ation viabi ity of t Snake River chinook sa Oncorhynchus tshawytscha

John M. Emlen

Abstract: In the presence of historical data, population viability models of intermediate complexity can be parameterized and utilized to project the consequences of various management actions for endangered species. A general stochastic population dynamics model with density feedback, age structure, and autocorrelated environmental fluctuations was constructed and parameterized for best fit over 36 years of spring chinook salmon (Oncorhynchus tshawytscha) redd count data in five Idaho index streams. Simulations indicate that persistence of the Snake River spring chinook salmon population depends primarily on density-independent mortality. Improvement of rearing habitat, predator control, reduced fishing pressure, and improved dam passage all would alleviate density- independent mortality. The current value of the Ricker a should provide for a continuation of the status quo. A recovery of the population to 1957-1961 levels within 100 years would require an approximately 75% increase in survival and (or) fecundity. Manipulations of the Ricker are likely to have little or no effect on persistence versus extinction, but considerable influence on population size.

RCsnmC : En presence de donnees historiques, il est possible de paramktriser des modkles de viabilitd d9une population qui sont de complexit6 intermkdiaire et de les utiliser pour prCdire les cons6quences de diverses mesures de gestion visant des espkces menackes. Nous avons construit un mod&le stochastiqate gCnCral de dynamique Bes populations tenant compte Be la rktroactisn sur la densitd, de la structure par 2ge et des fluctuations environnernentales aattocorrdldes; nous l'avons paramtitrisk pour obtenir l'ajustement optimal, sur 36 ans, de ddnombrements des nids de quinnat (Oncsrhynchus tshawytscha) de printemps effectuks dans cinq cours d'eau de l'ldaho servant d'indicateurs. Les simulations indiquent que la persistance de Ia population Be quinnats de primtemps dans la rivikre Snake dkpend avant tout de la mortalit6 indipendante de la densitk. L'amClisration de %'habitat de grossissement, la lutte contre les prkdateurs, la rCduction de %a pression de p$che et %'amClioratisn des passes migratoires devraient faire baisser la mortalit6 indkpendante de la densite. La valeur prCsente du param$tre a de Ricker devrait permettre le maintien du statu quo. Pour que la population remonte en 100 ans au niveau de 1957-1961, il faudrait une hausse d'environ 75% de la survie edou de Ia f6conditC. Bes manipulations du paramktre p de Ricker n9aatront vraisemblablement que peu d'effet sur la persistance par opposition 2i l'extinction, mais elles auront une influence considCrable sur la taille de la population. [TFPaduit par la RCdaction]

Introduction

Part of the recovery plan for any endangered species should be a risk assessment in which the probabilities of extinction over some finite period are related to various management options. Such a risk assessment consists of two steps: (1) relating management options to their impact on demo- graphic parameters and (2) determining the relationship between the demographic parameter changes and the

Received April 14, 1994. Accepted January 16, 1995. J 12340

J.M. Eden. Northwest Biological Science Center, National Biological Survey, Naval Station Puget Sound, Seattle, WA 98115, U.S.A.

prognosis for population persistence. The latter step is generally referred to as population viability analysis (PVA) and it involves the application sf population models utilizing the best information on the life history of the species in question.

Population viability analysis has at its disposal several classes of population models. At one extreme are the so- called '6systems9' models that incorporate significant detail into the processes to be modelled. The salmon life cycle model (SLCM; Lee and Hyman 19921, which includes considerable life-history detail and into which still more detailed submodels can be incorporated, is such a model. At the other extreme are the holistic models that, in theory? trade complexity for generality of application. The tkeo- retical models s f Goodman (1987), Ewens et al. (19871,

Can. J. Fish. Aquat. Sci. 52: 1442-1448 (1995). Printed in Canada / amprim6 au Canada

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and Dennis et al. (1991) are of this type. Both extremes have their advantages and drawbacks. With precise and complete knowledge of parameter values, systems mod- els should be the most accurate. Unfortunately, for most species, many parameter values are little more thm educated guesses. This opens the possibility of cascading errors in the projection of future population values. The simpler, holis- tic models are far less parameter intensive, and occasion- ally, as with the Dennis model, permit parameterization using time sequence data (see below). Essentially, they are bookkeeping models that optimize accuracy with only the most basic information. But these models generally are too simplistic to be reliable as trend predictors except over short time periods. The Dennis model, for example, does not consider density dependence. Thus, its accuracy falters during periods when the modelled populations rise close to carrying capacity (a later, still unpublished model corrects for this factor; B. Dennis, University of Idaho, Moscow, Idaho, personal communication). In addition, the Dennis model relies on a mathematical convergence (toward the predictions of more detailed and, presumably, accu- rate models) that requires time and so may be misleading over periods as short as 100 years.

