A probabilistic approach of flow-balanced network based on Markov chains

We used Markov chains to assess residence time, first passage time, rate of transfers between compartments, recycling index with a general mathematical formalism. Such a description applies to any flow-balanced system that can be modelled as a series of discrete stages or compartments through which matter flows. We derived a general set of equations from a probabilistic approach and applied them to a food web and a physical system derived from the literature. We therefore analysed preferential pathways of matter and behaviour of these systems and showed how it was possible to build up and exploit indices on the basis of a transition probability matrix describing the network, and to characterize with a generic algorithm: (1) the total indirect relationships between two compartments, (2) the residence time of one compartment and (3) the general recycling pathways including the amount of matter recycling and the implication of each compartment in recycling.