The authors have declared that no competing interests exist.

Conceived and designed the experiments: MJM SPC. Performed the experiments: MJM. Analyzed the data: MJM. Contributed reagents/materials/analysis tools: MJM SPC. Wrote the paper: MJM SPC.

Sockeye salmon (

The influence of environmental change on fish population productivity is a central problem in fisheries science [

Detecting trends in fish stock productivity in a timely manner is difficult because short-term variability in recruitment and noisy abundance data usually combine to obscure changes in mean productivity of individual stocks [

For sockeye salmon, multi-stock analyses have indicated widespread declines in productivity over the past two decades for stocks ranging from Washington (WA) to Southeast Alaska [

In this study, we asked whether productivity of wild North American pink and chum salmon stocks has declined over the past two decades and if so what is the spatial extent of the declines. In particular, our objectives were (1) quantify temporal trends in productivity for pink and chum salmon stocks throughout their North American range to determine the magnitude and direction of recent temporal shifts, and (2) investigate the extent of spatial heterogeneity in productivity trends to better understand the mechanisms driving temporal trends. To accomplish these objectives, we first estimated stock productivity trends for each of 99 pink and chum salmon stocks using a modified stock-recruit model and Kalman filter fitting procedure. We then estimated common productivity trends across all stocks using dynamic factor analysis (DFA). Together, this two-step modeling approach allowed us to quantify and summarize temporal trends in pink and chum salmon productivity across local, regional, and continental scales.

We used wild spawner abundance and total recruitment (catch plus escapement) data for 53 chum salmon stocks (

The 14 geographical regions are separated by dotted lines and the number of pink salmon and chum salmon stocks within a region are given by the numbers inside the circles (pink salmon) and squares (chum salmon). Map data from

Out of the 53 chum salmon data sets, 36 did not have full age-structured data. Without age-structure information, total returns in a given year cannot be properly allocated to a particular brood year of spawners. Therefore, to estimate total recruitment, we used assumptions about the age-structure of returning adults. Following Pyper et al. [

We chose to assume all returns were age-4 when little age data were available based on four lines of evidence that suggested this was an appropriate assumption. First, the dominant age of returning adults across the 17 stocks with full age data was age-4 (62% of all returns), with most chum salmon returning as age-3 and age-4 for WA and BC stocks (93% of all returns) and most salmon returning as age-4 and age-5 for Alaska stocks (86% of all returns). Second, recruitment series reconstructed using an age-4 assumption are strongly and positively correlated with observed recruitment series. For example, the average correlation between recruitment estimates calculated from observed age data and estimates reconstructed assuming all returns were age-4 across each of the 17 stocks with known age data was 0.82 (

We used two methods to estimate stock-specific time series of productivity for the 99 pink and chum salmon stocks. The first set of productivity indices were the residuals from a stationary Ricker spawner-recruit model, whereas the second set were time-varying Ricker

We used residuals from a stationary Ricker spawner-recruit model as estimates of annual stock productivity, which removed potential within-stock density-dependent effects [_{t} is the number of spawners in brood year _{t} is the number of recruits resulting from _{t}, _{t} is the residual error assumed to be normally distributed with 0 mean and variance

We estimated time-varying Ricker _{t} is the number of recruits in brood year _{t} is the number of spawners, _{t} is the annual stock productivity at low spawner abundances, _{t} is the observation error assumed to be normally distributed with a mean 0 and variance _{t} parameter,
_{t} is the process error assumed to be normally distributed with mean 0 and variance

The Kalman filter model estimated annual values for the _{t} parameter using an iterative Bayesian updating procedure whereby the prior value for _{t} (i.e., _{t−1}) was updated based on how well _{t−1} predicted the following year’s _{e}(_{t}/_{t}) [_{t} value only depended on data up through year _{t} parameters. Unlike the Kalman filter procedure, which estimated the earliest _{t} value first and moved forward through time, the smoothing procedure worked backwards starting with the most recent filtered _{t} value [_{t} value, the smoother calculated a weighted average between the estimate of the filtered value at time _{t} that were based on the whole time series, rather than only the previously estimated values. This smoothed time series of _{t}, standardized to a mean of 0 and a standard deviation of 1, was used as our second stock-specific productivity index.

