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.     

Ecological network determination of sectoral linkages, utility relations and structural characteristics on urban ecological economic system

Analyzing the structure and functioning of the urban system revealed ways to optimize its structure by adjusting the relationships among compartments, thereby demonstrating how ecological network analysis can be used in urban system research. Based on the account of the extended exergy utilization in the sector of urban socio-economic system, which is considered as the composition of extraction (Ex), conversion (Co), agriculture (Ag), industry (In), transportation (Tr), tertiary (Te) and households (Do) sectors, an urban ecological network model is constructed to gain insights into the economic processes oriented to sustainable urban development. Taking Beijing city as the case, the network accounting and related ecological evaluation of a practical urban economy are carried out in this study in the light of flux, efficiency, utility and structure analysis. The results showed that a large quantity of energy and resources have to be consumed to maintain the structure and function of a city. The thermodynamic efficiencies of individual sector in Beijing remain at a low level. The social system in Beijing is a highly competitive network, and there are 8 competitive relations and only two mutualistic ones. The Domestic and Agricultural sector are the major controlling factors of the system. Moreover, the assessment results of Beijing are compared with the other three socio-economic systems, Norway, UK and Italy, and the ecological network function and structure comparisons are correspondingly illuminated and discussed. The conclusions indicate that the exergy-based network analysis can be refined to become an integrative tool for evaluation, policy-making and regulation for urban socio-economic system management concerning structure and efficiency at urban levels.     

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.     

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.     

Topological analysis of the ecological importance of elasmobranch fishes: A food web study on the Gulf of Tortugas, Colombia

We built a trophic network based on a matrix of interspecific trophic relationships to assess the role of elasmobranch fishes in shaping community structure of the Gulf of Tortugas in the Colombian Pacific Ocean. We analyzed diet similarities to define trophic components (nodes) - rather than taxonomical groups - in the network. We evaluated the ecological function of species or trophic entities through topological analysis of their structural importance in trophic networks by applying one local and several mesoscale network indices. We found that top predatory elasmobranchs play an important ecological role in top-down control and in propagating indirect effects through the system owing to high values of the node degree, centrality and topological importance indices. However, invertebrates and teleost fishes had higher connectivity and topological importance than other elasmobranchs in the network before and after removal of top predators from the system. Results from our study thus suggest that elasmobranchs at intermediate trophic levels - commonly referred to as “mesopredators” - are not so important in all complex coastal ecosystems as previously reported.     

Response of balanced network models to large-scale perturbation: Implications for evaluating the role of small pelagics in the Gulf of Maine

Exploring the response of an ecosystem, and subsequent tradeoffs among its biological community, to human perturbations remains a key challenge for the implementation of an ecosystem approaches to fisheries (EAF). To address this and related issues, we developed two network (or energy budget) models, Ecopath and Econetwrk, for the Gulf of Maine ecosystem. These models included 31 network “nodes” or biomass state variables across a broad range of trophic levels, with the present emphasis to particularly elucidate the role of small pelagics. After initial network balancing, various perturbation scenarios were evaluated to explore how potential changes to different fish, fisheries and lower trophic levels can affect model outputs. Categorically across all scenarios and interpretations thereof, there was minimal change at the second trophic levels and most of the “rebalancing” after a perturbation occurred via alteration of the diet matrix. Yet the model results from perturbations to a balanced energy budget fall into one of three categories. First, some model results were intuitive and in obvious agreement with established ecological and fishing theory. Second, some model results were counter-intuitive upon initial observation, seemingly contradictory to known ecological and fishing theory; but upon further examination the results were explainable given the constraints of an equilibrium energy budget. Finally, some results were counter-intuitive and difficult to reconcile with theory or further examination of equilibrium constraints. A detailed accounting of biomass flows for example scenarios explores some of the non-intuitive results more rigorously. Collectively these results imply a need to carefully track biomass flows and results of any given perturbation and to critically evaluate the conditions under which a new equilibrium is obtained for these types of models, which has implications for dynamic simulations based off of them. Given these caveats, the role of small pelagics as a prominent component of this ecosystem remains a robust conclusion. We discuss how one might use this approach in the context of further developing an EAF, recognizing that a more holistic, integrated perspective will be required as we continue to evaluate tradeoffs among marine biological communities.     

