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Transactions of the American Fisheries Society 122:736-748. 1993
© Copyright by the American Fisheries Society 1993
Bioenergetics Modeling Today: Growing Pains on the Cutting Edge
JOHN J. NEY
Department of Fisheries and Wildlife Sciences
Virginia Polytechnic Institute and State University. Blacksburg, Virginia 24061, USA
Abstract. —Elaborations of the mass-balance equation that partitions energy of consumed food
into its various physiological fates have flourished in the past 15 years. These bioenergetics models
have been converted to powerful simulation tools and used in fisheries science, most often for
predicting consumption by predators or for projecting fish growth as a function of temperature
and prey availability. New uses of bioenergctics models are proliferating and range from predictions
of larval survival to analysis of ecosystem function. Companion technologies such as hydroacoustics and physiological telemetry promise to further broaden the spectrum of potential applications.
However, the data demands and uncertain accuracy of multiparameter models may constrain their
ability to address routine fish management questions. Field measures of consumption or growth
failed to corroborate bioenergetics estimates consistently (differences of at least 50%) in four of six
published tests. Poor agreement could be due to inaccuracies in field measures, bioenergetics
estimates, or both. Errors in bioenergetics estimates will accrue when input values for internal
parameters and external variables are deficient: problems can result from unknown activity costs,
extrapolation of weight-dependent power functions, unjustified borrowing of physiological values
from other species, and use of nonrepresentative field data. Remediation of these deficiencies will
require a major concerted research effort and extensive field corroboration. Simpler individual
and production-based models show promise for predicting long-term consumption or growth but
also require substantiation of input parameters and more corroboration. In the interim, I suggest
that bioenergetics models will remain better suited for making relative comparisons than for
making precise quantitative predictions.
The term bioenergetics refers to the ways in
which animals dispose of the energy they acquire.
Bioenergetics models are essentially mass-balance
equations in which the energy in consumed food
is partitioned into its various fates—growth, metabolism, and waste products (Winberg 1956). The
equations can be solved for any of these parameters when the others are known or estimated, although they are usually solved for growth or consumption. Application of bioenergetics models to
address fisheries research problems has flourished
in the computer age because of the models' inherent flexibility: parameters and their controlling
variables can be readily modified to calculate individual and population-level responses under
various biological and physical scenarios.
As the popularity of bioenergetics modeling has
risen, models themselves have been refined and
packaged for use by fisheries managers to aid in
traditional decisions on stocking strategies and
harvest regulations (Hewett and Johnson 1987,
1992). The bioenergetics modeling approach is also
being adapted to study a steadily expanding array
of questions, ranging from individual fish behavior to ecosystem function, as the papers in this
issue demonstrate. Predictably, bioenergetics
models have become more elaborate as modelers
strive to incorporate more realistic physiological
and behavioral responses to dynamic conditions.
As input parameters and variables increase, the
potential for error in model output also may rise.
However, the accuracy of predictions generated
by bioenergetics models have been evaluated infrequently.
In this paper, I review the development of bioenergetics models and their application in fisheries
research and appraise their present utility as predictive tools for fisheries management. Specifically, my objectives are to (1) review the development of the bioenergetics modeling approach, (2)
describe trends in its continuing evolution, (3)
compare model predictions with independent estimates of consumption and growth, and (4) identify areas of weakness in model parameter estimates and measures to remedy these weaknesses.
Development of Bioenergetics Modeling
7/7? Bioenergetics Equation
Winberg (1956) provided the first detailed energy budget for fish, partitioning the energy of consumed food (O as
C= G + R + W.
(1)
where G is somatic plus gonadal growth, R is total
metabolic costs, and W is the energy contained in
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ASSESSMENT OF BIOENERGETICS MODELING
waste products. Metabolic and waste costs can be
divided into subcomponents. Metabolism consists of energy costs for basic maintenance (standard metabolism, R$), activity (RA), and digestion
of food (RD)- Digestion costs include energy released in deamination of proteins (specific dynamic action, SDA), as well as energy used during mechanical digestion, assimilation, and storage
(Jobling 1985). Waste products are the total of
nonassimilated energy egested as feces (F) and assimilated energy later excreted (CO as urea and
ammonia. Consumed energy is now divided
among six fates
C = G + Rs + RA + RD + f + V.
(2)
This second Winberg equation is the basis of
most bioenergetics models in current use; modelers must provide input values for six components to solve the equation for the seventh. Energy
expenditures for metabolism and waste components of the equation are usually estimated from
laboratory studies and are weight- and temperature-dependent to varying degrees, increasing the
number of input parameters (Brafield 1985). Energy contained in consumed food or manifested
in growth is generally estimated from field measurements (Soofiani and Hawkins 1985; Ney
1990), as are water temperature and diet composition. Model accuracy should be enhanced if
the model is iterated with short step lengths (e.g.,
daily) over the period of estimation, and both
temperature and weight are varied to reflect realworld dynamics (Rice and Cochran 1984).
