NOAA Technical Memorandum NMFS-AFSC-37

A Bioenergetics Model of Walleye Pollock

(Theragra chalcogramma) in the Eastern

Bering Sea: Structure and Documentation

by

T. W. Buckley and P. A. Livingston

U.S. DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

National Marine Fisheries Service

Alaska fisheries Science Center

April 1994
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 new NMFS-NWFSC series will be used

by the Northwest Fisheries Science Center.

This document should be cited as follows:

Buckley, T. W., and P. A. Livingston. 1994. A bioenergetics model

of walleye pollock (Theragra chalcogramma) in the eastern Bering

Sea: Structure and documentation. U.S. Dep. Commer., NOAA Tech.

Memo. NMFS-AFSC-37, 55 p.

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

the National Marine Fisheries Service, NOAA.
NOAA Technical Memorandum NMFS-AFSC-37

A Bioenergetics Model of

Walleye Pollock (Theragra chalcogramma)

in the Eastern Bering Sea:

Structure and Documentation

by

T. W. Buckley1

 and P. A. Livingston2

1

Fisheries Research Institute

School of Fisheries WH-10

University of Washington

Seattle, WA 98195

2

Alaska Fisheries Science Center

7600 Sand Point Way N.E., BIN C- 15700

Seattle, WA 98115-0070

U.S. DEPARTMENT OF COMMERCE

Ronald H. Brown, Secretary

National Oceanic and Atmospheric Administration

D. James Baker, Under Secretary and Administrator

National Marine Fisheries Service

Rolland A. Schmitten, Assistant Administrator for Fisheries

April 1994
This document is available to the public through: 

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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 

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iii

ABSTRACT

The need for developing a bioenergetics model for walleye

pollock in the eastern Bering Sea has been previously established.

The Fish Bioenergetics Model 2'of Hewett and Johnson was adapted

to walleye pollock. Appropriate submodels for consumption,

respiration, egestion, and excretion were selected and

parameterized. Seasonal aspects of growth, reproduction, caloric

density, and diet composition of walleye pollock are described, as

well as the seasonal water temperature and the caloric density of

walleye pollock prey. The synthesis of published and unpublished

data required for parameter estimates and seasonal descriptions is

documented and discussed for each aspect of the bioenergetics

model.

V

CONTENTS

Page

Abstract . . . . . . . . . . . . . . . .

Introduction ..............

The Bioenergetics Model .........

. .

. .

. .

Bioenergetic Submodels and Parameters .

Consumption . . . . . . . .

Respiration . . . . . . . .

Egestion and Excretion . .

Seasonal Characteristics . . . .

Growth . . . . . . . . . . .

Predator Caloric Density . .

Reproduction . . . . . . . .

Temperature Regime . . . . .

Prey Caloric Density . . . .

Diet Composition . . . . . .

Conclusions . . . . . . . . . . . .

Acknowledgments . . . . . . . . . .

Citations . . . . . . . . . . . . . .

Appendix A. Qlo versus slope . . . . .

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Appendix B. Growth, walleye pollock caloric density,

temperature, prey caloric density, and,

diet composition data . . . . . . . . . .

Appendix C. Corrected calculations of energy losses

due to spawning by walleye pollock . . .

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iii

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53

INTRODUCTION

Walleye pollock (Theragra chalcogramma) support the world's

largest single-species fishery and comprise 67% of the total

groundfish biomass in the eastern Bering Sea (Wespestad 1993).

Cannibalism by adult walleye pollock has been identified as the

major source of predation mortality for juvenile walleye pollock

in the eastern Bering Sea (Livingston et al. 1986, Livingston

1991, Livingston et al. 1993).

Estimates of predation mortality exerted by adult walleye

pollock on economically important species in the eastern Bering

Sea are based on estimates of daily ration (Dwyer et al. 1987,

Livingston 1991, Livingston et al., 1993). Gastric evacuation

models and observed stomach fullness have been used to estimate

seasonal daily ration by size (Dwyer et al. 1987), but these are

biased low (Livingston et al. 1986, Dwyer et al. 1987). 

Livingston (1991) estimates more realistic daily rations by size

based on observed annual weight gain and a generalized food

conversion efficiency for fish. However, these estimates do not

incorporate seasonal differences, and they could be improved by

applying a bioenergetics model

variation in water temperature

(Livingston 1991).

that accounts for seasonal

and prey energy content

Developing a bioenergetics model for walleye pollock in the

eastern Bering Sea required a synthesis of information on

physiological processes and how they are affected by age and the

environment. The focus of our paper was to document and justify

the submodels, parameters,, and seasonal aspects of this
2

bioenergetics model. To facilitate future improvements to this

model, we describe in detail the methods used to calculate the

parameters and to approximate the seasonal patterns that

influence walleye pollock consumption in the eastern Bering Sea.

We also discuss some of the potential biases that may be

introduced by our methods and assumptions.

THE BIOENERGETICS MODEL

Bioenergetics models can be used to predict growth from a

specified feeding regime, or 'to predict consumption from

specified growth patterns. The Hewett and Johnson (1992) "Fish

Bioenergetics Model 2" (an improved and updated version of their

earlier generalized bioenergetics model of individual fish

growth) was parameterized for walleye pollock in the eastern

Bering Sea to predict daily consumption for walleye pollock.

Bioenergetics models are based on a balanced energy equation

which states that energy in the consumed food must be used for

respiration, reproduction, or growth; or be egested or excreted.

The basic unit of this model's daily accounting of energy input

and output is the calorie, which is translated to and from

weight-dependent processes using the caloric density (calories

per gram wet-weight, or cal * 9-1) of the predator and the prey.

Applying the Hewett and Johnson (19.92) bioenergetics model

to walleye pollock requires choosing submodels and estimating

parameters for consumption, respiration, egestion and excretion.

Incorporating seasonal variation in our model is made posible by
3

including seasonal patterns in reproduction, growth, diet

composition, predator and prey caloric densities, and water

temperature.

Bioenergetic Submodels and Parameters

Justification for submodel selection and derivation of

parameters for the consumption, respiration, egestion, and

excretion submodels are explained in this section. These weightand temperature-dependent processes are generally assumed to be

physiological constants for a species over time and among

populations (Hewett and Johnson 1992). Some of the following

descriptions of submodels and parameters used in the

bioenergetics model are paraphrased from Hewett and Johnson

(1992). Their manual is very complete, but in the course of

parameterizing their generalized model for walleye pollock, we

felt that a

noted a few

literature.

