or,| [Title Page] [Paper] [Figures and Tables] | Draft 18 December 1998 |
Growth rates and scope for Snake river chinook salmon are examined in order to 1) understand the spatial and temporal patterns of salmon growth; and 2) provide a foundation to model growth under simulated alternative river-conditions.
This analysis reveals that three basic measures of growth: instantaneous weight gain, instantaneous length gain and consumption rates are generally consistent but the differences between them are useful for making inferences about the growth process. Changes in "growth in length" do not necessarily accompany an equivalent change in the "growth in weight" because of changes in the morphology of juvenile salmon as they smolt, and changes in consumption do not necessarily accompany changes in growth or weight.
Growth of Snake River juvenile salmonids is a function of their run, rearing type, system of origin, temperature, position in the system and time of year.
There are several ways to measure growth. It can be determined by development of an individual organ or system, an increase in the mass or weight of the organism as a whole, an increase in the length of the organism, or (in principle) any positive or negative change in a morphometric parameter of the organism.
Growth records of Snake River juvenile chinook salmon are restricted to changes in either the length or weight of the fish. Not only are these measures nonlinearly related but their allometric relationship changes during the parr-smolt transition and varies between the runs (Hoar, 1988; Beckman et al. 1996; Beeman et al. 1994). These changes need to be understood for effective modeling of growth.
The ecological context of growth is examined through bio-energetic modeling. Much work on such ecological models for fish growth has been done and ultimately they depend on the fish's energy expenditure and prey consumption. Several assumptions about the fish and the system are necessary, but this mechanistic method ties growth to temperature profiles and biological parameters of the system as a whole. Since the parameters vary between "groups" of fish because they are distinct in space and time, it suggests that each group be modeled separately. For example, yearling hatchery chinook released into the Grand Ronde river in the spring of 1996 might be considered one group.
We are seeking to characterize the growth of a group of fish in a simple, yet distinct manner. Uni-modal distributions of parameters with as small a variance as possible are highly desirable. One of the central purposes of this analysis is to determine what those groupings are and characterize the parameters that make them unique.
The PIT tag recapture database was used to identify the over 55500 tag identities of released juvenile chinook that were subsequently recovered and remeasured. The tag-ids were used to obtain release and recapture information from PSMFC's PTAGIS database. The release information for each fish was obtained from the tagging database and related to the general release information through the release file id. Analogously, recapture information was obtained from the recapture or "observations" data. Each record therefore contained release information (e.g. location, date, temperature), individual fish information at release and at recapture (e.g. length and weight) and recapture information (similar to release information). From this superset of all possible fish, analysis was restricted to:
Over 35,000 individual records met all criteria. The data spanned 10 years of PIT-tag studies beginning in 1988 although it was not until 1992 that any significant recapture studies began.
Methods for calculating weight from length.
Length, though a useful measure of growth, is an insufficient measure for mass-balance bioenergetic models. However, length is an easily measured growth parameter, and is often used as an index for weight (Ricker 1979; Riddell & Leggett 1981; Beeman et al. 1994). All chinook salmon records were examined for availability of length and weight data. A summary of the data is in Table 2 and shows that 33028 - 18479 = 14549 recapture weights and 33028 - 11644 = 21384 release weights were missing for records where length is available. For fitting of a bioenergetic model, therefore, it was valuable to obtain these missing weights.
Allometric relationships for developing fish vary during development, likely in response to the priorities of vital functions at the particular life stage (Osse et al. 1995). The allometric weight-length relationship for a fish in a particular growth stanza is traditionally (Ricker 1979):
| or, |
(1) |
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(2) |
Modeling the log of the weights would have the form:
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(3) |
Eqn. (1) and Eqn. (2) apply to a given fish within a growth stanza and this requirement is gradually tightened in three stages of model fitting:
Stage 1: General relationship for all Snake River chinook
All chinook are considered the same and a general weight-length relationship is obtained by fitting Eqn. (2). The regression line is highly significant (p < .0001 and R2 = 0.9639) and the regression parameters are converted back for plotting on a weight vs. length graph. See Figure 1.
Stage 2: Releases and recoveries treated separately
Releases and recoveries are treated separately to determine if there is a system-wide change in the allometric relationship of weight to length between release and recovery.
The best fit for released chinook has the coefficients shown in Table 3 with p < .0001 and R2 = .958. The best fit for recovered chinook has the coefficients shown in Table 4 with p < .0001 and R2 = .957. Overlays of the two separate lines shows that the relationships are similar (both regression lines are drawn in both the left and right panels of Figure 2). A t-test of the slopes and intercepts of the regressions concludes that both the slope and intercepts are different (p < .001 for both slope and intercept.)
