by James F. Kitchell

The field of fish bioenergetics includes temporal scales that range from those of evolutionary time to cellular metabolism (Tytler and Calow 1985). It also includes spatial scales ranging from nutrition and growth in controlled aquaculture systems (Jobling 1994) to predator-prey systems in the largest ecological context (Adams and Breck 1990). Among the several reviews of the field, those by J. R. Brett offer the most insightful combination of basic laboratory studies and their application in the context most pertinent to fisheries science (Brett and Groves 1979). We recommend Brett’s lead chapter (Brett 1995) in the new volume edited by Groot et al. (1995) for a thorough review of the extensive work conducted on energetics of Pacific salmonids and for an insightful assessment of areas where knowledge of energetics should be improved.

The underpinnings of energetics have a firm theoretical base in the laws of thermodynamics (Kleiber 1975). Working from an energy budget requires that you satisfy the terms of a simple equation; outputs must equal inputs and the budget must balance. As detailed in Chapter 2, the terms of the energy budget for fishes are well known and each can be measured independently. The model allows the user to specify the important external regulators: temperature and diet. For fishes, the most easily measured component of the energy budgeting process is expressed as growth. Growth integrates the array of environmental variables affecting an individual fish. Thus the evidence provided in the observed growth rate is the rich and varied foundation of scientific inquiry and the basis for better understanding.

The modeling approach presented in this manual derived from the extension of energetics principles used in ecosystem-scale models of trophic interactions developed during the International Biological Programme (Kitchell et al. 1974). These models focused on biomass dynamics. They often included formulations requiring an estimate of carrying capacity which was used to characterize density-dependent constraints for growth rates of a given trophic level. While those kinds of models have utility in an ecosystem context, they had three important shortcomings when applied to fishes. First, units of biomass per area or volume did not allow for resolution of cause and effect at the species or individual scale. After all, it is individual fish that feed, grow, reproduce and die. Further, as a fish grows from first-feeding larvae to reproductive adult, it may ascend through three or four trophic levels. Second, biomass models did not allow an effective interface with either the long history of population-based models in fisheries science or the models of predator-prey interactions developed in the ecological sciences. Third, biomass models required an estimate of environmental carrying capacity. The latter is difficult to do and, more importantly, likely to change as a consequence of the ecological effects due to fishery exploitation and/or anthropogenic effects on fish habitats.

An alternative to biomass models is an energetics-based approach focused on the processes that regulate growth by individual fish (Kitchell et al. 1977). This model assembled individuals in age- or size-based populations, separated the agents of mortality (natural vs. fishing) and specified the trophic ontogeny of predator-prey interactions. It focused on using the kinds of data most frequently collected by biologists - the habitat that is occupied (thermal history), size at age (growth curves), stomach contents, size or age at sexual maturity, and size- or age-related mortality rates. The development of size- or age-based cohorts is elaborated in Chapter 3.

Starting the process with observed growth rate is different from that of many kinds of modeling practices. In this case, the strategy of model building is based on specifying rules that define the limit conditions, i.e., the maximum and minimum possible rates of growth for members of a population. The physiological parameters used to represent the rules derive from readily and oft-measured processes such as temperature dependence, thermal tolerance, thermal preference, size dependence, assimilation efficiency, etc., that can be accurately measured in the laboratory. Those physiological parameters are assembled as empirical rules that define the effect of temperature, body size and food quality on maximum feeding rates. The minimum is similarly defined by rules describing the effect of temperature and body size on metabolic rates when food consumption is set to zero. These limits define the boundaries of the scope for growth. Observed growth is somewhere between those limits and allows the user to estimate how that growth rate is being regulated.

The hierarchy of energy allocation is an important component of this modeling approach. Consumed energy is first allocated to catabolic processes (maintenance and activity metabolism), then to waste losses (feces, urine and specific dynamic action) and that left over is allocated to somatic storage (body growth and gonad development). This hierarchy is analogous to practical economics. The first costs paid are those for rent or mortgage (metabolism) that sustain the organism. The second set of costs (waste losses) are like taxes - they are proportional to income (food consumption) and must be paid. The energy resource remaining may then be allocated to savings (growth) or invested in the next generation (gonad development). In an ecological or evolutionary context, it is easy to imagine selection for behaviors that maximize benefits (growth rate or gonad development) and minimize costs. Like an account balance, a record of growth reveals how well the organism has resolved the complexities of its environment.

In a thorough review of previous energetics work, Brett and Groves (1979) presented a generalization about energy budgets for two classes of fishes. If the energy budget is stated in the following terms:

Energy Consumed = Respiration + Waste + Growth,

and normalized to percentages when energy consumption = 100, then fishes growing at "typical" rates would have energy budgets approximated as below.

