On some general properties of trophic networks

A new description in the class of non-linear Volterra models for such structures as trophic networks is suggested, and some fully plausible assumptions are formulated when it is possible. These assumptions allow us to construct a system of non-linear differential equations corresponding to the graphic representation of trophic networks in the form of a flow diagram. It is possible to calculate the Jacobi matrix for network equations, using data on the matter inside compartments and flows between them. It is very interesting that the Jacobi matrix does not depend on the type of interaction between compartments. With the help of the Jacobi matrix, some general properties of trophic networks, such as stability, sensitivity, etc. can be estimated. The sensitivity matrix and entropy function, as well as the other scalar measures, are calculated using the implicit function theorem and the Jacobi matrix, and then interpreted from the ecological point of view. A property of the Jacobi matrices such as stability, can be used as a criterion for selection of observed data in real trophic networks.