Ecological network analysis for water use systems—A case study of the Yellow River Basin

Ecological network analysis (ENA) is introduced in this paper as a promising approach to study water use systems. Information indices from ENA involving total system throughput (TST), ascendency and overhead are calculated here. Two related aspects including organization inherent in system structures and synthesized water use intensity related with sustainable development of water use systems are analyzed. The indices of ascendency and overhead are applied for analyzing and characterizing water use network organization. For comparison of sustainability of water use systems from integrated aspects of environment, society and economy and based on TST, a new indicator termed as total system throughput intensity (TSTI) is constructed incorporating parameters of land, precipitation, population, GDP and environmental flow, which can be used as a measure of sustainability in terms of synthesized water use intensity. The Yellow River Basin in China during 1998–2006 is chosen as the case study and divided into subsystems according to the six river sections as from source to Lanzhou (S1-L1), Lanzhou to Toudaoguai (L1-T), Toudaoguai to Longmen (T-L2), Longmen to Sanmenxia (L2-S2), Sanmenxia to Huayuankou (S2-H) and Huayuankou to the mouth of Bo Sea (H-B). The results show that (i) the organization levels of L1-T and H-B are better than those of S1-L1 and T-L2, with those of L2-S2 and S2-H the worst; (ii) the synthesized water use intensity has been improving, of which T-L2, L2-S2 and S2-H are at the highest levels while H-B the lowest. In addition, the comparison between TSTI and other metrics and the relationship between ascendency and TSTI are discussed, from which the importance of TSTI is reflected and the optimization criterions for sustainable development of six subsystems are derived. It can be concluded that the application of ENA in water use systems can provide new angles for water resource management to address the challenges of assessing and optimizing options to obtain more sustainable water use.     

Information indices as a tool for quantifying development of below-ground terrestrial ecosystems

Information indices from ecosystem network analysis (ENA) describe the size and organization of an ecosystem and are claimed to quantify ecosystem development [Ulanowicz, R.E., 1986, Growth and Development, Springler-Verslag, New York, 203 pp.]. To date, these indices were not used to describe a gradient of ecosystem development for a field situation. Here we used information indices to quantify soil succession with soils of different age on the island Schiermonnikoog, The Netherlands. We evaluated whether information indices describe ecosystem development as predicted by ENA.For the Island of Schiermonnikoog the biomasses of soil organisms and roots were measured on four stages of succession (0, 10, 25 and 100 years old soils). Organisms were grouped based on their feeding characteristics. With these data consumption, respiration, excretion, external input and output flows to, from and between groups were calculated. These flows, in turn, were used to calculate the information indices. Relative information indices describe the organization of an ecosystem; i.e. level of organisation (specialization of flows), diversity and evenness of flows, and disorganisation. Absolute indices describe both size (in terms of energy flow) and organisation of the system. System size is used to scale the absolute indices and will be analysed separately as well.We found that the absolute indices increased when succession processed, as predicted by theory. This pattern could have been due to the build-up of biomass, which apparently did not level off. Because the succession gradient deals mostly with young soils (0, 10 and 25 years old) and only one older field (100 years old), the gradient should include more soils of around 100 years old and older to exclude this possibility. Relative indices, on the other hand, increased initially, but then levelled off. We think that this was due to the strong aggregation of functional groups, especially at lower trophic levels, because information in some functional groups showed (expected) trends.Our results suggest that the absolute indices are able to describe ecological succession of terrestrial below-ground ecosystems. The relative indices, in contrast, appeared to be insensitive to subtle succesional changes.     

Evaluation of information indices as indicators of environmental stress in terrestrial soils