A major elaboration of this basic bioenergetics
model (equation 2) has been developed and promoted by J. F. Kitchell and colleagues at the University of Wisconsin (Kitchell et al. 1977). The
Wisconsin model has been adapted for microcomputer use (Hewetl and Johnson 1987, 1992) and
is now the most widely used version in North
American fisheries research. The chief innovation
of the Wisconsin model is that consumption is
estimated as a proportion of maximum possible
ration for a fish of a particular species at any weight
and temperature. Specifically,
C*
= C*
-n-r
C\\
where Q> is daily consumption, Cmax is maximum daily consumption, p is a proportion of
maximum ration ranging from 0 to 1, and rc is a
temperature-dependent sealer, also ranging from
0 to 1. The value of Cmax is determined as a power
function of weight (Cmax = a-W**); the coefficient
a and exponent b are estimated from ad libitum
737
feeding trials at optimum temperature. The value
of rc depends on species-specific inputs for optimum and maximum temperature as well as for
the rate of change in consumption with temperature. Consumption over a time interval is then
estimated by generating growth curves from known
or simulated initial and final weights with p as the
lone independent variable, values for metabolic
and waste parameters having been previously developed. The Wisconsin model is run through successive iterations, usually with a daily time length,
until a p value is obtained that results in the best
fit between predicted and known final weight.
Consumption over the time interval is the sum of
daily rations estimated with the best-fit p value,
which is sometimes then interpreted as an indicator of feeding efficiency (Stewart and Binkowski
1986). The Wisconsin bioenergetics model attempts to minimize error potential by forcing the
consumption estimate to agree with growth data,
at least at the end points of the time interval.
However, the accuracy of the p estimate depends
on the validity of the many other input variables
as well as on the actual pattern of growth over the
time interval and length of the interval itself (Rice
and Cochran 1984; Bartell et al. 1986; Boisclair
and Leggett 1989).
Applications of Bioenergetics Models
The bioenergetics approach has been used primarily to estimate consumption by or growth of
wild fish under different scenarios. The most frequent use of bioenergetics models in fisheries
management has been to quantify predator trophic demand and to relate demand to prey supply
(Ney 1990). Consumption estimates of average individuals have been expanded to cohorts and then
to populations to estimate predation impact on
fish or invertebrate prey resources. In this context,
bioenergetics models have been applied to determine optimal densities for put-grow-take stocking of salmonids in the Great Lakes (Stewart et al.
1981) and coolwater piscivores in a Virginia reservoir (Moore 1988). Prey consumption by selfsustaining populations of predators, such as walleye Stizostedion vitreum in Lake Erie (Hartman
and Margraf 1992) and largemouth bass Micropterus salmoides in Ohio reservoirs (Carline et al.
1984), also have been estimated by bioenergetics
models with an eye to modifying harvest rates to
maintain predator-prey balance. Conversely, predation impact can be addressed bioenergetically
with the objective of protecting desirable forage
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fishes, such as rainbow smelt Osmerus mordax in
Lake Champlain (LaBar 1993, this issue).
The bioenergetics equation can be solved for
growth rather than for consumption to assess the
effects of potentially limiting factors, notably temperature and prey availability (Kitchell et al. 1977;
Rice et al. 1983), or to compare projected growth
trajectories of species that are candidates for introduction into particular waters (Bevelheimer et
al. 1985). Because the bioenergetics equation can
be used to estimate both consumption and growth
rates, it also has been employed to model the dynamics of contaminants that bioaccumulate in fish,
such as PCBs and mercury (Weininger 1978;
Borgmann and Whittle 1992).
Bioenergetics models are readily adaptable for
the study of a host of other trophic-based phenomena, many of which are highlighted in this
issue. These include quantifying the description of
energy flow and nutrient processing rates across
trophic levels (Schindler et al. 1993;Heetal. 1993;
both this issue). To estimate nutrient cycling rates,
excretion and egestion may replace consumption
and growth as outputs of the model (Kraft 1993,
this issue). At the autecological end of the spectrum, bioenergetics models have a natural linkage
to emerging individual-based models of juvenile
fish recruitment that predict survival as functions
of consumption and growth rates (Adams and
DeAngelis 1987; Madenjian 1991; DeAngelis et
al. 1993, this issue; see also papers in Transactions
of the American Fisheries Society 122[3], 1993).
Investigation of the relationship between predator demand and prey supply through bioenergetics modeling is maturing beyond the first-order
accounting exercise of determining whether total
production of prey species is adequate to meet the
cumulative dietary needs of their predators. Incorporation of density-dependent population behavior and of ontogenetic role changes among and
within species is an important step in the refinement of predictions of predation impact (Post and
Rudstam 1992). The developing capability to describe predator and prey distributions on fine time
and space scales promises to define that fraction
of the prey resource that is encountered and can
be eaten by predators (Brandt et al. 1992).
