One of the most significant developments in ecological science is the development by Polovina [15] of a biomass budget box model of an ecosystem — ECOPATH. However, it is Christensen and Pauly’s [4] further development that has made it the most commonly used tool for analyzing the trophic interactions in fisheries resource systems, aquaculture ponds, farm systems, and natural systems. The widespread application of ECOPATH has generated many important inferences about the structure and function of some ecosystems. However, it provides only one or more snapshots of an ecosystem. Recognizing this limitation, Walters et al. [18] derived its system of differential equations, and hence made it dynamic, to become what is now known as ECOPATH with ECOSIM — the most commonly used tool for biologists for analyzing trophic interactions in fisheries resource systems, aquaculture ponds, farm systems, and natural systems. Unfortunately, questions must be asked about the logical consistency in their parameterization of the fishing mortality and utilized production, and about the mathematical and biological validity in deriving the fundamental equations of ECOPATH and its variants.

In this paper, I derive the fundamental equations of ECOPATH and its variants as a system of ordinary or partial differential-integral equations, subject to appropriate initial and boundary conditions, and examine the logical consistency in parameterizing their fishing mortality and utilized production, and the mathematical and biological validity in deriving their fundamental equations. I also show that the logically consistent fundamental equations of ECOPATH and its variants are not consistent with the basic equations of the currently used ECOPATH and its variants, thereby highlighting a need to revise all past work on ECOPATH and its variants. Finally, I discuss the general ecological and biological significance of this work as a solid foundation for developing a much needed practical method for biological and ecological modelling, and its significance to several areas of science, including food production, effective use and management of fisheries resources, marine and freshwater conservation, and the maintenance of a healthy aquatic environment.

ECOPATH, ECOSIM, multi-species models, population models, fish.