Consumption = Respiration + Waste + Growth

For carnivores: 100 = 44 + 27 + 29

For herbivores: 100 = 37 + 43 + 20

These budgets reveal two important features. First, as expected, herbivores exhibit lower growth rates and higher waste-loss rates per unit of energy consumed. That is the logical consequence of eating foods of lower energy density and higher indigestible content. Second, both types of fishes demonstrate high rates of growth efficiency compared to those known for mammals and birds. Although these budgets can serve as a first approximation, the 95% confidence intervals for each component are substantial (e.g., plus or minus 20% of the mean). Of course, the energy budget for an average fish in a typical habitat may be very different from that of fishes in some unique ecological context. Fishes are known to exhibit among the highest growth efficiencies recorded (approaching 50%) and are known to exhibit strikingly negative energy budgets, as in the case of migrating salmon (Brett 1995). Note, too, that the hierarchy of energy allocation operates in all cases. Growth efficiency is not a constant, and growth rates in fishes are highly variable. Observed growth is the integrated answer to a complex question about prey resources and environmental conditions. Deducing the quantitative components of cause and effect is the significant challenge.

In most of its applications, model users will seek an answer to questions about factors that constrain growth (e.g., diet quality or environmental stressors) or use the measured growth to estimate how much effect a predator has had on its prey populations. Assembled as a population, the model allows answers to those questions at the larger scales of ecological and management interest. This approach does not provide for feedback to future generations. Predator or prey population dynamics are not represented. Those must be characterized as simulations using specified assumptions about prey availability, mortality rates and environmental conditions.

We view the modeling process as having two general components. First is the "nuts-and-bolts" process of assembling the parameter tables and the input data. Much of the former is available in the manual or formatted in ways that welcome site-specific input. Second is the "arts-and-crafts" process of structuring analyses in ways that pose key questions and provide instructive answers. In these cases, it is often valuable to use the model as a way to create boundary conditions such as those for maximum possible growth or for maintenance requirements. Using the model in this way allows it to serve as a "deductive engine" in the more creative and challenging process of science (Walters 1986).

This manual represents the third version of what appeared first as Hewett and Johnson (1989, 1992), which was sold (at cost) to more than 1,000 users and served as the basis for several score of shortcourses and workshops taught since 1988. That version was labeled the "Wisconsin model" (Ney 1993). As evidenced by the diversity of parameter tables presented in Appendix A, previous uses of this modeling approach are many and varied. They range from autecological studies of highly active subtropical tunas (Boggs and Kitchell 1991) to those of the sedentary, slowly growing burbot (Rudstam et al. 1995). They include omnivorous minnows (Schindler et al. 1993) and hyper-predaceous sea lampreys (Kitchell 1990). They provide estimates of zooplanktivory rates by small fishes in small lakes (Luecke et al. 1990, Post 1990) and rates of piscivory by a guild of salmonids predators preying on an assemblage of forage species in Lake Michigan (Stewart and Ibarra 1991). They include estimates of cannibalism (Rice and Cochran 1984) and quantitative estimates linking three trophic levels (LaBar 1993). In addition, the framework has been modified to develop models for some invertebrates (Rudstam 1989, Schneider 1992).

As summarized in Chapter 2, this model has been evaluated through a rigorous sensitivity analysis. Model results have also been compared to independently derived field data in several cases; those by Rice and Cochran (1984), Beauchamp et al. (1989) and Hansson et al. (1996) are particularly instructive. The approach has been praised for its promise and criticized for its inadequacies; both are represented in the proceedings of a recent symposium (Brandt and Hartman 1993, Hansen et al. 1993). We encourage the process of rigorous evaluation because that represents the path to improvements. The model cannot be wrong because it is based on a budget that must be right. It will improve in proportion to our ability to estimate the physiological parameters that regulate growth and the errors or bias of data employed as inputs.

This version of the model includes several new and important features. First, it is developed in the Windows environment and provides for inputs through a spreadsheet interface. Second, it employs the principles of mass balance to allow calculations in alternative currencies. Accordingly, it can be used to estimate the ecological significance of nutrient flux rates owing to fishes. In addition, it can be implemented to evaluate bioaccumulation of contaminants such as PCBs or heavy metals. The basic frameworks described in Chapter 4 invite additional applications.

Adams, M. S., and J. E. Breck. 1990. Bioenergetics. Pages 389-415 In C. B. Schreck and P. B. Moyle (eds.). Methods of Fish Biology. American Fisheries Society, Bethesda, Maryland.

Beauchamp, D.A., D.J. Stewart and G.L. Thomas. 1989. Corroboration of a bioenergetics model for sockeye salmon. Trans. Am. Fish. Soc. 118:597-607.

Boggs, C.H., and J.F. Kitchell. l991. Tuna metabolic rate estimated from energy losses during starvation. Physiol. Zool. 64:502-524.

Brandt, S.B. and K.J. Hartman. 1993. Innovative approaches with bioenergetics models: future applications to fish ecology and management. Trans. Amer. Fish. Soc. 122:731-735.