The other parameters of the Kalman filter model, (i.e.,

To further characterize the Kalman filter models, we also calculated the signal-to-noise ratio (

To more clearly identify shared trends in productivity, we used DFA models, which are a class of multivariate autoregressive state-space models, to estimate common productivity trends across all stocks within a species. Dynamic factor analysis aims to estimate a specific number of common trends (_{t} is the vector of observed data at time _{t} is an _{t} is the observation error term assumed to be normally distributed with mean 0 and variance-covariance matrix _{t} is the process error also assumed to be normally distributed with mean 0 and variance-covariance matrix

We fit a total of 24 DFA models for each species using different combinations of trends and observation error variance-covariance matrices. All DFA models were fit using the residuals from the stationary Ricker models, rather than the Kalman filter productivity indices, because the DFA model already includes a Kalman filtering procedure. All productivity series were truncated to the period after 1979 because many stocks had considerable missing data or no data prior to 1980 (e.g., most stocks in BC). We fit models with 1–6 common trends and four different observation error variance-covariance matrices (i.e.,

We used the small-sample Akaike Information Criterion (AIC_{C}) as a model selection criterion [_{C} values were evaluated based on four criteria: (1) the most parsimonious model was defined as the model with the lowest AIC_{C} value, (2) equally plausible models were defined as models with AIC_{C} values within 3 AIC_{C} units of the lowest, (3) less plausible models had AIC_{C} values greater than 3 from the minimum and were rejected with caution, and (4) models with AIC_{C} values greater than 10 compared to the minimum were rejected with confidence [

We quantified spatial covariation in productivity series within and across geographic regions by calculating Pearson correlation coefficients for each unique pair of salmon stocks within a species. We estimated between-stock covariation using both the residual and Kalman filter _{t} productivity indices and only computed correlation coefficients between two stocks if the stocks had at least 10 years of overlap. Because previous research has indicated that the strength of spatial synchrony in productivity may change over time [

We initially assumed that because even and odd year pink salmon runs occupy the same physical habitat in alternate years that even and odd year runs could be treated as a single entity. However, pink salmon have a fixed 2-year life cycle where even and odd year brood lines are reproductively isolated. To check the sensitivity of our results to our assumption that even and odd year brood lines could be combined, we repeated the Kalman filter, DFA, and covariation analyses separately for even and odd year pink salmon brood lines.

Time series of the Kalman filter reconstructed _{t} values indicated widespread declines in chum salmon productivity since at least brood year 2000 (_{t} series showing recent declines in productivity. Among the stocks with recent declines in productivity, two qualitative trends were observed. The first trend, exemplified by stocks in the Outside WA and Northern BC regions, was characterized by gradual, but consistent declines in productivity since the mid 1980s (

Each time series shows the smoothed _{t} estimates from the Kalman filter model where each series is standardized to a mean of 0 and standard deviation of 1. The ordinate gives the stock, which are arranged south (bottom) to north (top) and grouped by geographic region. The area of the circle indicates the magnitude of the productivity values. Open circles represent negative values (red) and filled circles indicate positive values (blue). Small solid grey dots indicate zero values, whereas missing values are not shown.

For pink salmon, the Kalman filter _{t} series indicated a general pattern of declining productivity for WA and BC stocks and a more variable pattern for AK stocks (_{t} series showed declining or below average productivity values since at least brood year 1990 (_{t} series, 64% had increasing or above average productivity in recent years. However, only the Southeast Alaska and AK Peninsula regions had stocks that showed consistent increasing productivity trends in recent years with all five stocks with non-constant _{t} values having above average productivity since at least brood year 1990 (

Each time series shows the smoothed _{t} estimates from the Kalman filter model where each series is standardized to a mean of 0 and standard deviation of 1. The ordinate gives the stock, which are arranged south (bottom) to north (top) and grouped by geographic region. The area of the circle indicates the magnitude of the productivity values. Open circles represent negative values (red) and filled circles indicate positive values (blue). Small solid grey dots indicate zero values, whereas missing values are not shown.

The Kalman filter _{t} series for pink salmon had many more constant series (57% of pink salmon stocks) compared to chum salmon (23% of stocks; Figs

Region | Chum | Pink |
---|---|---|

Outside WA | 0.005 | - |

Inside WA | 0.046 | 0.008 |

Southern BC | 0.014 | 0.000 |

Central BC | 1.566 | 0.010 |

Northern BC | 0.188 | 0.012 |

Southeast Alaska | 0.389 | 0.068 |

Yakutat | 0.000 | 0.017 |

Prince William Sound | >10 | 0.000 |

Cook Inlet | 0.160 | 0.013 |

Kodiak | 0.032 | 0.003 |

Chignik | 0.117 | 0.034 |

Alaska Peninsula | 0.589 | 0.041 |

Bristol Bay | 0.331 | 0.015 |

AYK^{a} |
0.573 | 0.000 |

^{a} Arctic Yukon Kuskokwim.

