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 (Figure 3.1). 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 (see, 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 interspecific 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 (Levin 1992). 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 I am most interested in identifying in this analysis is whether there exists biological, or more generally ecosystem, production regimes of decades-long duration that are punctuated by abrupt shifts in their level of production. Therefore, in examining the interannual dynamics of various biological components of large marine ecosystems, what one sees 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 I am trying to interpret.
Pacific salmon are particularly appropriate for testing the effects of interdecadal climate variability. They are the dominant top-level predator in the Central Subarctic Domain (CSD, Ware and McFarlane 1989), an oceanographically distinct marine region covering most of the Northeast Pacific (Figure 3.2). The various species of salmon range across much of the CSD throughout their life histories and thus, in a sense, serve to integrate conditions within the region. Exceptionally long time series of catches on Pacific salmon exist as well as complete run (catch+escapement) estimates for certain watersheds. These lengthy time series, which are probably as high quality catch data as exists for virtually any fishery in the world, greatly expand the degrees of freedom beyond what is normally available for fisheries oceanography investigations.
I 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, I should find coherent shifts in mean production levels across both species and area. To test this hypothesis, I proceed by statistically analyzing catch statistics for Alaskan salmonids. I then focus on individual Bristol Bay sockeye salmon runs for which detailed catch and escapement data are available.
There have been several recent, and not so recent, papers documenting and/or analyzing historic variability in Pacific salmon production (e.g., Rogers 1980, 1984; Fredin 1986, Ward 1993). Two papers in particular - Quinn and Marshall (1989), Beamish and Bouillon (1993) - are somewhat related to this analysis. Quinn and Marshall (1989) used a time series analysis approach, fitting both univariate and transfer function models, to catch data of regional Alaska salmon stocks. Their analysis, however, simply involved fitting a large number of models using available environmental data to find a best fit. This lack of an a priori hypothesis relegates the study to the exploratory stage. Interestingly, the inclusion of environmental variables (air temperature, sea surface temperature, freshwater discharge) improved the fit to their univariate ARIMA models only to "a limited degree." I surmise this was due to the fact that they only examined interannual variability. The Beamish and Bouillon (1993) paper focused on variability at the national level. They examined, in a mostly graphical manner, the historic variability in Japan, Russia, Canada and the U.S. national catches of pink, chum and sockeye salmon. Forsaking a time series approach, Beamish and Bouillon (1993) used lowess smoothing (Cleveland 1985) to highlight trends in their data. Importantly, they advanced a hypothesis on the source of the observed variability, namely fluctuations in the size of the winter Aleutian Low pressure system. It should be noted, however, that they found very low correlation between salmon catch and an index of the Aleutian Low (ALPI) they developed. While smoothing of both the ALPI and salmon time series increased the correlations, they correctly identified statistical problems with such an approach and did not report the correlations. An important difference between the results of my study and Beamish and Bouillon (1993) concerns the characterization of the nature of the variability. Beamish and Bouillon (1993) contend, perhaps on the basis of their use of lowess smoothing, that the changes in abundance were gradual rather than precipitous. I demonstrate in this chapter that Alaskan salmon production is best explained as a series of alternating regimes with the transition being nearly instantaneous across species and regions. Finally, due to the high serial correlation (lack of independence between successive observations) in both the physical and biological datasets used here and by others, I believe that formal time series methods must be employed to characterize historical variability as well as any relation to environmental factors.
On the basis of physical regimes identified in the previous chapter, I use formal time series analysis and intervention analysis to identify the significance, magnitude, and form of structural shifts (interventions) in the salmon production time series. I identify and test the timing and significance 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 that has been recommended as a method for detecting and quantifying non-random change in situations involving unreplicated experiments, such as historical variability (Carpenter 1990). I follow the methods detailed in Chapter 1.
