western Alaskan populations has increased or varied only slightly over the same time period, suggesting different productivity dynamics between regions.
While our analysis identified regional covariability in Chinook salmon productivity, it Fig. 5. Covariate effects of the regional DFA models. Shown are maximum likelihood estimates and 95% confidence intervals for covariates included into the most parsimonious model for each region: WAK (left/blue), SCA (center/green), SEA (right/purple). The WAK and SCA models included three indicators, and the SEA model included two indicators (ICE, river ice break-up; NPGO, North Pacific Gyre Oscillation; RUS, Russian Chinook catches; BSAI, Bering Sea and Aleutian Islands Chinook bycatch; BOG, Bogoslof region pollock biomass). also indicated some degree of variation in the population-specific effects of environmental drivers. This is in line with recent studies that have demonstrated intraspecific variation in population responses to the same regional climate variables in Pacific salmon (Hilborn et al. 2003, Schindler et al. 2010, Braun et al. 2015. For instance, Braun et al. (2015) showed that ocean environmental conditions (e.g., offshore temperature) had contrasting effects on the survival of Chinook salmon populations in the Fraser River (Canada) that differed in life history. Population-specific responses may also reflect geographic variation in the relationship between broad-scale climate indices and local climate conditions, for instance, via differences in habitat characteristics (van de Pol et al. 2013).
The NPGO was associated with Chinook salmon productivity dynamics at large spatial scales (Fig. 3), indicating that the NPGO is more closely linked to variability in Chinook salmon dynamics than other broad-scale climate indices. The NPGO has previously been linked to the productivity of krill and higher trophic levels in the Northeast Pacific (Sydeman et al. 2013). Our results complement a recent study on hatcheryreared Chinook salmon indicating that the NPGO is an important driver of variability in Chinook salmon populations along the West Coast, from California to Southeast Alaska (Kilduff et al. 2015). Specifically, it was shown that variability in ocean conditions, as reflected by the NPGO, acts to synchronize survival rates of Chinook and coho salmon across a broad geographic range. At the regional scale, river ice break-up dates had significant effects on Chinook salmon productivity. Variability in river ice break-up dates reflects general changes in climate conditions and has been linked to larger climate indices such as the PDO (Schindler et al. 2005, Schindler andRogers 2009). Because stream-type Chinook spend one winter in freshwater, conditions such as river ice break-up that affect growth potential may affect survival during subsequent winters. Furthermore, ice break-up date may affect ocean survival through changes in the timing of smolt migration (Scheuerell et al. 2009, Satterthwaite et al. 2014). Thus, earlier ice break-up may affect productivity in Alaskan salmon populations through advanced outmigration of smolts or earlier warming of rivers leading to better growth conditions. Chinook populations at high latitudes may therefore benefit from changes in freshwater conditions due to a warming climate. In contrast, previous studies have suggested that Chinook salmon might be particularly vulnerable to future changes in ocean conditions due to climate change (Abdul-Aziz et al. 2011, Sharma et al. 2013. Forecast errors were used as a measure of predictive power to evaluate the degree to which environmental indicators could improve the models' ability to produce 1-yr-ahead projections of population productivity, as compared to random walk only and simple autoregressive models. Including the selected indicators generally improved the predictive ability of the models (Fig. 7). This was particularly evident for populations from Western Alaska. Consequently, obtaining information on environmental variables that are known to affect Chinook salmon at specific life stages, for instance, the timing of river ice break-up in the year that salmon smolts migrate to the ocean, can improve forecasts of population productivity.
The models presented here do not account for density dependence in the spawner-recruit relationship, because we used ln(R/S) time series as our index of population productivity. However, we also ran our analyses using the residuals of a Ricker stock-recruitment fit to account for density dependence effects. The results obtained using this alternative index of population productivity are largely in line with the findings reported for ln(R/S) time series (Appendix S1: Table S7, Figs. S2 and S3). The statewide model had the same number of trends, and included the NPGO index with sim ilar estimated effect sizes, though Shown are forecast errors for each population of the selected regional models including covariates (covar) in comparison with trend-only models (trend), models that in each year use the previous observation as predicted value (prev), and models that produce predictions by randomly drawing from a normal distribution with a mean and variance derived from the respective time series (rand). Circles and lines for the random forecast model represent median values and 95% confidence intervals based on 10,000 bootstraps. The selected covariate models tended to have the lowest forecast errors (square root of the mean squared prediction error) and thus the best predictive power.
v www.esajournals.org OHLBERGER ET AL. also included the BSAI Chinook bycatch as additional indicator (Appendix S1: Fig. S2). The regional models had either one or two trends and tended to select similar but fewer indicators in the top models (Appendix S1: Table S7, Fig. S3). The direction and strength of the covariate effects were mostly consistent ( Fig. 5 and Appendix S1: Fig. S3), for example, the strongest, most significant effects were found for river ice break-up in Western Alaska.
While the dominant life-history pattern across the study populations can be classified as "stream-type", that is, the majority of individuals spend a full year in freshwater habitats, it should be noted that the Situk river population in Southeast Alaska exhibits a distinct life history in that most individuals migrate to sea as sub-yearling smolts (McPherson et al. 2003). This may have limited our ability to identify important indicators of productivity dynamics in this region, because for this population indicators were tested for effects during the second (not first) year of marine life. Interestingly, the timing of river ice break-up in the first year was found to be significant for this population, which is in line with the expectation that ice break-up in the year of outmigration is an important driver of Chinook salmon productivity (Fig. 5). Another potential limitation of our approach is that the life history of the populations may have changed over time. Hence, changes in the proportion of the dominant age-class that migrates out to the ocean over the time period studied here cannot be ruled out.
Finally, other environmental drivers that were not included in this study may affect growth and survival of Chinook salmon, specifically trophic interactions that could not be accounted for due to a lack of long-term time series data. For instance, a potentially important factor is the prevalence of Ichthyophonus, a parasite that has recently increased in abundance and that may affect the spawning success of Alaskan Chinook salmon, such as has been hypothesized for the Yukon River population (Kocan et al. 2003).
In conclusion, our findings suggest that productivity dynamics of Chinook salmon populations strongly covary within regions and to some extend across large spatial scales. The estimated temporal trends further suggest that Chinook salmon productivity in Alaskan rivers has declined markedly in the early 2000s. Finally, this study illustrates the use of DFA for quantifying the spatial and temporal complexity of multiple population responses to changes in environmental conditions. This approach formally extracts trends that are common to populations but that are not explained by known covariates and therefore will provide insights to broad-scale processes that affect population dynamics across large regions.