On several measures concerning flow variables in ecosystems

Three measures—total residence time, total ecosystem throughput, and ratio of total standing stock to total system throughput—are investigated on the basis of an analysis of two types of structure matrices (or transitive closure matrices). The quantitative expression of total residence time given by Han (Han, B.P., 1997. Total residence time of ecosystem at steady state. Ecol. Modelling 95, 301–310) is proved to be equal to the ratio of total standing stock to total system outflow, that is, total residence time does not depend on ecosystem structure. Whereas total system throughflow is explicitly dependent on ecosystem structure, the ratio of total standing stock to total system throughflow not only depends on system structure but also on system state. Therefore, total system throughflow and the ratio of total standing stock to total system throughflow may measure ecosystem maturity or complexity. The ratio of total system throughflow to total system inflow or total system outflow is defined as the flow multiplying index instead of average path length, for the throughflow which equals the difference between total system throughput and total system inflow results from the interaction between compartments, i.e. reutilization of total system inflow. By dividing two types of structure matrices (transitive closure matrices) into cycling matrices and noncycling matrices, which correspond to first and subsequent passage flows, respectively, the contribution of cycling paths and noncycling paths to the three measures can be understood.