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

Network environ analysis is motivated by a desire to investigate ecosystems from a holistic perspective. It provides a quantitative measure of the integral (direct plus indirect) relationship between compartments and their within-system environments. In this analysis, each compartment within a system has an incoming interactive network that brings matter to it from the system's boundary inputs, and an outgoing network that takes matter from it to boundary outputs. These are, respectively, input and output environs. Methods described herein are used to compare environs from a time series of ecological networks for which the flow structure remains constant while flow quantities change. Observed differences in environs are analyzed with respect to: (a) differences between the steady-state seasonal ecosystem networks, and (b) which compartment receives the ‘analytical input’ in output-environ analysis. The Neuse River estuary is an ideal subject for this because a time series of 16 seasonal steady-state networks of nitrogen (N) storage and flow were constructed for the period spring 1985 through winter 1989 by Christian and colleagues. We explore two levels of analysis. The first is macro-level analysis of whole environs; total environ throughflow, an index of whole-environ activity, is computed and compared. The second is micro-level analysis which involves the individual intercompartmental flow and boundary output elements of output environs for two selected focal compartments, phytoplankton (x1-PN-Phyto) and nitrate/nitrite (x5-NOx). Our findings indicate that most of the observed variation in environs is being driven by differences in the seasonal networks analyzed. The macro-scale patterns observed for the environs show the same seasonal patterns evident in the whole steady-state network time series. These results support and extend the constancy of temporal indirect effects results reported by Borrett et al. [Borrett, S.R., Whipple, S.J., Patten, B.C., 2006. 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. Ecol. Model. 194, 178–188]. When comparing different environs within the same season, the macro-scale patterns show that the environs are quantitatively very similar; however, when micro-scale patterns are observed, it is found that the environs are indeed unique. Macro-scale similarities are thought to be driven by high cycling indices and high network homogenization. A conclusion from the comparative analysis of the Neuse estuary networks is that these environs display a weak autonomy. We hypothesize that the individuality of the environs is suppressed by two characteristics of the Neuse estuary networks: they are strongly connected graphs, and they contain many linked autocatalytic cycles. Two aspects of our results provide a means to link ecological measures important to the Neuse River estuary and environ analysis. Environ throughflow (TE¯T) is driven by boundary inputs, which is equivalent to the ecological measure of N loading, with dominance of total TE¯T by DON (x4-DON), nitrate–nitrite (x5-NOx), and ammonium (x6-NH4), which receive the largest boundary inputs. Previous network analysis demonstrated that, on average, one-half of the nitrogen needs of phytoplankton are met by nitrogen that once resided in the sediments. Phytoplankton (x1-PN-Phyto) and sediment (x3-Sed), and ammonium (x6-NH4) had distinctly different TE¯T pattern than the steady-state TST pattern. The key ecological driver of the sediment source for N needs of phytoplankton is the release of N from sediments in the warmer months as ammonium which is taken up by phytoplankton; low TE¯T during winter for phytoplankton (x1-PN-Phyto), sediment (x3-Sed), and ammonium (x6-NH4) reflects the low levels of ammonium release and low growth rates; high TE¯T during summer corresponds to greater release of ammonium (x6-NH4) from the sediments (x3-Sed) and greater uptake of ammonium (x6-NH4) by phytoplankton (x1-PN-Phyto).