NOAA Technical Memorandum NMFS-AFSC-170
 
 

The Influence of Sampling Location, 

Timing, and Hatching Origin on the 

Prediction of Energy Density in 

Juvenile Pink Salmon 

by 

C. Rodgveller, J. H. Moss, and A. M. Feldmann 

U.S. DEPARTMENT OF COMMERCE 

National Oceanic and Atmospheric Administration
 
 

National Marine Fisheries Service
 
 

Alaska Fisheries Science Center
 
 

April 2007 
NOAA Technical Memorandum NMFS 

The National Marine Fisheries Service's Alaska Fisheries Science Center 

uses the NOAA Technical Memorandum series to issue informal scientific and 

technical publications when complete formal review and editorial processing 

are not appropriate or feasible. Documents within this series reflect sound 

professional work and may be referenced in the formal scientific and technical 

literature. 

The NMFS-AFSC Technical Memorandum series of the Alaska Fisheries 

Science Center continues the NMFS-F/NWC series established in 1970 by the 

Northwest Fisheries Center. The NMFS-NWFSC series is currently used by 

the Northwest Fisheries Science Center. 

This document should be cited as follows: 

Rodgveller, C. J., J. H. Moss, and A. M. Feldmann. 2007. The influence 

of sampling location, timing, and hatching origin on the prediction of 

energy density in juvenile pink salmon U.S. Dep. Commer., NOAA 

Tech. Memo. NMFS-AFSC-170, 27 p. 

Reference in this document to trade names does not imply endorsement by 

the National Marine Fisheries Service, NOAA. 
NOAA Technical Memorandum NMFS-AFSC-170
 
 

The Influence of Sampling Location,
 
 

Timing, and Hatching Origin on the
 
 

Prediction of Energy Density in
 
 

Juvenile Pink Salmon
 
 

by 

C. J. Rodgveller, J. H. Moss, and A. M. Feldmann 

Auke Bay Laboratory
 
 

Alaska Fisheries Science Center
 
 

11305 Glacier Highway
 
 

Juneau AK 99801-8626
 
 

www.afsc.noaa.gov
 
 

U.S. DEPARTMENT OF COMMERCE 

Carlos M. Gutierrez, Secretary 

National Oceanic and Atmospheric Administration 

Vice Admiral Conrad C. Lautenbacher, Jr., U.S. Navy (ret.), Under Secretary and Administrator 

National Marine Fisheries Service 

William T. Hogarth, Assistant Administrator for Fisheries 

April 2007 
This document is available to the public through: 

National Technical Information Service 

U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

www.ntis.gov 
Notice to Users of this Document 

This document is being made available in .PDF format for the convenience of users; however, the 

accuracy and correctness of the document can only be certified as was presented in the original hard 

copy format. 

iii 

ABSTRACT

Accurate estimation of energy density of fish is important for biogenetic models. Our 

objectives for this study were to determine which variables could be used to predict energy 

density instead of estimating energy density directly with bomb calorimetry. Secondly, we 

examined the variability in energy density relative to the sampling location within the Gulf of 

Alaska, the stock of origin, and the year the fish was sampled. Juvenile pink salmon 

Oncorhynchus gorbuscha were collected from the Gulf of Alaska during July 2001 and 2002. 

Energy density (J/g of wet weight) was estimated using bomb calorimetry. Hatchery stocks were 

identified from otolith thermal marks, and non-thermally marked fish were assumed to be wild. 

Energy density differed significantly by transect (P < 0.000), year (P < 0.000) hatchery stock (P = 

0.001), and the interaction of origin and transect (P = 0.018). Body size was not related to 

energy density. However, % dry weight (dry weight/wet weight) was related to energy density 

(R2 = 0.93) and thus can be used in regressions to estimate energy density. We used energy 

densities predicted from a regression with % dry weight in bioenergetic modeling simulations. 

