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Posted by | October 25, 2012

Alan A. Berryman, Xin Chen and Jon Firehammer


We analyzed annual counts of steelhead trout ascending dams on the Columbia and Snake Rivers in Washington. Counts of fish returning to the Snake River separate naturally into 3 sequences; a period of relative stability (1962-1972), a period of recovery (1974-83) following a sudden collapse in 1973-5, and a period of oscillations of increasing amplitude with a period of 3 years (1984-93). The data suggest that the dramatic collapse in 1973-5 was caused by the closure of Dwarshak, a high dam on the North Fork of the Clearwater River, a dam with no fish ladders that removed most of the spawning grounds for a strain of large steelhead known as the B-run. Construction of low dams with fish ladders on the Snake River seemed to have little or no additive effect on the numbers of returning steelhead but may have had a cumulative effect. Fluctuations in the numbers of adult steelhead ascending the Snake River were analyzed by autocorrelation. Results indicate that the endogenous dynamics were affected by a first order negative feedback mechanism which we was possibly caused by competition between successive cohorts. In addition, a second order feedback effect became more evident in the later years, concurrently with an increasing production of hatchery reared fish. The data were fit to several theoretical population models with the two-lag logistic model generally providing the best fit. Stability analysis indicated increasing instability in the dynamics of steelhead populations, seemingly associated with the destabilizing second order effect. Simulation analysis showed that the modeled system has two stable states, a three-point limit cycle and a fixed point, depending on initial conditions. Suggestions are made for further research aimed at determining the causes of steelhead population fluctuations and the decline of wild fish populations.


The Snake River is one of the major watersheds in the western USA. Arising in Yellowstone Park, it runs about 1500 km before emptying into the Columbia River near Pasco, Washington, about 300 km from the Pacific Ocean. The river supports a diverse community of andromonous fish, including the steelhead trout, Oncorhynchus mykiss, a major sport fish in the Pacific Northwest (Fig. 1).

Two strains of steelhead ascend the Snake Rivers each fall: A-run fish averaging 2-4 kg begin to enter the river in August while the larger B-run fish (averaging 5-8 kg) enter a month or so later. The majority of the B-run fish spawn in Idaho’s Clearwater River, particularly its North Fork. In 1971 the North Fork was blocked by the closure of Dworshak, a high dam without fish ladders. To mitigate losses of salmon and steelhead spawning areas, a large fish hatchery was constructed at the mouth of the North Fork.

Beyond the Clearwater, steelhead still run up the free-flowing Grande Ronde, Imnaha, and Salmon Rivers, as well as many minor tributaries of the Snake. However, ascent of the upper Snake River was permanently blocked in 1967, 100 km beyond its confluence with the Salmon River, by Hell’s Canyon dam, another high dam without fish passage.

Other dams on the Columbia and lower Snake all have fish ladders and, therefore, allow passage of steelhead and salmon: Starting near Portland, Oregon, are Bonneville (completed in 1938), The Dalles (1957), John Day (1968), and Mcnary (1953) on the Columbia, and Ice Harbor (1962), Lower Monumental (1969), Little Goose (1970), and Lower Granite (1975) on the lower Snake below its confluence with the Clearwater River.

Steelhead trout spawn in the tributaries of the Snake River in early spring and the young fish feed actively in these streams and rivers before migrating as smolts to the Pacific Ocean in the spring of their second year. Considerable efforts have been made to facilitate the downstream migration of steelhead and salmon smolts, including transportation in barges, the use of screens to reduce fish passage through hydroelectric turbines, and increasing stream-flow by drawing down the Snake River dams. Once in the ocean, steelhead feed actively and grow rapidly. A-run fish spend one or two years in the sea while most B-run fish remain in the ocean for two or three years. Unlike Pacific salmon, adult steelhead can return to the sea after spawning but the likelihood of making it through or over eight dams seems remote.

To mitigate for losses of salmon and steelhead spawning areas due to dam construction, hatcheries on the Snake and its tributaries release up to 10 million smolts each year. Despite this, or because of it, returns of wild steelhead have continued to decline and have prompted some Snake River strains to be placed on the endangered species list. Because of the steelhead’s position as the premier game-fish in the region, the actions and reactions of the various agencies have generated heated public debate in the Pacific Northwest. Questions are being asked about the effects of dams on steelhead dynamics, including talk of removing some of the dams; whether commercial, native American and/or sport fisheries have significant impacts on wild steelhead populations; whether massive hatchery production is hurting rather than helping the recovery of wild populations; whether the stability of steelhead populations is being affected by any or all of these changes in the river environment?

