Abstract Two of the most significant developments in fisheries science are the single species virtual population analysis (SSVPA) and multi-species virtual population analysis (MSVPA). Since its development, MSVPA and its variants have been used in fish population studies, fish stock assessment, and the management of the fisheries in many parts of the world, including the North Sea, the Baltic Sea, the Barents Sea, the Bering Sea, Georges Bank, and the Benguela Current, and have been accepted as routine and essential tools for making efficient use of the world's major fisheries resources for food production, and for conserving and managing those resources. However, serious questions arise from the fact that some of their equations are “borrowed” straight from SSVPA, except for adding a species index. In this paper, I derive the fundamental equations of MSVPA and its variants as a system of ordinary differential equations (if the ages of fish are discrete) or as a system of first order partial differential–integral equations (if the ages of fish are continuous), both subject to appropriate constraints and boundary conditions (biological observations and data). Their formulation as well known mathematical problems has not only revealed their mathematical nature and hence laid the foundation for their speedy solution by use of a great variety of known and readily available mathematical techniques, but also revealed the logical inconsistency in the currently used MSVPA and its variants. This inconsistency highlights an urgent need to revise all past work on MSVPA and its variants, by replacing the existing equations of MSVPA and its variants with the fundamental equations derived above. Finally, I discuss (1) the conversion of data on the stomach contents of fish of different ages and of different species into their coefficients of suitability, (2) two possible extensions of the present work, (3) its general ecological and biological significance as a much needed practical method or routine for parameterizing a system of age- and time-dependent or more general Lotka–Volterra equations to understand the underlying mechanisms for the rapid changes of the ecosystems and for us to maintain a harmonious co-existence within a biological system, and (4) its significance to several areas of fisheries science, including food production, effective use and management of fisheries resources, marine and freshwater conservation, and the maintenance of a healthy aquatic environment.