Error associated with energy density predictions affected bioenergetic models of body growth by 

up to 7-8% over a 30-day period. This error increased as the water content of fish increased and 

as the energy density decreased. Biological factors should be considered when predicting energy 

densities so that errors are minimized. 

v 

CONTENTS

INTRODUCTION ............................................................. 1 
 


METHODS .................................................................. 3 
 


Sampling and Laboratory Methods .......................................... 3 
 


Analysis ............................................................... 4 
 


ANCOVA ....................................................... 5

 Regressions ...................................................... 5 
 

Bioenergetic Model ................................................ 6 
 


RESULTS ................................................................... 7 
 


Intrafish Variability ...................................................... 7 
 


ANCOVA ............................................................. 7 
 


Regressions ............................................................ 8 
 


Bioenergetic Model Simulations ............................................ 9 
 


DISCUSSION ................................................................ 9 
 


CITATIONS ................................................................. 15 
 


TABLES .................................................................... 20 
 


FIGURES ................................................................... 22 
 


INTRODUCTION 

Bioenergetic models have become so widespread that model parameters have been 

described for almost 40 fish species (i.e., reviewed in Hanson et al. 1997, Zhou et al. 2005). 

Bioenergetic models help fisheries biologists answer questions about multiple ecological 

processes, including fish growth as it relates to temperature (Walker et al. 2000), habitat quality 

(Nislow et al. 2000), energy costs (Holker and Breckling 2002), responses to varying rations of 

food (Walker et al. 2000; Paukert et al. 2003), and fish response to contaminants (Solvana and 

Roberto 2001. Trudel and Rasmussen 2001). Energy densities of predators and prey are key 

inputs of bioenergetic models. Sensitivity analyses have shown that bioenergetic models can be 

prone to errors in energy density when fish growth or growth-related parameters (Stewart et al. 

1983, Bartel et al. 1986). To generate accurate estimates from bioenergetic models, energy 

density values for predators and prey must reflect fluctuations from ontogeny, location, season in 

the environment. Because accurate estimates of energy density are difficult to obtain, published 

values are often used from closely related species (Hartman and Brandt 1995). These values can 

be misrepresentative of the actual energy content. 

There are several methods available for estimating energy density. The first method uses 

the proximate constituents of water, ash, lipids, carbohydrates, and proteins to estimate the total 

energy content. Because 98% of the constituents of fish are lipid and protein (Higgs et al. 1995), 

the energy equivalent of these tissues are used to calculate the total energy. Several energy 

equivalent values have been used for lipids and protein, but they may not provide accurate 

estimates of total energy (Craig et al. 1978), and the method is time-consuming and expensive. 

Lipid content is the primary determinant of energy density because protein remains fairly stable 

whereas lipids tend to fluctuate (Anthony et al. 2000). Because water content is a good 
 2

approximation of the amount of lipids and protein in the body (Groves 1970), the relationship 

between water content and energy density has been modeled with linear regressions to estimate 

energy density for many fish species (Brett et al. 1969, Hartman and Brandt 1995, Trudel et al. 

2005, Wuenschel et al. 2006). For this method to be successful, the relationship between energy 

density and the body water content must be established with direct measurements of energy 

density. The most accurate and time consuming method of obtaining energy density is to directly 

measure it with bomb calorimetry. 

Energy density is dynamic and can vary in marine fish species by season, ontogeny, and 

size class (Jansgaard 1974, Robards et al. 1999, Anthony et al. 2000, Vollenweider 2005, 

Wuenschel et al. 2006). Boldt and Haldorson (2004) found that pink salmon energy density 

varied by location within Prince William Sound, Alaska, which likely reflects differences in prey 

availability (Boldt and Haldorson 2002, 2004). Their results indicate that energy content, and 

therefore growth conditions, were location specific. Pink salmon (Oncorhynchus gorbuscha) 

have only one year at sea to grow so they must devote much of their energy toward body growth 

and not energy storage. The fast growth rate of pink salmon may make it more difficult to 

reserve calories for lipid storage than in other salmon species. So, above average energy 

densities, reflecting higher lipid concentrations, may dictate the survival of pink salmon more so 

than in other salmon species. Differences in energy density like those observed by Boldt and 

Haldorson (2004) should be included in bioenergetic models of pink salmon ecology because the 

differences may have large impacts on the growth and over-winter survival of pink salmon. 

