Introduction
In the mid-1970s, ocean conditions in the North Pacific Ocean underwent
a dramatic and abrupt change (Graham 1994).
Coincident with the physical regime shift, Alaskan salmonids entered
an era of greatly increased production that has persisted
into the 1990s (Fig. 1). Throughout their long (over 100 yr) commercial
exploitation history, several of the Alaskan salmon
species have demonstrated "red noise" variability, wherein periods
of high (low) production tend to persist for a lengthy period
before abruptly reversing to the opposite state. For example, in the
1930s and early 1940s, salmon landings were high,
followed by an era of low catches from the late 1940s to late 1970s.
As Alaskan landings increased in the late 1970s, several
North American west coast stocks, notably Oregon coho salmon (Oncorhynchus
kisutch; Pearcy 1992), went into a
prolonged period of decline.
Much early research on variability in salmon survival (and therefore
production and catch) focused on the freshwater stage of
their life cycle, attempting to link survival to conditions in their
spawning and rearing habitat. The period spent at sea was
regarded as relatively unimportant. There is now a growing awareness
of the importance of the marine environment in
determining salmon production (e.g. Pearcy 1984; Beamish and McFarlane
1989).
Variability in marine survival of salmon is poorly understood (Mathews
1984). Numerous studies have attempted to correlate
survival with environmental factors, though few have proven useful
in predicting salmon abundance or assisting in management
decision making (Pearcy 1992). Part of the difficulty in elucidating
the driving factors of survival is that the relationship between
the environment and survival is clouded by many factors. Biotic (e.g.
intra- and inter-specific competition, prey availability,
predation) and abiotic (environmental variables, habitat) factors not
only exhibit complex relationships with survival (non-linear,
threshold) but are themselves often highly correlated.
Despite these drawbacks, the importance of attempting to understand
the causes of variable survival should not be
underestimated (Francis and Sibley 1991). In particular, understanding
large-scale and long-term variability would benefit both
fishery managers and fishermen (Shepherd et al. 1984).
Large marine ecosystems fluctuate in response to physical forcings that
occur over a number of time intervals. There appears to
be a nested hierarchy of interacting processes occurring on different
time scales that are relevant to their dynamics, ranging from
relatively discrete processes that occur over times on the order of
1 yr or less (e.g., the 1970 North Pacific winter atmospheric
circulation pattern (Hollowed and Wooster 1992)), to processes that
persist over long time periods and fluctuate at the
inter-century level (Baumgartner et al. 1992). What we are most interested
in identifying in this analysis are regimes that define
points in time, separated by intervals on the order of decades, where
major jumps or shifts in the level of abundance occur in
large marine ecosystems. Therefore, in examining the interannual dynamics
of various biological components of large marine
ecosystems, what we see are responses to these nested hierarchies of
interacting processes occurring at different time scales
and working synergistically to create pattern. In this analysis, it
is pattern at the regime level that we are trying to interpret.
We hypothesize that regional variability in salmon production is driven
by large-scale climate change, reflected in North Pacific
atmospheric-oceanic regime shifts. Under this hypothesis, salmon populations
exhibit two characteristics: relatively stable
production while a particular regime persists, followed by a rapid
transition to a new production level in response to the
physical regime shift. If large-scale salmon production is closely
related to North Pacific climate processes, we should find
coherent shifts in mean production levels across both species and area.
In addition to the late 1970s regime shift, we surmise that an earlier
shift, opposite in character, occurred in the late 1940s.
Based on evidence summarized in the Discussion, we tentatively identify
the regime shifts as taking place in the winters of
1946-47 and 1976-77. Our hypothesis suggests that two shifts in Alaskan
salmon production should be detectable: a decrease
in the late 1940s and an increase in the late 1970s.
To test this hypothesis, we proceed by statistically analyzing the historical
production dynamics of four major Alaskan salmon
stocks: western and central sockeye salmon (Oncorhynchus nerka), southeast
and central pink salmon (Oncorhynchus
gorbuscha). While many researchers have noted the aforementioned swings
in production (e.g., Beamish and Bouillon 1994),
there remained the possibility that the changes might be either random
processes or nonsignificant, in a statistical sense. Owing
to the high serial correlation (lack of independence between successive
observations), the t-test for equality of means cannot be
used to test for production shifts. We utilize a time-series technique
known as intervention analysis to identify the significance,
magnitude, and form of structural shifts (interventions) in the four
time series. We identify and test the timing of the interventions
by matching the onset of the physical regimes with the life history
of the different species of salmon. Intervention analysis is a
relatively recent statistical technique recommended as a method for
detecting and quantifying non-random change in an
unreplicated experiment (Carpenter 1990).
To test for interventions, we fitted univariate time-series models of
the Box-Jenkins (1976) autoregressive integrated moving
average (ARIMA) class. These ARIMA models provide a baseline fit to
the correlation structure exhibited by the time series.
Interventions are subsequently identified by analyzing model residuals.
Model parameters are re-estimated incorporating the
intervention(s), and the models compared on the basis of several criteria.
After identifying the timing and nature of the
interventions, we then review the evidence for synchronous large-scale
physical regime shifts in the North Pacific.
Time-Series Modeling and Intervention Analysis
The use of time-series analysis to model fish population dynamics has
increased in recent years. Most of the theoretical
development and initial application has taken place in the econometric
and business forecasting literature. Recognition of the
potential applicability to ecological problems appears to have begun
with Moran (1949).
There are five classes of commonly applied time-series models (Jenkins
1979). The simplest, and most widely known,
comprise the so-called Box-Jenkins ARIMA univariate models. Simple
ARIMA models utilize only the history of the time
series to "explain" its observed variability. The second class comprises
the transfer-function noise (TFN) models, which relate
an output-series variability to both its own history and that of one
or more explanatory variables. A third class, related to TFN
models, comprises intervention models which incorporate the effects
of unusual events, natural or human-made, to modify
ARIMA models. The other two classes comprise multivariate models. Multivariate
stochastic models permit feedback among
several time series and are often referred to as vector ARIMA models.