Bioenergetics models will also be applied to totally new concerns, such as forecasting the role of
invaders like the zebra mussel Dreissenia polymorpha in the Great Lakes (Schneider 1992). Other novel uses of bioenergetics can be expected at
any trophic level when knowledge of the energyenvironment relationship is sought.
Current Trends
As bioenergetics modeling grows to confront new
questions, the approach itself is becoming more
sophisticated. Linkage of new technology to computer-based bioenergetics programs promises to
allow better descriptions of variables ranging from
individual to community energetics. Bioenergetics
models have also become more complex as modelers have strived to build fine-grain realism into
their depictions of fish physiology and behavior.
The data demands of increasingly elaborate models present an imposing obstacle to routine use of
the models as fisheries management tools. The
trend toward greater complexity has stimulated a
backlash effort to simplify bioenergetics models to
address coarse-grain management questions.
Technology
Hydroacousties and physiological telemetry appear to offer the most promising technological
couplings with bioenergetics. Hydroacoustics has
been used for more than a dozen years to estimate
pelagic forage-fish abundance and distribution
(Brandt 1975; Thorne 1983; Brandt et al. 1991).
Hydroacoustic technology now can resolve fish
numbers and sizes on fine spatial scales (e.g., 10-m
x 10-m x l-m grids). This information can be
cumulated over an entire water body and, in conjunction with temperature data and a bioenergetics growth model, used to generate spatially explicit estimates of the trophic efficiency, growth,
and production potential of the predator population (Brandt et al. 1992; Brandt and Kirsh 1993,
this issue; Goyke and Brandt 1993, this issue).
Color-coded snapshots of predators and prey distributions can be produced when hydroacoustics
data are translated by computer visualization imagery (see Brandt et al. 1992).
Values for the metabolic components of the bioenergetics budget ideally should be determined
from wild, free-swimming fish rather than from
captive specimens held in laboratory respirometers. Field measurement of metabolism finally has
been made possible by the invention of telemetry
devices to monitor those rates of bodily function
that are correlated with metabolism, including gill
ventilation rates, heart rates, and electromuscular
activity. Total metabolic energy expenditures can
be divided among standard, activity, and resting
components by concurrent observations of fish
behavior (Lucas etal. 1991, 1993, this issue). True
costs of metabolism, usually the principal fate of
ingested energy, should be defined as techniques
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ASSESSMENT OF BIOENERGETICS MODELING
of physiological telemetry evolve. However, not
all fish species may demonstrate a strong correlation between physiological rates and metabolic
energy expenditures (Sureau and Lagardere 1991).
Model Complexity
Parameter proliferation.— Winberg's formula
(equation 2) requires inputs for six components.
Because standard metabolism changes with weight
in an allometric fashion and is also temperature
dependent (e.g., R$ = a-Wb-e™?), T being temperature and m a coefficient), the total number of
input parameters is nine. The basic version of the
Wisconsin model has 15 input parameters (Kitchell et al. 1977). More recent elaborations of the
Wisconsin model incorporate parameters for
swimming speed (Stewart and Binkowski 1986) or
temperature dependence of excretion and egestion
(Beauchamp et al. 1989), bringing the total number of parameters to 22. External variables, including diet composition and predator as well as
prey energy densities (joules per unit mass offish),
can raise the total number of inputs that must be
valuated to more than 30 for fish with diverse
diets (Lyons and Magnuson 1987). Although these
data-hungry models may have the potential to
provide fine-scale estimates of a fish's energy intake and allocation, filling all the blanks with accurate inputs is an imposing task. Users of these
models must ensure that errors are small or assume that they cancel each other out rather than
being additive or multiplicative.
A better alternative is to weigh the potential
gain in resolution against uncertainties in accuracy
before any new parameter is added to a bioenergetic model. Sensitivity analysis by a variety of
statistical procedures can be used to identify those
parameters for which errors will have large or small
effects on model output. For example, Bartell et
al. (1986) used both individual parameter perturbation and error analysis techniques to determine
that variance in the excretion and egesion parameters of the Wisconsin model had little effect on
output; elaboration of these parameters to consider temperature or size dependence was unwarranted. Sensitivity analysis can and should be used
in this way not only to justify parameter proliferation but also to simplify existing models that
may be needlessly complex.
Parameter reduction.—Elaborate models may
not be necessary to provide satisfactory answers
to some bioenergetics questions of interest to fisheries managers. Simple models have been developed by eliminating or combining parameters, and
these could prove adequate for describing temporal patterns and the magnitude of growth and
consumption under alternative management
schemes. Models with few parameters facilitate
calculations, have less potential for data entry error, and focus concern on the accurate determination of only a small number of energetics parameters. However, these simple models
necessarily make encompassing assumptions about
fish energetics which, if unjustified, can result in
large errors in output. I offer three examples, an
individual-based model proposed by Winberg and
two versions that merge bioenergetics and population dynamics in a production-based approach.