Table 3 Coefficients for the weight-length relationship in Eqn. (3) for released chinook
| Value | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
 0 |
-11.3309 | 0.0334 | -339.6413 | 0.0000 |
| 1 |
2.9792 | 0.0075 | 397.8144 | 0.0000 |
Table 4 Coefficients for the weight-length relationship in Eqn. (3) for recovered chinook
| Value | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| 0 |
-11.6657 | 0.0202 | -577.3893 | 0.0000 |
| 1 |
3.0507 | 0.0043 | 715.6941 | 0.0000 |
Stage 3: Importance of covariates to weight-length relationship for recovered fish.
Since smolting chinook change in body form and behavior (Dickoff et al. 1995; Hoar 1988; Ricker 1979), the apparent bi-modal distribution of lengths at a given weight (Figure 3) could be a result of the pooling of data on actively migrating smolts and resident or slowly migrating parr. The recapture data clearly show two separate trajectories (Figure 2). Graphically the different runs and rearing types seem to have different relationships as shown in Figure 4.
We seek a general linear model to assess the importance of covariates that contribute to the variance of the weights and consider the following:
 |
(4) |
i = unmodeled variability (error) x (j or k) = regression parameters for x=1, 2, 3, ... 9The least squares fit of Eqn. (4) gave results tabulated in Table 5.
Table 5 Regression results for recaptured chinook. Run 1, Type H chinook (Hatchery yearlings) are considered to be the base case.
Analysis with single term deletions was used to find a more parsimonious model. The Pearson chi-squared version of AIC (Cp = 
2 + 2p, where p is the number of parameters) was used. With the large data set, model improvements as a result of adding terms are to be expected without a penalty to the AIC. Conventionally, if inclusion of a term reduces the AIC, then the resulting model is justified despite the loss of parsimony. For example, Cp = 355.170 using Eqn. (4). Dropping the recapture month and run interaction term increases this value to Cp = 372.849 and therefore should be retained in the model.
Table 6 Effect of dropping one term from Eqn. (4). "relmo" is the release month, "logreclen" is the log(recapture length), and ":" indicates the interaction of two variables.
Arguably, a biologically significant model is more desirable than the ideal statistical model and terms that contribute little to the overall SS (such as the release month and run interaction term) will be omitted.
Based on the results presented in Table 6, the recapture month and run are retained in the model along with their interaction term. If smolting is assumed to be a principle cause of the bimodality in the weight-length relationships, and we expect the different runs to smolt at different times during the year, then this model has a biological basis as well:
 |
(5) |
for all i and j = 2, 3, or 5 (corresponding to run types 2, 3, and 5 because the base condition is for run type 1--yearling chinook). All terms are significant at the p < 0.0001 level and R2 = 0.967. The coefficients are listed in Table 7. Although the common regression for the recovery data had an R2 = 0.957, and this is a small improvement for the population as a whole, we are interested in the fit of the curves for the larger fish where they clearly diverge into two different weight / length trajectories. The data is sparser for these larger fish and thus they have less influence over the overall fit.
Table 7 Coefficients for model in Eqn. (5)
Recapture weights will now be modeled as:
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(6) |
Transforming the equation and coefficients, we get the following relationships for the four different recapture runs:
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(7) |
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(8) |
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(9) |
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(10) |
Stage 4: Importance of covariates to weight-length relationship for released fish.
As for the recovery data, a general linear model was used to assess the importance of covariates that contribute to the variance of the release data:
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(11) |
i = unmodeled variability (error) x (j or k) = regression parameters for x=1, 2, 3, ... 6A summary of this analysis is shown in Table 8.
Table 8 Effect of dropping one term from Eqn. (11). "relmo" is the release month, "loglen" is the log(release length), and ":" indicates the interaction of two variables.
| Df | Sum of Sq | RSS | Cp | |
|---|---|---|---|---|
| <full model> | 206.319 | 206.944 | ||
| loglen | 1 | 2322.646 | 2528.965 | 2529.542 |
| relmo:run | 3 | 3.297 | 209.616 | 210.097 |
| relmo:type | 2 | 1.386 | 207.706 | 208.234 |
The type term (and its interactions are dropped) but the release month and run terms are retained to be consistent with the recovery models, even though "run" and "release month" are not as significant for released fish as "run" and "recovery month" are for recovered fish. The regression model for fish on release is then:
 |
(12) |
for all i and j = 2, 3, or 5 (corresponding to run types 2, 3, and 5 because the base condition is for run 1--yearling chinook). All terms are significant at the p < 0.01 level and R2 = 0.960. The coefficients are listed in Table 9. Despite their significance, there is only a small gain in understanding the variability in weights. Recall that R2 = 0.9585 for released chinook using the simpler model shown in Eqn. (3).