However, because bomb calorimetry is time consuming and expensive, it is desirable to use the 

less time intensive and inexpensive method of predicting energy density from the relationship 

between energy density and percent dry weight. 
 3 

Our first objective for this study was to examine the relationships between energy 

density, estimated directly with bomb calorimetry, and length, weight, condition, and % dry 

weight (water content) of juvenile pink salmon to determine which variables could be used to 

predict energy density. Our second objective was to examine the variability in energy density 

relative to the sampling location within the Gulf of Alaska, the stock of origin, and the year the 

fish was sampled. Finally, we estimated the error in the prediction of energy density from the 

relationship of % dry weight and energy density. We did this by examining the sensitivity of 

30-day bioenergetic models of growth to the errors in energy density prediction. In the case of 

pink salmon, small differences in body growth and the proportions of proximate constituents 

may have significant impacts on the prediction of energy density from water content. 

METHODS 

Sampling and Laboratory Methods 

In July of 2001 and 2002, cruises were conducted in the central Gulf of Alaska on board 

the FV Great Pacific, a 38-m long stern-trawling vessel. Although a more rigorous sampling of 

the entire Gulf of Alaska was conducted (Farley et al. 2001, Cokelet et al. 2002), samples from 

three transects were used for this study (Fig. 1). Juvenile salmon were collected with a 198-m 

long midwater rope trawl, which had a spread of 52 m horizontally and 18 m vertically, towed 

for 30 minutes. Fork length (to the nearest millimeter) and weight (to the hundredths of a gram) 

of juvenile age-0 pink salmon were recorded and otoliths were removed and examined for 

thermally induced markings to determine the hatchery of origin (either Armin F. Koernig [AFK], 

Wally Noerenberg [WN], or Solomon Gulch [SG]). Because thermal marks are added to otoliths 

in the hatchery to signify the hatchery or origin and the year of release, we assumed that fish 
 4

lacking thermal marks were of wild stock. Fish were frozen onboard until they were prepared for 

bomb calorimetry in the lab. 

We removed the stomachs contents from each juvenile pink salmon (n = 452) and then 

dried fish in a gravity convection oven for 2-7 days at 55-60 °C. We measured the weight of each 

fish every 24 hours until they lost less than 0.1 g of weight per day. Percent dry weight was 

calculated by dividing the final dry weight by the wet weight (excluding stomach contents and 

otoliths) × 100. We homogenized the dried fish into a fine powder using a Waring pulverizer and 

a mortar and pestle and then pressed a subsample of the powder into 0.15 g pellets. We stored the 

pellets in a desiccator cabinet to prevent reabsorption of water before they were bombed in the 

calorimeter. Energy density in cal/g of dry weight was estimated using a Parr 1425 Semimicro 

Bomb Calorimeter (Parr Instrument Co. 1991). We then converted these values to 

J/g wet weight for use in a bioenergetic model. Additionally, multiple calorimetry runs were 

performed on 10 pink salmon sampled in 2001 to determine if there was intra-fish variability that 

could be attributed to the bomb calorimeter, user error, or irregularities in the pellet composition. 

The calorimeter was calibrated for each user by performing a standardization run on a benzoic 

acid pellet of a known energy density. The bomb calorimeter calculates a correction factor for 

each user that is then used for the energy density estimation of future samples (Parr Instrument 

Co. 1991). 

