Indirect effects and distributed control in ecosystems

Compartmental, or “stock-and-flow”, models describe the storage and transfer of conservative energy or matter entering and leaving open systems. The storages are the standing “stocks”, and the intra-system and boundary transfers are transactional “flows”. Network environ analysis (NEA) provides network methods and perspectives for the quantitative analysis of compartment models. These emphasize the distinction between direct and indirect relationships between the compartments, and also with their environments. In NEA, each compartment in a system has an incoming network that brings energy or matter to it from the system’s boundary inputs, and an outgoing network that takes substance from it to boundary outputs. These networks are, respectively, input and output environs. Individual pathways in environs have an identity not unlike spaghetti in a bowl, each strand of which originates at some boundary input and terminates at some boundary output. All strands originating at the j’th input collectively comprise, no matter where they terminate, the j’th output environ; similarly, all strands terminating at the i’th output comprise, no matter where they originate, the i’th input environ. Thus, any substance freely mixing in the system as a whole runs in pathways consigned to one and only one output environ traced forward from its compartment of entry, and also one and only one input environ traced backward from its compartment of exit. The environs are partition elements – they decompose the interior stocks and flow according to their input origins and output destinations. Moreover, each environ’s dynamics and other systems and network properties are unique, and sum over all the environs to give the aggregate dynamics and properties of the whole. It is this composite, aggregate whole that empirical methods measure; empiricism unaided by theoretical analysis is blind to the environ pathways that actually compose the wholes.