Least-inference methods for constructing networks of trophic flows

The construction of material and energy budgets within ecosystems has long been accomplished via manual calculation. Recently, optimization techniques have been adapted to automate the procedure, but these methods require assumptions that may not square with biological reality. Two algorithms are developed to construct ecosystem budgets under minimal inference. Although the methods do not recapitulate the model used to generate the input data, analysis reveals that the results do not differ statistically from networks that were constructed manually.     

Implications of network particle tracking (NPT) for ecological model interpretation

Network particle tracking (NPT), building on the foundation of network environ analysis (NEA), is a new development in the definition of coherence relations within and between connected systems. This paper evaluates three ecosystem models in a comparison of throughflow- and storage-based NEA and NPT. Compartments in models with high indirect effects and Finn cycling showed low correlation of NEA storage and throughflow with particle repeat visits and numbers of particles in compartments at steady state. Conversely, the correlation between NEA and NPT results was high with two models having lower indirect effects and Finn cycling. Analysis of ecological orientors associated with NEA showed NPT to fully support conventional NEA results when the common conditions of donor control and steady state are satisfied. Particle trajectories are recorded in the new concept of a particle “passport”. Ability to track and record particle in-system histories enables views of multiple scales and opens the possibility of making pathway-dependent modeling decisions. NPT may also enable modeling of time, allowing integration of Newtonian, organismal and stochastic modeling perspectives in a single comprehensive analysis.     

Comparing discriminant analysis, neural networks and logistic regression for predicting species distributions: a case study with a Himalayan river bird

We assessed the occurrence of a common river bird, the Plumbeous Redstart Rhyacornis fuliginosus, along 180 independent streams in the Indian and Nepali Himalaya. We then compared the performance of multiple discrimant analysis (MDA), logistic regression (LR) and artificial neural networks (ANN) in predicting this species’ presence or absence from 32 variables describing stream altitude, slope, habitat structure, chemistry and invertebrate abundance. Using the entire data (=training set) and a threshold for accepting presence in ANN and LR set to P≥0.5, ANN correctly classified marginally more cases (88%) than either LR (83%) or MDA (84%). Model performance was assessed from two methods of data partitioning. In a ‘leave-one-out’ approach, LR correctly predicted more cases (82%) than MDA (73%) or ANN (69%). However, in a holdout procedure, all the methods performed similarly (73–75%). All methods predicted true absence (i.e. specificity in holdout: 81–85%) better than true presence (i.e. sensitivity: 57–60%). These effects reflect species’ prevalence (=frequency of occurrence), but are seldom considered in distribution modelling. Despite occurring at only 36% of the sites, Plumbeous Redstarts are one of the most common Himalayan river birds, and problems will be greater with less common species. Both LR and ANN require an arbitrary threshold probability (often P=0.5) at which to accept species presence from model prediction. Simulations involving varied prevalence revealed that LR was particularly sensitive to threshold effects. ROC plots (received operating characteristic) were therefore used to compare model performance on test data at a range of thresholds; LR always outperformed ANN. This case study supports the need to test species’ distribution models with independent data, and to use a range of criteria in assessing model performance. ANN do not yet have major advantages over conventional multivariate methods for assessing bird distributions. LR and MDA were both more efficient in the use of computer time than ANN, and also more straightforward in providing testable hypotheses about environmental effects on occurrence. However, LR was apparently subject to chance significant effects from explanatory variables, emphasising the well-known risks of models based purely on correlative data.     