The final class includes explanatory variables giving a
multiple input-multiple output mode and are sometimes referred to as
multivariate transfer-function models.
In addition to these time-series models, there has been a parallel development
of frequency-domain models, principally in the
engineering literature. In the frequency-domain models, processes are
modeled as combinations of cosine waves. While
theoretically translatable to time-domain models, there have been few
applications in ecology. More recently, state-space
models have generated a great deal of attention. In state-space, or
more generally, structural modeling, a time series is
decomposed into linear, seasonal, and irregular components (Harvey
1989). The central feature of structural models is the use
of the Kalman filter (Kalman 1960; Kalman and Bucy 1961) for parameter
estimation and forecasting. The principal difference
between traditional time-series and structural models is the manner
in which the error component is modeled. Though neither
method has emerged as clearly superior, structural models are likely
to receive increased attention.
The first published use of time-series modeling in the fisheries literature
was Dunn and Murphy (1976) and Murphy and Dunn
(1977), who used univariate and transfer-function models to forecast
fish catch in an Arkansas reservoir. Univariate and/or
transfer-function models have been used to model the population dynamics
of American lobster (Homarus americanus;
Boudreault et al. 1977, Fogarty 1988a, Campbell et al. 1991), rock
lobster (Jasus edwardsii; Saila et al. 1980), skipjack tuna
(Katsuwonus pelamis; Mendelssohn 1981), yellowtail flounder (Limanda
ferruginea: Kirkley et al. 1982), menhaden
(Brevoortia patronus; Jensen 1985), haddock (Melanogrammus aeglefinus;
Pennington 1985), Alaskan salmon (Quinn and
Marshall 1989; Noakes et al. 1987), winter flounder (Pseudopleuronectes
americanus; Jeffries et al. 1989), blue whiting
(Micromesistius poutassou; Calderon-Aguilera 1991), pilchard (Sardina
pilchardus; Stergiou 1989), and striped bass
(Morone saxatilis; Tsai and Chai 1992). Intervention analysis has been
applied to Dungeness crab (Cancer magister; Noakes
1986), geoduck clams (Panope abrupta; Noakes and Campbell 1992), power
plant impact on yellow perch (Perca
flavescens) and alewife (Alosa pseudoharengus; Madenjian et al. 1986),
and to forecast invertebrate yield (Fogarty 1988b).
Vector ARIMA models have been applied to Great Lakes pelagic species
(Cohen and Stone 1987; Stone and Cohen 1990)
and multivariate transfer-function models were used by Mendelssohn
and Cury (1987, 1989) to explore catch per unit of effort
in Ivory Coast pelagic fisheries.
In this paper, we use intervention models to determine if North Pacific
regime shifts are reflected in Alaska salmonid time series.
We provide a brief outline of the technique and explanation of time-series
terminology and notation. Those seeking a more
theoretical description should consult one of the numerous texts available
including the seminal works on ARIMA model
formulation (Box and Jenkins 1976) and intervention analysis (Box and
Tiao 1975).
Notation
ARIMA and intervention models have several different representations. We employ the following notation:
1)
is the discrete time series, which may be transformed
to stabilize the variance using the Box-Cox (1964) power
transformation. The most common transformations are square root (l=0.5),
natural logarithm (l=0.0), and inverse (l=-1.0).
No transformation is equivalent to a lambda value of 1.0. If required,
a power transformation must be done as the first step in
time-series modeling.
is an "integrating factor" (the "I" in ARIMA), better
defined as a differencing operation to induce stationarity in the mean
of
a series. The number of differences taken (which can be at various
lags) is indicated by d. If required, differencing is the second
step in ARIMA modeling.
is a seasonal integrating factor(s) where s
is the lag at which the Dth seasonal difference is taken. While seasonal
models
are generally applied to weekly, monthly, quarterly, etc. data, they
may also be applied to non-seasonal data that exhibit
seasonal (i.e., periodic) behavior.
plays different roles depending on the value of d
(order of differencing). For d = 0, q0 is equal to the estimated mean of
the
transformed input series multiplied by the sum of the autoregressive
components and moved to the right-hand side of the
equality. For d ³ 1, q0 is called the deterministic trend and
is often omitted unless clearly called for (Wei 1990, p. 72).
at is a random error component assumed to be normally independently distributed with mean 0 and constant variance s2a.
B is the backshift operator. By convention it is a special notation
used to simplify the representation of lagged values: Byt = yt-1,
Bsyt = yt-s. Note also the following definition: Ñ = 1 - B,
thus differencing is often represented by: Ñyt = (1 - B)yt.
is the autoregressive polynomial
of the form (1 - f1B - f2B2 - ... - fpBp). The term "autoregressive" is
in reference to
how the value of y is being regressed on its own past values plus a
random shock, thus relating the present value of a process to
a linear combination of its past values. An autoregressive process
can be written as yt = f1yt-1 + f2yt-2 + ... + fPyt-P + at..
An autoregressive process of order p is abbreviated AR(p), and lower
orders than p need not be non-zero.
is the multiplicative seasonal
autoregressive polynomial of the same form as the non-seasonal polynomial.
Multiple
seasonal autoregressive components may be included in the model, each
of seasonality S. The subscript P identifies the
presence of a seasonal component, and all coefficients other than that
of the seasonal lag are set equal to 0.
is the moving average polynomial
of the form (1 - q1B - q2B2 - ... - qqBq). The moving average term models
the
persistence of random effects over time and can be written as yt =
at + q1at-1 + q2at-2 + ... + qpat-p. A moving average
process of order q is abbreviated MA(q), and lower orders than q need
not be non-zero.
is the multiplicative seasonal
moving average polynomial of the same form as the non-seasonal polynomial.
Multiple
seasonal moving average components may be included in the model, each
of seasonality S. The subscript Q identifies the
presence of a seasonal component, and all coefficients other than that
of the seasonal lag are set equal to 0.
represents the jth intervention and is analogous
to a dummy variable in regression. Interventions can be either step (I
= 1 for
t ³ T, I = 0 otherwise) or pulse (I = 1 for t = T, I = 0 otherwise)
functions. A step intervention indicates a permanent shift in the
mean of a series, while a pulse indicates a one-time shock. There are
several different system responses to step and impulse
interventions, such as an abrupt permanent step, a step decay, and
impulse decay.
is a polynomial of the form (w0 - w1B - w2B2 - ... - wsBs) representing the initial impact of the intervention.
is a polynomial of the form (1 - d1B - d2B2 - ... - drBr) representing the long-term impact of the intervention.
models the delay in response associated with a particular intervention.