A special situation exists when historical data on pop- ulation size are available. In such cases it may be possible to utilize models that, while simple, incorporate more of the processes affecting population dynamics than do models of the bookkeeping variety. In this paper, I present such an intermediate model and apply it to the Snake River spring chinook salmon.

The purpose of this work is threefold: (1) to show how existing time sequence data can be used to parameterize a model; (2) to show how the parameterized model can be used to assess future extinction probabilities; and (3) to evaluate the effects on extinction probabilities of altering model parameter values manipulable through appropriate management.

The data utilized were redd numbers in several Idaho '"index streams" on the middle fork of the Salmon River supplied by the Idaho Department of Fish and Game for 1957-1992 (Table 1).

The model

In keeping with standard practice in fisheries biology, the basic structure of this model incorporates instantaneous density feedback in early life (Ricker 1958) and continuous hatch-to-adult density feedback (Beverton and Holt 1954). The model also incorporates age structure.

Define the following terms: n,(t), n,(t), n(t) are numbers of female, male, and total spawners in year t, N(t) is the number of redds produced in year t p(t) is the proportion of eggs spawned in year t that are female ~ ( t ) is the average number of fish hatched per redd in year t that live to age 3, were there no density-dependent mortality qfi(t) is the probability that a female hatched in year t t d still alive at age 3, survives to age a' and then spawns q,,(t) is the equivalent for males

P(t) is the Ricker p at time t p(t) is a Beverton-Molt parameter for year t 6(t) is the ratio of females to the redds they produce in year t before the influence of density feedback It follows from the above that

in the absence of density feedback. Applying Ricker-type feedback, and allowing for depensatory mortality as well (see Emlen 1984, pp. 1 17-1 18):

These redds subsequently produce fry that rear in trib- utaries, where they experience continuing (Beverton-Holt type) density influences, migrate to sea, and then return to spawn at age 3 (males only), 4, or 5. The number of spawners returning in year t is drawn from the pool pro- duced in years t - 3, t - 4, and t - 5.

Five-year-old females spawning in year t arose from N(t - 5) redds produced 5 years before and hence number:

in the absence of density-dependent mortality. When Beverton-Holt density dependence is incorporated, this becomes

The total number of female spawners in year t, then, includ- ing both five and four year olds, is

and for males is

The values of T vary year-to-year, and can be approxi- mated, after Peterman (1981), by

The value E(T) gives the number of fish per redd surviving to age 3 and is, thus, proportional to the standard Ricker a.

The values of the Beverton-Molt coefficient, p, also vary with time:

To avoid further proliferation of parameters, P was assumed constant.

Equations 1-4 define the general model except for three last considerations. Environmental fluctuations are more

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Can. J. Fish. Aquat. Sci. Vol. 52, 1995

Table 1. Redd counts from five Idaho index streams.

Year Bear Valley Elk Marsh Sulphur Upper Big

complex than simple white noise. It is, therefore, appropriate to allow for a certain amount of temporal autocorrelation in the process w(t) (see Eq. 3). Too much generality would reintroduce many more parameters, so we compromise by allowing for a single, I-year lag correlation, writing

for use in Eq. 3, where X is the autocorrelation coefficient and w*(t), w**(t) - N(0,l).

Second, fishing pressure on these populations has declined from about 40-6096 to less than 15% over the 1957-1992 period (Charles Petroski, Idaho Department of Fish and Game, Boise, Idaho, personal cornmunication). This decline has been modelled in the simplest manner possible, assuming a linear decrease from 58% in 1957 to 15% in 1992. In addition, effects of dam turbines and screens have been studied by Raymond (1988). Using his

data, and lumping data into periods (1964-1970, 197 1-1975, 1976-1980, 198 1-1985) a regression of -ln(survival to the Snake River) on number of turbine units (x,) and screens (x,) yields

This relation was used to rescale E(a) (Eq. 3) on a year-to- year basis. E(a), accordingly rescaled for the last year of data (1992), was used in subsequent population projec- tions.

