Indirect effects and distributed control in ecosystems: Temporal variation of indirect effects in a seven-compartment model of nitrogen flow in the Neuse River Estuary, USA—Time series analysis

Abstract

Indirect effects, the ability of one element in a system to impact another without direct interaction, are critical components of complex adaptive systems. Network environ analysis (NEA) is an environmental extension of economic input–output analysis that characterizes and quantifies indirect effects transmitted by a specific currency (e.g., carbon, nitrogen) within a steady state system. Previous NEA results suggest that indirect effects tend to dominate direct effects in ecosystems. Although steady state models may be useful, ecologists are often interested in system dynamics. In this article, we use NEA to investigate the temporal dynamics of indirect effects in 16 steady state models of nitrogen cycling in the Neuse River Estuary, USA. These models were originally constructed by Christian and Thomas [Christian, R.R., Thomas, C.R., 2003. Network analysis of nitrogen inputs and cycling in the Neuse River Estuary, North Carolina, USA. Estuaries 26, 815–828]. Our work had two primary objectives: (1) describe and quantify the temporal dynamics of indirect flows and (2) identify the importance of model factors in determining the magnitude of indirect flows. Our results indicate that indirect flows transmitted by the network of nitrogen transactions, especially microbial transformations, dominated direct flows in the Neuse River Estuary between spring 1985 and winter 1989. When we examined the indirect flow index (ratio of indirect to total system throughflow), we were surprised by the relatively small amount of temporal variation within the Neuse River Estuary. In all seasons, indirect flow was more than 80% of TST, and there was no significant interannual variation. Our analysis also revealed no clear relationship between boundary or direct flow and indirect flow, but a strong association between cycled and indirect flow. We conclude that while an increase in boundary, direct, and cycled flows can influence indirect flows, in the Neuse River Estuary models indirect flows are predominantly due to cycling. If nitrogen loading had been reduced during our study period, this system likely would have remained eutrophic for an extended period of time. If we assume the system remained similar in 1997, we would expect the legislated reduction of nitrogen loading to have little immediate effect, although this action will be important for long-term change. Dominance of indirect flow due to cycling makes this system state relatively difficult to change rapidly by external forcing. In this sense, the indirect effects stabilize the system, making it more resistant to external perturbations, though it may be more sensitive in the long-term.