Information indices from Ecosystem Network Analysis (ENA) can be used to quantify the development of an ecosystem in terms of its size and organization. There are two types of indices, i.e. absolute indices that describe both the size and organization of ecosystem (Total System Throughput (TST)—system size, Ascendancy (A)—size of organized flows and Development Capacity (C)—upper limit for A, Overhead (L)—size of unorganized flows) and relative indices that describe only the organization (Average Mutual Information (AMI = A:TST), Flow Diversity (H = C:TST), Relative Overhead (RL = L:TST)).It is theorized that environmental stress impair the ecosystem development and that the effect of stress can be quantified with the ENA information indices. Here we applied ENA on a case of environmental stress in a terrestrial ecosystem, i.e. soils that have endured long-term exposure to elevated copper concentration and altered pH.The absolute indices showed an unexpected pattern of response to pollution, suggesting that ecosystems in polluted soils are more active and better organized than these in unpolluted soils. The relative indices, alternatively, responded to pollution as predicted by theory, i.e. with decrease of stress (pollution level) the level of specialization increased (increase of AMI) and losses of energy, e.g. due to respiration, decreased (decrease of Overhead). The diversity and evenness of flows showed hump-backed relationship with stress. Less polluted soils appeared to be less vulnerable to external disturbances and more efficient in processing energy (higher Relative Ascendancy (RA = A:C)) than polluted soils. The relative information indices were rigid to changes in values of assumed parameters. The relative indices, opposite to absolute indices, appeared to be useful as indicators of environmental stress on the ecosystem level.     

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.     

Evaluation of ecological network analysis: Validation of output

Ecological network analysis (ENA) is a modeling approach increasingly being used to evaluate food webs and provide an ecosystem-based approach to resource management. Unfortunately, validation of ENA output is rarely performed. This study represents part of a larger effort to critically evaluate ENA. Here we validate ENA output using stable isotope analysis (SIA), and where validation is not met, determine the effects of modifying trophic networks to reflect validation.     

An overview of systems analysis methods in delineating environmental quality indices

Environmental quality indices (EQIs) have been developed for a variety of purposes ranging from enforcement of environmental standards, to analysis of trends of environmental degradation or improvement, to scientific research. EQIs currently in use are not organized within an integrated framework and thus it has been difficult to analyze adequately complex, multidisciplinary, large-scale, global phenomena. In this paper we compare four different approaches to developing EQIs within a systems perspective. Our analysis suggests that: (1) non-linear regression models that represent an ecosystem's response to different impacts within a stress-response framework (method of response functions) are useful tools for analysis of environmental data; (2) non-equilibrium thermodynamics models based on the concept of exergy, which represents the free energy a system possesses in relation to its environment, provide a common basis for representing many aspects of ecosystem development and response to environmental impacts as a single measure; (3) diagram models based on the concept of emergy, which represents both environmental values and economic values with a single measure, provide a common basis for integrating economic development and environmental protection values into one index; and (4) complex systems simulation models based on general systems theory, which use the methodologies of systems analysis and simulation to identify, quantify, and interrelate EQIs within a dynamic systems context, provide explicit linkages between causes and effects (vertical integration) and identify cross-linkages among different environmental issues (horizontal integration).     

Ecological network analysis: network construction

Ecological network analysis (ENA) is a systems-oriented methodology to analyze within system interactions used to identify holistic properties that are otherwise not evident from the direct observations. Like any analysis technique, the accuracy of the results is as good as the data available, but the additional challenge is that the data need to characterize an entire ecosystem's flows and storages. Thus, data requirements are substantial. As a result, there have, in fact, not been a significant number of network models constructed and development of the network analysis methodology has progressed largely within the purview of a few established models. In this paper, we outline the steps for one approach to construct network models. Lastly, we also provide a brief overview of the algorithmic methods used to construct food web typologies when empirical data are not available. It is our aim that such an effort aids other researchers to consider the construction of such models as well as encourages further refinement of this procedure.     

Validating graph-based connectivity models with independent presence–absence and genetic data sets

Habitat connectivity is a key objective of current conservation policies and is commonly modeled by landscape graphs (i.e., sets of habitat patches [nodes] connected by potential dispersal paths [links]). These graphs are often built based on expert opinion or species distribution models (SDMs) and therefore lack empirical validation from data more closely reflecting functional connectivity. Accordingly, we tested whether landscape graphs reflect how habitat connectivity influences gene flow, which is one of the main ecoevolutionary processes. To that purpose, we modeled the habitat network of a forest bird (plumbeous warbler [Setophaga plumbea]) on Guadeloupe with graphs based on expert opinion, Jacobs’ specialization indices, and an SDM. We used genetic data (712 birds from 27 populations) to compute local genetic indices and pairwise genetic distances. Finally, we assessed the relationships between genetic distances or indices and cost distances or connectivity metrics with maximum-likelihood population-effects distance models and Spearman correlations between metrics. Overall, the landscape graphs reliably reflected the influence of connectivity on population genetic structure; validation R² was up to 0.30 and correlation coefficients were up to 0.71. Yet, the relationship among graph ecological relevance, data requirements, and construction and analysis methods was not straightforward because the graph based on the most complex construction method (species distribution modeling) sometimes had less ecological relevance than the others. Cross-validation methods and sensitivity analyzes allowed us to make the advantages and limitations of each construction method spatially explicit. We confirmed the relevance of landscape graphs for conservation modeling but recommend a case-specific consideration of the cost-effectiveness of their construction methods. We hope the replication of independent validation approaches across species and landscapes will strengthen the ecological relevance of connectivity models.     

