Indirect effects and distributed control in ecosystems: Comparative network environ analysis of a seven-compartment model of nitrogen storage in the Neuse River Estuary, USA: Time series analysis

Abstract 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. A previous study of nitrogen dynamics in the Neuse River Estuary (NRE), North Carolina, USA ( Whipple et al., 2007 ) described within-environ transfers using a throughflow-based network analysis, NEA-T. Throughflow (Tin, Tout) is the sum of flows into or out of each compartment. This paper extends this work using a companion storage-based methodology, NEA-S, re-notated from its antecedent and originating contributions ( Barber, 1978a , Barber, 1978b , Barber, 1979 , Matis and Patten, 1981 ). Time-series data implementing 16 seasonal steady-state network models of nitrogen (N) storage and flow in the Neuse system were constructed for spring 1985 through winter 1989 by Christian and Thomas, 2000 , Christian and Thomas, 2003 . Network topology was constant over time, but the storage and transfer quantities changed. Environ analysis of this model showed that nitrogen storage and residence times differ within the different environs composing the compartments, and moreover, that these differences originate in the system’s interconnecting network as a whole. Thus, environs function within themselves as autonomous flow–storage units, but this individuality derives from, and at the same time contributes to the entire system’s properties. Environ autonomy is reflected in unique standing stocks and residence times, and whole empirical systems are formed as additive compositions of these. Because storage is durable and transfers ephemeral, storage environs revealed by NEA-S have more autonomy than flow environs computed using NEA-T. We quantified this autonomy by comparing the heterogeneity of extensive environs in models driven by actual inputs with intensive environs normalized to unit inputs. The former is more storage-heterogeneous than their unit reference counterparts, with dissolved nutrients NOx, DON, and NH4 exhibiting greatest heterogeneity. A previous NEA study of distributed control in this same model by Schramski et al. (2007) showed that NOx controls the system whereas sediment is controlled by the system. In the present study, NOx dominates storage in extensive environs, and therefore, is controlling in actuality. However, in the intensive unit, environs sediment accounted for most of the storage, reflecting greater control potential. This potential is expressed by the sediment acting like a capacitor for N, seasonally sequestering and releasing this element in the role of a biogeochemical regulator.

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