Comparing network analysis methodologies for consumer–resource relations at species and ecosystems scales

This research compares two existing methodologies, mixed trophic impact analysis and utility analysis, which use network analysis to evaluate the direct, pair-wise, and indirect, holistic, ecological relations between ecosystem compartments. The two approaches have many similarities, but differ in some key assumptions which affect both the final results and interpretations. Here, we briefly introduce both methodologies through a series of two simple examples; a 3-compartment competition model and a 3-compartment food chain model, and then apply the methodologies to a 15-compartment ecosystem model of the Chesapeake Bay. This example demonstrates how implementing the various conceptual and methodological assumptions lead to differing results. Notably, the overall number of positive relations is greatly affected by the treatment of the self-interactions and the handling of detritus compartments lead to a distinction between ecological or trophic relations. We recommend slight changes to both methodologies, not necessarily in order to bring them completely together, but because each has some points which are stronger and better defensible.     

The Reynolds transport theorem: Application to ecological compartment modeling and case study of ecosystem energetics

The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.     

Evidence for the dominance of indirect effects in 50 trophic ecosystem networks

Indirect effects are powerful influences in ecosystems that may maintain species diversity and alter apparent relationships between species in surprising ways. Here, we applied network environ analysis to 50 empirically-based trophic ecosystem models to test the hypothesis that indirect flows dominate direct flows in ecosystem networks. Further, we used Monte Carlo based perturbations to investigate the robustness of these results to potential error in the underlying data. To explain our findings, we further investigated the importance of the microbial food web in recycling energy-matter using components of the Finn Cycling Index and analysis of environ centrality. We found that indirect flows dominate direct flows in 37/50 (74.0%) models. This increases to 31/35 (88.5%) models when we consider only models that have cycling structure and a representation of the microbial food web. The uncertainty analysis reveals that there is less error in the I/D values than the ±5% error introduced into the models, suggesting the results are robust to uncertainty. Our results show that the microbial food web mediates a substantial percentage of cycling in some systems (median = 30.2%), but its role is highly variable in these models, in agreement with the literature. Our results, combined with previous work, strongly suggest that indirect effects are dominant components of activity in ecosystems.     

A hierarchical analysis of terrestrial ecosystem model Biome-BGC: Equilibrium analysis and model calibration

The increasing complexity of ecosystem models represents a major difficulty in tuning model parameters and analyzing simulated results. To address this problem, this study develops a hierarchical scheme that simplifies the Biome-BGC model into three functionally cascaded tiers and analyzes them sequentially. The first-tier model focuses on leaf-level ecophysiological processes; it simulates evapotranspiration and photosynthesis with prescribed leaf area index (LAI). The restriction on LAI is then lifted in the following two model tiers, which analyze how carbon and nitrogen is cycled at the whole-plant level (the second tier) and in all litter/soil pools (the third tier) to dynamically support the prescribed canopy. In particular, this study analyzes the steady state of these two model tiers by a set of equilibrium equations that are derived from Biome-BGC algorithms and are based on the principle of mass balance. Instead of spinning-up the model for thousands of climate years, these equations are able to estimate carbon/nitrogen stocks and fluxes of the target (steady-state) ecosystem directly from the results obtained by the first-tier model. The model hierarchy is examined with model experiments at four AmeriFlux sites. The results indicate that the proposed scheme can effectively calibrate Biome-BGC to simulate observed fluxes of evapotranspiration and photosynthesis; and the carbon/nitrogen stocks estimated by the equilibrium analysis approach are highly consistent with the results of model simulations. Therefore, the scheme developed in this study may serve as a practical guide to calibrate/analyze Biome-BGC; it also provides an efficient way to solve the problem of model spin-up, especially for applications over large regions. The same methodology may help analyze other similar ecosystem models as well.     