Table 9 Coefficients for model in Eqn. (12)
Transforming the equation and coefficients, we get the following relationships for the four different runs on release:
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(13) |
 |
(14) |
 |
(15) |
 |
(16) |
Application of formulas and relationship to each other
For fish that are grown for a very short period of time, the exact value of calculated release weight and the recapture weight can be very significant in determining growth. This is especially important for fish that are released very early or very late in the year. If separate release and recovery equations are used, a fish that does not change in length would have distinct weights calculated for release and recovery and that difference can be as much as 28% for a 100 mm fall chinook. This extreme example is for a fish released in December where the release formula predicts a 13.2 g fish and the recovery formula predicts an 18.3 gram fish. At the beginning of the year, the differences are reversed and a 100 mm fish would have weights modeled as 9.4 and 7.7 grams respectively. During the months of April, May and June this difference is less than 5%. Nearly half of the released and recovered fall chinook in the database were released in these months and 40% were released in July and August when the errors are 8 and 13% respectively. In the case of spring chinook, the difference is much less and varies linearly from -2.2% in January to -2.8% in December.
The longer that the fish grow in the system, the less significant is this difference, however to eliminate the cases of 1) incorrect growth direction (negative vs. positive) and 2) impossible growth rates; the recovery equations were used to model all weights. This insures that fish that grow only a small amount between release and recovery will have weights that reflect that growth. Nearly half the records are for fish that were in the river less than 10 days between release and recovery.
Perez-Gomas and Skalski (1997) examined changes in length of yearling chinook in the reach between LGR and LGS and conclude that they grow. This group took an average 9.3 days to travel the distance (median, 8.8) The length increment of these fish is certainly significant, however, their weight increment seems to be less upon examination of the graphs (see Figure 5). None of the fish they used in the study had release weights measured and only one fish had weight measured on recovery. In order to look at growth in weight, modeled weights have to be used. Using the single weight-length relationship for these fish on recovery, they appear to grow (shown), but using the separate relationships for the release and recaptured fish as detailed earlier, they did not appear to grow in weight (not shown). Indeed this begs the question of how to best to determine weight from length.
Arguably, the regressions are not calibrated for these fish (yearling hatchery chinook) in the impounded portions of the Snake river and therefore cannot be used reliably for that specific group, but given the biology of smolting, we do expect a change in their length-weight relationship as smolting progresses. Release-recovery studies that track both length and weight will be necessary to determine if weight growth is as significant as length growth.
A second group that they examined was a group of 43 PIT-tagged wild spring chinook that traveled from GRANDR to LGR in an average 33 days (median, 31). This group also increased significantly in length and their weight growth is also readily apparent (see Figure 6).
The "Wisconsin model" was developed by limnologists at the University of Wisconsin to model aquatic species interactions. There is an interface for it that exploits modern input and output methods and it has a users manual. All of the modeling assumptions are outlined therein and are not repeated in detail here, but an overview of the essential growth model follows.
Implementation of the model was done independently of the Wisconsin model interface in order to bundle it into a program that would quickly and efficiently read each of the records and then apply the bioenergetics model. In back-to-back comparisons, there were some differences in model predictions and these implementation errors are unresolved.
Growth in grams per day is defined:
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(17) |
I assumed that the basic parameters used for modeling consumption (C), respiration(R), excretion (U) and egestion (F) were constant for chinook (Hanson et al. 1997) (see Table A4). Simulations of growth require stream temperature, T, which must be known for each day that growth is simulated, and an ecological parameter, P, that is a temperature-independent proportion of the maximum consumption rate.
Fitting the P-values in this model requires a temperature history for each individual fish. Because the fish were moving in both space and time and the data is incomplete, several methods for generating temperature profiles were considered.
for each day i where day 0 is the release day (Release temperature). 
for each day i where day f is the recovery day (Recovery temperature). 
(Linear interpolation between release and recovery). Fish are assumed to move linearly from the release to the recovery site and for each day i (i = 0, 1, 2,... f) their position x is determined as decreasing from xrel to xrec = 0. Temperature records from the data sources at positions yj (j = 1,2,3,...n) are noted for days i=0 to i=f. If there is no single value of yj that matches x, then an upstream and downstream site with temperatures on day i are located and designated yu and yd respectively.
In creating a temperature profile for each fish, record "quality" is important. Temperature record quality is determined by proximity of date and location. For example, a fish is released at a known location on a known date and the temperature is recorded. This is higher quality than any estimates between sampling locations and between sampling dates.
The following criteria are used to create a temperature history for the growth of each fish. The highest quality temperature vector is created by applying the criteria in order. This ensures that the start and end values are determined first, followed by good quality intermediate values and concluded with lesser quality interpolated values. D was chosen to be 20 kilometers.
P-values are "proportion values" as opposed to "probability values". The terminology is maintained following model developers. In the bioenergetics model, P is a critical value that controls growth as the proportion of the maximum consumption rate that the individual fish can maintain, independent of temperature. In principle, it encompasses stream productivity, competition and other factors that may affect fish consumption and growth. In general applications of the Wisconsin model, these have to be fit to existing data before growth simulations can be run. The P-values can be calculated for individual fish that have the following attributes in their records: weights at the beginning and end of a small time frame, and a known temperature history between beginning and end (Stewart et al. 1983).