Recently there has been an increasing interest in analyzing population time series for the purpose of discovering the underlying causes and stability of observed fluctuations; sometimes called ecological diagnosis (Royama 1977, 1992; Berryman 1978, 1986, 1991a,b, 1994; Turchin 1990, Turchin and Taylor 1992). In this paper we analyze counts of adult steelhead ascending certain dams on the Snake and Columbia Rivers using the PAS (Population Analysis System), a time series approach developed specifically for biological populations, with the objective of understanding the causes and stability of fluctuations in these fish stocks, and to obtain some preliminary answers or hypotheses concerning the above questions.


During their passage over the dams on the Columbia River and its tributaries, steelhead trout are counted and classified from fish-ladder observatories. Hence, there exists a continuous inventory (time series) of all steelhead stocks ascending the Columbia River for 56 years (1938-1993) and the Snake River for 32 years (1962-1993). In 1995 we obtained fish count data to 1993 from the Coordinated Information System, now known as StreamNet (web site We first examined the time series of adult steelhead ascending 3 of the dams on the Snake River (counts from the fourth dam, Little Goose, were incomplete). As data from the 3 dams were remarkably similar, with correlations between dam counts exceeding 0.96, we used the numbers of adult steelhead ascending Ice Harbor, the first dam on the Snake River, as a measure of the adult steelhead population returning annually to the Snake River and its tributaries from 1962 to 1993. Steelhead counts at Bonneville, the first dam on the Columbia River, were also used because this was the only dam where the population was separated into A and B runs. (Although the method of separating the runs based on time of arrival is somewhat suspect, it does give a rough estimate of the relative size of the two runs.)

The data were analyzed with the PAS Single-species Time Series Analysis program P1a (Berryman and Millstein 1989). This program enables one to divide time series into sequences according to obvious discontinuities in the data, to detrend non-stationary sequences, to calculate autocorrelations, partial autocorrelations and rate correlations (see below), and to fit time series data to multiple-lag logistic and Gompertz single-species population models (e.g., see Royama 1977, Turchin 1990, Berryman 1994). Note that autocorrelations show the association between counts separated by different time lags (i.e., correlation between ln Xt and ln Xt-d, where Xt is the number of adult steelhead ascending the dam in year t and d is the time lag), and rate correlations show the association between the differenced sequence and lagged counts (i.e., the correlation between ln Xt ln Xt-1 and ln Xt-d,). We call this a rate correlation because the differenced data measure the per-capita rate of change of the population from one year to the next. Partial autocorrelation is the association between the lagged densities with the effects of shorter lags removed (the partial autocorrelation and partial rate correlation are identical at lag 2 and higher). Large negative rate correlations at lag 1 are indicative of first order dynamics while large negative partial auto (or rate) correlations at lags 2 or higher are indicative of higher order dynamics (Berryman and Millstein 1989, Royama 1992).

Following correlation analysis, models were fit to the steelhead counts with PAS, and the behavior of the models evaluated by simulation. We also used bifurcation graphs to evaluate the effects of parameters on the stability properties of the model. Bifurcation graphs were produced by running the model for 4,000 years and then plotting the last 200 simulated data points against the value of the parameter of interest. The value of that parameter was then incremented by a small amount and the procedure repeated for 100 increments.


Population dynamics result from the combined action of exogenous and endogenous processes acting on the reproduction and survival of individual organisms. In the former, environmental factors affect changes in population parameters but are themselves unaffected by the density of the population. In other words, environmental factors act as forcing or driving variables on population density rather than as feedbacks. Endogenous processes, on the other hand, involve feedbacks acting on population density through the demographic parameters and, thereby, determine the basic properties of stability and instability of the population system (Berryman 1981, 1989, 1994).

Exogenous dynamics

The first step in time series analysis is to evaluate and extract the effect of exogenous factors. Three distinct phases, or sequences, can be recognized in the adult steelhead counts at Ice Harbor (Fig. 2):

Sequence 1 (1962-1972). An 11-year period of oscillations around a relatively constant mean population of about 68,000 adult fish per year.

Sequence 2 (1975-1983). A 9-year period of recovery following a dramatic collapse of the population in 1973-4.

Sequence 3 (1984-1993). A 10-year period of oscillations with regular (period-three), or seemingly regular oscillations around a relatively constant average density of 109,000 fish per year.

We also examined the 57-year time series of steelhead ascending Bonneville, the first dam on the Columbia River and the only one where the A and B runs are separated, to see if there were any differences in the dynamics of these two runs (Fig. 3). This time series indicates that the B-run suffered major declines in 1948-51 and 1973-75 while the A-run had no major declines. It is interesting, and perhaps surprising, that the average steelhead returns over Bonneville have been somewhat higher in recent years than at any other time since Bonneville dam was built.