Determining factors that influence the dispersal of a pelagic species: A comparison between artificial neural networks and evolutionary algorithms

Because of increasing transport and trade there is a growing threat of marine invasive species being introduced into regions where they do not presently occur. So that the impacts of such species can be mitigated, it is important to predict how individuals, particularly passive dispersers are transported and dispersed in the ocean as well as in coastal regions so that new incursions of potential invasive species are rapidly detected and origins identified. Such predictions also support strategic monitoring, containment and/or eradication programs. To determine factors influencing a passive disperser, around coastal New Zealand, data from the genus Physalia (Cnidaria: Siphonophora) were used. Oceanographic data on wave height and wind direction and records of occurrences of Physalia on swimming beaches throughout the summer season were used to create models using artificial neural networks (ANNs) and Na?ve Bayesian Classifier (NBC). First, however, redundant and irrelevant data were removed using feature selection of a subset of variables. Two methods for feature selection were compared, one based on the multilayer perceptron and another based on an evolutionary algorithm. The models indicated that New Zealand appears to have two independent systems driven by currents and oceanographic variables that are responsible for the redistribution of Physalia from north of New Zealand and from the Tasman Sea to their subsequent presence in coastal waters. One system is centred in the east coast of northern New Zealand and the other involves a dynamic system that encompasses four other regions on both coasts of the country. Interestingly, the models confirm, molecular data obtained from Physalia in a previous study that identified a similar distribution of systems around New Zealand coastal waters. Additionally, this study demonstrates that the modelling methods used could generate valid hypotheses from noisy and complicated data in a system about which there is little previous knowledge.     

Comparative network analysis toward characterization of systemic organization for human–environmental sustainability

A preliminary study in comparative ecological network analysis was conducted to identify key assumptions and methodological challenges, test initial hypotheses and explore systemic and network structural characteristics for environmentally sustainable ecosystems. A nitrogen network for the U.S. beef supply chain – a small sub-network of the industrial food system analyzed as a pilot study – was constructed and compared to four non-human carbon and nitrogen trophic networks for the Chesapeake Bay and the Florida Everglades. These non-human food webs served as sustainable reference systems. Contrary to the main original hypothesis, the “window of vitality” and the number of network roles did not clearly differentiate between a human sub-network and the more complete non-human networks. The effective trophic level of humans (a partial estimate of trophic level based on the single food source of beef) was much higher (8.1) than any non-human species (maximum of 4.88). Network connectance, entropy, total dependency coefficients, trophic efficiencies and the ascendency to capacity ratio also indicated differences that serve as hypotheses for future tests on more comprehensive human food webs. The study elucidated important issues related to (1) the steady state assumption, which is more problematic for industrial human systems, (2) the absence or dearth of data on contributions of dead humans and human wastes to feed other species in an integrated food web, (3) the ambiguity of defining some industrial compartments as living versus non-living, and (4) challenges with constructing compartments and trophic transfers in industrial versus non-human food webs. The two main novel results are (1) the progress made toward adapting ecological network analysis (ENA) methodology for analysis of human food networks in industrial cultures and (2) characterizing the critical aspects of comparative ENA for understanding potential causes of the problems, and providing avenues for solutions, for environmental sustainability. Based on this work, construction and comparative network analysis of a more comprehensive industrial human food network seems warranted and likely to provide valuable insights for modifying structures of industrial food networks to be more like natural networks and more sustainable.     

EMERGY analysis for sustainability evaluation of the Baiyangdian wetland ecosystem in China

This study presents a quantitative and ecological benefit evaluation of the Baiyangdian wetland in China between the years 2000 and 2006. Methods of EMERGY analysis were applied to illustrate the wetland ecosystem, to evaluate the economic and environmental inputs and consequent yields, and to assess the sustainability of the Baiyangdian wetland. The indicators for the integrated ecological and economic system, such as EMERGY yield ratio (EYR) (7.51), EMERGY investment ratio (EIR) (4.52), environmental loading ratio (ELR) (2.92), EMERGY exchange ratio (0.41), and EMERGY sustainable indicator (ESI) (2.57) were calculated, compared, analyzed, and discussed. The non-renewable investment in Baiyangdian was greater than renewable investment, leading to the unsustainable development of the system. High EYR indicated that the Baiyangdian integrated system had created huge profits for its people, while ELR and ESI revealed that human behavior has been a heavy burden on the environment, and countermeasures should be taken by the Chinese government to relieve and resolve these problems. Potential management methods were also proposed in this paper.     