Bartell et al. (1986) and Kitchell et al. (1977) both observe that the model is better able to model consumption rate based on growth than predict growth based on consumption. This is due to the high sensitivity of growth to parameter P (Bartell et al. 1986; Beauchamp et al. 1989).
Several methods were used to measure juvenile chinook growth:
Proportion of maximum consumption as determined by fitting the bioenergetics model where temperatures are based on a temperature profile linear between the release and recapture temperatures. This indicator is the p-value from fitting the bioenergetics model with temperature method three.
A high P-value indicates that the fish are able to grow at a fast rate for the temperature they are experiencing. For a large group of fish with a common rearing history (i.e. same run, type and river system), P-values were aggregated and their distributions examined.
Comparison of p-value distributions based on different temperature profiling methods are not noticeably different, i.e. the plots of P value distributions in Figure 19 and Figure 20 show the same general patterns. Likely, only for an individual fish, will the exact method of temperature modeling be important.
There is some evidence that the P-values vary with temperature. This is likely due to changes in the productivity of the system since it intended to be de-coupled from the modeled activity level of the fish.
If the separate weight-length relationships are used to determine weights at release and recapture for fish that only have length recorded, it is quite likely to generate "impossible" weight changes especially for very short growing periods. To avoid this problem, the recovery equations were used to generate both release and recovery weights. (See Application of formulas and relationship to each other).
This is similar to indicator 1, but the proportion of maximum consumption is determined by fitting the bioenergetics model with temperature profiles based on all available temperature data. These are P-values from fitting the bioenergetics model with temperature method four.
Average daily increment of weight based on the release and recovery weight, where modeled weights are used if data is absent. Average daily growth rate is calculated as the change in weight from release to recovery divided by the time in days and the average weight of the fish. This is a good estimate of the average, daily, relative growth increment. It is defined as:
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(18) |
Average daily increment of weight based on a constant, average daily weight gain, where modeled weights are used if data is absent. Because growth indicator 1 is sensitive to the size of the fish on release (especially for smaller fish), growth indicator 2 is based on compounding of the relative growth rate. It is equivalent to a compound interest rate:
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(19) |
where G is the rate of growth in grams per gram per day. This is equivalent to a computationally simpler though less intuitive form (Ricker, 1979):
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(20) |
Eqn. (20) is less sensitive to positive growth rates and more sensitive to negative growth rates than Eqn. (19). To convert between these indicators:
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(21) |
These are analogous to growth indicators 3 and 4 but use length instead of weight.
Comparison of growth indicators
I found 33108 records of Snake River salmon growing for more than 1 day, less than 200 days and with lengths between 30 and 250 mm and with recovery weight less than 250 g. Many of these fish could not have a P-value (Indicators 1 and 2) calculated because data was missing or incorrect (no release or recovery temperatures, weights or lengths missing etc.) For fish that had valid weights and temperatures, the ones with the lowest growth rates were the most difficult to fit with the bioenergetics model. In some cases, the model failed to fit a consumption rate at all. This was not unreasonable since over 80% of the fish for which a P-value could not be calculated were yearling (Run 1) chinook and if they were moving through the system as smolts are likely to have a much slower growth rate than resident parr.
Despite this, over 17000 records had all six indicators calculated and four of these: (indicators 1,2,4 and 6) are compared and shown in Figure 7. The best correlated measures are Indicators 2 and 4. For indicator 2, all available temperatures are used to model the growth. We expect any two measures to be correlated, but not exactly. It is possible for fish to grow at fast or slow rates and still feed at a fixed proportion of their maximum consumption rate. Temperature, variation in the energy density of their prey, the proportion indigestible, etc. all affect the true growth rate for a fish feeding at a given P value.
Of the six indicators, some of them are considered undesirable. Indicator 4 is preferred for weight growth over indicator 3 because it better represents the curvilinear nature of growth in fish and requires no more information. Indicator 6 is chosen over indicator 5 for analogous reasons. A decision between indicator 1 and 2 is somewhat less simple. Indicator 1 requires only two temperature readings but is therefore sensitive to their exact values and their ability to represent the true thermal experience of the fish. Indicator 2 attempts to use as much temperature information as possible. Although more difficult to gather, the additional information is valuable since the bio-energetic dynamics are temperature dependent.
Figure 7 compares indicators 1, 2, 4, and 6 for all the fish records examined. The bottom row of three graphs shows the relationship between the three indicators chosen: 2,4, and 6.
There are several possible analyses for the data, once the growth indicators have been determined. This study screened the following:
Influence of release length on survival to recovery
Several studies have demonstrated the significance of release size on return survival (Bilton 1984; Martin and Wertheimer 1989; Ward et al. 1989) for salmon. Whether this size advantage is conferred at all stages of the life cycle is not clear. Examination of the relationship of release length on survival to recovery while the fish are juveniles may shed light on the influence of this factor during the early life history. Survival to recovery is not the same as general survival. The recovery database does not include all detections of PIT tagged fish, only those that were removed from the river and remeasured. Many fish that have length and or weight recorded at the time of tagging are subsequently detected at downstream locations, however, only a few of these are recovered and remeasured.