Brett, J. R. 1995. Energetics. Pages 3-68 In C. Groot, L. Margois, and W. C. Clarke (eds.). Physiological Ecology of Pacific Salmon. Univ. British Columbia Press, Vancouver.

Brett, J. R., and T. D. D. Groves. 1979. Physiological energetics. Pages 279-352 In W. S. Hoar, D. J. Randall, and J. R. Brett. (eds.). Fish Physiology. Volume 8. Bioenergetics and Growth. Academic Press, New York.

Groot C., L. Margois, and W. C. Clarke (eds.). 1995. Physiological Ecology of Pacific Salmon. Univ. British Columbia Press, Vancouver.

Hansen, M. J., D. Boisclair, S. B. Brandt, S. W. Hewett, J. F. Kitchell, M. C. Lucas, and J. J. Ney. 1993. Applications of bioenergetics models to fish ecology and management: Where do we go from here? Trans. Amer. Fish. Soc. 122: 1019-1030.

Hansson, S., L. G. Rudstam, J. F. Kitchell, M. Hilden, B. L. Johnson and P. E. Peppard. 1996. Predation rates by North Sea cod (Gadus morhua) - predictions from models on gastric evacuation and bioenergetics. ICES J. Marine Sci. 51:107-114.

Hewett, S.W. and B.L. Johnson. 1987. A generalized bioenergetics model of fish growth for microcomputers. University of Wisconsin Sea Grant Institute, Madison, Wisconsin. 47 pp.

Hewett, S. W. and B.L. Johnson. 1992. A generalized bioenergetics model of fish growth for microcomputers. University of Wisconsin Sea Grant Institute, Madison, Wisconsin. UW Sea Grant Tech. Rep.WIS-SG-92-250. 79 pp.

Jobling, M. 1995. Fish Bioenergetics. Chapman and Hall, London.

Kitchell, J.F., J.F. Koonce, R.V. O'Neill, H.H. Shugart, Jr., J.J. Magnuson, and R.S. Booth. 1974. Model of fish biomass dynamics. Trans. Am. Fish. Soc. 103:786-798.

Kitchell, J.F., D.J. Stewart, and D. Weininger. 1977. Applications of a bioenergetics model to perch (Perca flavescens) and walleye (Stizostedion vitreum). J. Fish. Res. Board Can. 34:1922-1935.

Kitchell, J.F. l990. The scope for mortality caused by sea lamprey. Trans. Amer. Fish. Soc. 119:642-648.

Kleiber, M. 1975. The Fire of Life: An Introduction to Animal Energetics. R. E. Krieger Publ, Huntington, New York.

LaBar, G. W. 1993. Use of bioenergetics models to predict the effect of increased lake trout predation on rainbow smelt following sea lamprey control. Trans. Amer. Fish. Soc. 122:942-950.

Luecke, C., M.J. Vanni, J.J. Magnuson, J.F. Kitchell, and P.T. Jacobson. 1990. Seasonal regulation of Daphnia populations by planktivorous fish: implications for the spring clear water phase. Limnol. Oceanogr. 35(8):1718-1733.

Ney, J. J. 1993. Bioenergetics modeling today: growing pains on the cutting edge. Trans. Amer. Fish. Soc. 122:736-748.

Post, J.R. 1990. Metabolic allometry of larval and juvenile yellow perch (Perca flavescens): in situ estimates and bioenergetic models. Can. J. Fish. Aquat. Sci. 47:554-560.

Rice, J. A., and P. A. Cochran. 1984. Independent evaluation of a bioenergetics model for largemouth bass. Ecology 63:732-739.

Rudstam, L.G. 1989. A bioenergetic model for Mysis growth and consumption applied to a Baltic population of Mysis mixta. J. Plankton Res. 11:971-983.

Rudstam, L.G., P.E. Peppard, T.W. Fratt, R.E.Bruesewitz, D.W.Coble, F.A. Copes and J. F. Kitchell. 1995. Prey consumption by the burbot (Lota lota) population in Green Bay, Lake Michigan, based on a bioenergetics model. Can. J. Fish. Aquat. Sci. 52: 1074-1082.

Schindler, D. E., J. F. Kitchell, X. He, S. R. Carpenter, J. R. Hodgson and K. L. Cottingham. 1993. Food web structure and phosphorus cycling in lakes. Trans. Amer. Fish. Soc. 122:756-772.

Schneider, D.W. l992. A bioenergetics model of zebra mussel feeding and growth in the Great Lakes. Can. J. Fish. Aquat. Sci. 49(7):1406-1416.

Stewart, D.J. and M. Ibarra. 1991. Predation and production by salmonine fishes in Lake Michigan, 1978-88. Can. J. Fish. Aquat. Sci. 48:909-922.

Tytler, P., and P. Calow (eds.). 1985. Fish Energetics: New Perspectives. Croom Helm, London.

Walters, C.J. 1986. Adaptive Management of Renewable Resources. Macmillan, New York.