Alaska salmon landings data are aggregated by several regional schemes. In this analysis, I use the statistical areas developed by the International North Pacific Fisheries Commission (INPFC) and reported in their Statistical Leaflet Series through 1980 (Figure 3.3). Salmon data is now generally aggregated, and reported, by Alaska Department of Fish and Game (ADFG) Management Regions, Areas and Subareas, though the older INPFC aggregations are still maintained for historical purposes. I elected to continue using the INPFC aggregation for two reasons. First, the data remain consistent over the time frame I chose to use (1925-1992). Secondly, the regional groupings combine individual runs together in a broad geographic range based on their marine entry location. Thus the Southeast Region includes salmon that spawn in (and entered the ocean from) rivers along the Alaskan panhandle. The Central Region includes rivers from the panhandle out to Unimak Pass. The Western Region includes all Bering Sea rivers and the few salmon producing streams far out the Aleutian chain. The ADFG grouping by Management region places runs from the Bering Sea in the same group as those originating in Prince William Sound, two marine areas generally of highly different conditions (though the freshwater rearing areas may be somewhat similar due to latitudinal proximity).
The salmon landings data used in this study were principally taken from an Alaska Department of Fish and Game annual report (ADFG 1991). Data for 1992 were taken from Pacific Fishing (1994). I focus on the four major regional groups of stocks: Western Alaska sockeye, 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 average annual Alaskan salmon catches (by number) for the period 1925-1992 (Table 3.1). Note that the terms "catch" and "landings" are used interchangeably throughout this study.
Catch data for these regional stocks are available from as early as the 1870's. I have restricted my analysis to 1925-1992, which I consider to be the period of full exploitation. If there is a "fishing up" effect (the appearance of increasing production which, in reality, is just a mirror of the increasing effort directed at the fishery) in the early part of the record, the time series analysis would be affected by this form of nonrepresentative dynamics. These time series span 68 years which is fully adequate for a proper time series analysis (Newton 1988).
Due to concerns over the impact of high seas and other interceptions, the catch data were adjusted to account for incidental catch of Alaska origin salmon and U.S. catch of non-Alaska origin salmon. Incidental catch data through 1989 were taken from Shepard et al.(1985), Harris (1989), and the Pacific Salmon Commission (1991). Data for 1990-1992 were computed by using the average interception ratio for 1985-1989. Between 1952 (start of the Japanese mothership fishery) and 1992 (demise of high seas salmon fishing), estimated interceptions of Alaska origin sockeye averaged 6.6% of the Western and Central Alaska origin sockeye catch, topping 20% in several years. Based on Harris (1989), I assigned 75% of the intercepted fish to Western Alaska, the other 25% to Central Alaska. The change in the catch time series for Western Alaska sockeye is illustrated in Figure 3.4. The other category of interception involved Canadian/Alaskan tradeoffs. I applied all corrections involving Canada to the Southeast Alaska salmon time series. Compared to Western Alaska sockeye, changes to the three other time series were minor, rarely accounting for a yearly change of more than 5% (not shown). More substantive changes occurred with the coho and chinook time series, however they are not formally modeled in this study. The final corrected time series for all fifteen species/area aggregations is illustrated in Figure 3.5.
True production data (catch plus escapement), while preferable to work with, are not available for many Alaska salmon runs. However, salmon catches are believed to mimic production, at least for very large runs, such as those used in this analysis (Beamish and Bouillon 1993). I was able to test this assumption by regressing 1950-1984 run size estimates (Rogers 1987) on the catch time series. The results (Table 3.2) support my use of the time series I assembled as a means of analyzing historical variability in salmon production.
To further analyze the breadth and significance of the regime shifts in salmon production, I collected total production (catch + escapement) data for Bristol Bay sockeye salmon. The Bristol Bay system is the largest producer of sockeye salmon in the world and relatively complete data exists on both spawners and recruits (production) since the 1956 brood year class (Stratton and Crawford 1992, Rogers 1994). These time series have also been corrected for estimated interceptions by the Japanese high seas salmon fleet. Under the ADFG run classification (Figure 3.6), there are nine major sockeye salmon producing rivers: Branch, Egegik, Igushik, Kvichak, Naknek, Nushagak, Togiak, Ugashik, and Wood. In both this analysis, and the stock-recruitment analysis in Chapter 5, I use data for all runs except the Nushagak for which good spawner-recruit data exists only since the mid 1970s. The Bristol Bay sockeye salmon data can be examined in either of two ways: by brood year or by return year (Figure 3.7). For this analysis I elected to do a return year analysis principally because the time series are longer, and they correspond better to the landings data. Full brood year data is available for the 1956-1987 year classes (assuming no significant numbers of fish older than six years have yet to return). Full return year data is available for 1956-1993, resulting in a time series of 38 data points. Bristol Bay sockeye, on average, tend to return at age five, though significant numbers return at ages four and six (Figure 3.8), with considerable interannual variability. In general, the fish spend one or two years in fresh water and two or three full years in the marine environment. There is, therefore, no uniform rule as to when fish of a given brood year or a given return year first encountered the marine environment. This becomes an important point when deciding upon the year to test for a regime shift in each population (see next section).
