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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 736 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 738 NEY 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 739 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 NEY 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 742 NEY 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. 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