Finally, p(t) was determined using a binomial distrib- ution with a mean of one-half.

Metagogulation considerations Spring chinook spawn and spend their early life stages (largely) in tributaries. Therefore, fish inhabiting each trib- utary might be thought of as comprising a single population unit. However, even if no fish returned to a tributary over a 5 -yea period (meaning all year-classes have died out), recolonization from other tributaries via straying may stave off extinction.

There is a philosophical issue regarding recolonization by strays that has not been dealt with satisfactorily in the PVA literature. If recolonization is by individuals of different genetic constitution from those whose home turf is being invaded, resulting in genetic change of the native stock, is that native stock enhanced or compromised? In particular, if extinction is avoided by virtue of gradual replacement of the native population by genetically different immigrants, should the local stock nevertheless be considered extinct because its genome no longer exists? Furthermore, how different must the native md immigrmt stocks be before we reach this conclusion? This matter is probably not of con- cern where only natural, wild populations exist because current stray rates are likely to be similar to the historic pat- terns that, in fact, defined the local stocks (unless some significant anthropogenic habitat alteration has taken place), but the presence of hatchery strays is problematic. To avoid such nasty issues, the current work focuses on index streams largely free of hatchery influence (Bear Valley Creek, Elk Creek, Marsh Creek, Sulphur Creek, and Upper Big Creek) in the middle fork of the Salmon River drainage in Idaho.

Given the paucity of data, straying has to be dealt with in a somewhat simplistic fashion. For example, no con- sideration is given in the present treatment to variations in stray rate mong close versus more distant tributaries, and no consideration is given as to whether immigration is more or less likely into areas of low or high resident pop- ulation density. These simplifications might have significant impacts on the conclusions reached in this report.

Quinn and Fresh (1984) showed that straying from a local spring chinook population increased with age of the fish and decreased with population size. The relations are close to linear. Hence, I modelled the percent outmigra- tion of the population (8) using the function

C71 @ = y + ~y + pn,

where y is average age in the population, n is population size (number of potential spawners), and y, K, and p are parameters to be fit with real time sequence data.

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Estimation of model parameters Because the precise trajectory of a population depends on a series of stochastic events (environmental fluctuations, deviations in sex ratio about a mean, variations from mean straying rates) any appropriate model, of necessity, must be stochastic. As such, each run of the model can be thought of as a random selection from a universe of possible pop- ulation trajectories specific to the values of the parame- ters used and the initial population conditions. If, out of 100 runs, 80 result in extinction within 100 years, then the probability of persistence over 180 years can be esti- mated at 20%. This fact must be reflected not only in pop- ulation projections, but also when using the existing time sequence data to fit the model parameters.

Initial parameter values (E(T), p, E(p), etc.) were used, along with output from normal random number generators and redd count data, to generate for each of the five index streams, year-by-year: (1) T and y. values (Eqs. 3 and 4); (2) predicted number of spawners in the absence of stray- ing (Eq. 2), based on redd counts 3, 4, and 5 years in the past; (3) predicted number of spawners after straying (Eq. 7). Numbers of emigrants were determined using a binomial distribution with parameter 8, with a binomial (mean = 0.5) split among the sexes. Number of immi- grants, male and female separately, were randomly (bino- mially) determined for each population from the total pool of outmigrants; (4) predicted number of redds (Eq. 1); and (5) squared error (squared difference between predicted and observed redd number). The chain of calculations was repeated over all 36 years for which redd count data were available, and the sum of errors squared tallied. Finally, the above excercise was incorporated into a nonlinear least squares routine (Ecker and Kupferschmid 1983) and run repetitively to find those parameter values that best predicted the 36 years of redd data. This entire procedure was then repeated 100 times, with different random number sequences, to produce 100 equally likely parameter con- figurations, which thus constituted a probability distribution from which expected (mean) parameter values and confi- dence intervals could be calculated.

The initial parameter values (input to the best fit routine) were obtained as follows.