Analysis 

ANCOVA 

Of the 452 pink salmon samples bombed in the calorimeter, 312 were collected in 2001 

and 140 in 2002. Samples from all transects (Fig. 1) and all hatcheries of origin were represented 

in the 2001 and 2002 samples. We used an analysis of covariance (ANCOVA; Sall et al. 2005) to 
 5

test for differences in the energy densities of the pink salmon by origin (Ok [AFK, WN, or SG 

hatcheries, or wild]), year sampled (Ai), survey transect (Tj), and % dry weight (Dl) using the 

following full model: 

Yijklm = μ + Ai + Tj + Ok + β 0(Dl - D ) + Ai ×Tj + Ai ×Ok + Ai × β 1(Dl 

- D ) + Tj ×Ok + Tj × β 2(Dl - D )+ Ok × β 3(Dl - D ) + Ai ×Tj ×Ok + Eq. 1 

Ai ×Tj × β 4(Dl - D ) + Tj ×Ok × β 5(Dl - D )+ Ai ×Tj ×Ok × β 6(Dl - D ) 

+ eijklm , 

where Yijklm is the energy density from bomb calorimetry, μ is the theoretical population 

mean, D is the mean % dry weight for all individuals, β 0-6 are the regression coefficients for the 

covariate term D, and eijklm is the normally distributed random error. The main effects were year, 

origin, and transect, while % dry weight was treated as a continuous covariate. All possible 

interactions were included in the full model. For significant interactions (α= 0.05), we performed 

separate ANOVA models for each level of the significant effect and used a Tukey Kramer 

honestly significant different (HSD) test to compare levels within the ANOVA (Engqvist 2005, 

Sall et al. 2005). In these ANOVA models, significant effects from the full model were also 

included. 

Regressions 

We examined the correlations of energy density (directly estimated with bomb 

calorimetry) with more easily measured variables (length, weight, condition factor, and % dry 

weight [dry weight/wet weight]) to determine if linear regressions could be used to predict 
 6

energy density. The standard deviation of the residuals of the regression between % dry weight 

and energy density was then used in bioenergetic models to assess the sensitivity of these models 

to errors in energy density predictions. 

Bioenergetic Model 

We used the predicted energy densities from the regression (Fig. 2) in Wisconsin 

bioenergetic modeling simulations (Hanson et al. 1997) to quantify the difference in growth 

estimates from directly estimated energy densities and predicted energy densities. We first used 

predicted values from the regression at fixed % dry weights as the consumer energy densities. In 

other simulations, we used the same predicted energy density at each % dry weight plus/minus 

two standard deviations of the residuals of the regression (Fig. 2). This measured the sensitivity 

of the bioenergetic model to prediction error associated with estimating the energy densities from 

a regression. The Wisconsin model calculates the consumption of prey required to satisfy the 

observed growth over a given time interval, or the growth rate that should result from a specified 

amount of consumption, and is based on the energy-balance equation: 

C = G + M + W , Eq. 2 

where C is the total energy consumed, G is the growth, M is metabolic costs (e.g., respiration, 

activity, and specific dynamic action), and W is waste (excretion and egestion). Physiological 

parameters used to represent juvenile pink salmon were taken from the pink/sockeye parameter 

set (Beauchamp et al. 1989). Bioenergetic model simulations were run for a 30-day time period 

using data collected on all stations of the Seward line transect (Transect No. 2, Fig. 1) during the 

2001 survey. Model input data from the transect included average 10-m surface temperature, 
 7

average pink salmon body size (wild and hatchery combined, 19.2 g), and literature energy 

density values for prey items (Davis et al. 1998). Consumer end weight was fit to a constant 

proportion of daily maximum consumption (0.80). Previous studies have shown that juvenile 

pink salmon in the Gulf of Alaska feed at 90-95% of their maximum daily ration (Cross et al. 

2005); therefore, we believed a constant proportion of 0.80 was a conservative estimate. 

RESULTS 

Intra-fish Variability 

Three calorimetry runs were conducted on 10 fish, and the intra-fish variability of energy 

density ranged from 0.12 - 0.99% ( x = 0.60%), which was 5.7 - 0.7 J/g wet weight ( x = 28.1 

J/g wet weight; Fig. 3). This variability can be attributed to slight differences in the subsample 

composition, and error from the bomb calorimetry unit. The calorimeter has a margin or error of 

0.5% (Parr Instrument Co. 1991), so the variability we observed seemed reasonable. 

