Ecosystem network analysis indicators are generally robust to parameter uncertainty in a phosphorus model of Lake Sidney Lanier, USA

Understanding how data uncertainty influences ecosystem analysis is critical as we move toward ecosystem-based management. Here, we investigate how 18 Ecological Network Analysis (ENA) indicators that characterize ecosystem growth, development, and condition are affected by uncertainty in an ecosystem model of Lake Sidney Lanier (USA). We applied ENA to 122 plausible parameterizations of the ecosystem developed by Borrett and Osidele (2007, Ecological Modelling 200, 371-387), and then used the coefficient of variation (CV) to compare system indicator variability. We considered Total System Throughput (TST) as a measure of the underlying model uncertainty and tested three hypotheses. First, we hypothesized that non-ratio indicators whose calculation includes the TST would be at least as variable as TST if not more variable. Second, we postulated that indicators calculated as ratios, with TST in the numerator and denominator would tend to be less variable than TST because its influence will cancel. Last, we expected the Average Mutual Information (AMI) to be less variable than TST because it is a bounded function. Our work shows that the 18 indicators grouped into four categories. The first group has significantly larger CVs than the CV for TST. In this group, model uncertainty is amplified rendering these three indicators less useful. The second group of four indicators shows no significant difference in variability with respect to TST. Finally, there are two groups whose CV values are significantly lower than that for TST. The least variable group includes the ratio-based indicators and Average Mutual Information. Due to their low variability, we conclude that these indicators are the most robust to the parameter uncertainty and most useful for ecosystem assessment and comparative ecosystem analysis. In summary, this work suggests that we can be as certain, or more certain, in most of the selected ENA indicators as we are in the parameters of the model analyzed.     

The dual nature of ecosystem dynamics

Mechanistic simulation modeling has not generally delivered on its promise to turn ecology into more of a “hard” science. Rather, it appears that deeper insights into ecosystem functioning may derive from a new set of metaphysical assumptions about how nature functions. Force laws from physics are fundamentally incompatible with the heterogeneity and uniqueness that characterizes ecosystems. Instead, coherence, selection and centripetality are imparted to ecological systems by concatenations of beneficial processes—a generalized form of autocatalysis. These structure-enhancing configurations of processes are opposed by the ineluctable tendency of structure to decay (as required by the second law of thermodynamics). The dual nature of this agonism can be quantified using information theory, which also can be used to measure the potential of the system for further evolution. The balance point for these countervailing tendencies seems to coincide with the state of maximal potential for the system to evolve. In an ostensible paradox, the same locus seems to attract stable, persistent system configurations.     

Using social network analysis tools in ecology: Markov process transition models applied to the seasonal trophic network dynamics of the Chesapeake Bay

Ecosystem components interact in complex ways and change over time due to a variety of both internal and external influences (climate change, season cycles, human impacts). Such processes need to be modeled dynamically using appropriate statistical methods for assessing change in network structure. Here we use visualizations and statistical models of network dynamics to understand seasonal changes in the trophic network model described by Baird and Ulanowicz [Baird, D., Ulanowicz, R.E., 1989. Seasonal dynamics of the Chesapeake Bay ecosystem. Ecol. Monogr. 501 (59), 329–364] for the Chesapeake Bay (USA). Visualizations of carbon flow networks were created for each season by using a network graphic analysis tool (NETDRAW). The structural relations of the pelagic and benthic compartments (nodes) in each seasonal network were displayed in a two-dimensional space using spring-embedder analyses with nodes color-coded for habitat associations (benthic or pelagic). The most complex network was summer, when pelagic species such as sea nettles, larval fishes, and carnivorous fishes immigrate into Chesapeake Bay and consume prey largely from the plankton and to some extent the benthos. Winter was the simplest of the seasonal networks, and exhibited the highest ascendency, with fewest nodes present and with most of the flows shifting to the benthic bacteria and sediment POC compartments. This shift in system complexity corresponds with a shift from a pelagic- to benthic-dominated system over the seasonal cycle, suggesting that winter is a mostly closed system, relying on internal cycling rather than external input. Network visualization tools are useful in assessing temporal and spatial changes in food web networks, which can be explored for patterns that can be tested using statistical approaches. A simulation-based continuous-time Markov Chain model called SIENA was used to determine the dynamic structural changes in the trophic network across phases of the annual cycle in a statistical as opposed to a visual assessment. There was a significant decrease in outdegree (prey nodes with reduced link density) and an increase in the number of transitive triples (a triad in which i chooses j and h, and j also chooses h, mostly connected via the non-living detritus nodes in position i), suggesting the Chesapeake Bay is a simpler, but structurally more efficient, ecosystem in the winter than in the summer. As in the visual analysis, this shift in system complexity corresponds with a shift from a pelagic to a more benthic-dominated system from summer to winter. Both the SIENA model and the visualization in NETDRAW support the conclusions of Baird and Ulanowicz [Baird, D., Ulanowicz, R.E., 1989. Seasonal dynamics of the Chesapeake Bay ecosystem. Ecol. Monogr. 501 (59), 329–364] that there was an increase in the Chesapeake Bay ecosystem's ascendancy in the winter. We explain such reduced complexity in winter as a system response to lowered temperature and decreased solar energy input, which causes a decline in the production of new carbon, forcing nodes to go extinct; this causes a change in the structure of the system, making it simpler and more efficient than in summer. It appears that the seasonal dynamics of the trophic structure of Chesapeake Bay can be modeled effectively using the SIENA statistical model for network change.     

Network calculations and ascendency based on eco-exergy

Ascendency is an index of activity and organization in living systems calculated in terms of flows. The concern here is with how that quantity behaves when the flows in question are measured in terms of eco-exergy. The storage of eco-exergy has served as a goal function in assessing parameter values for structurally dynamic models, but network magnitudes and topologies can change in response to significant changes in the forcing functions. As storages are relatively insensitive to such changes, it is advisable in such cases to explore how changes in a flow variable, like ascendency, might capture network adaptations. It happens that changes in ascendency calculated in terms of flows of simple energy are small in comparison to corresponding variations in the storages of eco-exergy. But when ascendency is reckoned in terms of flows of eco-exergy, its changes in response to network changes are more comparable to those in the storages. Ascendency seems to be more sensitive to changes in flow topology, however, so that a combination of eco-exergy storage and eco-exergy ascendency would probably be most appropriate for situations where changes in flow topology are significant.