Observed spawning groups in the index streams are composed of approximately 2% jacks (3 year olds), and 4 and 5 year olds in a ratio of 0.31:0.67 (61. Petroski, per- sonal communication). Values of q., were set accordingly.

Initial parameter input values for E(T) were based on estimated delta and (Ricker) a-values. Petrosky and Schaller (1995) estimated a for these index streams at between about 1.9 and 2.8. Data collected on spring chinook spawn- ers and redds on the middle fork of the Salmon River in 1988 (T. Bjornn, University of Idaho, Moscow, Idaho, per- sonal communication) indicate a redd-to-spawning female ratio of 3.5 to 4 (but see discussion of redd count data, below). Under present densities of about 40-80 redds per stream and a beta value of 0.082 (see below), this translates to a 6-value of 0.20-0.26. The initial value of 6 was set at 0.25. Letting n represent stock, n' recruits, we can write, on average, n' = E(T)N = E(~)n,/6 -- E(~)n /26 in the absence of density feedback. But also in the absence of density

Table 2. Sensitivity to stray rate.

Stray rate Number sf redds relative to Probability in year 100 estimated sf for persisting true value persistence populations

Note: Values are means k SE.

Table 3. Effects of potential measurement error.

Sigma Number of redds relative to Probability 0% in year 100 for

estimated value persistence persisting populations

Note: Values are means A SB.

feedback, n' = an. Hence E(T) = 2a6. Therefore, E(T) lies somewhere in the neighborhood of 0.76-1.46.

Petrosky and Schdler (1995) estimated p-values for these streams (over indexed reaches) as 0.0008-0.0026. The input value used in data fitting for this paper was 0.002.

The initial estimate of E(y.) was obtained by estimat- ing the historic number of redds per stream at 200, two to four times present levels. Then, if Beverton-Holt feed- back reduced the population at those levels by, say, 8-lo%, E(y.) = -1n(0.92)/200 = 0.0004.

With respect to a and a ' , suppose initially that envi- ronmental fluctuations result in a 95% confidence swing of 20% about the average values of T and p. Then the val- ues of a and a h u s t be on the order of 0.17. The value of the environmental autocorrelation must lie between 6 and 1; a pure guess of 0.4 was used.

A regression of the fraction of the population composed of strays at Cowlitz hatchery (Quinn and Fresh 1984) on average age at return and escapement level provided initial estimates of y, K, and p of -0.6, 1-00, and -0.0002, respectively. Finally, in the absence of any information as to possible bias of density feedback by depensatory mor- tality, a and b were set initially to zero.

Constraints utilized in the fitting procedure involved holding E(T), P, E(p), Q, a ' , 8, a, and b, as well as out- migration rate over all years non-negative, and 0 < bb < 1.

Redd count data were based on indexed reaches that constituted different proportions of the various index streams. By treating these counts as absolute, the model, in effect, scales the population counts of the different streams in different units. Therefore, because E(T), P, and E(p) are in per-individual units, this fact alone leads to different values for these parameters among the streams. Predic- tions as to probability of persistence or (appropriately weighted) projected redd counts should not be affected.

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1446 Can. J. Fish. Aquat. Sci. Vol. 52, 1995

Table 4. Fitted parameter values.

Population

Parameter Bear Valley Elk Marsh Sulphur Upper Big

Note: Values are means + SE. Average stray rate (1988-1992) = [-7 4- E(age) -$(no. redds per population in 1988-1992)]/1W = [(-0.6048) + (1.0160)(4.65) - (-0.0002)(8).1184)(66.9)]/100 = 0.0412 Bars indicate average over all five populations.

Resuits its estimated true value. The results (Table 3) indicate that

Sensitivity tests Because the five index streams do not comprise the full metapopulation, projections of population survival and size based on them might be biased by omission of other streams. It seems likely, because the five populations are positively correlated with respect to year-to-year redd counts and because they are currently well below carry- ing capacity, that their dynamics are, in fact, nearly inde- pendent. That is, metapopulation structure seems likely to prove a minimal factor in population projections, at least so long as the population remains well below historic levels. To test this expectation, 100-year simulations were run, 10 replicates (different w*, w** sequences) for each of the 100 parameter solution sets, for various stray rates (y-, K-,

m d p-values of 0.001, 0.50, 1.00, and 2.00 times their esti- mated true values), and with E(T) set at two thirds of its estimated true vdue to assure a fair number of extinctions for comparison purposes. All projections were initiated with 5 years (1988-1992) of observed redd counts. The results (Table 2) indicate minimal influence of stray rate. Therefore, simulation bias introduced by incomplete metapopulatiora data also should be minimal.

