Before revision:  These mathematical system analysis tools are quantitative ecological indicators that monitor the flow distribution and URLanization, quantify the  effect and utility of one compartment directly or indirectly on another, identify the system efficiency and stress, measure the compartmental exposure to system flows, determine the residence time and compartmental activity levels, and ascertain the restoration time and resilience in the case of disturbances.
After revision:  These mathematical system analysis tools are quantitative ecological indicators that monitor the flow distribution and URLanization, quantify the direct, indirect, acyclic, cycling, and transfer (diact) effect and utility of one compartment directly or indirectly on another, identify the system efficiency and stress, measure the compartmental exposure to system flows, determine the residence time and compartmental activity levels, and ascertain the restoration time and resilience in the case of disturbances.