ANCOVA 

All origins were present at all transects in both years (Table 1). A series of models were 

run with one non-significant variable (α = 0.05) excluded each time until all variables left were 

significant. In all models, year, % dry weight, transect, origin, and the interaction of origin and 

transect all accounted for a significant amount of the variation in energy densities (Table 2). 

Separate ANOVA were run for each origin and for each transect in order to test for pairwise differences among hatcheries of origin within each transect and among transects within 

each origin (Tukey Kramer HSD test, α = 0.05, Sall et al. 2005). For example, because hatchery 

× transect was a significant interaction, we performed one ANOVA for transect one in which the 

explanatory variables were % dry weight, year, and hatchery. Within this ANOVA we compared 
 8

all origins to each other using a Tukey Kramer HSD test, which tests for pair-wise differences. 

Additionally, we ran similar ANOVA for each transect and then for each hatchery. For AFK 

hatchery fish, there were significant differences in energy density between Transect numbers 1 

and 3, and between Transect numbers 1 and 2. Wild fish were significantly different between 

Transect numbers 1 and 2 and Transect numbers 3 and 2. SG energy densities were not 

significantly different between transects, while WN hatchery energy densities were significantly 

different between Transect numbers 1 and 3 and between Transect numbers 3 and 2. Overall 

there were no patterns, except that both AFK and WN hatchery energy densities differed 

between Transect numbers 1 and 3. Because there were many significant pair-wise differences 

due to transect, it appears that location is an important factor in determining a fishes’ energy 

density. 

Pair-wise differences were also found between hatcheries at each transect. At Transect 

number 1, WN and wild fish had significantly different energy densities. At Transect number 2, 

there were no significant differences between origins, and AFK and wild fish were significantly 

different at Transect number 3. There was no pattern to the pair-wise differences between origins 

nor between transects. However, there were fewer significant differences between origins within 

a transect than there were transects within hatcheries. This may indicate that location has a 

stronger effect on energy density than origin. 

Regressions 

No strong relationships existed between length, weight, or condition factor and energy 

density (range of R2 = 0.07-0.14; Fig. 4). Therefore, the size of the fish is not a good predictor of 

caloric density. The coefficient of determination of the relationship of % dry weight and energy 

density was very high (R2 = 0.93; Fig. 2). We subtracted each energy density measured directly 
 9

from the predicted value to get a residual (Fig. 2). The residuals had a standard deviation of 112 

J/g of wet weight (two standard deviations = 224) and the largest residual was 607. A difference 

of up to about 25 J/g of wet weight (0.5%) is the acceptable margin of error of the bomb 

calorimeter (Parr Instrument Co. 1991, Trudel et al. 2005); however, 84 % of the residuals were 

over 25 J/g of wet weight. 

Bioenergetic Model Simulations 

In the bioenergetic models, low % dry weights yielded higher variability in growth 

estimates. The difference in end weight at two standard deviations from the predicted energy 

density was 6 g, which is an error of 8% (Fig. 5). This error decreased as % dry weight increased 

(Fig. 5). The largest residual of the pooled regression (607 J/g wet weight) would have a much 

greater error than what we observed in this simulation. 

DISCUSSION 

The condition factor, length, and weight of juvenile pink salmon were not highly 

correlated with energy density (Fig. 4). Body size and energy density were also poorly correlated 

in recently out-migrated pink salmon from Prince William Sound, Alaska (Boldt and Haldorson 

2004) and in coho (Oncorhynchus kisutch) and Chinook salmon (O. tshawytscha) (Trudel et al. 

2005). Additionally, coho salmon and Chinook salmon energy densities are not correlated with 

condition (Madenjain et al. 2000), nor with protein content (Trudel et al. 2005). However, we 

found a strong correlation between % dry weight and energy density, which has also been 

documented in coho and Chinook salmon (Trudel et al. 2005), and other groups of fish including, 

clupeids, pleuronectids, cyprinids, and osmerids (reviewed in Hartman and Brandt 1995). 
 10 

We found that the energy density of pink salmon differed significantly by the transect, 

year, origin, and the interaction of origin and transect (ANCOVA; Table 2). Two hatcheries 

(AFK and WN) had significantly different energy densities at Transect numbers 1 and 3. There 

were other significant pair-wise comparisons, but no other patterns were present. The number of 

significant differences between transects within hatcheries was higher than the number of 

significant differences among hatcheries within a transect. This may indicate that location has a 

stronger effect on energy density than origin. Boldt and Haldorson (2004) also found that 

location had a significant effect on energy density of juvenile pink salmon. 