There is some question as to the accuracy of the redd counts. The impact of counting error on accuracy of pop- ulation projections can be explored, at least crudely, as follows. Because redd counts are constrained to be positive, it is not unlikely that the measurement error tern should be approximately lognomally distributed. Thus, measurement error affects redd count in the same manner as environ- mental fluctuations and can be incorpsrated into the o tern. Population projections were run using a equal to zero (equivalent to a situation in which all 66envirsnmental" error is, in fact, measurement emor), equal to its estimated true value (no measurement error), and equal to one half of

extreme count errors may lead to low projections of redd numbers (although the differences for different emor rates are statistically insignificant) and have no influence on projected probability of population persistence.

Although the mean best fit parameter values were sim- ilar to expectation (initial values used), considerable vari- ation occurred among the 100 solution sets in each of the five populations. This raised the possibility of different solution sets corresponding to different local optima on the response surface. To check for this, frequency distrib- utions were examined for all 12 parameters for each of the five populations. There is no evidence of multimodal- ity in any of the populations. The best fit p a m e t e r values are given in Table 4.

Average stray rate is predicted to be about 4%. Data on actual stray rates are poor for the middle fork of the Salmon River, but the expected rate for spring chinook spawning at the Cowlitz hatchery, projected for the popu- lation density levels and spawning age structure seen in the index streams, is also about 4% (based on the afore- mentioned regression of percent strays on population size and age at return (Quinn and Fresh 15884).

Projections Following the above sensitivity tests and final parameter fit- ting, simulations were run, again over 100 years and with 10 replicates for each of the 100-parameter solution sets, varying the value of E(T) from 0.50 to 2.5 times its esti- mated value, and letting range between 0.001 and 5.00 times its estimated value. Results are provided in Figs. I and 2.

The parameter E(s) is proportional to a and describes density-independent survival and reproductive output. It is convenient, then, to speak of proportional changes in

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a rather than E(T). Varying E(T) (or a, Fig. 1) clearly has a profound influence on both likelihood of persistence and expected redd count in the 100th year. The present esti- mated a-value apparently is sufficient to virtually ensure population persistence over the next 100 years, and to lead to considerable increases in the number of redds over pre- sent counts (1988-1992), the lowest 5-year counts on record. If a were to further decrease to below 0.50 its pre- sent level, however, there seems little doubt that extinc- tion would follow. Population recovery, also, might be expected under present a. Indeed, in the absence of adverse weather conditions, environmental deterioration, or unex- pected setbacks, the 1957-1961 Ievels should be regained within about 160 years.

Alterations in p (mediated primarily through increased spawning habitat) seem to have virtually no impact on prob- ability of population persistence. As P varies from 0.061 to 5.00 times its present value, the likelihood of persistence drops from 100 to 95%. On the other hand, a doubling of spawning habitat (halving the present value of P) might increase the redd count by as much as 2.25-fold.

Fig. 1. Relation sf persistence probability over 100 years, and expected number of redds in year 100 as a function of cu, relative to its existing (estimated) value.

ax 1 Estimated Existing a

Discussion On the optimistic side, the model projections indicate a virtually certain persistence of Snake River spring chi- nook over the next 100 years. Models can be misleading, however. Notice in Fig. 1 that the mean redd count over the last 5 yeas corresponds to an a-value of only about 0.4 its estimated value. This may be a consequence merely of stochastic events, i.e., the recent redd count does not line up with the estimated ew for purely statistical reasons. On the other hand, i t could mean that important events, not accounted for in the model, are occurring; that is, param- eter values are changing over time. Have we merely wit- nessed a short series of unusually 66unlucky" years, or is something more sinister going on? Kf the latter is true, then a shift to the right is indicated for the redd count ver- sus a curve, suggesting an even dimmer prognosis for stock recovery. Consider also, when reading predictions from Fig. 1, that as a population grows with increased a, the role s f the density feedback parameters, P and E(b), becomes increasingly strong. Because of the insensitivity of population dynamics to these parameters at present den- sities, the values obtained for them using the best fit row tines may be inaccurate. Projections of redd counts with high a values, therefore, must be considered tenuous; pro- jections might be either overly pessimistic or overly rosy, and given present data it is impossible to say which.