I determined the year in which to test for a statistically significant intervention (i. e., regime shift effect) in the salmon time series in the following manner. I first (Chapter 2) identified the timing of the interventions in the physical time series. These years were 1925, 1947, and 1977. I assumed that the year of effect on salmon was the first year of marine residence, following the evidence and arguments of Pearcy (1992). The interventions were then set at the appropriate lag and tested for significance. Thus, for example, assuming a change in the marine environment in the winter of 1976/77, the response would be noted in 1978 for pink salmon, in 1979 for fish returning after two ocean years (most western Alaska salmon runs) and in 1980 for fish returning after three ocean years (central Alaska salmon, a few Bristol Bay runs).
As noted earlier, this analysis focuses only on the four major salmon catch groups (Western and Central sockeye, Central and Southeast pink) largely due to the unreliability of the catch data to accurately index overall production. Basic time series diagnostics, however, are reported for all fifteen area/species groups to help illustrate the necessity of a time series approach to modeling the historic variability of Alaskan salmon. The first step in time series modeling is, if necessary, to transform the time series to stabilize the variance. Only square root and natural logarithm transformations were considered. All 15 time series were positively skewed and thus required transformation (Table 3.3).
The second step is to plot and examine the autocorrelation functions (ACF, Figure 3.9) and partial autocorrelation functions (PACF, Figure 3.10) functions. The plots indicate the following: 1) substantial autocorrelation is present in all 15 time series, 2) nonstationarity in certain groups (particularly coho and chinook); 3) complex historical dynamics are evident from the large number of significant ACF and PACF lags.. None of the four major groups require differencing to stabilize the mean though such an option was considered for Central Alaska sockeye due to the slow decline in both the ACF and PACF. Another curious aspect of the plots is that very few lag correlations (including the partials) are negative. Negative values in the PACF can be indicative of density dependent mortality (Turchin 1990). Only the Western Alaska sockeye lag 6 and Central Alaska chum lag 3 partial autocorrelations are significantly negative. Considering the number of time series examined, these negative relationships may be purely coincidental with no actual interpretation. This result supports Pearcy's observation that there is not strong evidence for density-dependent survival in salmonids, though density-dependent effects on growth are well documented (e.g., Rogers 1980, Peterman 1984).
I develop for each of the four time series, three models: a univariate model, a model incorporating a late 70s intervention and a model incorporating a late 40s and late 70s intervention. The final models, in traditional ARIMA form, and associated parameter standard errors are given in Table 3.4. Model diagnostics for all time series models are given in Table 3.5. Model fits are illustrated in separate figures and referenced within each section.
The Western Alaska sockeye data required a square root transformation to stabilize the variance. Examination of the ACF and PACF indicates very complex dynamics in this time series, substantially different from the three other salmon time series. 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 non-seasonal 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.
Based on the physical regime shifts that I identified occurring in the winters of 1946/47 and 1976/77, the interventions in the Western Alaska sockeye salmon time series should be detected in the late 1940s and late 1970s. The dominant Western Alaska sockeye life history is 2.2 (i.e., age five returning after two full ocean residence years), thus I used 1949 and 1979 as the years to test for interventions.
I 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 < .01), and in the 2-intervention model, both interventions were highly significant (p<.01). In both cases, the best statistical fit was provided by simple step (i.e. no ramp, decay, or delay) interventions. Both intervention models substantially outperformed the nonintervention model. The coefficient of determination, r², improved from .459 to .575 with the 1979 intervention and further increased to .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 1-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 Figure 3.11. 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 regime means were estimated at: 13.287 (1925-1948), 8.359 (1949-1978), and 25.843 million (1979-1992).
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 indicated 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 no-intervention models (r2=.644). Model residuals showed no residual autocorrelation.
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 my hypothesis that the climate effect occurs during the first year of marine life, I tested for interventions in 1950 and 1980 for the Central Alaska sockeye salmon time series. In the 1-intervention (1980) model, the step intervention was highly significant (p<.01) and led to an improvement in all diagnostic statistics. The 2-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 (Figure 3.12). 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 3.746 million) 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.