The residual productivity series had considerably more short-term high-frequency variability than the reconstructed Kalman filter _{t} series, making patterns harder to discern (_{t} series were also observed in the residual series. For chum salmon, the residual series also indicated widespread declines in productivity for WA and BC chum salmon stock, although the recent trends tended to be more similar to those of the Northern BC _{t} series with steep declines in productivity since brood year 2000 (_{t} estimates (

For chum salmon, there was strong support from the data for a DFA model with two common trends and the north-south variance-covariance matrix (

(a) The first (solid line) and second (dashed line) common productivity trends and (b) stock specific loadings for the first (solid horizontal bars) and second (dashed horizontal bars) common trends. In the bottom panel, stocks are ordered south (bottom) to north (top) and are grouped by geographic region.

Species | N | Parameters | Trends | Var-covar | Log-likelihood | AICc | |
---|---|---|---|---|---|---|---|

Chum | 1213 | 98 | 2 | north-south | -1508.8 | 3230.9 | 0.0 |

1213 | 52 | 1 | north-south | -1563.8 | 3236.3 | 5.3 | |

1213 | 95 | 2 | equal-var-covar | -1519.2 | 3244.7 | 13.7 | |

Pink | 1075 | 47 | 1 | north-south | -1392.4 | 2883.3 | 0.0 |

1075 | 88 | 2 | north-south | -1365.6 | 2923.2 | 39.9 | |

1075 | 44 | 1 | equal-var-covar | -1418.3 | 2928.4 | 45.2 |

N gives the number of data points included in the model; Parameters gives the total number of parameters in the model; Trends gives the number of trends the model was fit with; Var-covar gives the variance-covariance matrix structure used to fit the model where north-south indicates variances and covariances were equal across stocks but were allow to differ between northern (i.e., AK) and southern (i.e., WA and BC) stocks and equal-var-covar indicates variances and covariances were equal for all stocks.

The pink salmon DFA model with the lowest AIC_{C} value included a single common trend and the north-south variance-covariance matrix (

(a) the single pink salmon common trend and (b) the stock specific loadings for the single common trend. In the bottom panel, stocks are ordered south (bottom) to north (top) and are grouped by geographic region.

Productivity indices for both chum and pink salmon stocks within a region were, on average, strongly and positively correlated (

(a) between-stock correlation coefficients calculated using all available brood years, (b) correlations for brood years 1950–1990, and (c) correlations for brood years 1991–2007. The magnitude of the between-stock correlation is given by the area of the circle with larger circles representing larger correlations than smaller circles. Negative correlations between stocks are shown as open circles (red) and positive correlations are shown as filled circles (blue). Stocks are grouped by geographic region, which are arranged south (bottom, left) to north (top, right).

(a) between-stock correlation coefficients calculated using all available brood years, (b) correlations for brood years 1950–1990, and (c) correlations for brood years 1991–2009. The magnitude of the between-stock correlation is given by the area of the circle with larger circles representing larger correlations than smaller circles. Negative correlations between stocks are shown as open circles (red) and positive correlations are shown as filled circles (blue). Stocks are grouped by geographic region, which are arranged south (bottom, left) to north (top, right).

Ricker | Kalman | |||
---|---|---|---|---|

Region | Chum | Pink | Chum | Pink |

Outside WA | 0.96 | - | 0.99 | - |

Inside WA | 0.58 | 0.68 | 0.43 | 0.81 |

Southern BC | 0.87 | 0.63 | 0.74 | 0.36 |

Central BC | 0.79 | 0.64 | 0.81 | 0.90 |

Northern BC | 0.47 | 0.50 | 0.65 | 0.69 |

Cook Inlet | 0.62 | 0.68 | 0.68 | 0.53 |

Kodiak | 0.46 | 0.62 | 0.46 | 0.44 |

Chignik | 0.59 | 0.66 | 0.36 | 0.40 |

Alaska Peninsula | 0.64 | 0.80 | 0.68 | 0.91 |

Bristol Bay | 0.74 | - | 0.81 | - |

AYK^{a} |
0.57 | 0.77 | 0.46 | 0.49 |

Average correlations are shown for both the Ricker residual and Kalman filter _{t} productivity series for each geographic region. Average correlations were only calculated if at least two stocks had sufficient data within a region, therefore, some regions (e.g., Prince William Sound, Southeast Alaska, and Yakutat) are not shown or have no values.