Nonseasonal ARIMA models use the notation (p, d, q) to compactly represent
autoregressive, difference, and moving average
orders. Seasonal models are expressed as (p, d, q) x (P, D, Q)S, with
each seasonal component separately represented. Thus,
a (1, 0, 5) model indicates the presence of additive lag 1 AR and lag
5 MA terms with smaller lag MA terms possibly present.
A (1, 0, 0) x (0, 0, 1)5 model also has lag 1 AR and lag 5 MA terms,
but the parameters are multiplicative rather than additive.
Model development
Univariate time-series model building, in the methodology of Box and Jenkins (1976), proceeds in the following fashion:
1) Model Identification. In this step, tentative models are identified.
Determination of the need for power transformation (for
variance stabilization) and differencing (to render the series stationary
in the mean) are first evaluated. Plots of the
autocorrelation and partial autocorrelation functions (ACF and PACF
respectively) of the possibly transformed series are
examined to assist in determining the order of the AR and MA components
(Box and Jenkins 1976). Several other
identification tools are also available, such as the extended sample
autocorrelation function (ESACF; Tsay and Tiao 1984),
generalized partial autocorrelation coefficient (GPAC; Woodward and
Gray 1981) and the prediction variance horizon (PVH;
Parzen 1981).
2) Parameter estimation. Following selection of a potential model(s),
estimates of the parameters are calculated. Access to
time-series software is almost essential as ARIMA model parameters
must be fitted using a nonlinear estimation routine (though
the models themselves are usually linear). Maximum likelihood procedures,
usually based on the Cholesky decomposition or
the Kalman filter, have been developed as an alternative to the early
methods of least squares and approximate likelihood
utilized by Box and Jenkins (1976). Standard errors are also computed,
and parameters judged to not be significantly different
from zero can be dropped. The remaining parameters are then re-estimated.
3) Model diagnostic checking. With a tentative model selected and parameters
estimated, the adequacy of the model must be
assessed to determine if model assumptions are met. One basic assumption
is that the residuals at form a white-noise series. A
common test is the portmanteau test of Box and Pierce (1970), which
uses the residual ACF to test the joint null hypothesis
that all serial correlations are equal to zero. It is also common in
time-series analysis that several models may be adequate in the
sense that the model residuals are reduced to white noise. Several
model selection criteria have been developed to assist in
model selection. In this analysis, we compared competing models using
five criteria: mean absolute error (MAE), which
measures the average one-step-ahead prediction error; the unbiased
residual variance s2a, equal to the residual sum of squares
divided by degrees of freedom; the coefficient of determination r²,
which is the amount of variance "explained" by the model;
Akaike's Information Criterion (AIC; Akaike 1974); and Schwarz's Bayesian
Criterion (SBC; Schwarz 1978). The AIC and
SBC are performance statistics that balance statistical fit with model
parsimony. The SBC utilizes a larger penalty function than
the AIC, thus often suggesting a model with fewer parameters. Formulas
for the model diagnostic and selection criteria are
contained in the appendix.
Intervention detection and estimation
In intervention analysis, the correlation structure is initially assumed
to be unaffected by the interventions that are modeled as
deterministic functions of time. Once the best ARIMA model has been
selected, the three-step modeling sequence is repeated
to identify and test the significance of interventions.
The original intervention methodology developed by Box and Tiao (1975)
permitted estimation of intervention effects when the
timing of the interventions was known a priori. To handle the situation
where the number and timing of potential interventions
are unknown, Chang and Tiao (1983) proposed an iterative detection
technique using a likelihood ratio test. Interventions are
identified in a stepwise fashion beginning with the residuals from
the univariate model. Following detection and estimation of an
intervention, model parameters are estimated and the resultant intervention
model compared with the univariate model using the
criteria cited above. The new model residuals can then be re-analyzed
for evidence of other interventions.
A good general review of intervention models is contained in Wei (1990),
while Noakes (1986) discusses the applicability of
intervention analysis to fisheries problems.
There are two types of interventions, pulse and step. The first represents
a discrete system shock; the second a permanent
change in the mean level of a process. In this analysis, we model step
interventions that result in permanent shifts in the mean
level of salmon production. Step interventions can be modeled as abrupt
(i.e., a one time-step jump) or delayed (e.g., ramp,
impulse decay) processes. It should be noted that testing for different
types of interventions increases the probability of
identifying a spurious intervention. However, our use of the AIC and
SBC performance statistics should minimize this risk. Two
software packages, AUTOBOX (Automatic Forecasting Systems, Inc. 1992),
and SPSS Trends (SPSS, Inc. 1993), were
used for all analyses.
Data
The salmon landings data used in this study were principally taken from
an Alaska Department of Fish and Game (ADFG
1991) annual report. Data for 1992 were taken from Pacific Fishing
(1994). We selected the four major regional groups of
stocks: western Alaska sockeye salmon, central Alaska sockeye and pink
salmon, and southeast Alaska pink salmon. Landings
data for these regional stocks are more likely to reflect actual production
than other Alaskan salmon stocks, as they have been
the most intensively exploited stocks because of their high abundances
and value. These four regional stocks accounted for
over 80% of total Alaskan salmon catches (by number) for the period
1925-1992. To more accurately reflect salmon
production by area (Fig. 2), we corrected the Alaskan landings for
interceptions using data provided in Shepard et al. (1985),
Harris (1989) and the Pacific Salmon Commission (1991). Details of
the adjustments are provided in Francis and Hare (1994).
Catch data for these regional stocks are available from as early as
the 1870s. We have restricted our analysis to 1925-1992
which we consider to be the period of full exploitation. If there is
a "fishing up" effect in the early part of the record, the
time-series analysis would be affected by this form of nonstationarity.