An inverse model for the analysis of the Venice lagoon food web

A steady-state model of the Venice lagoon food web was constructed, based on a comprehensive set of data, which were collected in the years 2001-2005. Energy flows were estimated by means of an inverse methodology of constrained optimization based on the Minimum Norm criterion, i.e. on the minimization of both the sum of squares of the residuals and of the sum of squares of energy flows. The solution was constrained by a set inequalities, which were derived from general eco-physiological knowledge and site specific data on energy flows. The trophic network was represented by thirty-two nodes, including single-species compartments for the species of high economical or ecological relevance. Mass balance equations were weighted, in order to obtain meaningful results in presence of large differences, up to 5 orders of magnitude, among biomasses. A perturbation technique was applied, with the purpose of reducing the risk of finding solutions heavily affected by the set of constraints and of obtaining a more robust representation of the energy flows. The main patterns of energy flow are consistent with those obtained in previous attempts at modelling the Venice lagoon food web. Micro- and macro-phytobenthos account for the largest fraction of the primary production. Energy is then transferred towards higher trophic levels by means of two main pathways: the recycling of dead biomass through the detritus compartment and the direct consumption by grazers. The first pathway is the most important and accounts for approximately two/thirds of the energy transferred to the second trophic level.     

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.     

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.     

Emergy analysis of the urban metabolism of Beijing

Cities can be modeled as if they were superorganisms with a range of metabolic processes. Research on this urban metabolism can contribute to solving urban environmental problems by revealing details of the metabolic throughput of the system. A key issue is how to find a common basis for measuring the environmental and economic values. By providing a single unified unit, emergy theory integrates the natural and socioeconomic systems and thoroughly evaluates a system's metabolism. We analyzed Beijing's urban metabolic system using emergy synthesis to evaluate its environmental resources, economy, and environmental and economic relations with the regions outside the city during 14 years of development. We compared Beijing's emergy indices with those of five other Chinese cities and of China as a whole to assess Beijing's relative development status. These indices are the emergy self-support ratio (metabolic dependence), the environmental load ratio (metabolic loading), empower density (metabolic pressure), emergy used per person (metabolic intensity per capita), and the monetary equivalent of emergy (emdollars; metabolic intensity). Based on our emergy analysis, Beijing's socioeconomic system is not self-sufficient, and depends greatly on external environmental resources. Its GDP is supported by a high percentage of emergy purchased from outside the city. During the study period, Beijing's urban system showed an increasing dependence on external resources for its economic development. Beijing's loading and pressure on the ecological environment is continuously increasing, accompanied by continuously increasing human emergy consumption. In the future, it will become increasingly necessary to improve Beijing's metabolic efficiency.     

What is hidden behind the concept of ecosystem efficiency in energy transformation?

The number of energy transformation levels in trophic webs is usually below five, but can be extended up to ten when parasites and hyper-parasites are included. Research on the structure and function of food webs is relevant to the complexity–stability–productivity debate. The aim of this theoretical analysis is to link energetic and connectional aspects of ecosystems with information theory. Updating an energetic model reported by Ricklefs [Ecologia, Zanichelli Editore S.p.A., Bologna, Italy, 1993, p. 896], our approach is integrated with a static analysis of food webs. The length of food webs is theoretically associated with the average ecological efficiency which can be empirically correlated with the effective connectance between species. Furthermore, the advantage of greater complexity when applied to a signalling network is qualitatively addressed.The overall efficiency of energy transformation into biomass throughout a trophic web, in an ecosystem with a given number of species, is the resultant of the various ecological efficiencies, η, at the transitions between the trophic levels. However, we propose that an increment in effective connectance and interspecies connectivity based on a superimposed signalling web may increase the η values, despite the fact that signalling per se has an energetic cost. According to this hypothesis, ecosystem stability would not be necessarily reduced by increasing the number of trophic levels, N, whenever stability in terms of persistence is improved by a cost-efficient regulatory network.     