The effect of initial length on survival to recovery and remeasurement was determined by examining the frequency distribution of weights of recovered fish sizes compared to released fish. For this analysis, large releases (counts) were identified and subset based on recoveries of 20 or more fish. To ensure the largest possible number of groups, the SNAKER-released, wild sub-yearling chinook designated "1,5,W" were included with the other wild sub-yearling chinook. The recovered fishes' release lengths (y) were considered to be a random sample from the release lengths (x). Three tests were performed on the release and recovery data: 1) Kolmogorov-Smirnov goodness-of-fit for the distributions as a whole, 2) Welches modified t-test for comparison of the means, and 3) an equal variance test. The null hypotheses are respectively:
.Although there are some discrepancies in the actual number of released fish and the number of records for each release, it was assumed that the meta-data was wrong in these cases and that the individual records were in fact valid, i.e. the meta-data may indicate a release of n fish, there may in fact be >n records of individual fish from that release.
Table A5, through Table A8 show detailed results for these comparisons. In the case of wild yearling chinook, in only seven out of 120 tests of H2, the null hypothesis was rejected it appears that recovered fish are randomly distributed from the releases. Similarly for the wild sub-yearling chinook, in only two out of 22 cases of H2, the null hypothesis was rejected and it appears that the recovered fish were randomly distributed from the releases.
In the cases of hatchery fish, in 27 out of 63 tests of H2 for sub-yearling chinook, the null hypothesis was rejected, and for 22 out of 150 tests of H2 for yearling chinook, the null hypothesis was rejected. This suggests that the influence of release size on survival to recovery varies between the rearing types. Growth indicators for a population of fish that have differential survival based on release size will be biased if the individual growth indicators are correlated with the release size (see below).
Unexplored potential biases include:
Influence of release size on growth
The influence of release size on growth is important because it examines:
Release size (length) is a significant predictor of subsequent growth. Figure 8 through Figure 10 show how the three indicators relate to eight groups of fish. In almost all cases, the negative correlation suggests that the smaller fish are growing better than their larger counterparts. This could be due to prey selectivity, habitat availability, or other factors that contribute to growth opportunities. Larger fish may have trouble finding suitable prey or may grow more slowly due to smoltification and migration energy requirements. The most significant lines are for the subyearling chinook that are more likely to be active feeders in the system. Regression lines for the yearling fish (run 1) are very flat and some are insignificant.
Indicator 2 required creating a temperature profile. Method 3 and Method 4 for temperature profile modeling were considered. For many fish, the methods produced identical profiles, but for some fish the differences are significant. Figure 11 compares the average temperature of the method 3 and 4 profiles for each record.
Indicator 2 showed a very strong signal in response to temperature. Figure 12 shows the relationship of indicator two to the average temperature from method 4. Since the P-value calculated with the bioenergetics model is designed to be independent of temperature, this suggests that it reflects productivity in the system. The negative or zero correlation that exists for Run 1 may simply demonstrate that these fish are doing very little feeding in the system.
Indicators 4 and 6 are perhaps less informative. Figure 13 shows the relationship of growth indicator 4 (weight) to average temperatures from methods 3 and 4 respectively. Figure 14 shows the relationship of growth indicator 6 (length) to average temperatures from method 4.
Both indicator 4 and indicator 6 are very similar for a given type and run. The results for comparisons of different types and runs are more complicated. Hatchery and wild fish have somewhat opposite patterns in their growth-temperature relations, with hatchery sub-yearling chinook showing an increase in growth rate with temperature and wild sub-yearling chinook showing a negative or non-existent relationship of growth rate to temperature. A summary of the regression relations are shown in the table that follows.
Table 10 Relationship of Indicators to average temperatures determined by method 4.
Arguably, these regressions have many problems. Most notable is the inconsistency of the length of time between release and recapture, the longer that time difference, the less likely that the growth rate is correlated to this average, because the intervening temperature experience of the fish has an increasing chance of being different than that average. A weighted regression (using 1/days as the weight; not shown) gave slightly different results but these differences were small.
Growth in warm waters is important because reservoir temperatures as well as lower Snake river temperatures regularly exceed 20 °C in the summer while the optimum growing temperature for chinook salmon is closer to 15 °C. Identifying fish that were exposed only to warm temperatures is little more difficult. Only 50 fish were reported to have been released and recovered in water > 20 °C. Forty eight of them were Snake river hatchery sub-yearling chinook released at SNAKER or LGRCOL sites and recovered at LGR or LGS. Many more records (>680) show recovery in temperatures > 20 °C but the release temperatures varied from 13.5 to 20.5 For fish that are released in comparatively cooler water and recovered in warm water, it is not known precisely what portion of their in-stream growth occurred under the warm conditions.