Endogenous dynamics

The observed oscillations of animal populations around their average densities can be caused by sampling errors, random variations in an external factor like weather (= exogenous dynamics), or by feedback processes, such as density-dependent competition for food or predator-prey interactions (= endogenous dynamics). As attempts are made to count all fish passing over the dams, and as the counts from all Snake River dams are highly correlated (r2 > 0.96), sampling error does not seem to be a major component of the observed variations. Hence, we can assume that most of the year-to-year variability of fish numbers in the stationary sequences (1 and 3) were caused by endogenous processes or random exogenous effects.

Because the second sequence in the Ice Harbor series was non-stationary, we were only able to evaluate the endogenous dynamics of the first and third sequences (Fig. 2). The autocorrelation functions for the two stationary sequences are presented in Figure 4. Notice the small autocorrelations in the first sequence and the strong positive autocorrelation at lag 3 in the third sequence. The latter indicates a periodic oscillation that repeats itself every three years, as is visible in the data (Fig. 2). Also note that the third sequence had fairly strong negative autocorrelations at lags 1 and 2 which suggests the possibility of first and/or second order negative feedback.

The partial rate correlations for the two stationary sequences are presented in figure 5. Of particular interest are the very strong negative correlations at lag 1 in both sequences and the fact that third sequence showed a strong negative correlation at lag 2. These results indicate that the endogenous dynamics of the steelhead population were regulated by a first order negative feedback process (rapid negative feedback between year classes), but that a second order process (delayed negative feedback) became evident in the later series.

Model fitting and analysis

Because changes in numbers of steelhead returning to the Snake River from one year to the next (the differences ln Xt ln Xt-1) were strongly correlated with the numbers present in the initial year (ln Xt-1) and the year before that (ln Xt-2) (Fig. 5), we decided to fit a second order model to the first and third Ice Harbor sequences. A second order logistic model (e.g., Turchin 1990) generally provided the best fit, so this model was used to investigate the dynamics and stability of the Snake River steelhead population. The two-lag logistic can be written

ln Xtln Xt-1 = AB Xt-1 – C Xt-2 (1)

where A is the maximum per-capita rate of change from one year to the next in the absence of density-induced negative feedback, B is the coefficient of first order negative feedback, and C is the coefficient of second order negative feedback. This model is easy to fit to the time series by linear multiple regression (Berryman and Millstein 1989). Parameter values and the results of numerical stability analysis are presented in Table 1. Notice that the model for the first sequence has a stable equilibrium but that for the third sequence exhibits complex dynamics. With this in mind we explored the latter model in more detail.

Stability analysis

Figure 6 shows two numerical solutions of equation (1) with parameters estimated from the third sequence (Table 1, column 3). The first solution, which has a stable point-equilibrium, began with an initial number of 140,000 fish while the second, which exhibits a period-three stable cycle, began with an initial population of 180,000. Hence, the model has two solutions, an inner solution that converges to a stable point and an outer solution that converges to a three-point limit cycle (Fig. 6). Notice that the limit cycle varies from a high of about 280,000 fish to a low of around 24,000. The fact that fluctuations in the steelhead returns seem to be increasing in amplitude (Fig. 2) may lead us to suspect that the dynamics are responding to the outer attractor and that even greater fluctuations may be seen in the future.


Counts of steelhead ascending the Snake River over the past 32 years can be divided into 3 distinct periods, or sequences, with characteristically different dynamics. During the first 11 years the population remained relatively stable around an average of 68,000 fish per year. The oscillations where mainly first order indicating that a large returning cohort in year t tends to be followed by a weaker cohort in year t+1, and vice versa. This implies that there is a negative feedback between successive cohorts. A possible explanation is that asymmetrical competition occurs between year classes, as may happen if two-year-old fish out-compete one-year-olds in fresh water, or 4-year-olds out- compete 3-year-olds in the ocean. It is also important to remember that, during this period, returning steelhead populations were composed mainly of wild fish spawned naturally in the Snake River and its tributaries whereas later counts were composed of increasing numbers of hatchery reared fish.