Testing Accuracy of Finite Element and Random Walk Schemes in Prediction of Pollutant Dispersion in Coastal Waters

Distribution of pollutants in coastal waters is usually represented by depth averaged twodimensional convection-dispersion equation. Under very specific conditions this equation can be solved analytically. Although such a solution is restricted to simplified situations it provides a very useful case for testing the performance of various numerical solution techniques currently available for the simulation of convective-dispersion of pollutants in natural water systems. In this paper the analytical solution of the convective dispersion equation is used as a benchmark against which the accuracy of other techniques are assessed. These assessments are based on quantitative comparisons between the results of the solution of two-dimensional convection-dispersion equation by the deterministic finite element and stochastic random walk methods. Both Eulerian and Lagrangian frameworks are employed to obtain the finite element solution of the convection-dispersion problem. It has been shown that the Lagrange–Galerkin finite element scheme yields the most accurate results for the case under study. However, computational costs of the Lagrange–Galerkin method can be relatively high and under certain conditions it may be reasonable to use a less accurate but cost effective random walk scheme to make water quality management decisions.     

On the consequences of aggregation and balancing of networks on system properties derived from ecological network analysis

In the ecological network analysis (ENA) of complex flow food webs the assumption is often made that the models characterizing the flows and stocks of ecosystems occur in a steady state where inflows equals outflows. An assessment of the system indices derived from ENA of six balanced and unbalanced system models, respectively, indicate to differences between indices. The aggregation of highly articulated flow models into models with fewer compartments also has drastic effects on the system metrics, particularly on the information indices.     

Prediction of response of zooplankton biomass to climatic and oceanic changes

This paper examines the long-term variation in zooplankton biomass in response to climatic and oceanic changes, using a neural network as a nonlinear multivariate analysis method. Zooplankton data collected from 1951 to 1990 off the shore of northeastern Japan were analyzed. We considered patterns of the Kuroshio and the Oyashio, sea surface temperature, and meteorological parameters as environmental factors that affect zooplankton biomass. Back propagation neural networks were trained to generate mapping functions between environmental variables and zooplankton biomass. The performance of the network models was tested by varying the numbers of input and hidden units. Changes in zooplankton biomass could be predicted from environmental conditions. The neural network yielded predictions with smaller errors than those of predictions determined by linear multiple regression. The sensitivity analysis of networks was used to extract predictive knowledge. The air pressure, sea surface temperature, and some indices of atmospheric circulation were the primary factors for predictions. The patterns of the Kuroshio and the Oyashio demonstrated different effects among sea areas.     

Invasive species impacts on ecosystem structure and function: A comparison of Oneida Lake, New York, USA, before and after zebra mussel invasion

Exotic species invasion is widely considered to affect ecosystem structure and function. Yet, few contemporary approaches can assess the effects of exotic species invasion at such an inclusive level. Our research presents one of the first attempts to examine the effects of an exotic species at the ecosystem level in a quantifiable manner. We used ecological network analysis (ENA) and a social network analysis (SNA) method called cohesion analysis to examine the effect of zebra mussel (Dreissena polymorpha) invasion on the Oneida Lake, New York, USA, food web. We used ENA to quantify ecosystem function through an analysis of food web carbon transfer that explicitly incorporated flow over all food web paths (direct and indirect). The cohesion analysis assessed ecosystem structure through an organization of food web members into subgroups of strongly interacting predators and prey. Our analysis detected effects of zebra mussel invasion throughout the entire Oneida Lake food web, including changes in trophic flow efficiency (i.e., carbon flow among trophic levels) and alterations of food web organization (i.e., paths of carbon flow) and ecosystem activity (i.e., total carbon flow). ENA indicated that zebra mussels altered food web function by shunting carbon from pelagic to benthic pathways, increasing dissipative flow loss, and decreasing ecosystem activity. SNA revealed the strength of zebra mussel perturbation as evidenced by a reorganization of food web subgroup structure, with a decrease in importance of pelagic pathways, a concomitant rise of benthic pathways, and a reorganization of interactions between top predator fish. Together, these analyses allowed for a holistic understanding of the effects of zebra mussel invasion on the Oneida Lake food web.     