Our time series span 68 years which is fully adequate for
a proper time-series analysis (Newton 1988).
Results
Western Alaska Sockeye
The western Alaska sockeye data required a square-root transformation
to stabilize the variance. Differencing was not
required. Examination of the ACF and PACF indicates rather complex
dynamics in this time series, substantially different from
the three other salmon time series (Fig. 3) Lags 1, 4, and 5 in the
ACF and lags 1, 4, and 6 in the PACF were significant. A
variety of models were fitted and compared. Initial identification
indicated three candidate univariate models: (6, 0, 0), (1, 0, 5),
and the seasonal model (1, 0, 0) x (1, 0, 0)5. Diagnostics indicated
residual serial correlation at lag 3 for the seasonal model,
thus a moving average term was added and the resultant (1, 0, 0) x
(1, 0, 0)5 x (0, 0, 1)3 model compared with the
nonseasonal models. On the basis of the diagnostic statistics, the
(6, 0, 0) model was judged to be the most parsimonious at
representing the catch dynamics. Within this model, the lag 2, 3, and
4 autoregressive terms were statistically insignificant and,
therefore, dropped from the final model. Residual analysis indicated
that all serial correlation had been accounted for by the
model. The final fitted model parameter estimates and standard errors
for the univariate and subsequent intervention models are
given in Table 1. Model diagnostics for the univariate and intervention
models are given in Table 2.
Based on the physical regime shifts that we tentatively identify occurring
in the winters of 1946-47 and 1976-77 (Francis and
Hare 1994), we hypothesize that interventions in the western Alaska
sockeye salmon time series should be detected around
1949-50 and 1979-80. Sockeye salmon from this region spend 1 or 2 years
rearing in freshwater before migrating to sea
where they are first exposed (and, probably, most vulnerable) to oceanic
conditions. Bristol Bay sockeye salmon, which
comprise most of the western Alaska sockeye salmon, generally spend
two years at sea, thus the year classes that entered the
ocean in 1977 would be caught in 1979.
We fitted two intervention models, the first incorporating a 1979 step,
the second also incorporating a 1949 step. For the
one-intervention model, the 1979 step was highly significant (p <
0.01), and in the two-intervention model, both interventions
were highly significant (p < 0.01). In both cases, the best statistical
fit was provided by simple step (i.e. no delay) interventions.
Both models substantially outperformed the nonintervention model. The
coefficient of determination, r², improved from 0.459 to
0.575 with the 1979 intervention and further increased to 0.623 with
inclusion of the 1949 intervention (all model diagnostics
reflect model fit in the transformed metric; thus for western Alaska
sockeye salmon, the statistics result from model fitting in
square root space). Both the AIC and SBC decreased substantially with
the addition of each intervention.
The 2 intervention model differed slightly from the two other models
in its ARIMA components. The lag 1 AR term, which had
decreased in significance from the no intervention to the one-intervention
model, dropped out of the model and a lag 3 AR term
was added. The AR(5) coefficient was positive and highly significant
in all three models, likely reflecting the pseudo-regular 5
year cycle (Eggers and Rogers 1987). The decrease in significance of
the AR(1) term with incorporation of interventions was a
feature of the model building sequence for each of the salmon time
series. One explanation for this result is that a time series that
alternates between different levels (or regimes) will have the statistical
appearance of a low frequency series with high apparent
autocorrelation. Removing the "regime effect" from the time series
often accounts for most of the low frequency (i.e., lag 1)
autocorrelation.
Resultant model fits and pre- and post-intervention means for the three
models are illustrated in Fig. 4. For the one intervention
(1979) model, estimates of the pre- and post-intervention means were
10.443 and 27.748 million respectively, resulting in an
estimated step intervention of 17.305 million. In the two-intervention
model, the 1949 step was estimated at -4.928 million and
the 1979 step at 17.484 million. The three means were estimated at:
13.287 (1925-1948), 8.359 (1949-1978), and 25.843
million (1979-1992).
Central Alaska Sockeye
The central Alaska sockeye salmon time series dynamics were much less
complex than those of the western Alaska sockeye
salmon. The ACF and PACF for the natural logarithm transformed series
(Fig. 3) indicated either a (2, 0, 0) or a (1, 0, 1)
model. Model diagnostics indicated a better fit for a (2, 0, 0) model.
The univariate model fit was the best among the four
salmon time series (r2=0.644). Model residuals showed no residual autocorrelation.
Parameter estimates for the univariate and
intervention models are given in Table 3, and model statistics in Table
4.
A large fraction of the central Alaska sockeye salmon (e.g., Kenai River,
Chignik Lake runs) spend three years in the ocean
before returning to spawn (Cross et al. 1983). In keeping with our
hypothesis that the climate effect occurs during the first year
of marine life, we tested for interventions in 1950 and 1980 for the
central Alaska sockeye salmon time series. In the
one-intervention (1980) model, the step intervention was highly significant
(p < 0.01) and led to an improvement in all
diagnostic statistics. The two-intervention model provided an equally
large improvement as both interventions (1950, 1980)
were highly significant. The lag 2 AR term, present in the no-intervention
model, dropped out in each of the subsequent models.
In addition, for reasons noted earlier, the magnitude of the AR 1 term
also decreased with the incorporation of interventions.
The effective change in mean catch for the one intervention model (1980)
was 6.937 million (Fig. 5). The estimated mean for
the 1980-1992 period was 11.555 million, compared to an estimated mean
of 4.618 million prior to the intervention effect. For
the two-intervention model, the interventions were estimated to have
decreased mean catch by 1.919 million (from 5.665 to
3.746million) between the 1925-1949 and 1950-1979 periods, and then
increased mean catch by 8.086 million (to 11.832
million) for the 1980-1992 period.
Southeast Alaska Pink
The southeast Alaska pink data required a natural logarithm transformation
to stabilize the variance. The resultant ACF and
PACF resembled central Alaska sockeye, indicating similar dynamics.