Other studies have also found significant effects of area, season, and species on energy 

density. White crappie (Pomoxis annularis) energy density varied among reservoirs in Ohio 

(McCollum et al. 2003). Wuenschel et al. (2006) found an effect of ontogeny on the relationship 

of % dry weight and energy density in juvenile grey snapper (Lutjanus griseus) and spotted 

seatrout (Cynoscion nebulosus). Trudel et al. (2005) suggested that seasonal, species, and area 

differences should be considered when using regressions to estimate energy density. In a study of 

the energy density of eight North Sea fish species, the energy density of all species studied 

differed significantly by season (Pederson and Hislop 2001). The energy density can change in 

response to seasonal feeding changes including starvation (Oliver et al. 1979, Pangle and Sutton 

2004), increases in rations (Hayes and Taylor 1994, Pangle and Sutton 2004), prey switching 

(Breck 1998), reproductive status (Anthony et al. 2000), or season (Anthony et al. 2000; 

Vollenweider 2005). Conversely, some studies have found little variation in energy density, and 

concluded that related species be pooled by taxonomic group for energy density prediction from 

regressions with % dry weight (Hartman and Brandt 1995; Pederson and Hislop 2001). 

Variability in the regression is caused by fluctuations in the proportions of lipids and 

protein that can not be explained by water content. Although the ANCOVA did not detect 
 11

significant effects of year, transect, or stock on the slope of the % dry weight and energy density 

relationship, they still are affecting the slope in a biologically significant way, as seen by the 

differences in end weight after 30-days in the bioenergetic model. At a fixed % dry weight, the 

discrepancy in the actual energy densities can be attributed to differing proportions of lipids and 

protein in an individual fish. Even small changes in the proportion of constituents can cause a 

marked increase in energy density because lipids have almost double the energy content as 

protein (Brett 1995). Year, location, origin, and possibly other variables, are contributing to the 

variability in the relationship between energy density and % dry weight, or in other words 

affecting the proportion of lipids and proteins. Because these variables affect the relationship of 

% dry weight and energy density, the regression systematically biases estimates of energy 

density. Some of the variability between the regression lines at 16% dry weight can be attributed 

to a small sample size (Fig. 2); however, there is a strong increasing trend in variability as % dry 

weight decreases which is independent of sample size (Fig. 5). The increase in variability at low 

% dry weight means that the proportion of lipids and proteins is more variable when water 

content is high. Wuenschel et al. (2006) also found variability in regressions of % dry weight and 

energy density that was attributed to ontogeny. This variability caused estimates in energy 

density to be overestimated by up to 25%. 

The trend of increasing variability in energy density was apparent for fish with low % dry 

weights (Fig. 5) and smaller fish (Fig. 6). This may be because the smaller, less energy-dense 

fish have high water content, are under energetic stress, and are starting to use protein reserves as 

well as lipid reserves. Age-0 pollock, Theragra chalcogramma, and capelin, Mallotus villotus, 

use a greater proportion of protein than lipids when energetically stressed, whereas age-1 fish 

used lipids before protein (Ron Heintz, NMFS-ABL, pers. commun.). So it is possible that the 
 12

age-0 juvenile pinks in this study are using protein reserves as well as lipids, and are therefore 

experiencing fluctuations in the ratio of protein and lipids as they become less energy dense. 