A dramatic collapse of the steelhead population occurred in 1973-5 with only 12,000 fish climbing Ice Harbor dam in 1974. This collapse occurred 2-3 years after the closure of Dwarshak dam on the North Fork of the Clearwater River, 3-4 years after the completion of Little Goose on the Snake, and 4-5 years after John Day was closed on the Columbia River. Lower Granite on the Snake was completed in 1975 and, therefore, is unlikely to have been involved in the collapse, though it could have hindered the recovery. Examination of steelhead returns at Bonneville (Figure 3), the only dam where attempts are made to separate A from B run fish, suggest that the collapse was mainly in the B run (in fact the B run over Bonneville in 1975 was the lowest in the entire series). Since both A and B runs pass over all the dams on the Snake and Columbia rivers, and since there was no evidence of a collapse of the A run, we are lead to conclude that the collapse was mainly caused by the closure of Dwarshak dam, an event that caused the loss of all steelhead spawned in the North Fork of the Clearwater River, most of which would have returned as B-run fish in 1974 and 1975. This leads us to believe that the wild B run is in considerable danger.

It is surprising that none of the other dams showed any impact on returning steelhead populations. The only other large decrease in the B-run was in 1951, prior to the major dam-building period. In fact the Bonneville steelhead counts have remained remarkably steady for almost 60 years. If anything, the total returns have increased during the last decade, presumably because of large-scale hatchery production. At the same time, wild steelhead have continued to decline, prompting their listing as an endangered species.

Following the 1994 collapse, returning steelhead populations contained increasing numbers of hatchery fish. Hatchery production almost tripled over the period 1976 to 1990 and this undoubtedly contributed to the recovery of the runs over the next 10 years, as well as the high dam counts in recent years.

During the final 10 years (1984-93), steelhead populations in the Snake have fluctuated around a new and higher average density of about 109,000 fish per year. However, these oscillations are quite different from those prior to the collapse. Not only are the oscillations much greater than before, but their amplitude seems to be increasing with time. In addition the oscillations are much more regular, having a dominant period of three years. Finally, observation of a strong negative correlation at lag 2 in the partial rate correlation function for this sequence suggests that the change in numbers of adult steelhead from one year to the next (the differenced series) is inversely related to numbers in the previous year (a second order negative feedback effect). The lack of a strong second order effect in the first sequence, when steelhead populations were largely composed of wild fish, suggests that increased hatchery production may be the cause of instability as well as the higher average returns in recent years. It is not clear, however, how increasing hatchery output could cause such a delayed second order effect. A mechanistic explanation of this phenomenon will probably have to await further research and modeling efforts.

Our analysis leads us to the following conclusions relevant to the conservation of endangered steelhead stocks. Of first concern are the wild stocks in the Snake River drainage. Our analysis, as well as simple logic, suggests that the wild B-run is in greatest danger because the construction of Dwarshak dam removed most of the spawning habitat for this strain. It is not clear if the low dams on the Columbia and Snake Rivers are a real threat to the wild populations. There is little evidence in the time series for an additive effect of these dams, for if there was, we should see a decline in returning fish 3-5 years after the construction of each dam. It is possible, however, that dam construction could have had a cumulative effect not visible in the time series. For instance, if wild steelhead populations are regulated at carrying capacity by typical negative feedback processes, then losses due to sequential dam construction could be compensated for by increased density-dependent survival. As long as the cumulative annual mortality from dams and all other agents was less than annual reproduction, the population could be sustained near to the carrying capacity of its environment. There could come a point, however, where the cumulative effect of 8 dams had reduced the survival of wild fish to the point where mortality exceeded reproduction, at which point the population would be doomed to extinction. This is a case of “the last straw breaking the camel’s back”. Because hatchery fish are protected for two years within hatcheries, their net reproduction could be considerably higher than wild fish so that similar mortality rates would not bring them to an extinction trajectory.

The apparent decrease in the stability of steelhead dynamics is another matter of concern. There is some indication that this instability may be associated with increasing hatchery production. In addition, hatchery reared fish could compete directly with wild fish and, because of their high juvenile survival under hatchery protection, may have a competitive advantage over their wild cousins. If this is true, then this mechanism alone could explain the collapse of the wild stocks.

Although diagnostic time series analysis is highly objective, in the sense that no preformed assumptions or hypotheses are made about the specific causes of population fluctuations prior to analysis, it cannot be considered definitive evidence for the biological causes of those fluctuations. Rather it should be treated as a pointer, or as a generator of hypotheses, for further research. As a start, we should probably test the above ideas on mechanistic computer models that describe the hypothesized competitive interactions between cohorts. If we can reproduce the dynamics observed in the time series under simulated dam-induced mortality and hatchery releases, it would give us some confidence in our diagnosis and may indicate which hypothesis is the more plausible. The next step should be to test the more plausible hypotheses by carefully designed experiments. For example, we may want to suspend hatchery production on particular watersheds or to remove certain dams to see if these actions stabilized adult returns and increased wild fish productivity.


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