The analyses and conclusions presented here account for temporal and other stochastic variation over the period between 1957 and 1992. They do not address risk arising from catastrophes. The effects of a series of unusually low water years, high reservoir mortality, a toxicant spill, or any other major environmental disruption might well fall outside the range of fluctuations implied by events over those 36 years and implicitly incorporated into the 100-year projections. Thus the predictions given in Fig. 1 are probably optimistic. In addition, no consideration is given to the importance of maintaining genetic diversity in the populations. While the model predicts little danger

Fig. 2. Relation of persistence probability over 100 years, and expected number of redds in year 100 as a function of p relative to its existing (estimated) value.

0 1 2 3 4 5 2 p 1 Estimated Existing p

of extinction for the population as a whole, local popula- tions can be expected to die out at a more rapid rate and to be recolonized by others. The consequent genetic deterio- ration can be expected to lower adaptedness and lessen resilience of the species to further environmental change. Again, the projections provided here probably paint an overly optimistic picture of the species' true status. From a management perspective, the projections given in this paper should be considered a best case scenario.

Acknowledgements I would like to thank Dr. Steve Cramer, Dr. Doug Neely, Dr. Ted Bjornn, Dr. Charles Petroski, and Dr. W. Miller for data, ideas, and discussion.

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References Beverton, R.J.H., and S.J. Holt. 1957. On the dynamics of

exploited fish populations. Fish. Invest. Lond. Ser. 2: 533. Chapman, D.W., A. Giorgi, M. Hill, D. Park, W.S. Blatts, and

K. Pratt. 1990. Prefatory review of status of Snake River chinook salmon. Report prepared by Don Chapman Con- sultants, Inc., for the Pacific Northwest Utilities Confer- ence Committee, Nov. 1 3, 1990.

Dennis, B., PL. Mulholland, and J.M. Scott. 1991. Estimation of growth and extinction parameters for endangered species. Ecol. Monogr. 61 : 1 15-143.

Ecker, J.G., md M. Kupferschmidt. 1983. An ellipsoid algorithm for nonlinear programming. Math. Program. 27: 83-186.

Emlen, J.M. 1984. Population biology: the coevolution of pop- ulation dynamics and behavior. MacMillan, New York. 527 p.

Ewens, We, P.J. Brockwell, J.M. Gani, and R.1. Resnick. 1987. Minimum viable population size in the presence of cata- strophes, p. 59-68. In M.E. Soule [ed.] Viable populations for conservation, Cambridge University Press, Cambridge, U.K.

Goodman, D. 1987. Consideration of stochastic demographics in the design and management of biological reserves. Nat. Resour. Modell. 1 : 205-234.

Lee, D.C., and J.B. Hyman. 1992. The stochastic life cycle model (SLCM): Simulating the population dynamics of anadromous salmonids. USDA For. Ser. Res. Pap. INT-459.

Peterman, R.M. 1981. Form of random variation in salmon smolt-to-adult relations and its influence on production esti- mates. Can. J. Fish. Aquat. Sci. 38: 1113-1 119.

Petrosky, C., and H. Schaller. 1995. A comparison of produc- tivities for Snake River and lower Co%umbia River spring and summer chinook stocks. In Proceedings of Salmon Man- agement in the 21st Century. 1992 Northwest Pacific Chinook and Coho Workshop, Boise, Idaho. American Fisheries Soci- ety Publication, Idaho Water Resource Research Institute. In press.

Quinn, TOP., and K. Fresh. 1984. Homing and straying in chinook salmon (Oncorhynchus tshawytseha) from Cowlitz River Hatchery, Washington. Can. J. Fish. Aquat. Sci. 41: 1078-1082.

Raymond, H.L. 1988. Effects of hydroelectric development and fisheries enhancement on spring and summer chinook salmon in the Columbia River Basin. N. Am. J. Fish. Man- age. 8: 1-25.

Ricker, W.E. 1958. Handbook of computations for biological sta- tistics of fish populations. J. Fish. Res. Board Can. 119: 1-300.

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