The same two initial models, (2, 0, 0) and (1, 0, 1),
were tested. The (2 ,0, 0) was eventually selected, the same model
as for the central Alaska sockeye series. Model fit,
however, was the poorest among the time series, as indicated by the
r2 value (0.348). Univariate and intervention model
parameter estimates are listed in Table 5, and model statistics in
Table 6.
Pink salmon migrate to the ocean in the spring following the year they
were spawned and return the following year. Therefore,
we tested for interventions in 1948 and 1978. In the one-intervention
model, the 1978 intervention was highly significant, but
the AR 1 term dropped out as its p-value increased above 0.05 (to 0.09).
The one-intervention model actually had a slightly
worse fit than the no intervention model. Had the AR 1 term been retained,
however, most diagnostics would have favored the
one-intervention model. In the two-intervention model, both interventions
(negative in 1948, positive in 1978) were also highly
significant (p < 0.01). Interestingly, though, no ARIMA terms were
significant after inclusion of the two interventions. The
interpretation of this result is that Southeast Alaska pink salmon
production (as indicated by catch) varies randomly about the
various regime levels of production. Nearly half (r2=0.446) of the
total variation in Southeast Alaska pink salmon catch was
accounted for by the two interventions.
The mean change in catch under the one-intervention model was 12.378
million, from a level of 15.280 million for the
1925-1977 period to a level of 27.658 million for the 1978-1992 period
(Fig. 6). Estimated average catch under the
two-intervention model decreased by 17.169 million (from 26.678 to
9.509) from the 1925-1947 period to the 1948-1977
period and then increased by 16.480(to 25.989) million during the 1978-1992
period.
Central Alaska pink
The central Alaska pink time series required a square-root transformation
to stabilize the variance. Both the ACF and PACF of
the transformed series show significant correlation at lags 1 and 2,
indicating a mixed ARMA process. The best model we
found was a (1,0,2) model with no MA(1) term. Parameter estimates and
model statistics for the univariate and intervention
models are listed in Tables 7 and 8, respectively.
In the one-intervention model, the highly significant step intervention
identified in 1978 resulted in a mean level increase of
21.216 million, from 14.829 to 36.045 million (Fig. 7). The two-intervention
model resulted in a further improvement of the
model fit. Under this model, the mean level of production was 19.156
million during 1925-1947, then dropped by 7.383 million
to a level of 11.773 million for the 1948-1977 period, then increased
by 25.509 million to reach the modern catch level of
37.282 million.
Incorporation of the interventions reduced both the AR(1) and MA(2)
parameters substantially as the "regime effect" accounted
for an increasingly large part of the serial correlation. The AR(1)
term was highly significant (p < 0.01) in the no-intervention
model, remained barely significant (p ~ 0.05)in the one-intervention
model, and was not retained in the two-intervention model,
resulting in a (0, 0, 2) model. The MA(2) term reduced in magnitude
from -0.566 (no-intervention model) to -0.241
(two-intervention model).
Discussion
Over the past seven decades, Alaskan salmon populations appear to have
alternated between high and low production
regimes. We propose that Alaskan salmon are responding to changes in
North Pacific climate regimes. Under this hypothesis,
each salmon population exhibits a unique smaller-scale variability
about some mean level of production during a climatic regime.
The transition from one regime to another occurs relatively rapidly,
resulting in a shift in the mean production level of Alaskan
salmon populations.
In support of this hypothesis, we have demonstrated nearly synchronous
production shifts in four regional Alaskan salmon
stocks. These stocks include two different species from three widely
separated geographic regions. Using the technique of
intervention analysis, we identified three production regimes defined
by two major production shifts, one in the late 1940s, the
other in the late 1970s.
Alaskan pink and sockeye salmon spend the majority of their marine life
cycle in the Central Subarctic Domain (CSD; Ware
and McFarlane 1989) which encompasses the Gulf of Alaska (Fig. 8).
The principal feature within the CSD is the Alaska Gyre,
with an area of active upwelling at its core. The southern boundary
of the CSD is defined by the Subarctic Current, whose
latitudinal location varies yearly (Roden 1991, Ward 1993). During
the seaward and return migrations, pink and sockeye
salmon pass through the Coastal Downwelling Domain, a region extending
from Queen Charlotte Sound to Prince William
Sound dominated by the Alaska Current.
Any attempt to link physical processes in the marine environment to
Alaskan salmon production must involve oceanographic
conditions within these two regions. We now examine the two production-regime
shifts in greater detail, summarize the change
in production, and consider the evidence for concurrent climate-regime
shifts. We then discuss potential mechanisms linking the
physics and biology.
Late 1970s Shift
The increase in salmon production was highly significant in all four
time series. In the two-intervention models, the smallest
t-value (based on roughly 63 degrees of freedom) of the four late 1970s
step intervention variables was 5.492 (p < 0.0001,
southeast pink salmon). Both pink salmon time series showed a significant
jump in 1978 to a higher production level. Because
of the strength of the change in production, the timing of the intervention
could also have been placed in 1977 or 1979, but
model diagnostics indicated the best fit occurred in 1978. Additionally,
we chose to test for a 1978 effect because, according
to our hypothesis, the returning 1976 brood year class, first to be
exposed to the new oceanic regime, should be the first to
show a regime effect. A similar argument, based on the sockeye salmon
life history, should lead to a 1979 or 1980 intervention
for the two sockeye salmon time series, depending on whether the returning
fish spent two or three years in the ocean. For the
western Alaska sockeye, a 1979 intervention was statistically more
significant than a 1980 intervention. The reverse was true
for central Alaska sockeye.
Each of the four production groups is faced with a unique set of environmental
conditions between their freshwater rearing
habitat and entry into the marine feeding and migration grounds. The
three geographic regions each contain numerous
salmon-bearing rivers. Localized factors will, therefore, lead to some
amount of unique variability added to the effect of the
climatic regime on the population as a whole. This is reflected in
the differing ARIMA structures among the four time series as
well as the remaining unexplained variance. It is clear, however, that
the four stocks entered an era of increased production in
the late 1970s and have remained at that level in the 1990s. Combining
the four series, we estimate that the increased
production resulted in an annual mean catch increase of greater than
69 million salmon. This translates to a threefold difference
in production between the previous regime of the late 40s-late 70s
and the present regime beginning in the late 70s.
