A comprehensive understanding of the structure, function, and regulation of major ecosystems is necessary to face the world's ever-growing environmental problems (Mann 1988; Pahl-Wostl 1993; Gaedke 1995). Mass-balance biomass models (Ecopath approach, inverse methods) are being used globally as an efficient and useful method to systematically describe ecosystems and to explore their properties (Vézina and Platt 1988; Christensen and Pauly 1993; Christensen 1995; Pauly and Christensen 1996; Savenkoff et al. 2001). They constitute a simple approach to represent the complexity of an ecosystem, and they involve a mass-balance description of trophic interactions between all the functional groups of the ecosystem. Such scientific tools will provide valuable information on the health of marine habitats, as well as the capacity to support biological production and sustainable development of Canada's marine waters.

The Ecopath approach uses mass balance principles to estimate flows (Polovina 1984; Christensen and Pauly 1992; Bundy et al. 2000). Each group is represented by one balanced equation and requires six input parameters: biomass (B), production (P), consumption (Q), ecotrophic efficiency (EE; the fraction of the production that is either passed up the food web or exported), diet composition, and catch of each group. The linear equations are solved via matrix algebra to produce estimates of the flows that balance inputs and outputs; any missing parameters are estimated (EE is estimated if all parameters have been entered). Export and diet composition must always be entered while of the four remaining basic input parameters (B, P, Q, and EE), three must be entered. In most cases, when all the information to run an Ecopath model is assembled, the model will not balance due to the inconsistencies in the information. In this case, the values of one or more of the terms can be changed iteratively until a balance is obtained. Indeed, there is more than one way to construct a Ecopath model and there is no unique solution to any model. However, where there are areas of the model that are well known and on which the modeller can place some certainty, then the number of plausible solutions is reduced. For the less certain parameters, sensitivity analysis can be used to examine their effects on the model. The ecotrophic efficiency provides an immediate check for mass balance (Christensen and Pauly 1992). If the model is not balanced, then there are negative flows to the detritus and ecotrophic efficiencies (EE) are greater than one. Arriving at a balanced network with the Ecopath approach is left largely to trial and error, either through user intervention or Monte-Carlo simulations.

Another approach to solving for the flows is to compute the solution that minimizes the imbalances between inputs and outputs. This inverse approach provides a global criterion for an optimal (balanced) solution (Parker 1977; Enting 1985; Vézina and Platt 1988; Vézina et al. 2000; Savenkoff et al. 2001). When the system of equations is strongly underdetermined, additional constraints (inequality relations) must be added to constrain the range of possible solutions and thus to obtain a meaningful solution. Each flow must be non-negative. Further, the flows (consumption, production, and export) or ratios of flows (metabolic and ecotrophic efficiencies) are assumed to fall within certain ranges. The mass-balance equations and the additional constraints reduce the potential range of flux values, and trophic flows are estimated using an objective least-squares criterion for an optimal (balanced) solution (sum of flows in the system is as small as possible). The solution process generates thus the simplest flow network that satisfies both the mass conservation and constraints. The best solution is the model that produces the smallest sums of squared residuals for the compartmental mass balances. The solution minimizes thus the imbalances between inputs and outputs. The mass balance is thus closed by residuals (inputs-outputs) instead of ecotrophic efficiencies as in the Ecopath approach.

Based on the data availability and ecological and commercial significance of the species, the trophic food web is depicted by a number of compartments or functional groups (30 to 35 functional groups representing the main pelagic and benthic species present) to which all organisms are allocated and which are interconnected by fluxes of matter. To estimate the magnitude of these fluxes, measurements or estimates of major process rates such as consumption, production, and commercial catch are required for each living compartment, as well as quantitative information on the diet composition of the different groups.