^{a} Arctic Yukon Kuskokwim.

Covariation patterns for the Kalman filter _{t} productivity indices were similar to those of the residual series including (1) positive covariation between stocks within a region, (2) positive covariation between stocks in different regions in WA and BC, although this pattern was not as strong for chum salmon _{t} series, and (3) weak covariation between stocks that enter the ocean at distant locations (

Our results were not sensitive to our assumption that even and odd year pink salmon brood lines could be treated as a single entity. In particular, Kalman filter _{t} series for stocks with even and odd year runs tended to show similar trends (_{t} series showed recent declines in productivity, similar to the trends observed when odd and even years brood lines were combined (_{C} values included a single common trend and the north-south variance-covariance matrix, which corresponds to the DFA model selection results for the combined pink salmon analysis. The common trends for even and odd year brood lines showed similar patterns to the combined DFA analysis with no evidence for strong declines in productivity in recent years (

Our results provide evidence that productivity of wild chum salmon stocks, and to a lesser extent wild pink salmon stocks, has declined over the past two decades throughout WA and BC. Specifically, (1) productivity for the majority of chum salmon stocks in WA and BC has declined over the past two decades, although the functional form of declines varied across regions with Central BC stocks showing an abrupt and steep decline in productivity starting around brood year 2000 and stocks in the Outside WA and Northern BC regions showing a more gradual declining trend, (2) trends in productivity for AK pink and chum salmon stocks were more variable with some regions and stocks showing declines in productivity and others showing increases, (3) there was strong positive covariation of productivity series within regions, and (4) covariation between productivity series for stocks in WA and BC has become stronger in recent years for both pink and chum salmon. In general, our results suggest that productivity of pink and chum salmon stocks is driven by common processes operating at the regional or multi-regional spatial scale, and the effects of these drivers may not be constant through time.

Evidence for widespread declines in productivity was stronger for chum salmon than for pink salmon. With the exception of the Kalman filter results for Inside WA chum salmon stocks, both the DFA and Kalman filter analyses indicated that chum salmon stocks throughout WA and BC have experienced declines in productivity over the past two decades. In contrast, the Kalman filter analysis for pink salmon indicated that the low frequency signal (i.e., trend) tended to contribute less to the total variability for many stocks in WA and BC. This corresponded with the single common DFA trend for pink salmon that did not show strong increasing or decreasing trends in productivity over the past two decades. However, across the WA and BC pink salmon stocks where a trend in productivity was observed, the trend was consistently downward over the past two decades. This finding that most chum and some pink salmon stock productivities have declined markedly throughout WA and BC is consistent with the findings of Peterman and Dorner [

Despite the general coherence in productivity trends across species, there were some important differences between our pink and chum salmon productivity trends and those previously reported for sockeye salmon. In particular, Peterman and Dorner [_{t} series indicated above average or increasing productivity trends for all three Southeast Alaska pink salmon stocks since at least brood year 1990 (

We observed a general increasing trend in productivity for chum salmon stocks in the Inside WA region, which was opposite of the declining productivity trends observed for chum salmon stocks in the four other geographic regions in WA and BC. More specifically, the South Sound and Hood Canal chum salmon stocks had increasing trends in the Kalman filter _{t} series and weak covariation with other WA and BC chum salmon stocks, particularly during the 1950–1990 period. Surprisingly, these southern Puget Sound stocks also differed from chum salmon stocks that enter the ocean in northern Puget Sound (e.g., the Bellingham stock). One potential explanation for why productivity trends of southern Puget Sound chum salmon stocks are different is differences in physical and biological conditions in different parts of Puget Sound. For example, Duffy et al. [

Similar to Peterman and Dorner [

The observed patterns of covariation in productivity are also consistent with previously reported covariation patterns for wild pink and chum salmon abundances [

Our results broadly agree with those of several previous studies that suggested spatial covariation between demographic rates of nearby sockeye and chinook salmon stocks have increased in recent decades [

Regardless of the underlying mechanisms driving the trends, our results indicate that productivity of most chum salmon and some pink salmon stocks is non-stationary, which has important management and conservation implications if non-stationarity is not accounted for when setting management targets. Our results support the idea that the use of stationary spawner-recruit models to estimate stock productivity may be inappropriate for setting management targets, such as harvest rates or escapement goals, particularly in situations where large changes in productivity have occurred, such as those observed for chum salmon throughout BC [