柠檬酸固态发酵过程的研究

本文研究了以甘薯为原料，以黑曲霉为菌种，固态发酵制柠檬酸的最佳发酵条件和发酵动力学。探讨了接种方式、灭菌与否以及温度、含水量、ｐＨ值、颗粒度、通气速率等因素对柠檬酸固态发酵过程的影响，提出了适宜的发酵参数。在此基础上，进一步研究甘薯固态发酵制取柠檬酸的动力学模型，确定了模型参数与操作条件的关系。该模型反映了基质消耗、产物生成、菌体生长及ＣＯ２释放速率的变化过程和温度、颗粒度的影响。模型的模拟结果与     

Modeling changes in the coastal ecosystem of the Pearl River Estuary from 1981 to 1998

The coastal ecosystem of the Pearl River Estuary (PRE) has been overfished and received a high level of combined pollution since the 1980s. Ecopath with Ecosim was used to construct two ecosystem models (for 1981 and 1998) to characterize the food web structure and functioning of the ecosystem. Pedigree work and simple sensitivity analysis were carried out to evaluate the quality of data and the uncertainty of the models. The two models seem reliable with regards to input data of good quality. Comparing the variations of outputs of these two models aimed to facilitate assessment of changes of the ecosystem during the past two decades.The trophic structure of the ecosystem has changed with an increase in the biomass proportion of lower trophic level (TL) organisms and a decrease in top predator biomass proportion. All the indices of ecosystem maturity examined show that the system was in a more mature condition in 1981 than in 1998, although the system has been in a condition of stress due to anthropogenic disturbances, such as environmental pollution and habitat destruction since 1981. The ecosystem was aggregated into six and seven integral TLs in 1981 and 1998, respectively, using the trophic aggregation routine of Ecopath. Most of the total system biomass and catch took place at TL II and III in both years. But the distribution of the total system biomass and catch at different TLs changed with decreasing proportions in higher TLs in 1998. The mean transfer efficiency was 9.1% and 10.2% in 1981 and 1998, respectively.Comparative network analysis allowed quantification of the importance of direct and indirect trophic interactions among functional groups. Moreover, a method derived from the mixed trophic impact (MTI) analysis allowed estimating importance of groups in terms of “keystoneness” and identifying the keystone species in the two models over the past two decades. The results indicate that there were no clear keystone species in 1998 but two keystone species at medium trophic levels were identified in 1981. Moreover, organisms located at low trophic levels such as phytoplankton, zooplankton and benthic invertebrates were identified to have relatively high keystoneness in the ecosystem.     

Are network indices robust indicators of food web functioning? A Monte Carlo approach

Indices based on network theory are often used to describe food web functioning. These indices take as input food web flows that are estimated based on merging of (scarce) data with linear inverse methods (LIMs). Due to under sampling, most food webs are highly uncertain and can only be quantified within a specific uncertainty range. The linear inverse method (LIM) can estimate food web flows using a variety of techniques, e.g. the parsimonious or minimum norm (MN) solution, which selects one food web, based on a quadratic minimization technique or the Monte Carlo solution where a finitely many random solutions are generated which are then averaged. We use the Monte Carlo approach (MCA) to estimate the values of several indices from four published food webs, the Gulf of Riga for the autumn, summer and spring seasons, and the Takapoto atoll system. We first show that network indices are much better constrained than the uncertain food webs from which they are calculated. Therefore, even in the face of food web uncertainty, they are robust estimators of food web functioning. We then use the MCA-derived network indices to generate cumulative density functions for each index. These serve to compute the probabilities of the MN indices estimates being an extreme solution as compared to the median values. Our findings show that 82% of the MN solutions are smaller than the MCA solutions, and 63% of the network indices are significantly under-estimated.     