Consumption

few parameters needed clarification. In addition, we

inconsistencies and errors in the walleye pollock

Consumption (C), in "grams-prey- * 'grams-predator' * day-1",

is described by the general equation;

c = cmax * P * f(T),

where Cmax is the maximum specific feeding rate (in g * g-1 * d-1),

f(T) is the water temperature (oC) dependence function of the

specific feeding rate, and P is the proportion of the maximum
specific feeding rate that is achieved by the predator. In the

model, Cmax is an allometric function of-the form'

cmax = CA * WcB,

where CA is the intercept (for a 1g fish at 0oC), CB is the

weight dependence coefficient, and W is the predator weight in

grams

There is a choice of three equations for the form of

temperature dependence in the consumption submodel. We chose

consumption model Equation 1,

where CQ is the water temperature dependence coefficient. This

is a simple exponential function and is only appropriate when the

water temperatures are below "optimum" (the temperature at which

consumption is highest) or stressful levels. For walleye

pollock, the optimum temperature for consumption is notknown,

but is probably greater than 7.8oC because maximum consumption

increases from 3o to 7.8oC for 30 to 60 g walleye pollock (Smith

et al. 1986). The average seasonal temperature regime for

walleye pollock in the Bering Sea does not exceed 5oC (Chen 1983,

Dwyer, et al. 1987), which appears to be well below the optimum

temperature for consumption. Consumption model Equation 2 is

recommended for warm-water species, and consumption model

Equation 3 requires more information than is currently available
5

on the changes in maximum consumption at higher temperatures, so

these two equations were not selected.

The parameter estimates required for the submodel of

consumption are CA, CB, and CQ. Curves of the form required by

the model were fit to raw data from Smith et al., (1986,. 1988)

relating Cmax to weight (W) and Cmax to temperature (T). Smith et

al. (1986, 1988) fit a different form of weight dependent curve',

(using consumption as percentage of body weight) for 16 to 440 g

walleye pollock at 5.0° and 5.5oC. To satisfy the parameter

requirements of this bioenergetics model, we fit the curve

to the same data. The fit of this curve was only slightly poorer

than the fit obtained using Smith et al.'s (1986, 1988) form.

Smith et al. (1986) show a linear relationship between Cmax

(percent body weight) and temperature for 30 to 60 g walleye

pollock,

1

The number e is omitted from this equation in Table 2 and.

Figure 1 of Smith et al. (1986) 'and in Smith et al. (1988). The

number e is also omitted from the equation relating maximum growth

to initial weight in Table 2 and Figure 8 of Smith et al. (1986).
6

however, the exponential curve used in this model,

(Eq. B)

fits slightly better.

The weight intercept in Equation A was corrected for

temperature- to arrive at an intercept for a 1 g fish at 0oC. In

essence, we solved for CA by dividing 0.02075 (which represents

CA * ecQ*T in Equation A) by e0.3763*5.25 (which represents ecQ*

T

 in

Equation B). The values of the consumption parameters are

CA = 0.02878, CB = ,-0.6292, and CQ = 0.3763, and the resulting

consumption submodel is,

c = 0287.8 * w -0.6292 * p * e0.3763 * T

Respiration

The total metabolic rate, in ,"grams-energy * grams-predator-'

* days1" , is described by the general equations,

and

Respiration (R) is calculated with an allometric function (RA *

W

RB) , a temperature dependence function (f(T)), and an activity

dependence- function (Activity).

The specific dynamic. action (S, also known as the apparent

heat increment) is added to standard respiration (R) to give the
7

total respiration. Specific dynamic action can be described as

the increase in standard respiration caused by digesting and

assimilating prey into usable energy or tissue. It is expressed

as a

C is

(see

proportion (SDA) of the digested food energy (C - F), where

the total consumption and F is the amount egested as feces

Egestion and Excretion section below). Harris (1985)

calculated the specific dynamic action to be 10% of the consumed

energy and he estimated the digested food energy to be 80% of the

consumed energy. Therefore,- the specific dynamic action is 12.5%

of the digested food energy, and SDA = 0.125.

The respiration allometric function (RA * WRB) describes the

weight (W) dependence of respiration where RA is the intercept

(for a 1 g fish at the temperature causing-the highest 

respiration), measured in "grams-O2 * grams-predator" * day-'",

and RB is the weight dependence coefficient.

There is a choice of two equation sets to describe the

temperature dependence function in the respiration submodel.

Respiration model Equation Set 2 was chosen for walleye pollock

because respiration model Equation Set 1 requires information

about the dependence of the metabolism on swimming-speed, which

is not available for walleye pollock. The respiration model
8

Equation Set 2 is

and

Activity = ACT

requires, estimates for -four parameters; RTO, RTM, RQ, 'and ACT.

The parameter RTO is the optimum water temperature for

respiration (the temperature at which respiration is highest), 

RTM is the lethal water temperature, RQ is the temperature

coefficient, and ACT is a constant times the resting metabolism.

The respiration temperature dependence curve described by the

series of equations above is analogous to the temperature

dependence curve for consumption model Equation 2, illustrated in

Figure. 5 of Hewett and Johnson (1992).

Our estimates of RTO and RTM are based on the general trends

among studies examining walleye pollock respiration over a fairly

narrow range of temperatures. Paul (1986) shows an increase in

respiration for 40 to 90 g walleye pollock from lo to 7.5oC

followed by nearly constant levels of respiration from 7.5o to

12oc. Smith et al. (1988) show a more mild increase in

respiration for 345 to 750 g walleye pollock from 1.5o to 7.l°C.

Harris (1985) examined the effect of temperature on respiration
9

for 50 to 250 g walleye pollock and, although his data are biased

high (Harris 1985), he found that the respiration increased more

rapidly with temperature between 6o and 10°C than between 3o and

6oC. The temperature which yields the highest respiration (RTO)

is likely to be between 7.5o and 10°C, therefore RTO is set at

9oc. The lethal temperature for walleye pollock is greater than

15oC (Yoshida and Sakurai 1984), and RTM is set at 16oC. Lacking

further information, we make the assumption that RTO and RTM are

the same for all walleye pollock 2 years of age or older.