The error in end weight after 30 days from the bioenergetic model is likely biologically 

significant and may be large enough to warrant concern. It has been hypothesized that juvenile 

salmon must reach a critical size to meet minimum metabolic requirements before the end of the 

first growing season in order to survive the winter at sea (Mortensen et al. 1999, Beamish and 

Mahnken 2001). Moss et al. (2005) examined pink salmon scales from Prince William Sound, 

Alaska and found that fish that survived to adulthood were comparatively larger and faster 

growing than juvenile fish sampled at sea. They concluded that size-selective mortality occurs 

during the winter at sea after the fish have the opportunity to reach a critical size during the first 

summer. Differences in end weight, like we saw in our bioenergetic model (Fig. 5), may be large 

enough to draw false conclusions about the over-winter survival of pink salmon. The error we 

saw in our bioenergetic models is systematically biased by the factors we examined (year, 

transect, origin), so any growth and survival predictions will also be systematically biased. 

There are a few options to consider when deciding how many samples should be bombed 

in a calorimeter and how many should be predicted with the dry weight method. The first option, 

which is the most accurate and most expensive, is to perform calorimetry on all of the samples. 

The second approach is to perform calorimetry on a sample of the fish, and save resources by 

predicting the energy densities of a portion of the fish. If there is a reason to believe that there 

may be other factors affecting energy density, such as maturation, prey switching, or seasonal 

growth patterns, then several regressions can be used to capture this variability. Using 

exploratory analyses like these can be helpful in deciding how many samples should be bombed 

in a calorimeter and what sources of variation should be accounted for when using regressions 

for prediction. 
 13

When energy densities are going to be used for purposes other than bioenergetic models 

that are sensitive to energy density, more error in the estimates may be acceptable. In these cases, 

performing calorimetry on fewer samples would make sense. Estimating a portion of the samples 

may be adequate for bioenergetic models that are less sensitive to energy densities, such as 

consumption rate models (Stewart et al. 1983). This method may also be appropriate when 

energy density is used as an index of health (McCollum et al. 2003, Boldt and Haldorson 2004). 

For example, it may be a valuable parameter for models of population dynamics, such as 

spawner-recruit relationships. Climate variables often are used to help the predictive power of 

these models, but the addition of a direct index of health may help fisheries scientists to 

formulate more accurate models (Shotwell and Adkison 2004). 

When predicting energy density values with a regression of % dry weight and energy 

density, it is important to dry a large number of fish at the same time and then decide which fish 

samples should be bombed. For a robust regression with minimal error, it is necessary to have 

samples that represent a variety of % dry weights, thus providing contrast in the data. To get the 

best possible estimates of energy density, the bomb calorimeter should be used on fish that have 

% dry weights that are uncommon. This will help with prediction error due to small sample sizes 

at rare % dry weights. If there is increasing error at certain % dry weights like we observed at 

low % dry weight (Figs. 5, 6), these should also be bombed instead of estimated. It is helpful to 

examine the predicted and actual energy density values throughout the process to interpret the 

residuals of the regression and decide how many more and which samples should be run in the 

calorimeter. 

 15 

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Table 1. -- Mean energy density ( x , J/g wet weight), standard 

error (SE), and number of samples (n), of juvenile 

pink salmon sampled from the Gulf of Alaska. 

Summary statistics are stratified by year (2001 and 

2002), transect number (1-3), and stock (one of 

three hatcheries: Armin F. Koernig (AFK), Wally 

Noerenberg (WN), or Solomon Gulch (SG), or 

wild). Energy density was estimated using bomb 

calorimetry. 

Year Transect Origin x SE n 

2001 1 

AFK 4,275 234 7 

SG 4,205 86 18 

WN 4,391 95 12 

Wild 4,247 91 22 

2 

AFK 4,188 63 35 

SG 4,038 45 41 

WN 4,169 60 29 

Wild 4,082 66 31 

3 

AFK 4,294 86 25 

SG 4,418 70 27 

WN 4,501 48 32 

Wild 4,556 58 33 

2002 1 

AFK 4,081 192 7 

SG 4,334 127 25 

WN 4,534 94 14 

Wild 4,601 142 21 

2 

AFK 4,272 143 20 

SG 4,379 85 13 

WN 4,476 110 9 

Wild 4,059 215 6 

3 

AFK 4,570 447 3 

SG 4,697 179 10 

WN 4,814 164 8 

Wild 4,935 118 4 
 21 

Table 2. -- ANOVA F-test of factors affecting the energy density 

of juvenile pink salmon. df denotes the degrees of 

freedom, F-ratio is the F-test statistic used for 

hypothesis testing, and P is the significance of the test. 