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.     

From data and theory to environmental models and indices formation

A prerequisite for environmental indices is that they represent environmental pressure, and the state of, and impact on environmental conditions. In other words, they should capture as much as possible of the cause-effect chains they represent and relate pressure and effect to criteria of environmental quality. The approach proposed in the article attempts to link the pressure–state–impact–response framework of indicators to the integrated environmental model, based on the method of response function (MRF). The MRF allows to construct purposeful, credible models from data and prior knowledge or information. The data are usually time series observations of system inputs and outputs, and sometimes of internal states. The output of such models is presented with highly aggregated environmental indices, reflecting the main pressure–state–impact–response cause-effect chains. The proposed approach is illustrated with the example of soil erosion indices.     

Throughflow analysis: A stochastic approach

Ecological network analysis (ENA), predicated on systems theory and Leontiev input–output analysis, is a method widely used in ecology to reveal ecosystem properties. An important ecosystem property computed in ENA is throughflows, the amount of matter/energy leaving each compartment of the ecosystem. Throughflows are analyzed via a matrix representing their relationships to the driving input at the boundary. Network particle tracking (NPT) builds on ENA to offer a Lagrangian particle method that describes the activity of the ecosystem at the microscopic level. This paper introduces a Lagrangian throughflow analysis methodology using NPT and shows that the NPT throughflow matrix, , agrees with the conventional ENA throughflow matrix, , for ecosystems at steady-state with donor-controlled flows. The matrix is computed solely from the pathways (particles’ histories) generated by NPT simulations and its average over multiple runs of the algorithm with longer simulation time agrees with the Eulerian matrix (Law of Large Numbers). While the traditional NEA throughflow analysis is mostly used with steady-state ecosystem models, the Lagrangian throughflow analysis that we propose can be used with non-steady-state models and paves the way for the development of dynamic throughflow analysis.     

Prediction of longitudinal dispersion coefficients in natural rivers using artificial neural network

An artificial neural network (ANN) model is developed for predicting the longitudinal dispersion coefficient in natural rivers. The model uses few rivers’ hydraulic and geometric characteristics, that are readily available, as the model input, and the target output is the longitudinal dispersion coefficient (K). For performance evaluation of the model, using published field data, predictions by the developed ANN model are compared with those of other reported important models. Based on various performance indices, it is concluded that the new model predicts the longitudinal dispersion coefficient more accurately. Sensitive analysis performed on input parameters indicates stream width, flow depth, stream sinuosity, flow velocity, and shear velocity to be the most influencing parameters for accurate prediction of the longitudinal dispersion coefficient.     

Natural control mechanisms in models of aquatic ecosystems

Based on cybernetic categories of natural control mechanisms, four generations of ecosystem models are distinguished: feed-forward, feedback, self-adaptation and self-organization models. The analysis of the natural control mechanisms in aquatic ecosystems suggests that different processes are controlled in different ways, and, although the four mechanisms were identified in historical sequence, they all operate simultaneously. The concept of self-organization of an ecosystem is introduced and specified for a model of an aquatic pelagic ecosystem. The concept of the ecosystem as a multilayer, multigoal and multiechelon hierarchical system with hierarchy of the levels of biological organization is also introduced.     

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.     

Forest growth in the light of the thermodynamic theory of ecological systems

The observed growth of a particular forest stand can be described by many models and explained by some of them. The forest growth models are also successfully applied for extrapolating the growth curve. However, the known models of forest growth are not “one-point” models. They are not designed to predict the future growth of a forest stand from its current state: the model parameters either are not directly measurable or cannot be measured with relevant accuracy. This article is an attempt to use Jørgensen–Svirezhev theory as a new clue to the choice of variables that determines forest growth. The postulates of this theory combined with the pipe theory of tree growth lead to conclusion that biomass of a stand should be proportional to the four-fifths power of its age. Empirical validation, however, disclosed that calendar age is rather approximate measure of ecosystem ontogeny. Delayed development or intensive thinning of a forest stand at the early stages leads to rejuvenation bias. Thus derived 4/5-law model approximates well-known Chapman–Richards model in the neighborhood of the inflection point, and is applicable to middle-aged forest stands.