The respiration temperature coefficient, RQ, is not clearly

described in Hewett and Johnson (1992), but they say the

analogous parameter in consumption model Equation 2, CQ,

"approxrmates a Qlo for the rate at which the function increases

over relatively low temperatures." Respiration equation set 2

was first used by Kitchell et al. (1977) and they describe RQ as

the slope for temperature dependence of standard respiration or

approximately the Qlo for respiration. A Qlo is the increase in a

rate associated with a 10°C increase in temperature (Paul 1986)

and is defined mathematically as

where rate, is the rate at a temperature (T1) and rate, is the

rate at a higher temperature (T2) (Harris 1985). A Qlo is

independent of the units used to measure a rate, but the slope

for temperature dependence is not (Appendix A). For walleye

pollock, the parameter RQ is estimated by the Qlo of respiration-
10

temperature relationships reported in the literature, and the

parameters RA and RB are estimated using the respiration rates

converted from "1-0, * g-' * h-'I' in the literature to "g-O,'* g-' *

d-1 II in the model using "24 hr * d-l", "1~ 1 * l,OOO,OOO pl-'" and 

"1.429 g-02 * (l-02)-l/

Paul (1986) found the linear increase in respiration for 40

to 90 g walleye pollock to be

R(g-02 * g-l * d-l) = 0.000433 + 0.000273 * T, r2

 = 0.98

between loand 7.5oC with a Qlo of 6.04. Smith et al. (1988)

found the increase in respiration for 345 to 750 g walleye

pollock to be

R(g-0, * g

I * d-l) = 0.000681 + 0.000053 * T, r2

 = 0.999

between 1.6o and 7.1°C with a Qlo of 1.8. Harris (1985) found

intermediate respiration Qlo values for intermediate-sized walleye

pollock. The RQ values determined for walleye pollock decrease

with increasing' size, therefore the RQ (weight) values input into

the model approximately correspond to weight ranges as follows,:

RQ(<100 g) = 6.04; RQ (100-299 g) = 4.5; RQ(300-400 g) = 3.0;.and

RQ(>400 g) = 1.8.

The parameters RA and RB are derived from the allometric

relationship defined by the equation'

for 6 to 750 g walleye pollock at 5.5oC (Smith et al. 1988).
11

In respiration model Equation Set 2 the specific standard

metabolism, RA, should be in terms of a 1 g fish at the optimum

temperature for respiration (RTO =.9oC), and the change in

metabolism with the 3.5oC difference in temperature will be

greater for smaller walleye pollock. Using the slopes of

respiration with temperature given by Paul (1986; walleye pollock

cl00 g) and Smith et al. (1988; walleye pollock >400 g), and

intermediate slopes for walleye pollock (100-299 g and

300-400 g), the values for RA that correspond to approximate size

ranges are calculated by

RA(<lOO g) = 0.005933 t 0.000273 * 3.5;

RA(lOO-299 g) = 0.005933 t 0.000200 * 3.5;

RA(300-400 g) = 0.005933 + 0.000127 * 3.5; and

RA(>400 g) = 0.005933 + 0.000053 * 3.5

with RA (<100 g) = 0.0069, RA(lOO-299 g) = 0.0066, RA(300-400 g) =

0.0063, and RA(>400 g) = 0.0061. The weight dependence

coefficient, RB, is -0.26.

The activity multiplier, ACT, depends on the average level

of active respiration above the level described by the other

parts of the respiration submodel. A resting, non-feeding level

of respiration is described by the above parameters, and the

respiration of active, feeding walleye pollock is about double

the resting, non-feeding level (Smith et al. 1988). Smith et al.

(1988) calculated the metabolic rate of walleye pollock fed a

maintenance ration in aquaria to be 1.55 times higher than

resting, non-feeding levels. If walleye pollock respiration in
12

the Bering Sea is 2 times the resting, non-feeding levels; and

specific dynamic action accounts for respiration that is 1.55

times resting, non-feeding levels, then the activity multiplier,

ACT', is 2/1.55 which equals 1.3. This is generally in agreement

with Johnston and Battram (1993) who' found that the elevation of

respiration above resting,. non-feeding levels appears to be

caused primarily by specific dynamic action.

Using the weight-specific parameters for walleye pollock

greater than 400 g as an example, the equations for the

respiration submodel are

where

'and

S = 0.125 * (C - F).

Egestion and Excretion

There is a choice of three equation sets to describe the

egestion of feces and excretion of nitrogenous waste, and we

chose equation set 1. Egestion and excretion equation sets 2 and

3 incorporate water temperature and consumption to describe these
13

processes. Bartell et al. (1986) conclude that this is

unnecessarily complex when computing growth or consumption.

Egestion (F) and excretion (U) are modelled is constant

proportions in "grams-waste * grams-predator-1' * day-1" in equation

set 1, as

F=FA*C

and

U = UA * (C - F),

where FA is the fraction of consumed 'food (C) that is egested and

UA is the fraction of the digested food energy that is excreted.

Harris (1985) estimates that 20% of the food consumed by walleye

'pollock is egested (based

Harris et al. (1986)

11% for ammonia-excreting

on Winberg 1956), so FA = 0.2.

suggest using a nitrogen correction of

predators that feed on walleye pollock.

The nitrogen correction is based on the energy released during

the combustion of nitrogenous compounds to N2 that cannot be

obtained when these compounds are metabolized to NH, or urea

(Harris et al. 1986). The 11% nitrogen correction is represented

in the excretion parameter, and UA = 0.11.

Seasonal Characteristics

Seasonal patterns in individual growth, spawning, caloric

density, diet composition, and frequented temperatures have been

observed for walleye pollock. Many of these seasonal patterns

appear to differ substantially between the northwest and
southeast areas of the eastern Bering Sea shelf (Fig. l), as -do

the oceanographic conditions (Smith 1981).

Seasons in the bioenergetics model are based primarily on

observed seasonal growth and caloric density patterns. When

estimating consumption from observed growth of an individual, the

model must calculate the amount of calories needed to get from

the total body calories at the beginning of the time period to

the total body calories at the end of the time period.