In conclusion, our results indicate that the majority of North American chum and some pink salmon stocks have experienced large shifts in productivity over the past two decades, and at least for WA and BC stocks, these shifts have been downward. The coherence of these declines over regional and multi-regional spatial scales suggests that physical or biological factors operating at similar spatial scales are likely driving the observed trends. Because productivity is an important determinant of marine and anadromous fish stock dynamics, the sharp or gradual shifts in productivity observed here for pink and chum salmon can have important consequences for management and conservation. In particular, this research further demonstrates the need to account for time varying demographic rates in stock assessments to quickly detect temporal changes that may otherwise lead to an increased risk of overexploitation.

Recruitment series are standardized to a mean of 0 and standard deviation of 1. Correlation coefficients between the two recruitment series are given within each panel (

(PDF)

The residual series are standardized to a mean of 0 and standard deviation of 1. The ordinate gives the stock, which are arranged south (bottom) to north (top) and grouped by geographic region. The area of the circle indicates the magnitude of the productivity values. Open circles represent negative values (red) and filled circles indicate positive values (blue).

(PDF)

The residual series are standardized to a mean of 0 and standard deviation of 1. The ordinate gives the stock, which are arranged south (bottom) to north (top) and grouped by geographic region. The area of the circle indicates the magnitude of the productivity values. Open circles represent negative values (red) and filled circles indicate positive values (blue).

(PDF)

Correlations were calculated using all available brood years. The magnitude of the correlation is given by the area of the circle with larger circles representing larger correlations than smaller circles. Negative correlations between stocks are shown as open circles (red) and positive correlations are shown as filled circles (blue). Stocks are grouped by geographic region, which are arranged south (bottom, left) to north (top, right).

(PDF)

Correlations were calculated using all available brood years. The magnitude of the correlation is given by the area of the circle with larger circles representing larger correlations than smaller circles. Negative correlations between stocks are shown as open circles (red) and positive correlations are shown as filled circles (blue). Stocks are grouped by geographic region, which are arranged south (bottom, left) to north (top, right).

(PDF)

Each time series shows the smoothed _{t} estimates from the Kalman filter model where each series is standardized to a mean of 0 and standard deviation of 1. Even and odd year brood lines are shown concurrently for each stock with the even year brood lines offset slightly above the odd year brood lines. The ordinate gives the stock, which are arranged south (bottom) to north (top) and grouped by geographic region. The area of the circle indicates the magnitude of the productivity values. Open circles represent negative values (red) and filled circles indicate positive values (blue). Small solid grey dots indicate zero values, whereas missing values are not shown.

(PDF)

(a) Even brood year (solid line) and odd brood year (dashed line) common productivity trends and (b) stock specific loadings for the even year (solid horizontal bars) and odd year (dashed horizontal bars) common trends. In the bottom panel, stocks are ordered south (bottom) to north (top) and are grouped by geographic region.

(PDF)

(a) between stock correlation coefficients for odd year runs and (b) correlations for even year runs. The magnitude of the correlation is given by the area of the circle with larger circles representing larger correlations than smaller circles. Negative correlations between stocks are shown as open circles (red) and positive correlations are shown as filled circles (blue). Stocks are grouped by geographic region, which are arranged south (bottom, left) to north (top, right).

(PDF)

Brood years gives the range of years available for each stock; N gives the total brood years with data; R/S gives the average spawner to recruit ratio over all available brood years; Stationary _{t} gives the average _{t} value and SD gives the standard deviation for the _{t} series; Kalman filter S/N gives the signal-to-noise ratio for that stock.

(PDF)

Brood years gives the range of years available for each stock; N gives the total brood years with data; R/S gives the average spawner to recruit ratio over all available brood years; Stationary _{t} gives the average _{t} value and SD gives the standard deviation for the _{t} series; Kalman filter S/N gives the signal-to-ratio for that stock.

(PDF)

We are thankful to the many biologists from the Washington Department of Fish and Wildlife, Fisheries and Ocean Canada, and the Alaska Department of Fish and Game for collecting and providing us with the numerous salmon time series analyzed here. We also thank Randall Peterman and Brigitte Dorner for helpful discussions, Michelle Jones for helpful comments on an earlier draft, and two anonymous referees for their useful comments on our manuscript.