The best data available are records of fish that are release and recovered in 20°C water (for higher) A comparison of the warm-exposed fish to those released and recovered in water temperatures strictly below 20°C shows very little difference in the growth indicators.
It is not clear whether this growth data set can be used to determine the effects of warm water on the growth of these fish. Indicators 1 and 2 were difficult to obtain for these fish and those that did have P-values calculated were at a very high level. This may indicate that the true temperature experience of these fish is not well represented by the release and recovery temperatures. Alternatively, behavioral modifications of the fish affect their true temperature experience or the productivity issues are significant.
Influence of total number of fish on growth indicators.
The mean and median of the growth indicators was used to characterize the different distributions by system, run, and type. These, in turn were compared to the smolt indices for the years 1971 to 1997 when good records were available. Correlations are weak and any interpretation should be done carefully. For example, positive correlation does not necessarily imply that more smolts and the growth rate are linked. Perhaps, a year that is good for smolt numbers will be good for smolt growth--an intuitive but non-informative conclusion. Figure 17 and Figure 18 show the relationship between the mean and median values of the growth indicators of Snake River wild sub-yearling chinook to the smolt indices at LGR. The lines shown are the least-squares regression line.
Characteristics of juveniles that return as adults
Very few of the fish in this database subsequently returned as adults. There are over 2200 records of PIT-tagged fish returning to GRA, however, most of these were not recovered prior to being detected as adults. As a result, it is questionable as to whether the recovery data will be helpful for determining the effect of growth rate on survival. Only 30 of these fish were recovered as juveniles and remeasured, and of these, 11 were wild chinook.
The release length is generally available and the released sizes of the fish that returned as adults appears to be slightly greater than for the fish in the recovery data base.
Two method for examining spatial differences in growth use multiple recovery records. A third method uses all the records and distinguishes between fish in different locations.
Multiple recapture records were examined for differences in growth between the first and second recapture. The data was screened to find fish that had been recovered exactly twice. For individual fish that were recovered three or more time, only two of the recovery records were used. The priority system for omitting extra recovery records was:
Table 11 Counts of available data according to run and rearing type for chinook recaptured more than once.
| Run | Hatchery | Unknown | Wild |
|---|---|---|---|
| 1 | 148 | 0 | 220 |
| 2 | 11 | 0 | 28 |
| 3 | 72 | 0 | 139 |
| 5 | 8 | 61 | 154 |
Second, the multiple recapture records were further screened to identify records where the second recapture point was distinct from (and downstream of) the first point.
The results of these methods are summarized in Table 12 through Table 15. Results for the distinct recovery site method are shown in Figure 15 and Figure 16.
The fish differ in how their growth indicators change in time. Whether this is the result of productivity, temperature, or behavior of the fish is not clear. Although we can be confident that the "different locations" screen for fish (second method) virtually ensures that the second recovery is downstream from the first, the spatial difference may be slight although for many of the fish the distinction is between a "SNAKER" site for the first recovery and "LGR" site for the second recovery.
Indicator 4 drops significantly for all groups except the subyearling wild fish as they move lower in the system and the season progresses, whereas only for the yearling hatchery fish does indicator 6 drop.
Growth in different regions of the system
This is the third method of examining spatial differences in growth. The records were divided into two groups based on whether the fish were both released and recovered above or below a certain specified point in the system. (There is actually a third group of course that was released above the point and recovered below, but they are not included in this discussion.) This is similar to the second method in that the growth of the different groups is not overlapping, but the division point is specified and the groups consist of different individuals. Though Lower Granite Dam was considered, the specified point was the confluence of the Snake and the Clearwater as representing a boundary between the free-flowing and impounded portions of the system.
Figure 19 and Figure 20 show distributions of growth indicators for fish released and recovered exclusively above the confluence. Note that they are mostly unimodal with some possible exceptions.
Tests of the mean do not assume equal variance. Test of the median are valid but are less powerful (about 65% depending on the details of the test) than tests of the mean when such tests are possible (Zar, 1996). Figure 21 shows the distribution of Indicator 2 for fish grown either above or below the confluence and Table 16 compares these distributions. Similarly, Figure 22 shows the distribution of Indicator 4 for fish grown either above or below the confluence and Table 17 compares these distributions; and Figure 23 shows the distribution of Indicator 6 for fish grown either above or below the confluence and Table 18 compares these distributions.
The bimodal distribution of the wild yearling chinook growth distributions prompted a more detailed examination of the growth indicator distributions. General linear models to explain the variance in the p-values are very unbalanced due to gaps in the spatial and temporal heterogeneity of the distribution of these fish.