Therefore, it is important to specify at least those points that

are near observed minima and maxima of annual weight and caloric

density patterns. The model has been set up with four equal

seasons. with the model year beginning on 15 March:

The seasonal patterns used in our model, and how they are

established,- are explained for each seasonal characteristic

below. Generally, these patterns are based on long-term averages

and are meant to represent the seasonal conditions experienced by

an average walleye pollock.- Individual and interannual

differences can be explored by changing the seasonal

characteristics used in the model. To aid in this, we discuss

how the behavior of walleye pollock may influence the seasonal
Figure 1. --Map showing the southeast (SE) and northwest (NW) areas of the eastern Bering

Sea shelf and the 200 m isobath.
16

patterns in the data, and identify some of the potential biases

introduced by our assumptions about the data. In addition, some

comments are provided that may be helpful to users of the Hewett

and Johnson (1992) bioenergetics model and we attempt to correct

a few of the errors that we found in the literature.

Growth

Growth of walleye pollock is given to the model in "grams"

for the beginning and ending weight of each time period for an

individual. Seasonal variations in walleye pollock growth were

proposed by Maeda (1972) and investigated by Chen (1983). Chen's

(1983) results indicate that the monthly weight increment in the

"feeding season" (June-September) was greater than the weight

increment in the "transitional season" (October-May). Seasonal

differences in growth (with negative growth in some areas and

seasons) were found in length-at-age data from 1976 through 1983

by Lynde et al. (1986). They concluded that the observed pattern

could be due to seasonal migration and length-dependent swimming

speed of the migrating' walleye pollock.

The growth rate of walleye pollock inhabiting the southeast

shelf of the eastern Bering Sea is faster than that of walleye

pollock inhabiting the northwest shelf (Lynde et al. 1986,

Hinckley 1987). The seasonal growth patterns of walleye pollock

from these two areas were examined using monthly weight-at-age
17

data from 1981 through 1990, provided by Vidar Wespestad (pers.

commun.

2

). The-variance of the monthly weight-at-age data is

high for each year, as it, is in other studies (Chen 1983), and a

consistent seasonal trend in the growth among years is unclear.

The weighted mean of the monthly weight-at-age was calculated for

all years combined. For March, June, September and December, the

mean was calculated using monthly weight-at-age data for these

and their respective preceding and following months (e.g., the

mean for March was calculated using weighted means of the monthly

weight-at-age data from February, March, and April),. An areaspecific seasonal pattern of growth emerged for the northwest and

southeast areas of the eastern Bering Sea shelf (Fig. 2) that is

consistent with the seasonal observations by Chen (1983) and with

the areal differences found by Lynde et al. (1986) and Hinckley

(1987). The general seasonal pattern is visible by age 2, but it

breaks down in these data at ages 8 and 10 in the northwest and

southeast areas respectively. This is apparently due to low

sample sizes and increased measurement error for older walleye

pollock.

It is likely that seasonality in the growth of walleye

pollock exists based on the seasonality in condition factor

(Harris et al. 1986) and feeding rates (Dwyer et al. 1987, Maeda

1972), but the potential influence of seasonal and lifetime

movement patterns should be considered. Lynde et al. (1986)

2

Alaska Fisheries Science Center, 7600 Sand Point Way N.E., BIN

C15700, Seattle, WA 98115-0070, U.S.A., March 1993.
Figure 2.-- The weight.(g) of walleye pollock by season from age 2 to age 8 in the

northwest (NW) area and to age 10 in the southeast (SE) area of the eastern

Bering Sea shelf as calculated from monthly weight-at-age data.
describe how seasonal on- and off-continental shelf migrations,

stratified by size, can affect the observed size-at-age in areas

with migrating fish. It is likely that the apparent extremely

negative winter growth in the southeast area is the result of

slower growing walleye pollock immigrating from the Aleutian

Basin in the spring (Lynde et al. 1986), and we think it may be

more conservative to assume there is no winter weight loss in the

southeast area.

While seasonal movements may have a large effect on the

apparent growth pattern, long-term movements can also have some

influence. A general southeastward movement (or dispersal) with

age was inferred from the spatial distribution of walleye pollock

by age over the eastern Bering Sea shelf (Pierre Dawson, pers.

commun.

3

) . The growth curve for walleye pollock in the southeast

area will be biased low as smaller size-at-age fish immigrate

from the northwest area. In addition, if this general movement

is size-dependent with larger size-at-age fish moving faster,

then the growth curve for walleye pollock in the northwest area

will be biased low as well.

It may be impossible to determine the degree of influence

that movement patterns, size-dependent movement rates/and

spawning losses (see Reproduction section below) have on the

actual seasonal growth pattern of walleye pollock. In the model,

the weights in Appendix Table B-l can be input as the beginning

3

A1aska Fisheries Science Center, 7600 Sand Point Way N.E., BIN

C15700, Seattle, WA 98115-0070, U.S.A., June 1993.
2 0

and ending weights for each season. This seasonal pattern of,

growth is in general agreement with seasonal patterns in

frequency of empty stomachs (Dwyer et al. 1987); in mean stomach

weight (Dwyer et al. 1987), in condition factor (Chen 1983) and

in caloric density (Harris et al. 1986) of walleye pollock, and

these may all be related to prey availability (Cooney 1981). A

reasonable but unlikely lower bound on the seasonality of growth

may be to assume that growth is constant among seasons (however,

fluctuations in caloric density will retain some of the

seasonality in the model).. This assumption will- generally cause'

the consumption to be underestimated in seasons of high growth

and overestimated in seasons of low or negative growth:

. ' Predator Caloric Density

The caloric density (using wet weight) of the predator, in

"calories * grams-predator'", can be modelled as a linear

function of body weight or input as a seasonal function for each

age class. The caloric density (using- dry weight) of juvenile

walleye pollock has been shown to vary seasonally, and to a

lesser extent, vary with body size, (Harris et al. 1986). Several

sources of data on the caloric density of walleye pollock (using

wet weight) from different areas were examined and a seasonal

pattern emerged (Appendix Table B-2). Although the data are

limited, the seasonal pattern. appeared to be somewhat independent

of body size for walleye pollock, age 2 and older. Therefore,

seasonal caloric density changes were input into the model, but

weight-dependent change's in caloric density were not.
21

The seasonal pattern for the caloric density of walleye

pollock is given as a low of 950 cal * g-1 on 15 March (day 1 in

the model year) and a high of 1,400 cal * g-1 on 15 September (day

185 in the model year). All intermediate values are calculated

by linear interpolation

section below).