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 (.348).
Pink salmon migrate to the ocean in the spring following the year they were spawned and return the following year. Therefore, I 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 .05 (to .09). The 1-intervention model actually had a worse fit than the no intervention model. Had the AR 1 term been retained, however, most diagnostics would have favored the 1-intervention model. In the 2-intervention model, both interventions (negative in 1948, positive in 1978) were also highly significant (p<.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=.446) of the total variation in Southeast Alaska pink salmon catch was accounted for by the two interventions.
The change in mean catch under the 1-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 (Figure 3.13). Estimated average catch under the 2-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 million during the 1978-1992 period.
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 I found was a (1,0,2) model with no MA(1) term
In the 1-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 (Figure 3.14). The 2-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<.01) in the no-intervention model, remained barely significant (p=.05) in the 1-intervention model, and was not retained in the 2-intervention model, resulting in a (0,0,2) model. The MA(2) term reduced in magnitude from -.566 (no-intervention model) to -.241 (2-intervention model).
All eight Bristol Bay sockeye salmon production time series were log transformed to stabilize the variance and render them normally distributed for modeling. The resultant ACF and PACF plots are illustrated in Figures 3.15 and 3.16, respectively. Two of the time series, Egegik and Ugashik, were determined to be non-stationary and were differenced to stabilize the mean. The difference ACFs and PACFs for these two time series are given in Figure 3.17. As with the regional salmon landings, the diagnostic plots indicate a wide range of complex behavior in these time series. They are discussed separately in the following section. The univariate ARIMA time series fits for all eight series are illustrated in Figure 3.18; the intervention model fits are illustrated in Figure 3.19. The time series models for the ARIMA and intervention models are given in Table 3.6 and model diagnostics are given in Table 3.7.
The Kvichak run is strongly dominated by a 5-year cycle in which the peak year run can result in more than 40 million returning fish. As this run often forms the dominant component of the Bristol Bay run, its dynamics would be expected to be similar to those described above for the Western Alaska sockeye landings data. In fact, the same ARIMA (6,0,0) model provided the best time series fit to the data. In both cases, the AR(1) and AR(5) coefficients were positive, the AR(6) coefficient negative and the AR(2), AR(3), and AR(4) coefficients statistically insignificant and, therefore, not retained in the final model.
For the intervention model, I fit a 1979 step function based on the prevalence of age 5 fish (dominated by the 2.2 age group) in the Kvichak run. The intervention coefficient was positive and significant (p~.05); however, the overall model fit was inferior to the non-intervention model. The change in mean production was estimated at 5.388 million fish annually, a doubling in average run size. The increased production is mostly reflected in the non-peak year cycle runs; the peak year run size changed very little with the new regime. Addition of the intervention resulted in a decrease of the lag 1 AR coefficient below the .05 level and this is likely one factor in the overall poorer intervention model fit.
The Egegik time series could be adequately fit by a variety of univariate time series models. Due to the recent large upswing in run size, the Egegik time series has become borderline non-stationary. Four different univariate models were eventually selected for detailed evaluation. Three of the models: (1,0,0), (1,0,4), and (5,0,4) were fit to the non-differenced data; while the fourth model (3,1,0) was fit after differencing. Among the three non-difference model, the (5,0,4) was superior with an SBC value of 52.1. Besides the intercept term, there were lag 1 and 5 autoregressive and a lag 4 moving average term. The differenced series ACF and PACF plots indicated significant autocorrelated dynamics up to lag three. In the (3,1,0) model, all three AR terms were statistically significant. The SBC value for this model was much lower (47.2) than those of the non-differenced models. Additionally, the r2 value (.78) was the highest among any of the Bristol Bay univariate ARIMA models.
The Egegik intervention model was fit with a 1980 step. Among the Bristol Bay stocks, Egegik sockeye are, on the average, the oldest fish at return with more than 30% being age six (principally 2.3 fish). The 1980 intervention was significant (p~.03) and led to an improvement in all five diagnostic statistics. The change in mean annual production was estimated at 4.752 million fish, which represents a tripling in run size during the present regime.