Evidence for the timing and strength of the late 1970s regime shift
has been documented in numerous environmental and
biological variables (Ebbesmeyer et al. 1991). The most obvious physical
manifestations of the late 1970s shift include a
strengthening and eastward shift of the Aleutian Low (Trenberth 1990)
and warming of the surface waters in the Gulf of Alaska
(Royer 1989). Defining the event as the onset of a new regime rather
than a temporary system shock reflects the persistence of
the new state variables. Most evidence pinpoints the winter of 1976-77
as the critical transition period. The shift appears to
have been forced by an increasingly vigorous winter circulation over
the North Pacific (Graham 1994), leading to more severe
and frequent winter storms (Seymour et al. 1984), decreases in mid-Pacific
sea-surface temperatures (SSTs), and basin-wide
decreases in sea-level pressure (Trenberth 1990). The large-scale increase
in central Pacific chlorophyll (and thus
phytoplankton) during the 1970s has been attributed to persistence
of warm SSTs in the summer months (Venrick et al. 1987).
The increase in Alaskan air and sea-surface temperatures probably derived
from warm air advected from the south by a
strengthened Aleutian Low.
Hollowed and Wooster (1992) have hypothesized that the North Pacific
alternates between two environmental states, with one
transition occurring in 1977. The cool period prior to the transition,
what they call a type A regime, is characterized by a weak
winter Aleutian Low, enhanced westerly winds in the eastern Pacific,
decreased advection into the Alaska Current, and
negative coastal SST anomalies. A warm era (type B regime) is characterized
by a strong winter Aleutian Low displaced to the
east, enhanced southwesterly winds in the eastern Pacific, increased
advection into the Alaska Current, and positive coastal
SST anomalies.
The mechanisms driving the late 1970s regime shift are the subject of
much intensive research. Several hypothesized
mechanisms have suggested links between this regime shift in the North
Pacific and an abrupt climate shift in the tropical Pacific,
which occurred in the late 1970s. Kashiwabara (1987) and Nitta and
Yamada (1989) have hypothesized that changes in the
tropical Pacific forced the change in North Pacific winter circulation
patterns. Trenberth (1990) noted that, in the period
between 1976 and 1988, there were three warming El Niño events,
but no cooling La Niña events. Graham (1994) holds that
the El Niño-La Niña cycle continued but the background
state was set to a different state. Miller et al. (1994) were able to
reproduce the 1976-77 shift with a general circulation model driven
by heat flux input, suggesting that the atmosphere (as
opposed to an ocean-atmosphere feedback loop) was the primary force.
On the basis of observational analyses, Trenberth and
Hurrell (1994) attribute North Pacific atmosphere-ocean variability
to both local (atmospheric) and remote (tropical oceanic)
processes with mid-latitude feedback serving to emphasize decadal scale
variability.
Late 1940s Shift
The negative production shifts identified in the late 1940s were all
significant, but of lesser magnitude than those of the late
1970s. The t-values for the step interventions in the two-intervention
models ranged from 6.45 (p < 0.0001, southeast pink
salmon) to 3.27 (p < 0.01, central pink salmon). The timing of the
interventions we tested were selected in the same manner as
for the late 1970s shift. Assuming a climate shift in the winter of
1946-47, the appropriate years to test are 1948 (both pink
time series), 1949 (western Alaska sockeye), and 1950 (central Alaska
sockeye). We estimate the combined drop in catch
following the late 1940s intervention at approximately 30 million salmon
annually, a decrease of nearly 50%.
Evidence for an late 1940s regime shift is less confirming than for
the late 1970s. To some extent, this may be due to the
relative lack of data in comparison with that available for the later
event. Also, if the salmon data are indicative of the physical
data, the shift in physical variables is expected to be smaller and,
therefore, more difficult to detect.
Francis and Hare (1994) found a statistically significant negative step
in 1947 in Trenberth and Hurrell's (1994) North Pacific
Index, a measure of winter atmospheric variability. Several researchers
(Dzerdzeevskii 1962, Kutzbach 1970, Kalnicky 1974,
Brinkmann 1981) have noted sharp changes in upper level atmospheric
circulation patterns occurring in the late 1940s to early
1950s. Balling and Lawson (1982) and Granger (1984) showed that rainfall
patterns over the southwestern United States
changed in the early 1950s. Rogers (1984) presented average winter
air temperatures for Kodiak and Bristol Bay from
1920-1983. With only a few exceptions, coastal Alaskan air temperatures
remained anomalously low between the 1946-47
and the 1976-77 winters. Surface-temperature trends in the northern
hemisphere were shown by Jones (1988) to be in a cool
period between the late 1940s and late 1970s. The frequency and intensity
of El Niño-Southern Oscillation events have
undergone several changes in the past century (Trenberth 1990; Trenberth
and Shea 1987) with strong events between 1880
and 1920, and 1950 and the present, and weak events between 1920 and
1950. Trenberth (1990) also noted the
preponderance of cold (La Niña) tropical events during the 1950-1977
period compared with the present (1977-1990)
imbalance marked by a greater number of warm (El Niño) events.
Several data sets that we examined dated back only to the late 1940s.
While not capable of demonstrating a shift in the late
1940s, they do indicate a similarity of conditions for the 1947-1976
period. Between 1949 and 1976, Emery and Hamilton
(1985) classified 22 of 28 North Pacific sea-level pressure patterns
as either weak or near normal. Hollowed and Wooster
(1992) identified 24 of 31 winter atmospheric circulation patterns
between 1946 and 1976 as type A regimes (cool periods).
Potential Mechanisms
Establishing the mechanism whereby salmon production is driven by large-scale
climate processes can only proceed by
speculation at present. We alluded earlier to the general inability
of most studies to establish predictable relationships between
environmental variables and salmon survival and production that stand
the test of time. Quinn and Marshall (1989), for
example, found that inclusion of air and water temperature and freshwater
discharge provided limited improvement to their
time-series models of southeast Alaska salmon variability.