The energy content

in the model (see Prey Caloric Density

of organisms is measured in several

different units in the literature and most conversions to cal *

g

-1 (wet weight) are easily obtainable. The following conversions

may be useful in some instances: 1 cal = 4.1868 absolute joules

(J), and 1 British thermal unit (Btu) = 251.996 cal = 1055.07 J.

In addition, the caloric density, or heat of combustion, is

commonly expressed in "cal * g-1", "J * g-'" and "Btu * lb-1" , and 1

cal * g-l = 1.8 Btu * lb-1.

Reproduction

Energy lost to reproduction is modelled as a fraction of

weight (or total body energy) lost on a given day, beginning at a

given year of life. Spawning dates of 1 April (day 17) on the

southeast shelf (Smith 1981, Hinckley 1987) and 15 July (day 123)

on the northwest shelf (Hinckley 1987) were set in the model.

The age at first spawning was set at 4 years (Wespestad 1993).

Although the spawning loss is modelled as a l-day event,

walleye pollock have a protracted spawning period (about 4 to 6

weeks) during which they apparently do not feed (Smith 1981).

However, when the total spawning energy loss is known, the 

average daily ration for the time period will be very similar
22

whether the total energy loss of spawning is modelled as a l-day

loss of energy or a protracted loss of energy (Hewett and Johnson

1992 ). 1

The energy lost during the spawning event, including any 

starvation that may occur, is about 25.2% of the total body

energy (Smith et al. 1988)4. This is composed of a 14.35% weight

loss from the pre-spawning weight accompanied by a reduction in

caloric density. We assumed that the weight loss due to spawning

was included in the quarterly weight-at-age data (see Growth

section above). We made an additional assumption that the

reduction in caloric density resulting from spawning was not

represented in the seasonal predator -caloric density file; known

post-spawning caloric densities were omitted from the calculated

averages (see Predator Caloric Density section above).

The measurement of energy losses due to spawning were

conducted in the Gulf of Alaska (Smith et al. 1988.) where the

walleye pollock spawn at about the same time as in the 'southeast

area of the eastern Bering Sea shelf (Hinckley 1987, Smith et al.

1988), and they appear to follow a similar seasonal caloric

density pattern (Appendix Table B-2). Therefore, the spawning

loss parameter was first, calculated for walleye pollock on the

southeast shelf-. The total energy loss is 25.2% and we assumed

that 14.35% was accounted for by lost weight, so the remaining

10.85% must be accounted for by the spawning loss parameter.

4

Due to calculation errors, this paper concludes that about 46%

of the body energy is lost during spawning. The' correct

calculation of their published data is presented in Appendix C.
23

This 10.85% of the pre-spawning, total body energy divided by the

remaining body weight (85.65%) yields the proportion of the

remaining body energy (0.127) that is lost. Hence, the spawning

loss parameter was set at 0.127 for walleye pollock on the

southeast shelf.

The weight-fecundity relationship appears to be similar in

the southeast and northwest shelf areas (Hinckley 1987).

Therefore, the weight-specific energy loss that resulted in the

southeast area due to spawning,

was applied in the northwest area to correct for differences in

the specified seasonal caloric density on the day of spawning,

and the spawning loss parameter for the northwest shelf was set

at 0.101.

Different values of the spawning loss parametermay be used

under alternative assumptions. If we assume the total spawning

energy loss is already represented, then the spawning loss

parameter would be set at 0.0. If we assume none of the spawning

energy loss is represented, then the spawning loss would be set

at 0.252. The spawning loss values of 0.127 and 0.101 for

walleye pollock on the southeast and northwest shelf are

intermediate of these two extreme possibilities.-
2 4

Under- or overestimation of the spawning losses may result

respectively in under- or overestimation of the consumption by

walleye pollock. Setting the first year of spawning at age 4 may

underestimate the average energy loss during the spawning season

for age-3 walleye pollock, especially on the southeast shelf, and

overestimate the average energy loss for age-4 walleye pollock on

the northwest shelf. Smith (1981) found 50% of walleye pollock

males and females to be sexually mature at 31 cm (about 206 g)

and 34 cm (about 275 g), respectively. The first spawning season

when these sizes are attained, on average, is at age-3 in the

southeast and age 4 in the northwest areas of the eastern Bering

Sea shelf (see Growth section above) .

The effect that the weight' loss due to spawning has on the

weight-at-age data can only be estimated, and it may cause some

bias in the observed seasonal growth, and therefore the predicted

seasonal consumption. 'The' observed growth during the season

preceding a weight estimate reduced by spawning. may be biased low

and the observed growth-during the season following a weight

estimate reduced by spawning may be biased high.

Temperature Regime

Seasonal temperature (oC) changes were input by specifying

temperatures on chosen days. The specified temperatures

(Appendix Table B-3) were based on observed mean bottom

temperatures for 1953 through 1982 (Ingraham 1983) in areas where

walleye pollock are-the most common (Wilson and Armistead 1991,

Bakkala et al. 1992) 'in the eastern Bering Sea. The daily
25

temperatures between the days where temperatures are specified in

the input file are interpolated by the model (Fig. 3).

Although sea surface temperature and bottom temperature data

are available for much of the-Bering Sea shelf throughout the

year, the degree of behavioral thermoregulation in walleye

pollock is unknown. The temperatures given in Appendix Table B-3

are similar to what larger juveniles and adult walleye pollock

are believed to "prefer" in the eastern Bering Sea (Chen 1983).

The model

temperature."

occurs and the

also requires input of a "maintenance

This is the temperature below which zero growth

predator consumes food at a rate equal to its

energy expenditure each day. This temperature must be, set above

the above input temperatures to have any effect on the model's

output. The maintenance temperature will be set at O.O°C and

will have no effect on the model because the temperature regime

that we input into the model never drops below 1.5oC.