For Naknek, only the lag 1 terms in the ACF and PACF are significant, indicative of a relatively simple ARIMA model. Only (1,0,0) and (0,0,1) models were considered, with the (1,0,0) providing a much better fit to the data. The univariate fit, however, was the worst among the eight stocks, with an r2 of .230. The Naknek sockeye are the second oldest, on average, at return thus I also fit a 1980 step intervention to this time series. The addition of the intervention, which was highly significant (p<.01), resulted in elimination of the AR(1) term. This model is the same as that found for the Southeast Alaska pink salmon landings data, indicating random variability about the regime level of production, which more than doubled , from a level of 2.053 to 4.547 million, with the mid 70s regime shift. The variance explained by the intervention model (r2=.428) was more than twice that of the univariate model.
The Ugashik time series had dynamics similar to Egegik, particularly in the recent period when continued increasing landings has led to a possibly non-stationary series. The same tentative models fit to Egegik were also fit to Ugashik with the same result. The difference model (3,1,0) was selected as best representing the dynamics as the SBC value of 99.0 was considerably lower than the best non-differenced SBC value of 104.7 for the (1,0,4) model. Unlike Egegik, the lag 1 AR term was insignificant. The univariate fit was second only to Egegik with a r2 value of 0.637.
The intervention model for Ugashik had a 1979 step that was highly significant and resulted in the best intervention fit of the Bristol Bay stocks (r2=.811). The step matched the beginning of the recent period of much higher production. Prior to 1979, the average annual run size was .830 million, subsequently runs have averaged 4.150 million, an increase of 400%.
The ACF and PACF plots indicate significant autocorrelation at lags 1 and 4 for Wood River sockeye. Wood River has the largest fraction of age four fish of the eight runs (roughly 43 percent), thus there is evidence of cyclicity in Wood River sockeye. Several univariate time series models incorporating lag 1 and 4 terms were evaluated. Fits among the four possible combinations: (4,0,0), (0,0,4), (4,0,1), (1,0,4) were fairly similar with the (1,0,4) model selected on the basis of lowest SBC. The fit was rather poor (r2=.330) largely because the ARIMA model could not "catch up" to the late 70's jump in production. Addition of a 1979 intervention parameter yielded a significantly better fit (r2=.449) despite the fact that the lag 1 AR term dropped out. The mean level of production doubled, from 1.569 to 3.192 million, with the late 70s regime.
On the basis of the simple ACF and PACF plots, I fit a (1,0,0) model to Igushik. Residual analysis, however, indicated significant lag 3 autocorrelation, hence a MA(3) term was also required in the model. The intervention model, with a 1979 step, provided a substantially better fit and increased the r2 value from .450 to .574. The effect of the intervention was to increase mean annual production from .443 to 1.046 million.
The Branch time series contains one highly irregular data point, the 1960 return year. Time series models were constructed including, and excluding, this datum. In both cases, the best ARIMA model was a (4,0,1). The overall fit was not particularly good either for the full time series (r2=.310) or when excluding the extreme value (r2=.328). The real influence of the extreme data point was exerted in the intervention model. Using the full data set, the 1979 step intervention was only significant at the 0.1 level. Excluding the data point lowered the p-value below 0.05. The statistics for the complete time series are what is reported in Table 3.6 and 3.7. The estimated change in mean production between the two regimes was .293 million, rising from .346 to .639 million.
The ACF and PACF plots for the Togiak time series showed significant autocorrelation at lag 1 and possibly lag 5. The best ARIMA fit was provided by a (5,0,1) model and resulted in an r2value of .351. A 1979 step intervention was found to be statistically insignificant, however a 1980 intervention was significant (p~.02). Togiak sockeye generally return at age 4 or 5. The large majority of the 5 year old fish are 1.3 age, thus 1980 is the appropriate year to test for an intervention for this time series. Mean annual production increased from .302 to .565 million.
Over the past seven decades, Alaskan salmon populations appear to have alternated between high and low production regimes. I 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 my hypothesis, I have demonstrated nearly synchronous production shifts in four regional Alaskan salmon stocks, and the eight principal sockeye runs from the Bristol Bay region. These stocks include two different species from three widely separated geographic regions. Using the technique of intervention analysis, I identified three production regimes defined by two major production shifts, one in the late-1940s, the other in the late-1970s. I now summarize the above results and estimate the combined impact of the regime shifts on Alaskan salmonid populations.