(1) Individual-based model. Winberg (1956)
considered his six-parameter model (equation 2)
to be unnecessarily cumbersome and simplified
it as
2RS
1 -(RD
V)'
(4)
In this version, the energies allocated to digestion,
egestion, and excretion are fixed fractions of the
energy of the consumed food, an assumption retained in most versions of the Wisconsin model.
These total 35-40% of C in carnivorous fish (see
Brett and Groves 1979 for a review). The denominator in equation (4) thus reduces to a decimal
(0.60-0.65). Winberg's second assumption was that
activity metabolism (RA) was equal to standard
metabolism (the Winberg II multiplier) in wild
fish (the assumption that activity metabolism is
an integer multiple of standard metabolism is also
common to the basic versions of the Wisconsin
model). Equation (4) requires inputs only for
growth, usually derived from field data, and standard metabolism, obtained from laboratory study.
The total number of input parameters is reduced
to five (standard metabolism is weight and temperature dependent). This simplified Winberg
equation has been used with some modification
to estimate growth of sauger Stizostedion canadense in Tennessee (Minton and McLean 1982)
and stream fishes in Poland (Penczak 1985).
(2) Production-based models. Many questions
in fisheries management focus on populations, but
most bioenergetics models provide estimates for
individual fish and must be merged with data on
abundance, mortality, and recruitment to obtain
population-level predictions. A developing alternative for management questions concerning
predator consumption is to relate population production to one or two bioenergetics variables. Two
versions of this approach, the conversion efficien-
740
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applied to individual age-groups over 1-year intervals. The model is based on broad assumptions
concerning annual maintenance ration and average conversion efficiency of piscivorous fish (Brown
1946; Kelso 1972; Lane et al. 1979). In energetics
terms, it is approximately equivalent to the apportionment of energy intake as 60% for metabolism, 20% for growth, and 20% for wastes, which
appears reasonable (Brett and Groves 1979).
P=G-£,
(5)
This simple production-biomass (P-B) equawhere G is the instantaneous rate of growth (nat- tion has produced estimates of annual consumpural log of the ratio of final to initial weight) and tion that agree well with independent values obB is mean biomass over the interval. For preci- tained from field measurements and from the
sion, production is often calculated separately for Wisconsin bioenergetics model. Production-bioeach cohort, then totaled to achieve the popula- mass estimates of the annual ration of individual
fish were within 2% of field determinations (by
tion estimate.
If the average gross food conversion efficiency the gut content x evacuation rate method) for
(G/C) for the population or its individual cohorts largemouth bass in a Tennessese reservoir (Adams
is known, then total consumption (Cyoj) over a et al. 1982a, 1982b) and sauger in the Ohio River
(Wahl and Nielsen 1985). Somewhat poorer cortime interval can be calculated as:
respondence was obtained between the P-B and
(6) Wisconsin bioenergetics models when both were
used to estimate total annual consumption by
multicohort populations. The P-B estimate of toThe production-conversion efficiency approach tal annual consumption summed over nine cowas used by Eck and Wells (1983) to estimate prey horts of trout in Lake Michigan was 17% higher
consumption by the population of lake trout Sal- than that projected by the Wisconsin model (Stewvelinus namayacush in Lake Michigan; conver- art et al. 1983; Ney 1990). Similarly, P-B estision efficiencies were obtained from captive lake mates were 9% above the corresponding Wiscontrout. However, estimated total consumption of sin model estimate for an eight-cohort population
alewives Alosa pseudoharengus was only 38% of of striped bass Morone saxatilis in Virginia (Moore
the estimate developed by Stewart et al. (1983) 1988), and 18% higher than the bioenergetics esusing the Wisconsin bioenergetics model. Eck and timate of aggregate annual consumption by four
Wells (1983) believed that their estimate was too age-groups of largemouth bass in an Ohio reserlow and attributed their error in part to overes- voir (Carline et al. 1984). In each of these three
timation of age-specific conversion efficiencies. comparisons, the P-B and bioenergetics estimate
This example provides a cautionary lesson: as the were in close agreement for younger age groups,
number of input parameters decreases, the effect but diverged progressively for older cohorts (Figof each parameter on output rises accordingly. It ure 1). In the Wisconsin bioenergetics model,
is thus imperative to have accurate estimates of maintenance ration effectively declines with age,
gross conversion efficiencies to use this method. whereas the production-biomass model holds
Deriving these estimates for wild fish from labo- maintenance ration constant (at three times mean
ratory experiments is problematic.
biomass). Energy budgets of large adult piscivores
I have proposed an even simpler model to es- have not been well studied; the accuracy of contimate annual cohort consumption that requires sumption estimates generated by any bioenergetonly production and mean biomass estimates as ics model thus probably declines with age.
input (Ney 1990). These parameters can be obThe production-biomass method requires adtained from abundance, growth, and mortality data ditional corroboration (as do all extant bioenerthat are often routinely collected in fisheries man- getics models) before it can be routinely adopted.
agement investigations. The model for temperate- The assumption that annual maintenance rations
latitude, freshwater piscivorous fish is
and conversion efficiencies can be considered
identical across species and water bodies obvi2/> + IB.
ously requires further investigation; species- and
Parameters are as in equations (5) and (6) and are system-specific variations of the P-B equation may
cy and production-biomass models, are illustrated here.