Table 16 Comparison of Indicator 2 (P-value) above and below the confluence
Table 17 Comparison of Indicator 4 (Weight growth indicator) above and below the confluence
Table 18 Comparison of Indicator 6 (Length growth indicator) above and below the confluence
Table 19 Significance tests for differences between upstream and downstream growth parameters. Null hypothesis for mean: "Downstream growth is not less than upstream growth". Null hypothesis for median: "Median values are the same for upstream and downstream growth". Indicator 2 is the P-value, Indicator 4 is the weight growth rate, and Indicator 6 is the length growth rate.
This is a biologically diverse group of fish, coming from headwaters in the Salmon, Clearwater and other tributaries throughout the Snake River drainage. None of the growth indicators (means) decrease for these fish below the confluence and the null hypothesis of growth below the confluence being greater than or equal to the growth above the confluence is not rejected for any of the three indicators. Note however that these indicators are all at much lower levels than for the other three groups.
The bimodal distribution of indicator 2 for the "released below the confluence" (Figure 21, lower panel, title: "1 W") was also bi-modal for release date, comprised of those released in the spring and those released in the late summer or fall (Table 20) and the above-below analysis of growth indicators is repeated (Table 21) and shown in Figure 24. The late and early releases are essentially opposite. One interpretation is that the autumn releases of wild yearling chinook remain as parr (i.e. do not smolt), pass the winter in the river system with very low growth and as they move into the spring and summer, their growth rate increases (compared to the winter) is much higher even if they are low in the system. Note that the effect is less pronounced for indicator 2 which is consistent with the fact that this is a temperature dependent proportion of the maximum consumption rate.
Table 20 Details of wild yearling chinook. Summary of indicator 2 distributions.The early fish were released prior to Julian day 175, i.e. in the spring or early summer. The late fish were released after Julian day 175, i.e. in the late summer or fall.
Table 21 Significance tests for differences between upstream and downstream growth parameters for wild yearling chinook only. Early fish were released pre Julian day 175 and late fish post Julian day 175. H0 for mean: "Downstream growth not less than upstream growth". H0 for median: "Median values are = upstream and downstream".
| Growth indicator | Type | Run | release group |  |
 |
|---|---|---|---|---|---|
| 2 (P-value) | W | 1 | early | 1 | 0 |
| 2 (P-value) | W | 1 | late | 0.9923 | 0 |
| 4 (Weight) | W | 1 | early | 1 | 0 |
| 4 (Weight) | W | 1 | late | 0 | 0 |
| 6 (Length) | W | 1 | early | 1 | 0 |
| 6 (Length) | W | 1 | late | 0.1621 | 0 |
We can not reject the null hypothesis for length (indicator 6) for the late fish below the confluence even though it is rejected for the weight indicator. These different results for the growth indicators could be due to the changes in body shape for these fish as they smolt. Wild fish above the confluence move significantly slower than their downstream counterparts (average 0.548 vs. 5.26 km/day respectively). The "early" wild yearling chinook travelled at an average speed of 5.23 km/day--indistinguishable from the downstream group.
All growth indicators decrease for these fish below the confluence compared to their counterparts above the confluence. Hatchery yearling chinook are released in the spring and early summer, with those above the confluence generally released slightly ahead of those in the lower river.
Hatchery yearling chinook are significantly larger than their wild counterparts on release and live in a river system more like the early releases of wild yearling chinook, than the over-wintering late releases. The hatchery fish upstream of the confluence grew faster than their downstream counterparts by all indicators and traveled faster (16.53 vs. 10.87 km/day). If the Imnaha river hatchery releases from site "522.308.074" are excluded, the average speed for upstream hatchery fish is reduced to 9.74 km/day. These migration rates are comparable to rates determined from PIT tag interrogation data (Zabel et al. 1998). This shows that the "system" is important for distinguishing the growth of different groups of chinook. Beckman et al. (1996) confirm the positive correlation of size with migration rate. Their growth indicators below the confluence are consistently the lowest for any of the four groups examined.
Comparison of above and below is difficult for this group of fish. There were very few of these fish released below the confluence. Drawing general conclusions from this small sample is tricky and we fail to reject the null hypotheses for any of the three indicators. Thirteen of these 14 fish were released during a 20 day period in 1993. They were all released at a SNAKER site and recovered at LGR. Several issues are pertinent to interpreting these results: Temperature effects could allow higher consumption without accompanying growth. The travel rates both above and below the confluence are very slow compared to the yearling chinook (mean and median < 1) but increase below the confluence.
Growth indicators for these fish suggest they are consuming more but growing less below the confluence compared to above the confluence. Indicator 2 (P-value) is greater, but indicator 4 (weight growth) is decreasing.
The hatchery fish move very quickly compared to the wild fish--by more than an order magnitude and their rates are comparable above and below the confluence. They are also released at a larger size then the wild fish.