Prey Caloric Density

Model inputs of caloric densities of the prey (up to 10 prey

categories in the model), in "calories * grams-prey-'", were

seasonally varied. The seasonal changes in caloric density for

the 10 prey categories (Fig. 4 and Appendix Table B-4) were

estimated from published and unpublished literature (Davis 1993)

with an emphasis on values determined for Bering Sea samples

(Harris 1985), as well as estimates based upon the trophic level

of the prey category. The seasonal trend in caloric density for

the prey categories of walleye pollock, other Gadidae and other

Figure 4.--The seasonal caloric density (cal * g-1 wet weight) of major prey categories of

walleye pollock. (WPOL - walleye pollock, WPEG - walleye pollock eggs, ,GAD -

gadidae that are not walleye pollock, EUPH - euphausiids,. COPD - copepods, AMPH

- amphipods, MPSD - mysids, CRUS - crustaceans not included in the above

categories, FISH - fishes not included in the above categories, MISC -

miscellaneous prey not included in the above categories)
28

fish was taken from the caloric density of predator walleye

pollock. No distinction was made between the southeast and

northwest shelf areas in the timing or magnitude of changes in

the caloric densities, however differences probably do exist.

-The model interpolates the caloric density between days

where it is specified in the prey caloric density input file.

However, the overall caloric density of the diet on a given day

is dependent on the prey composition, therefore large changes in

the caloric density of the diet can occur if the compositionof

the diet changes.

Diet Composition

The proportion by weight of each prey in the diet (up to 10

prey categories in the model), can be seasonally varied for each

walleye pollock age group. The model will interpolate between

the days where diet proportions are specified. The methods used

to collect the diet, data and to calculate the proportion by

weight for the prey categories can be found in Livingston (1991).

The four time periods used to calculate the diet composition

begin on the 1st of January, April, July and October. These time

periods are offset by about 15 days from the growth seasons. The

diet composition was maintained as a constant mean over the time

period for which it was calculated by specifying the mean diet

composition at both the beginning and, end of the, time period. To

ensure complete coverage in all seasons for all ages in each

area, the proportion by weight of each prey category was

calculated using the diet data pooled from 1985 through 1989.
Fork length intervals were

the predator walleye pollock in

29

used to approximate the age o-f

the food habits database:

Diet proportions of walleye pollock ages 2 through 4 were pooled.

The seasonal diet composition of the three age groups in the

southeast and northwest shelf is presented in Appendix Tables B-5

and B-6.

CONCLUSIONS

This model can be used to provide insight into the effects

of different conditions on walleye pollock consumption. The

physiological processes are described as well as the data

available will allow. As more data on the physiological

processes of-walleye pollock become available, the parameter

estimates (Table 1) may be improved, or perhaps different

submodels may be used. One benefit to our choice of the

submodels available in the "Fish Bioenergetics Model 2" is that

they require the fewest parameter estimates.

The seasonal characteristics experienced by walleye pollock

in the eastern Bering Sea are also 'described as well as the data
Table 1.--Parameter values for the bioenergetics model' of walleye

pollock in the eastern Bering Sea. See text for explanation of

the parameters and bioenergetic equations.
31

will presently allow. The seasonal patterns observed for many of

these characteristics must be considered in terms of the behavior

of walleye pollock and also in terms of interactions between the

characteristics. As we have discussed, some of the observed

seasonal characteristics may be somewhat biased, and thus

estimates of consumption generated by the bioenergetics model may

be somewhat biased. However, we feel that the bioenergetics

model, in its present form, will allow us to make relatively good

seasonal estimates of daily rations for walleye pollock in 'the

eastern Bering Sea.
3 2

ACKNOWLEDGMENTS

We are grateful to A.J. Paul for digging up and sharing raw

data that substantially improves our confidence in some of the

parameter estimates: Nancy Davis provided helpful comments on an

early draft of this paper, and later versions were thoughtfully

reviewed by Sarah Hinckley, Vidar Wespestad, and Richard Brodeur.
CITATIONS

Bakkala, R.G., W.A. Karp, G.F. Walters, T. Sasaki, M.T. Wilson,

T.M. Sample, A.M. Shimada, D. Adams, and C.E. Armistead.

1992. Distribution, abundance, and biological

characteristics of groundfish in the eastern Bering Sea

based on results of U.S.-Japan bottom trawl and midwater

surveys during-June-September 1988. U.S. Dep. Commer., NOAA

Tech. Memo. NMFS F/NWC-213, 362p.

Bartell, S.M., J.E. Breck, and R.H. Gardner. 1986. Individual

parameter perturbation and error analysis of fish

bioenergetics models. Can. J. Fish. Aquat. Sci. 43:160-168.

Chen, L.F. 1983. The effects of water temperature on the

seasonal distribution and growth of walleye pollock,

Theragra chalcosramma (Pallas), in the southeast Bering Sea.

M.S. Thesis, Univ. Alaska, Fairbanks, 92p.

Cooney;R.T. 1981. Bering Sea zooplankton and micronekton

communities with emphasis on annual production. In: D.W.

Hood and J.A. Calder (eds.), The Eastern Bering Sea Shelf:'

Oceanography and Resources, 2:947-74. Univ. Washington

Press, Seattle, Washington.
34

Davis, N.D. 1993. Caloric content of oceanic zooplankton and

fishes. for studies of salmonid food habits and their

ecologically related species. (NPAFC DOC.) FRI-UW-9312.

Fisheries Research Institute, Univ. Washington,- Seattle.

10p.

Dwyer, D.A., K.M: Bailey, and P.A. Livingston. 1987. Feeding

habits and daily ration of walleye pollock (Therasra

chalcosramma) in the eastern Bering Sea, with special

reference to cannibalism. Can. J. Fish. Aquat. Sci.

44:1972-1984.

Harris, R.K. 1985. Body composition (carbon, nitrogen and

calories) and energetics of immature walleye pollock,

Theragra chalcogramma (Pallas), in the southeast Bering Sea.

 M.S. Thesis, Univ. Alaska, Fairbanks, 116p.

Harris, R.K., T. Nishiyama, and A.J. Paul. 1986. Carbon,

nitrogen and caloric content of eggs, larvae, and juveniles

of the walleye. pollock, Theragra chalcogramma. J. Fish

Biol. 29:87-98. 