Production is classically defined as all growth
in the population over a specified interval, including growth of individuals that die within the
time period. Production can be calculated with
only initial and final numbers and initial and final
mean weights as
ASSESSMENT OF BIOENERGETICS MODELING
741
ow
^ 300-
u
7T 250
1 15°
3
100-
0-
1
2
3
4
Irlj.
5
6
7
8
Year of Life
FIGURE 1.—Total consumption in successive years for a cohort of 1,000 striped bass fingerlings stocked into
Smith Mountain Lake, Virginia, as estimated by the Wisconsin bioenergetics model (Moore 1988; white bars) and
the production-biomass method (black bars).
be required. Multipliers of production and biomass will probably differ most among species that
experience markedly different thermal regimes and
activity levels (e.g., cod, tuna) or noncarnivorous
diets.
Equations (4), (6), and (7), as well as other simple formulations based on bioenergetics principles, should complement multiparameter bioenergetics models. They are best suited for first-order
analysis of relatively long-term growth or consumption phenomena. Before they can be applied
with confidence, these simple models will require
research to establish the accuracy of critical parameters such as activity metabolism (reduced
Winberg model) or food conversion efficiency and
maintenance requirements (production-based
models) of noncaptive fish. Multiparameter models have the potential to provide finer resolution
on temporal and spatial scales and mechanistic
explanations of observed or simulated patterns of
energy allocation (e.g., the effect of climate change
on growth and consumption of Great Lakes fishes:
Hill and Magnuson 1990). Model choice will depend on needed accuracy, feasibility, and objective.
Growing Pains
The trend toward more elaborate bioenergetics
models has not proceeded with stepwise assurances of the accuracy of output. In my appraisal,
I review results of field tests of bioenergetics es-
timates, diagnose perceived deficiencies, prescribe
remedial measures, and offer a prognosis on the
future health of bioenergetics modeling.
Model Accuracy
Bioenergetics models have a sound theoretical
framework because they account for all possible
fates of consumed energy. However, the output of
bioenergetics models is susceptible to error in the
input of the values for both external variables and
internal parameters as well as in the mathematical
description of physiological rate processes. External variables include field estimates of growth or
consumption, water temperature, diet composition, and energy densities of predators and prey.
Accurate in situ estimates of growth are usually
easier to obtain than accurate estimates of consumption, which require intensive field sampling
(Ney 1990). Water temperature as experienced by
the fish is a critical input to bioenergetics models
because of the temperature dependence of physiological processes and should be measured frequently in thermally heterogenous environments
(see Hewett et al. 1991 for an illustration). The
more common practice is to measure water temperature independent offish location and then assume that the fish resided at the available temperature nearest its preferendum. Values for
internal parameters include the coefficients and
exponents that quantify the effects of influencing
factors such as weight and temperature on consumption, metabolism, and waste processes. The
third source of potential error in the output of
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TABLE 1. —Field tests of bioenergetics models. Sauger estimates are for growth; all others are for consumption.
Species
Age
Period
Sauger
1
2
1
Mar-Get
Mar-Oct
Oci-Mar
Winberg
Winberg
Winberg
Northern pike
3
3
Annual
Monthly
Wisconsin
Wisconsin
Model
Percentage
difference:
I00(model field) field
-- 2
+ 10
+ 770
Source
Minton and McLcan (1982)
-1 to +16
-86 to +59
Diana (1983)
Largemouth bass
3
Jun-Sep
Wisconsin
+8
Rice and Cochran (1984)
Sockeye salmon
0
Jul-Fcb
Wisconsin
+ 10
Beauchampet al. (1989)
Yellow perch
1
May-Sep
May-Sep
May-Sep
Wisconsin
Wisconsin
Wisconsin
+3
-34
-51
Boisclairand Lcggctt (1989)
Kerr
Kerr
Kerr
+ 91
+ 34
-10
Boisclairand Leggctt (1989)
Wisconsin
3
Yellow perch
1
3
May-Sep
May-Sep
May-Scp
Ksox spp.
0
Scp-Fcb
bioenergetics models is the choice of mathematical formulations to express relationship of influencing factors to physiological processes (e.g..
whether the rate of change in Cmax with temperature is best expressed by a £10 function or the
Thornton and Lessem 1978 algorithm). Formulations and values for internal variables should be
determined through rigorous experimentation under controlled conditions.