During 1992 and 1993, Tom Curet (1993) studied the food habits of sub-yearling chinook in Lower Granite reservoir. During his sampling period, he excluded fish over 75mm during April and May and over 85mm during June. However, the average release size of sub-yearling chinook (all wild) in the recapture database recovered below the confluence of the Snake and Clearwater Rivers during these years (n= 119) was 79 mm and they had a mean recovery length of 133.5. Two possible explanations are:
He also concludes that the P-value (indicator 1 or 2 in this analysis) is .274 for these fish, whereas I conclude it is much higher (almost .6). This difference could be due to:
Although he does not declare prey density or digestibility values for the bioenergetic model runs, I inferred prey density from the stomach content analyses (Curet 1993) and published prey energy density calculations (Groot et al. 1995; Hanson et al. 1997; Hoar 1997). I assumed that ranges of prey density published by Hanson et al. represented minimum and maximum values for certain prey types and that the proportions of prey types found in the stomachs sampled by Curet represented consumption overall. Prey energy densities by this method were therefore between 2700 and 4220 J/g. Since the prey density and P-values compensate each other to a certain extent in the bioenergetics model, using his values of 2700 to 4200 J/g for prey density means that for a 100 g chinook at 15°C in my formulation of the bioenergetics model, the P-value should be between ~.2 - .25 to get the same growth increment. I believe that in general, Curet's growth conclusions are not comparable to the ones presented in this analysis.
Distributions of weight or length increments could be used to model the growth of any particular group of fish, but to take advantage of temperature and spatial effects, growth can be best modeled through the P-value. Some caution should be taken in modeling growth in this manner because the bio-energetics model is sensitive to certain inputs. Bartell et al. concluded that the model was most sensitive to P-values and the allometric consumption parameters ca. Attempts have been made to reduce the variability of P although it will still be possible to grossly over- or under-grow fish. The allometric parameters for consumption are assumed to be constant for juvenile chinook, even though we have seen that the weight-length allometric parameters change with smolting.
A simple method is to calculate P-values with a deterministic and stochastic component that incorporates the spatial differences in growth between groups and the temperature effect on P-value. The deterministic part as a linear function of temperature--the coefficients particular to the group and location, and the stochastic part as a random normal deviate. Growth of the fish will then be calculated through the bioenergetics model given a temperature profile and initial weight.
The P-value for a fish will be calculated in two steps. First the "normalized proportion" is determined from:
 |
(22) |
. The arcsine transform is commonly used to normalize proportion data. 
= intercept from regression 
= slope from regression Second, the true proportion value (P-value) is then back-calculated as:
 |
(23) |
The table that follows details the fit and parameters for Eqn. (22).
| Table 22 Regression coefficients for Eqn. (22), using the arcsine transformed proportion data. NA indicates too few fish. | |||||||||
|
| |||||||||
| Run (i) | Type (j) | early or late (julian 175 cutoff) (l) | System (k) | R2 | p | intercept  |
slope  |
Variance of residuals | Count |
|---|---|---|---|---|---|---|---|---|---|
|
| |||||||||
| 1 | W | early | Snake | NA | NA | NA | NA | NA | NA |
| 1 | W | early | Clwtr | 0.0022 | 0.7608 | 0.6204 | -0.0056 | 0.0887 | 48 |
| 1 | W | early | GR | 0.0045 | 0.1954 | 0.5355 | -0.0043 | 0.0328 | 373 |
| 1 | W | early | Imnaha | 0.0230 | 0.6969 | 0.4846 | 0.0097 | 0.0306 | 9 |
| 1 | W | early | Salmon | 0.0180 | 0.1261 | 0.4437 | 0.0086 | 0.0682 | 133 |
|
| |||||||||
| 1 | W | late | Snake | NA | NA | NA | NA | NA | NA |
| 1 | W | late | Clwtr | 0.1227 | 0.0000 | 0.5394 | -0.0221 | 0.0396 | 335 |
| 1 | W | late | GR | 0.0485 | 0.0000 | 0.3972 | -0.0096 | 0.0154 | 1315 |
| 1 | W | late | Imnaha | 0.0447 | 0.0033 | 0.3621 | -0.0054 | 0.0019 | 191 |
| 1 | W | late | Salmon | 0.0696 | 0.0000 | 0.5474 | -0.0193 | 0.0410 | 563 |
|
| |||||||||
| 3 | W | NA | Snake | 0.0594 | 0.0000 | 0.2861 | 0.0278 | 0.0252 | 969 |
| 3 | W | NA | Clwtr | 0.0124 | 0.4314 | 0.4592 | 0.0088 | 0.0183 | 52 |
| 3 | W | NA | GR | NA | NA | NA | NA | NA | NA |
| 3 | W | NA | Imnaha | NA | NA | NA | NA | NA | NA |
| 3 | W | NA | Salmon | NA | NA | NA | NA | NA | NA |
|
| |||||||||
| 1 | H | NA | Snake | NA | NA | NA | NA | NA | < |
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