Hewett, S.W., and B.L. Johnson. 1992. Fish Bioenergetics Model

2, an upgrade of "A Generalized Bioenergetics Model of Fish

Growth for Microcomputers." Univ: Wisconsin, Sea Grant

Tech. Rep. No. WIS-SG-92-250, 79p.
35

Hinckley, S. 1987. The reproductive biology of walleye pollock,

Theragra chalcogramma, in the Bering Sea, with reference to

spawning stock structure. Fish. Bull., U.S. 85:481-498.

Ingraham, W.J., Jr. 1983. Temperature anomalies in the eastern

Bering Sea 1953-82 for the Dynumes 24 x 24 ecosystem model

grid. NWAFC Processed Rep. 83-21, 348p. Alaska Fish. Sci.

Cent., Natl. Mar. Fish. Serv., NOAA, 7600 Sand Point Way

NE., BIN C15700, Seattle, WA 98115-0070.

Johnston, I.A., and J. Battram. 1993. Feeding energetics and

metabolism in demersal fish species from Antarctic,

temperate and tropical environments. Mar. Biol. 115:7-14.

Kitchell, J.F., D.J. Stewart, and D. Weininger. 1977.

Applications of .a bioenergetics model to yellow perch (Perca

flavescens) and walleye (Stizostedion vitreum vitreum). J.

Fish. Res. Board Can. 34:1922-1935.

Livingston, P.A. 1991. Groundfish food habits and predation on

commercially important species in the eastern Bering Sea

from 1984 to 1986. U.S. Dep. Commer., NOAA Tech. Memo. NMFS

F/NWC-207, 240p.
36

Livingston, P.A., D.A. Dwyer, D.L. Wencker, M-S. Yang, and G.M.

Lang. 1986. Trophic interactions of key fish species in

the eastern Bering Sea. Int. N. Pac. Fish. Comm. Bull.

47:49-65.

Livingston, P.A., A. Ward, G.M. Lang', and M-S. Yang. 1993.

Groundfish food habits and predation on commercially

important prey species in the eastern Bering Sea- from 1987

to 1989. U.S. Dep. Commer., NOAA Tech. 'Memo. NMFS-AFSC-11,

192p.

Lynde, C.M., M.V.H. Lynde and R.C. Francis. 1986. Regional and

temporal, differences in growth of walleye pollock (Theragra

chalcogramma) in the eastern Bering Sea and Aleutian basin

with implications for

10, 48p. Alaska Fish

NOAA, 7600 Sand Point

98115-0070.

management. NWAFC Processed Rep. 86-

sci. Cent., Natl. Mar. Fish. Serv.,

Way NE., BIN C15700, Seattle, WA

Maeda, T. 1972. Fishing grounds of Alaska pollock. Bull. Jap.

Soc. Sci. Fish. 38:362-711

Miller, L.K. 1978. Energetics of the northern, fur seal in

relation to climate and food resources of the Bering Sea.

U.S. Marine Mammal Comm. Rep. MMC-75/08, 27p. (Available

from Natl. Tech. Inf. Serv., Springfield, VA,, as PB-275296.)
37

Paul, A.J. 1986. Respiration of juvenile pollock, Theragra

chalcogramma (Pallas) , relative to body size and

temperature.' J; Exp. Mar.. Biol. 'Ecol. 97:287-293.

Perez, M.A. 1994. ,-Calorimetry measurements of energy value of

some Alaskan fishes and squids. U.S. Dep. Commer., NOAA

Tech. Memo. NMFS-AFSC-32, 32p.

Smith, G.B. 1981. The biology of walleye pollock. In: D.W.

Hood and J.A. Calder (eds.), The Eastern Bering Sea Shelf:

Oceanography and Resources, 1:527-551. Univ. Washington

Press, Seattle, Washington.

Smith, R.L., A.J. Paul, and J.M. Paul. 1986. Effect of food

intake and temperature on growth and conversion efficiency 

of juvenile walleye pollock (Theragra chalcogramma

(Pallas)): A laboratory study. J. Cons. int. Explor. Mer

42:241-253.

Smith, R.L., A.J. Paul, and J.M. Paul. 1988. Aspects of

energetics of adult walleye pollock, Theragra chalcogramma

(Pallas), from Alaska. J. Fish Biol. 33:445-454.

Smith, R.L., J.M. Paul, and A.J. Paul. 1989. Gastric evacuation,

in walleye pollock, Theragra chalcogramma. "Can. J. Fish.

Aquat. Sci. 46:489-93.
38

Steimle, F.W., Jr., and R.J. Terranova. 1985. Energy

equivalents of marine organisms from the continental shelf

of the temperate northwest Atlantic. J. Northwest Atl.

Fish. Sci. 6:117-124.

Stewart, D.J., D. Weininger, D.V. Rottiers, and T.A. Edsall.

1983. An energetics model for lake trout, Salvelinus

namaycush: Application to the Lake Michigan population.

Can. J. Fish. Aquat. Sci. 40:681-698.

Tyler, A.V. 1973. Caloric values of some North Atlantic

invertebrates. Mar. Biol. 19:258-261.

Wespestad, V.G. 1993. The status of Bering Sea pollock and the

effect of the "Donut Hole" fishery. Fisheries 18:18-24..

Wilson, M.T., and C.E. Armistead.: 1991. 1989 bottom trawl

survey of the eastern Bering Sea continental shelf. U.S.

Dep. Commer., NOAA Tech. Memo. NMFS F/NWC-212, 212p.

Winberg G.G. 1956. Rate of metabolism and food requirements, of

fishes. Belorussian State Univ; Minsk. Fish. Res. Board

Can. Transl. Ser. 194, 239p.
39

Yoshida, H., and Y. Sakurai. 1984. Relationship between food

consumption and growth of adult walleye pollock Therasra

chalcosramma in captivity. Bull. Jap. Soc. Sci. Fish.