Despite these potential errors, the capability of
bioenergetics models to accurately predict consumption or growth of noncaptive fish has seldom
been assessed. Sensitivity analyses have been performed with some frequency, but these serve primarily to identify model parameters with the
greatest potential for affecting output values
(Stewart et al. 1983: Bartell et al. 1986). Validity
tests that compare model predictions with observed data are direct checks of the accuracy of
model output. True validity tests of bioenergetics
models have not been performed because of the
difficulties inherent in obtaining accurate field
measurements of the growth or consumption of
fish. Instead, bioenergetics estimates have been
compared with estimates obtained by other means,
such as gut content x evacuation rate measures
of consumption. Because one or both estimates in
these comparisons could be wrong, they serve to
corroborate rather than validate the model being
evaluated.
Even corroboration tests of bioenergetics models, such as those cited for production-based models in the preceding section, have been reported
rarely. I found six studies in which bioenergetics
-39 to -52
Wahl and Stein (1991)
and field estimates of growth or consumption were
compared (Table 1). Although several of these
studies included both consumption and growth
comparisons, I chose to focus on consumption
rather than growth where possible (five of six studies) because bioenergetics estimates of consumption should be the more accurate (Hewett and
Johnson 1987). Percentage difference between
model and field estimates was calculated as
(model - field)
x 100.
field
(8)
Minton and McLean (1982) used a modified
Winberg bioenergetics model (see equation 4) and
field measurement of ration to estimate growth of
sauger in a Tennessee reservoir. Bioenergetics estimates agreed closely with observed growth over
the March-October period but greatly exceeded it
over the winter, despite high food consumption.
The poor fit was blamed on unexpectedly high
winter activity of sauger; activity metabolism in
the model was assumed to be negligible (activity
multiplier of standard metabolism = 1).
The Wisconsin bioenergetics model was used by
Diana (1983) to develop energy budgets for age-3
northern pike Esox Indus in an Alberta lake. Field
measures of average annual consumption summed
from monthly totals concurred with bioenergetics
estimates for both females (-1%) and males
(+ 16%) (Table 1). However, the congruence was
due to the balancing of model versus field differences that varied widely and erratically in the 18
comparisons (nine months for each sex). Poor
ASSESSMENT OF BIOENERGETICS MODELING
agreement was attributed to errors in the field estimates of ration for northern pike, which consume large meals irregularly. Activity metabolism
was assumed to be negligible on the basis of telemetry observations. Lucas et al. (1991) used
physiological telemetry to determine that activity
metabolism of northern pike was grossly underestimated by conventional telemetry. However,
activity metabolism still accounted for only 10%
of total metabolic costs (RA + R$ + RD) in this
Scottish study.
Rice and Cochran (1984) obtained a good fit
between field and bioenergetics estimates of consumption for an age-3 largemouth bass in a Minnesota lake over a 4-month period. However, biweekly estimates of growth were entered into this
Wisconsin model, and consumption was estimated and totaled over three successive intervals.
When only initial and final endpoints of growth
were used, the fit between model and field estimates of total ration was poor, indicating the need
for periodic determination of input values for external variables. This model represented activity
as a constant swimming speed (5 cm/s).
Strong corroboration of the Wisconsin model
as a predictor of consumption was also reported
by Beauchamp et al. (1989). Cumulative ration of
a zooplanktivorous juvenile sockeye salmon Oncorhynchus nerka in Lake Washington projected
by the model over a 7-month period differed by
only 10% from an earlier estimate obtained by
intensive field sampling. Swimming speed (Rj) was
modelled as a temperature- and weight-dependent
function, as were Cmax and R$.
Efforts to corroborate bioenergetics models for
yellow perch Perca Jlavescens in Canadian lakes
failed (Boisclair and Leggett 1989). Ages 1-3 yellow perch were sampled in 12 populations to derive estimates of May-September consumption by
the gut content-evacuation rate method. Cumulative consumption generated by the Wisconsin
model (with RA = 1 as a multiplier of R$) was
virtually identical to the field estimate for age-1
fish (average of all populations) but was lower by
half for age-3 fish. An alternative bioenergetics
model, in which activity metabolism is coupled
to food consumption (Kerr 1982), fared even worse
(Table 1). Poor agreement of field estimates with
the output of both models was attributed primarily to inadequate description of the activity metabolism parameter. Boisclair and Leggett (1989)
rearranged the bioenergetics equation and entered
field data on consumption as well as growth to
estimate activity expenditures. They found that
743
activity metabolism was extremely variable among
yellow perch age-groups and populations, ranging
from zero to almost three times the energy expended in standard metabolism (RA = 1 to 3.9 as
a multiplier of RS). The authors concluded that
the Wisconsin model could not be trusted to reliably predict consumption by actively foraging
fish. This conclusion was challenged by Hewett et
al. (1991) on the basis of methodological weaknesses in field measurements of temperature, energy densities, and evacuation rate. The methods
and findings were defended by the investigators
(Boisclair and Leggett 1991).