The increase in salmon production was highly significant in all four landings 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 5.498 (p<.0001, Southeast pink). 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 was for 1978. Additionally, I chose to test for a 1978 effect because, according to my 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 into the 1990s. Combining the four series, I estimate that the increased production resulted in an annual mean catch increase of greater than 60 million salmon. This translates to a nearly threefold difference in production between the previous regime of the late 40s-late 70s and the present regime beginning in the late 70s.
All eight Bristol Bay runs increased in mean production following the late 1970s regime change. Seven of the eight step interventions were significant at the .05 level, the other (Branch) at the .10 level. The increase in production ranged from 87% (Togiak) to 400%(Ugashik), with an overall increase of 142%.
The negative production shifts identified in the late-1940s were all significant, but generally of lesser magnitude than those of the late-1970s. The t-values for the step interventions in the two-intervention models ranged from 6.436 (p<.0001, Southeast pink) to 3.272 (p<.01, Central pink). The timing of the interventions I 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). I estimate the combined drop in catch following the late-1940s intervention at approximately 31 million salmon annually, a decrease of nearly 50% from the previous regime.
Evidence for an late-1940s regime shift is less convincing than for the late-1970s shift. To some extent, this may be due to the relative lack of data in comparison to 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.
Establishing the mechanism whereby salmon production is driven by large-scale climate processes can only lead to speculation at present. I 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. Several speculative mechanisms have been advanced to help explain the late-1970s rise in Alaskan salmon production. A detailed analysis of the evidence for these mechanisms and advancement of my own mechanistic explanation is the subject of the next chapter in this thesis.
Perhaps the most interesting feature of the salmon regimes I 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 what they termed Type A and Type B regimes. They characterized Type B regimes by warmer waters in the Gulf of Alaska resulting from a deepening of the Aleutian Low, whereas Type A regimes were periods of a weaker Aleutian Low. 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 I have documented for Alaskan salmon. In addition, the average duration of Type A and B regimes was 7-10 yr, whereas I 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) 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.
| Species | Avg. catch | % of total | cum. % | |||
| Southeast pink | 21.742 | 28.64 | 28.64 | |||
| Central pink | 20.704 | 27.27 | 55.92 | |||
| Western sockeye | 14.485 | 19.08 | 75.00 | |||
| Central sockeye | 6.287 | 8.28 | 83.28 | |||
| Central chum | 3.207 | 4.22 | 87.50 | |||
| Southeast chum | 3.114 | 4.10 | 91.61 | |||
| Western chum | 1.483 | 1.95 | 93.56 | |||
| Southeast coho | 1.426 | 1.88 | 95.44 | |||
| Central coho | 1.121 | 1.48 | 96.92 | |||
| Southeast sockeye | 1.088 | 1.43 | 98.35 | |||
| Western coho | 0.720 | 0.95 | 99.30 | |||
| Western chinook | 0.277 | 0.36 | 99.66 | |||
| Central chinook | 0.182 | 0.24 | 99.90 | |||
| Southeast chinook | 0.075 | 0.10 | 100.00 | |||
| Total | 75.911 | 100.00 | ||||
| Western Alaska sockeye | |
| Central Alaska sockeye | |
| Southeast Alaska pink | |