50:763-769.
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THIS PAGE INTENTIONALLY LEFT BLANK
APPENDIX A

Qlo versus Slope
THIS PAGE INTENTIONALLY LEFT BLANK
43

The Qlo of a rate. (k) is the increase in that rate associated

with a 10°C increase in temperature (T) and is defined

mathematically as

A Qlo will approximate the slope of the change in respiration (R)

with temperature if respiration is measured in "μ1-02 * g-1 * hr-1"

as in Kitchell et al. (1977), but not if respiration is measured

in “g-02 * g-1 * d-l" as in the bioenergetics model of Hewett and

Johnson (1992). Respiration rates are converted between these

two units of measure using "24 hr * d-1", "1 1 * 1,000,000 μ1-1",

and "1.429 g-02 * (1-O2)

-1". Paul (1986) found the linear increase

in respiration for 40 to 90 g walleye pollock between lo and

7.5oC to be

or

R(g-02 * g-1 * d-1) = 0.000433 + 0.000273 * T.

The Q10 of the first equation can be calculated for T1 =

1.0oC and T2 = 7.5oC as follows:
44

The slope of the first equation (7.961) approximately equals the

Qlo (6. 915) .

The Qlo of the second equation can be calculated for T1 =

1.0oC: and T2 = 7.5oC as follows:

log Q10 = 10 * (log R2 - log R1)/ (T2 - T,)

log Qlo = 10 * (log 0.0024802 - log 0.0007057)/(7.5 - 1.0)

log Q1 0.= 0.83980

Qlo = 6.915. 

The slope of the second equation (0.000273) is not approximately

equal. to the Qlo (6:915), but the Q1O of both respiration equations

is the same. 
APPENDIX B

Growth, walleye pollock caloric density,

temperature, prey caloric density, and

diet composition data.
THIS PAGE INTENTIONALLY LEFT BLANK
47

Table B-l.--Weight-at-age data input into the bioenergetics model

for walleye pollock from the southeast (SE) and

northwest (NW) areas of the eastern Bering Sea shelf.

Weight is in grams and age is the number of December

31sts survived.
48

Table B-2.--Caloric density values (cal * g-1 wet weight) of

walleye pollock. Monthly averages omit known postspawning samples (lb). BS = Bering Sea samples.

Month
49

Table B-3.--Dates, corresponding model day and the temperature

input for the southeast (SE) and northwest (NW) areas

of the eastern Bering Sea shelf.

Temperature (OC)

Date

Model

Day SE NW
5 0

Table B-4.--The date and caloric densities (cal * g-1, wet weight)

for 10 prey categories specified in the model. A

'description of each prey category and the major

information sources are described below.

Prey categories*

Date WPOL WPEG GADS EUPH COPD AMPH MYSD CRUS FISH MISC

*Prey category definitions and data sources:

WPOL

WPEG

GADS

EUPH

COPD

AMPH

MYSD

CRUS

FISH

MISC

Walleye-pollock caloric densities are taken directly from

the predator caloric densities.

Walleye pollock egg caloric density is derived from the.

average caloric. density of Harris (1985).

Gadidae, that are not walleye pollock, have caloric

densities taken directly from the walleye pollock caloric

densities.

Euphausiid caloric densities are derived. from the seasonal

caloric densities given in Harris (1985).

Copepod caloric densities are 'derived from the average

caloric density given in Harris (1985) and seasonal changes

are inferred from the May and June spring "bloom" (Cooney

1981).

Amphipod caloric densities are based on Harris (1985).

Mysid caloric densities are based on Harris (1985).

Crustaceans not included in the above categories are mostly

decapods and some isopods, and their caloric densities were.

based on Harris (1985) and Davis (1993) .

Fishes not included in the above categories have caloric

densities taken directly from walleye pollock.

Miscellaneous prey include molluscs, echinoderms, other

invertebrates and unidentified prey, and their caloric

densities were based on Davis (1993), Steimle and Terranova

(1985), and Tyler (1973).
51

Table B-5.--Diet proportions by weight and season of the 10 prey

categories and three age groups used in the model of

walleye pollock on the southeast shelf of the eastern

Bering Sea. (WPOL - walleye pollock, WPEG - walleye

pollock eggs, GADS - gadidae that are not walleye

pollock, EUPH - euphausiids, COPD - copepods, AMPH -

amphipods, MYSD - mysids, CRUS - crustaceans not

included in the above categories, FISH - fishes not

included in the above categories, MISC - miscellaneous

prey not included in the above categories)

*Winter = 1 January to 31 March- (model days 293 to 17).

Spring = 1 April to 31 June (model days 18 to 108).

Summer = 1 July to 30 September (model days 109 to 200).

Autumn = 1 October to 31 December (model days 201 to 292).
52

Table B-6.--Diet proportions by weight and season of the 10 prey

categories and three age groups used in the model of

walleye pollock on-the northwest shelf of the eastern

Bering Sea. (WPOL - walleye pollock, WPEG - walleye

pollock eggs, GADS - gadidae that are not walleye

pollock, EUPH - euphausiids, COPD -copeppds, AMPH -

amphipods, MYSD - mysids, CRUS - crustaceans not

included in the above categories, FISH - fishes not

included in the above categories, MISC - miscellaneous

prey not included in the above categories.)

Prey categories 

*Winter = 1 January to 3l March (model days 293 to 17).

Spring = 1 April to 31 June (model days 18 to 108).

 Summer = 1 July to 30 September (model days 109 to 200).

Autumn = 1 October to 31 December (model days 201 to 292).
APPENDIX C

Corrected calculations of energy losses

due to spawning by walleye pollock.
THIS PAGE INTENTIONALLY LEFT BLANK
55

Table C-l.--Table II of Smith et al. (1988) is reproduced below

with the corrected values underlined. Based on the

corrected values, adult walleye pollock will lose

about 14.4% (males, 7.3%; females, 21.4%) of their

pre-spawning body weight and about 25.2% (males,.

14.1%; females, 36.3%) of their total body energy

during spawning.

TABLE II. Energy content and partitioning of that energy in ripe

and spent adult walleye pollock. In this exercise, [Smith et al.

(1988)] assumed a ripe weight of 1,000 g for both males and

females; corresponding lengths (49.6 cm for males, 48.3 cm for

females) were calculated for ripe fish, based on average condition

of ripe males (0.82) and ripe females (0.89) in March 1986;

weights of spent adults were predicted based on lengths and

average condition of spent fish (0.76 for males; 0.70 for females)

in April, 1986; liver, gonad and somatic indices were those

calculated for ripe fish in March 1986 and for spent fish in April

1986

kcal

Compartment % body g g (dry) g (dry) kcal % total
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