Effect df F-ratio P 

Origin 3,434 5.38 0.001 

Year 1,434 106.09 < 0.000 

Transect 2,434 14.42 < 0.000 

% dry weight 1,434 7754.51 < 0.000 

Origin×Transect 6,434 2.59 0.018 
 22

Figure 1. -- Transects and sample locations for juvenile pink salmon on research cruises in July 

of 2001-2002. 
 23

6400 

5700 

5000 

4300 

3600 

2900 

2200 

0.12 0.17 0.22 

% dry weight 

0.27 0.32 

J/g w

et w

eight

SD of residuals = 112 

y = 21795x - 352.63 

R2

 = 0.94 

Figure 2. -- Linear regression of energy density and % dry weight of juvenile pink salmon. The 

formula is presented with the coefficient of determination (R2), as well as the 

standard deviation (SD) of the residuals (│observed – predicted│). 
 24

J/g we

t w

eig

h

t

5200 

5100 

5000 

4900 

4800 

4700 

4600 

4500 

4400 

4300 

0 1 2 3 4 5 6 7 8 9 10 11 12 

Fish ID 

Figure 3. -- Intra-fish variability in energy density measured using bomb calorimetry. Error bars 

represent 95% confidence intervals. Three energy density values were obtained for 

each of the 10 juvenile pink salmon. The mean of all 10 fish and the mean of all the 

error bars are in grey. 
60 

80 

100 

120 

Length (

m

m) 

25 

y = 79.401e0.0001x 

R2 = 0.1204 

160 

140 

Wet Weight (g) 

50 

40 

30 

20 

10 

0 

y = 7.5829e0.0002x 

R2 = 0.0414 

2.0 

1.8 

1.6 

1.4 

1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

0.0 

y = -0.0001x + 1.4075 

R2

 = 0.149 

Condition 

2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 

Energy Density (J /g wet weight) 

Figure 4. -- Regressions of condition factor, length, and wet weight versus the energy density of 

juvenile pink salmon. A linear formula is presented with its coefficient of 

determination (R2

). Exponential models are presented for length and weight. 
 26

80 

70 

60 

50 

40 

9 

a Average 

+ or - 2 SD 

b 

% difference i

n end End weight (g) 

w

eight 

3 

+2 SD 

-2 SD 

6

0 

0.16 0.2 0.24 0.28 

% dry weight 

Figure 5. -- Bioenergetic model simulation of weight after 30 days, when all variables are held 

constant except energy density. (a) The solid line is the estimated growth when 

energy density is predicted from a regression with dry weight. The large dashed line 

represents estimated growth when the predicted energy density +/- 2 standard 

deviations (SD) of the residuals is used in the model. (b) The % difference in end 

weight between the growth estimated from predicted energy, and the growth 

estimated when energy density is -2 (long dash) and +2 standard deviations of the 

residuals (solid black) from the predicted energy density. The % difference 

describes the error in growth estimates that can be attributed to using predicted 

energy densities instead of using energy densities directly measured with bomb 

calorimetry. 
 27

% dr

y w

eight 

J/g wet weig

ht 

6500 

6000 

5500 

5000 

4500 

4000 

3500 

3000 

2500 0.30 

10 20 30 40 50 0.28 0 

0.26 

0.24 

0.22 

0.20 

0.18 

0.16 

0.14 

0.12 

0 10 20 30 40 50 

Wet weight (g) 

Figure 6. -- Energy density measured with bomb calorimetry and % dry weight of juvenile pink 

salmon from the Gulf of Alaska, plotted against the wet weight. The linear 

regression is also shown in black to demonstrate the trend. 
RECENT TECHNICAL MEMORANDUMS


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