| Central Alaska pink |
| Species | |||
| Pink | |||
| Sockeye | |||
| Chum | |||
| Coho | |||
| Chinook |
| Model | Parameter estimates and standard errors | |
| Western sockeye | (1 - .538B - .505B5 + .369B6)ÖYt = 1.209 + at
(.107) (.111) (.122) (.107) | |
| Central sockeye | (1-.568B - .316B2)ln Yt = .216 + at
(.119) (.123) (.034) | |
| Southeast pink | (1 - .277B - .410B2)ln Yt = .906 + at
(.112) (.115) (.073) | |
| Central pink | (1 - .482B)ÖYt = 2.238 + (1+.566B2)at
(.110) (.178) (.117) | |
| Model | Parameter estimates and standard errors | |
| Western sockeye
(1979) | (1 - .299B - .499B5 + .253B6)ÖYt = 1.468 + at + 2.036It1979
(.121) (.109) (.131) (.105) (.415) | |
| Central sockeye
(1980) | (1-.572B)ln Yt = .655 + at + .917It1980
(.102) (.040) (.188) | |
| Southeast pink
(1978) | (1 - .495B2)ln Yt = 1.377 + at + .593It1978
(.108) (.084) (.310) | |
| Central pink
(1978) | (1 - .252B)Ö Yt = 2.893 + (1+.362B2)at + 2.0887It1978
(.128) (.163) (.135) (.433) | |
| Model | Parameter estimates and standard errors | |
| Western sockeye
(1949, 1979) | (1 + .305B3 - .377B5 + .225B6)ÖYt = 4.206 + at - 0.754It1949 + 2.192It1979
(.121) (.114) (.117) (.161) (.188) (.223) | |
| Central sockeye
(1950, 1980) | (1-.310B)ln Yt = 1.197 + at - .409It1950 + 1.145It1980
(.120) (.058 ) (.112) (.135 | |
| Southeast pink
(1948, 1978) | ln Yt = 3.284 + at - 1.032It1948 + 1.005It1978
(.121) (.160) (.183) | |
| Central pink
(1948, 1978) | Ö Yt = 4.377 + (1 + .241B2)at - .946It1948 + 2.675It1978
(.219) (.122) (.289) (.327) | |
| Model | ||||||||
| Western sockeye | ||||||||
| Central sockeye | ||||||||
| Southeast pink | ||||||||
| Central pink | ||||||||
| Model | ||||||||
| Western sockeye | ||||||||
| Central sockeye | ||||||||
| Southeast pink | ||||||||
| Central pink | ||||||||
| Model | ||||||||
| Western sockeye | ||||||||
| Central sockeye | ||||||||
| Southeast pink | ||||||||
| Central pink | ||||||||
| Run | Parameter estimates and standard errors |
| Kvichak | (1 - .387B - .551B5 + .562B6)ln Yt = 5.348 + at
(.133) (.109) (.133) (.131) |
| Egegik | (1 + .283B + .307B2 + .551B3)Ñln Yt = at
(.143) (.145) (.142) |
| Naknek | (1 - .474B)ln Yt = 4.174 + at
(.148) (.084) |
| Ugashik | (1 + .350B2 + .375B3) Ñln Yt = at
(.140) (.141) |
| Wood | (1 -.448B)ln Yt = 4.220 + (1 + .535B4)at
(.147) (.100) (.157) |
| Igushik | (1-.801B)ln Yt = 1.288 + (1 - .622B3)at
(.122) (.040) (.166) |
| Branch | (1 - .429B4)ln Yt = 3.474 + (1 + .535B)at
(.156) (.133) (.151) |
| Togiak | (1 - .455B5)ln Yt = 3.236 + (1 + .412B)at
(.165) (.104) (.155) |
| Run | Parameter estimates and standard errors |
| Kvichak (1979) | (1 - .548B5 + .305B6)ln Yt = 6.509 + at + .690It1979
(.118) (.118) (.172) (.341) |
| Egegik (1980) | (1 + .344B + .337B2 + .644B3)Ñln Yt = at + .668It1980
(.133) (.137) (.129) (.299) |
| Naknek (1980) | ln Yt = 7.627 + at + .795It1980
(.093) (.093) |
| Ugashik (1979) | (1 + .378B2 + .500B3) Ñln Yt = (1 - .352B)at + 2.777It1979
(.123) (.121) (.167) (.452) |
| Wood (1979) | ln Yt = 7.358 + (1 + .559B4)at + .710It1979
(.116) (.153) (.168) |
| Igushik (1979) | (1-.328B)ln Yt = 4.095 + (1 - .707B3)at + .860It1979
(.166) (.047) (.145) (.137) |
| Branch (1979) | (1 - .503B4)ln Yt = 2.905 + (1 + .516B)at + .613It1979
(.155) (.145) (.153) (.360) |
| Togiak (1980) | (1 - .330B5)ln Yt = 3.286 + (1 + .384B)at + .627It1980
(.196) (.120) (.159) (.254) |
| Stock | |||||||
| Kvichak | |||||||
| Egegik | |||||||
| Naknek | |||||||
| Ugashik | |||||||
| Wood | |||||||
| Igushik | |||||||
| Branch | |||||||
| Togiak |
| Stock | |||||||
| Kvichak | |||||||
| Egegik | |||||||
| Naknek | |||||||
| Ugashik | |||||||
| Wood | |||||||
| Igushik | |||||||
| Branch | |||||||
| Togiak |