Wahl and Stein (1991) monitored rations of juvenile esocids (northern pike, muskellunge Esox
masquinongy, and their hybrid) stocked into five
Ohio reservoirs and compared field estimates with
outputs from a version of the Wisconsin model.
Consistently poor agreement between model and
field estimates (Table 1) was attributed to a seasonal reduction in metabolism of the fish that was
not a function of temperature. The authors recommended that the influences of season and photoperiod on standard metabolism be considered
in future bioenergetics modeling. They concluded
that the bioenergetics model could predict consumption reliably within only a factor of two and
cautioned that the predictions of bioenergetic
models should not be accepted without more field
corroboration.
Diagnosis of Deficiencies
These corroboration studies illustrate both the
potential and the problems of applying bioenergetics models in their present state of development. Four of the six investigations showed discrepancies between model and field estimates that
might be considered too great for many management uses. Only one of these studies (Diana 1983)
identified weaknesses in field estimates of growth
or consumption or in choice of values for external
variables; the remaining three studies indicated
uncertainties in the values of internal parameters
of the bioenergetics models associated with metabolism. None of the corroborations found fault
with the mathematical formulations of the bioenergetics models they tested, although Wahl and
Stein (1991) suggested that additional internal parameters may sometimes be needed. The models
thus appear to be sound and fit for field applications. However, the credibility of the bioenergetics
approach for estimating consumption or growth
of noncaptive fish will continue to be compromised if critical input values of either external
744
NEY
variables or internal parameters are inaccurate. I
believe that considerable attention must be devoted to refining the values for the internal parameters of bioenergetics models to better describe the physiological behaviors of fish. More
intensive field sampling may also be required to
obtain representative values for external variables. The major areas of potential deficiency can
be summarized in four categories.
(1) Unknown activity costs.—It is reasonable to
assume that swimming encompasses most activity
offish (Soofiani and Hawkins 1985), but the energy costs of swimming by noncaptive fish have
only been approximated. The simplest approach
to incorporating activity metabolism (RA) into the
bioenergetics equation originated with Winberg
(1956), who considered activity to be a simple
integer multiple of standard metabolism. The
multiplier approach has endured, despite its obvious imprecision. Multiples ranging from 1 (no
energy expenditure for activity) to 3 have been
assigned to various species from perceptions of
their lifestyles (Ney 1990). Swimming speed has
been sometimes incorporated into models based
on telemetry or laboratory observations (e.g., Rice
andCochran 1984; Stewart and Binkowski 1986).
Telemetric observations of movement must be
considered underestimates of average velocity because fish rarely travel between two points at a
constant rate and in a straight line. Careful observation of laboratory swimming rates may be accurate (if confounding variables can be removed)
for pelagic cruisers, but not for species that are
start-stop swimmers. A third approach to modeling activity costs is to couple them with consumption. Such models have been used primarily
with North Atlantic gadoids (Ursin 1979; Majkowski and Waiwood 1981; Kerr 1982), and they
may be realistic for species whose feeding success
is determined by area searched. Madon and Culver (1993, this issue) found that consumption varied with activity for juvenile walleyes. However,
these models may not apply to more sedentary
stalkers and ambush predators. A further complication in the effort to accurately model activity
metabolism will occur if the species of interest
displays highly variable patterns of activity, as
Boisclair and Leggett (1989) reported for yellow
perch. Effort would then be required to identify
factors influencing activity and incorporate them
in the activity metabolism component of the bioenergetics model.
(2) Extrapolation of allometric functions. —
Sensitivity analyses have shown that biases in the
power functions describing the changes in maximum consumption (Cmax) and standard metabolism (R$) with weight produce the greatest error
in model output (Rice et al. 1983; Bartell et al.
1986). The functions take the form a-W* with
coefficients and exponents derived from laboratory data. These relationships are frequently developed from juvenile specimens, which are most
amenable to laboratory treatment, but then extrapolated to younger and adult life stages. Such
extrapolations have not been justified and may
introduce substantial error, especially for larval
fish (Post 1990; Madon and Culver 1993).
(3) Unjustified species borrowing.— Fisheries
science has been hurt by a general reluctance to
support basic research to quantify physiological
and behavioral variables of fishes. As a consequence, even the simplest demands (e.g., for evacuation rates or conversion efficiencies) are often
met by using off-the-shelf values obtained for a
species that must be presumed to behave identically to the one under investigation. Data-hungry
bioenergetics models are especially demanding,
and species borrowing is frequent. Substitutions
are usually justified on the best available grounds,
which are often tenuous (e.g., similar sizes or body
forms). The degree to which fish species may vary
in their expression of bioenergetics parameters is
unknown. Brett and Groves (1979) found that the
few reported energy budgets of carnivorous fish
were quite similar in the fractions of consumed
energy allocated to growth, metabolism, and waste.