At least two speculative mechanisms have been advanced to help explain
the late 1970s rise in Alaskan salmon production.
Rogers (1984) proposed that the increase in catch derived from increased
marine survival of migrating salmon in their last
winter at sea. Anomalously warm surface temperatures in the Gulf of
Alaska altered both the migration paths and timing of
returning salmon thus lessening their vulnerability to predators (principally
marine mammals). Additional evidence for this
hypothesis may be provided by the 1970s and 1980s decline in northern
fur seal (Callorhinus ursinus) and Steller's sea lion
(Eumetopias jubatus) (Merrick et al. 1987; York 1987).
The second mechanism relates improved feeding conditions in the Alaska
Current and Alaska Gyre to increased salmon
production. Brodeur and Ware (1992) documented a twofold increase in
zooplankton biomass between the 1950s and 1980s
in the subarctic Pacific Ocean. They suggest that the primary beneficiaries
of the elevated zooplankton biomass are juvenile
salmon that migrate around the coastal margin of the CSD foraging on
zooplankton advected to the oceanic shelf. Transport of
zooplankton-rich waters derives from increased flow into the Alaska
Current from the Subarctic Current (Pearcy 1992).
Chelton (1984) has proposed that transport into the California and
Alaska Currents fluctuates out of phase. This scenario
suggests that the observed decrease in west coast salmon production
may be due to poor feeding conditions resulting from
decreased advection of subarctic water into the California Current
(Pearcy 1992). Francis and Sibley (1991) illustrated
opposite trends in production between Gulf of Alaska pink salmon and
west coast coho salmon. The nature of the transitions
from high (low) to low (high) production in both stocks suggests a
single cause.
Perhaps the most interesting feature of the salmon regimes we have identified
is the nature of the level of persistence exhibited
by the different stocks. Hollowed and Wooster (1992) found synchronous
recruitment patterns in several groundfish species
corresponding to switches between type A and type B regimes. Strong
year-classes apparently derived from the onset of type
B regimes. Subsequent year-classes, however, were much smaller. This
appears to be quite different from the situation we have
documented for Alaskan salmon. In addition, the average duration of
type A and B regimes was 7-10 yr, whereas we have
identified much longer period regimes based on Alaskan salmon dynamics.
This suggests that different components of the North
Pacific large marine ecosystem respond to forcing factors of different
scales.
Little is known about what causes low-frequency shifts in the structure
and dynamics of large marine ecosystems. Margalef
(1986) challenges us to develop a new paradigm in this regard. He suggests
that infrequent and discontinuous changes in
external (physical) energy are the most important factors affecting
fluctuations in the biological production of these systems.
These inputs, which he refers to as "kicks," disrupt established ecological
relationships within an ecosystem.
Dr. John Steele (Woods Hole Oceanographic Institution, Woods Hole, MA
02543, personal communication) puts it another
way. He feels that, in the ocean, the variances of biological processes
that respond to both physical and biological forcings are
inversely proportional to their frequencies. If the variance of a process
is forced beyond certain bounds or tolerances, that part
of the system "snaps," such as when an earthquake occurs, forcing repercussions
throughout the ecosystem. As in the case of
an earthquake, many system variables that "snap" at the time of the
earthquake demonstrate no aberrant behaviors prior to the
earthquake itself. So perhaps it is with large marine ecosystems.
Acknowledgments
This research was funded by Washington Sea Grant. We are indebted to
Ray Hilborn, Jim Ianelli, Don Percival, Michael Ward
and two anonymous reviewers for critically reviewing the manuscript.
We also acknowledge Steven Riser, Warren Wooster,
and Anne Hollowed for discussions that helped develop many of the ideas
that appear in the paper.
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Appendix
The following time-series model diagnostic and selection criteria were used.
Box-Pierce Portmanteau test
The joint null hypothesis Ho: r1 = r2 = ... = rK = 0 is tested with the statistic
(A1)
The hypothesis of white noise is rejected if Q > c2a,K-m, where K is
the number of residuals calculated from the model and m is
the number of estimated parameters.
Mean Absolute Error (MAE)
(A2)
Unbiased residual variance s2a
(A3)
where RSS is the residual sum of squares and m is the number of estimated
model parameters
Coefficient of determination r²
(A4)
where z represents the (possibly) transformed and differenced observed
values.
Akaike's Information Criterion (AIC)
(A5)
where RSS is the residual sum of squares, K is the number of residuals,
m is the number of estimated parameters, and s2a is the
biased residual variance.
Schwarz Bayesian Criterion (SBC)
(A6)
where the parameters have the same interpretation as for the AIC.
0
Table 1. Univariate and intervention ARIMA models with parameter estimates
and associated standard errors developed for
western Alaska sockeye salmon. Standard errors are given in paretheses
below the equations.
Model
Parameter estimates and standard errors
Univariate
(1 - 0.538B - 0.505B5 + 0.369B6)ÖYt = 1.209 + at
(0.107) (0.111) (0.122) (0.107)
One intervention
(1979)
(1 - 0.299B - 0.499B5 + 0.253B6)ÖYt = 1.468 + at + 2.036It1979
(0.121) (0.109) (0.131) (0.105) (0.415)
Two interventions
(1949, 1979)
(1 + 0.305B3 - 0.377B5 + 0.225B6)ÖYt = 4.206 + at - 0.754It1949 +
2.192It1979
(0.121) (0.114) (0.117) (0.161) (0.188) (0.223)
Table 2. Summary statistics for univariate and intervention ARIMA models
developed for western Alaska sockeye salmon.
MAE = mean absolute error of fitted values, s²a = unbiased residual
variance, r² = coefficient of determination, AIC =
Akaike's Information Criterion, SBC = Schwarz's Bayesian Criterion,
and Q = portmanteau residual autocorrelation test (up to
lag 20) and associated p-value. All statistics are calculated in the
transformed metric.
Model
MAE
s²a
r²
AIC
SBC
Q
p value
Univariate
0.741
0.836
0.459
186.6
195.5
15.17
0.767
One intervention
0.632
0.667
0.575
172.0
183.1
13.64
0.848
Two interventions
0.603
0.607
0.623
166.4
179.7
17.43
0.625
Table 3. Univariate and intervention ARIMA models with parameter estimates
and associated standard errors developed for
central Alaska sockeye salmon. Standard errors are given in paretheses
below the equations.
