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.
versus inverse modelling
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
used in modelling
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
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