Conversely, some parameters may vary at the intraspecific level, as has been reported for the influence of temperature on growth of northern pike
(Bevelheimer et al. 1985).
(4) Inadequate estimation of external variables.—Bioenergetics models do not free the users
from the obligation for rigorous field sampling to
obtain representative data. All external variables
are subject to error that can render model output
inaccurate. Sensitivity analysis has shown that errors in the determination of diet composition can
have a major effect on estimates of prey consumption (Lyons and Magnuson 1987). Energy
densities of predator and prey are known to vary
with season, size, and sex (Adams et al. 1982b;
Soofiani and Hawkins 1985), but these have frequently been assumed to be constant in bioenergetics applications. The assumption that fish continually reside at the available temperature nearest
their preferenda has been disproved (e.g., Spigarelli et al. 1982; Bevelheimer 1990), but it is still
widely used when temperature values are entered
ASSESSMENT OF BIOENERGETICS MODELING
into bioenergetics models. The challenge of obtaining representative data is further exacerbated
by the inherent behavioral and physiological variability among individual fish (see Hartman and
Brand! 1993, this issue) and the biases associated
with most sampling techniques (Nielsen and
Johnson 1983).
745
not now available for many fishes (Ney 1990). The
tedium involved in determining accurate evacuation rates was an original motivation for the development of bioenergetics models, but without
evacuation rates to conduct validity checks, bioenergetics outputs will remain suspect.
Prognosis
Prescription for Remedial Measures
In my view, these remedial measures may be
These deficiencies require prompt attention to
prevent a credibility gap between the developers viewed as bitter medicine by bioenergetics reand promoters of bioenergetics models and their searchers. Much relatively mundane effort will be
clientele in fisheries management. Remedial ac- required to assure accuracy in internal variables,
tions are straightforward. Activity cost must be effort that may be subordinated in the rush to craft
quantified through in situ study of noncaptive fish. another generation of models to apply to exciting
This can be accomplished by field measures of new problems. But these measures are crucial if
consumption and solution of the bioenergetics the bioenergetics approach is to realize its potenmodel for activity metabolism (Adams et al. tial as a powerful predictive tool for population
1982b; Boisclair and Leggett 1989), by physiolog- and ecosystem management. The time necessary
ical telemetry (Lucas et al. 1993), by underwater to complete these refinements is also considerable,
observation (Boisclair and Sirois 1993, this issue), but bioenergetics models should not be used rouor by a combination of these approaches. The in- tinely until all uncertainties are resolved. In their
fluence of weight on maximum consumption and present state of development, bioenergetics modstandard metabolism must be examined over an els are best suited for making relative rather than
entire size range of species, despite the logistic absolute predictions. The models provide infordifficulties this might present. An in situ approach mative simulations of interspecific or intersystem
for determining allometric parameters of bioen- performance (e.g., Stewart et al. 1981; Lantry and
ergetics models for larval and juvenile fish was Stewart 1993, this issue) and of comparative outdeveloped by Post (1990) and substantiated by comes of different habitat and food availability
Madon and Culver (1993). A combination of lab- scenarios (e.g., Hill and Magnuson 1991; Jones et
oratory and field measurements may be required al. 1993, this issue). However, they should be used
to quantify allometric parameters for large adult very conservatively to balance predator with prey
fish. Species borrowing can only be justified when populations, to set harvest regulations from proa particular parameter has been quantified for a jected growth trajectories, and to serve other rouwide variety of fish, and the degree of similarity tine but important management purposes requircan be directly evaluated on the basis of taxonom- ing quantitative estimates. Uncertainties
ic or functional relationships. The field compo- concerning the accuracy of bioenergetics paramnent of bioenergetics programs must be designed eters mandate that the simplest model be chosen
to obtain representative samples that account for that can produce output within the confidence
gear bias as it affects analyses of growth, diet com- limits of study objectives, and that the best pracposition, and energy densities. Accurate descrip- ticable effort be made to obtain accurate inputs
tions of thermal histories of fish can now be for the parameters that are essential.
achieved by combining simultaneous hydroacoustic and thermographic data (Brandt et al. 1992) or
Acknowledgments
by the use of temperature-sensitive telemetry. Finally, more laboratory and field corroborations of
I thank symposium participants for sharing their
bioenergetics models must be conducted as qual- perspectives on where bioenergetics is and where
ity control measures. Laboratory experiments can it is going. The symposium editors, J. F. Kitchell,
control sampling error but do not simulate the W. Van Winkle, and an anonymous reviewer pronatural experience; they should be used as pre- vided comments to improve the manuscript. Vircursors of field corroborations. Corroborative ginia Polytechnic Institute and State University
studies of consumption require data on evacua- provided me the time to develop this paper. I am
tion rates (which can vary with temperature), prey particularly grateful to Carolyn W. Linkous for
type, and prey as well as predator size, and are processing this paper with skill and diligence.
746
NEY
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