Model-based analysis of the influence of ecological processes on forest point pattern formation—A case study

Many different spatio-temporal individual-based models (IBM) for forests have been developed for studying the development of trees in space and time. Such models typically depend on various numerical parameters that represent the ecological processes of growth (G), inter-plant competition (C) and birth-and-death (B&D; also called regeneration and mortality). Until now little work has been done to systematically trace the influence of these processes and their model parameters on the spatial structure of forest ecosystems.This paper attempts to fill this gap by addressing an important aspect of forest structure, spatial variability, characterised by the mark variogram as a summary characteristic. The model used was inspired by components of various well-established IBMs including a shot-noise competition field. Time series data from monospecies forests in three different countries of the northern hemisphere provided ecological reference scenarios. Though a case study, the paper's methodology is rather general and can be applied to any model and forest ecosystem.Methods of sensitivity analysis revealed that only a small number of model parameters is crucial for forming spatial variability. Particularly important is the range of competition between trees; with increasing range the variability increases. Growth processes have considerable importance particularly with short observation periods and in young forests, whereas mortality processes become more influential in the long-term. Naturally, these statements depend upon the initial structure and on the length of the observation period.     

Ecological network and emergy analysis of urban metabolic systems: Model development,and a case study of four Chinese cities

Analysis of the structure and function of urban metabolic systems is an important goal of urban research. We used network pathways and network utility analysis to analyze the basic network structure of the urban metabolic system and the complex ecological relationships within the system, providing a new way to perform such research. Using four Chinese cities as examples, we developed an ecological network model of the urban metabolic system. By using network pathway analysis, we studied the changing relationships between metabolic length and the number of metabolic pathways, and between metabolic length and reachability. Based on the distribution of the number of metabolic pathways, we describe the basic structure and intercompartment relationships of the system. By using the sign distribution in the network utility matrix, we determined the ecological relationships and degree of mutualism between the compartments of the system. The basic components of the system consisted of the internal environment, the external environment, and the agricultural, industrial, and domestic sectors. With increasing metabolic length, the ecological relationships among the components of the system became more diverse, and the numbers of metabolic paths and their reachability improved. Although the basic network structure of the four cities was identical, the mutualism index differed. Beijing's mutualism index was superior to that of Shanghai, and much higher than those of Tianjin and Chongqing. By analyzing the structure and function of the urban metabolic system, we provide suggestions for optimizing the structure and adjusting the relationships, and propose methods for the application of ecological network analysis in future urban system research.     

Invasive species impacts on ecosystem structure and function: A comparison of the Bay of Quinte, Canada, and Oneida Lake, USA, before and after zebra mussel invasion

As invasion rates of exotic species increase, an ecosystem level understanding of their impacts is imperative for predicting future spread and consequences. We have previously shown that network analyses are powerful tools for understanding the effects of exotic species perturbation on ecosystems. We now use the network analysis approach to compare how the same perturbation affects another ecosystem of similar trophic status. We compared food web characteristics of the Bay of Quinte, Lake Ontario (Canada), to previous research on Oneida Lake, New York (USA) before and after zebra mussel (Dreissena polymorpha) invasion. We used ecological network analysis (ENA) to rigorously quantify ecosystem function through an analysis of direct and indirect food web transfers. We used a social network analysis method, cohesion analysis (CA), to assess ecosystem structure by organizing food web members into subgroups of strongly interacting predators and prey. Together, ENA and CA allowed us to understand how food web structure and function respond simultaneously to perturbation. In general, zebra mussel effects on the Bay of Quinte, when compared to Oneida Lake, were similar in direction, but greater in magnitude. Both systems underwent functional changes involving focused flow through a small number of taxa and increased use of benthic sources of production; additionally, both systems structurally changed with subgroup membership changing considerably (33% in Oneida Lake) or being disrupted entirely (in the Bay of Quinte). However, the response of total ecosystem activity (as measured by carbon flow) differed between both systems, with increasing activity in the Bay of Quinte, and decreasing activity in Oneida Lake. Thus, these analyses revealed parallel effects of zebra mussel invasion in ecosystems of similar trophic status, yet they also suggested that important differences may exist. As exotic species continue to disrupt the structure and function of our native ecosystems, food web network analyses will be useful for understanding their far-reaching effects.     