Model
Parameter estimates and standard errors
Univariate
(1-0.568B - 0.316B2)ln Yt = 0.216 + at
(0.117) (0.121) (0.034)
One intervention
(1980)
(1-0.572B)ln Yt = 0.655 + at + 0.917It1980
(0.102) (0.040) (0.188)
Two interventions
(1950, 1980)
(1-0.310B)ln Yt = 1.197 + at - 0.409It1950 + 1.145It1980
(0.120) (0.058) (0.112) (0.135)
Table 4. Summary statistics for univariate and intervention ARIMA models
developed for central Alaska sockeye salmon.
MAE = mean absolute error of fitted values, s²a = unbiased residual
variance, r² = coefficient of determination, AIC =
Akaike's Information Criterion, SBC = Schwarz's Bayesian Criterion,
and Q = portmanteau residual autocorrelation test (up to
lag 20) and associated p-value. All statistics are calculated in the
transformed metric.
Model
MAE
s²a
r²
AIC
SBC
Q
p value
Univariate
0.255
0.101
0.644
41.3
47.9
15.14
0.768
One intervention
0.234
0.094
0.672
35.7
42.4
14.13
0.824
Two interventions
0.213
0.087
0.704
31.1
40.1
9.92
0.970
Table 5. Univariate and intervention ARIMA models with parameter estimates
and associated standard errors developed for
southeast Alaska pink salmon. Standard errors are given in paretheses
below the equations.
Model
Parameter estimates and standard errors
Univariate
(1 - 0.277B - 0.410B2)ln Yt = 0.906 + at
(0.112) (0.115) (0.073)
One intervention
(1978)
(1 - 0.495B2)ln Yt = 1.377 + at + 0.593It1978
(0.108) (0.084) (0.310)
Two interventions
(1948,1978)
ln Yt = 3.284 + at - 1.032It1948 + 1.005It1978
(0.121) (0.160) (0.183)
Table 6. Summary statistics for univariate and intervention ARIMA models
developed for southeast Alaska pink salmon. MAE
= mean absolute error of fitted values, s²a = unbiased residual
variance, r² = coefficient of determination, AIC = Akaike's
Information Criterion, SBC = Schwarz's Bayesian Criterion, and Q =
portmanteau residual autocorrelation test (up to lag 20)
and associated p-value. All statistics are calculated in the transformed
metric.
Model
MAE
s²a
r²
AIC
SBC
Q
p value
Univariate
0.484
0.397
0.348
133.7
140.3
14.43
0.808
One intervention
0.515
0.413
0.317
136.3
143.0
22.18
0.331
Two interventions
0.452
0.334
0.446
121.4
128.1
18.02
0.586
Table 7. Univariate and intervention ARIMA models with parameter estimates
and associated standard errors developed for
central Alaska pink salmon. Standard errors are given in paretheses
below the equations.
Model
Parameter estimates and standard errors
Univariate
(1 - 0.482B)ÖYt = 2.238 + (1 + 0.566B2)at
(0.110) (0.178) (0.117)
One intervention
(1978)
(1 - 0.252B)Ö Yt = 2.893 + (1 + 0.362B2at + 2.089It1978
(0.128) (0.163) (0.135) (0.433)
Two interventions
(1948, 1978)
Ö Yt = 4.377 + (1 + 0.241B2at - 0.946It1948 + 2.675It1978
(0.219) (0.122) (0.289) (0.327)
Table 8. Summary statistics for univariate and intervention ARIMA models
developed for central Alaska pink salmon. MAE =
mean absolute error of fitted values, s²a = unbiased residual
variance, r² = coefficient of determination, AIC = Akaike's
Information Criterion, SBC = Schwarz's Bayesian Criterion, and Q =
portmanteau residual autocorrelation test (up to lag 20)
and associated p-value. All statistics are calculated in the transformed
metric.
Model
MAE
s²a
r²
AIC
SBC
Q
p value
Univariate
0.726
0.915
0.583
191.2
197.9
9.63
0.974
One intervention
0.628
0.797
0.653
181.9
190.8
10.81
0.951
Two interventions
0.608
0.745
0.672
177.1
1846.0
20.03
0.456
Figure captions
Figure 1. Trend in total Alaskan salmon catch, 1925-1992.
Fig. 2. ADFG statistical areas and regional salmon stocks used in this study.
Fig. 3. Plots of the autocorrelation (ACF) and partial autocorrelation
(PACF) functions for the four salmon time series. The
ACF and PACF are computed for the appropriately differenced and transformed
time series.
Fig. 4. Plots of model fits for ARIMA and intervention models developed
for western Alaska sockeye salmon time series,
1925-1992. Landings data are indicated by dashed lines, fitted values
by thick lines. Estimated means before and after
interventions are shown by straight lines. Timing of the step interventions
and resultant change in mean are also shown.
Fig. 5. Plots of model fits for ARIMA and intervention models developed
for central Alaska sockeye salmon time series,
1925-1992. Landings data are indicated by dashed lines, fitted values
by thick lines. Estimated means before and after
interventions are shown by straight lines. Timing of the step interventions
and resultant change in mean are also shown.
Fig. 6. Plots of model fits for ARIMA and intervention models developed
for southeast Alaska pink salmon time series,
1925-1992. Landings data are indicated by dashed lines, fitted values
by thick lines. Estimated means before and after
interventions are shown by straight lines. Timing of the step interventions
and resultant change in mean are also shown.
Fig. 7. Plots of model fits for ARIMA and intervention models developed
for central Alaska pink salmon time series,
1925-1992. Landings data are indicated by dashed lines, fitted values
by thick lines. Estimated means before and after
interventions are shown by straight lines. Timing of the step interventions
and resultant change in mean are also shown.
Fig. 8. Summary of major oceanographic features of the North Pacific.
This page last updated on February 19, 1997.
Copyright © Steven R. Hare