The effects of aggregation on the performance of the inverse method and indicators of network analysis

Food webs are usually aggregated into a manageable size for their interpretation and analysis. The aggregation of food web components in trophic or other guilds is often at the choice of the modeler as there is little guidance in the literature as to what biases might be introduced by aggregation decisions. We examined the impacts of the choice of the a priori model on the subsequent estimation of missing flows using the inverse method and on the indices derived from ecological network analysis of both inverse method-derived flows and on the actual values of flows, using the fully determined Sylt-Rømø Bight food web model. We used the inverse method, with the least squares minimization goal function, to estimate ‘missing’ values in the food web flows on 14 aggregation schemes varying in number of compartments and in methods of aggregation. The resultant flows were compared to known values; the performance of the inverse method improved with increasing number of compartments and with aggregation based on both habitat and feeding habits rather than diet similarity. Comparison of network analysis indices of inverse method-derived flows with that of actual flows and the original value for the unaggregated food web showed that the use of both the inverse method and the aggregation scheme affected indices derived from ecological network analysis. The inverse method tended to underestimate the size and complexity of food webs, while an aggregation scheme explained as much variability in some network indices as the difference between inverse-derived and actual flows. However, topological network indices tended to be most robust to both the method of determining flows and to the inverse method. These results suggest that a goal function other than minimization of flows should be used when applying the inverse method to food web models. Comparison of food web models should be done with extreme care when different methodologies are used to estimate unknown flows and to aggregate system components. However, we propose that indices such as relative ascendency and relative redundancy are most valuable for comparing ecosystem models constructed using different methodologies for determining missing flows or for aggregating system components.     

Bibliometric analysis of ecosystem monitoring-related research in Africa: implications for ecological stewardship and scientific collaboration

Regional ecosystem monitoring is a central form of knowledge sharing and collaboration amongst scientists and decision makers on environmental health, land use change, and science-policy development. Despite the proliferation of such research networks on long-term monitoring on many continents, little has been achieved in Africa. This study aims to assess and examine the spatiotemporal trend and categorical patterns in ecosystem monitoring-related research in Africa for the benefits of conserving biodiversity and sustaining natural resource sectors for well-being and livelihood security, environmental planning, and ecological stewardship. A systematic review was conducted using bibliometric tools. Based on a set of search terms and peer-reviewed publications retrieved from various ecosystem monitoring networks and journal databases, further analysis was conducted using social network approaches, mapping tools, and content analysis. About 1442 scientific publications on ecosystem monitoring and related research were documented from 1987 to 2014 mostly published in English. The number of publication increased progressively since 1992 after the Convention on Biodiversity was signed and this trend peaked till 2008. South African Journal of Science was the most leading journal and Nature the most cited. Internationally coauthored and collaborative articles represented majority of the findings with the United Kingdom at the central position in the research network due to colonial relationships. Regional collaboration amongst countries is limited owing to language barriers and other institutional constraints such as funding and short-term projects. These findings have implication for prioritizing national and regional policies toward biodiversity science and its contribution to human well-being, food security, and global change responses.     

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.