Assessment of impacts of invasive fishes on the food web structure and ecosystem properties of a tropical reservoir in India

A network model of trophic interactions in a tropical reservoir in India was developed with the objective to quantify matter and energy flows between system components and to study the impact of invasive fishes on the ecosystem. Structure of flows and their distribution within and between trophic levels were analysed by aggregating single flows into combined flows for discrete trophic levels. The trophic flows primarily occurred in the first four trophic level (TL) and the food web structure in this reservoir ecosystem was characterized by the dominance of low TL organisms, with the highest TL of only 3.57 for the top predator. Highest system omnivory index (SOI) was observed for indigenous catfishes (0.422), followed by the exotic fish Mozambique Tilapia (0.402). Nile Tilapia and Pearl spots show the highest niche overlap which suggests high competition for similar resources. The mixed trophic impact routine reveals that an increase in the abundance of the African catfish would negatively impact almost all fish groups such as Indian major carps, Pearl spots, indigenous catfishes and Tilapines. The other invasive fish Mozambique Tilapia adversely affects the indigenous catfishes. The most interesting observation in this study is that the most dominant invasive fish in this reservoir, the Nile Tilapia does not negatively impact any of the fish groups. In fact it positively impacts the Indian major carps. The direct and indirect effects of predation between system components (i.e. fish, invertebrates, phytoplankton and detritus) are quantitatively described and the possible influence and role in the ecosystem's functioning of the invasive fish species are discussed.     

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.     

Evaluation of urban metabolism based on emergy synthesis: A case study for Beijing (China)

Cities (“urban superorganisms”) exhibit metabolic processes. Disturbance of these processes results from the high throughput of the socioeconomic system as a result of the flow of resources between it and its surroundings. Based on systematic ecology and emergy synthesis, we developed an emergy-based indicator system for evaluating urban metabolic factors (flux, structures, intensity, efficiency, and density), and evaluated the status of Beijing's environment and economic development by diagramming, accounting for, and analyzing the material, energy, and monetary flows within Beijing's metabolic system using biophysically based ecological accounting. We also compared the results with those of four other Chinese cities (Shanghai, Guangzhou, Ningbo, and Baotou) and China as a whole to assess Beijing's development status. From 1990 to 2004, Beijing's metabolic flux, metabolic intensity, and metabolic density increased significantly. The city's metabolic processes depend excessively on nonrenewable resources, but the pressure on resources from outside of the city decreased continuously. The metabolic efficiency increased by around 12% annually throughout the study period. Beijing had a highest metabolic fluxes and density compared with the four other cities; its metabolic efficiency was lower, and its metabolic intensity was higher. Evaluating these metabolic indicators revealed weaknesses in the urban metabolic system, thereby helping planners to identify measures capable of sustaining these urban metabolic processes.     

A simple random path method for the analysis of flow networks

The path of a particle through an ecosystem is modelled as a Markov chain. For a given flow network, powers of the transition matrix are used to calculate the distribution of the particles over the network after each transition. The method may be applied for the definition and calculation of trophic levels in food webs. The algorithm yields the trophic level distribution of species, the species composition of trophic levels, and the path length distribution of output flows. In addition, the network can be described as a linear chain, with the throughflows at each step identified. Data from several ecosystems are analyzed by the method, showing that surprising insights may result.     

Cyclic energy pathways in ecological food webs

Standard ecology textbooks typically maintain that nutrients cycle, but energy flows in unidirectional chains. However, here we use a new metric that allows for the identification and quantification of cyclic energy pathways. Some of these important pathways occur due to the contribution of dead organic matter to detrital pools and those organisms that feed on them, reintroducing some of that energy back into the food web. Recognition of these cyclic energy pathways profoundly impacts many aspects of ecology such as trophic levels, control, and the importance of indirect effects. Network analysis, specifically the maximum eigenvalue of the connectance matrix, is used to identify both the presence and strength of these structural cycles.     

Environ indicator sensitivity to flux uncertainty in a phosphorus model of Lake Sidney Lanier, USA

Effective environmental impact assessment and management requires improved understanding of the organization and transformation of ecosystems in which independent agents are linked through an intricate network of energy, matter, and informational interactions. While advances have been made, we still lack a complete understanding of the processes that create, constrain, and sustain ecosystems. Network environ analysis (NEA) provides one approach for building novel ecosystem insights, but it is model dependent. As ecological modeling is an imprecise art, often complicated by inadequate empirical data, the utility of NEA may be limited by model uncertainty. Here, we investigate the sensitivity of NEA indicators of ecosystem growth and development to flow and storage uncertainty in a phosphorus model of Lake Sidney Lanier, USA. The indicators are total system throughflow (TST), total system storage (TSS), total boundary input (Boundary), Finn cycling index (FCI), ratio of indirect-to-direct flows (Indirect/Direct), indirect flow index (IFI), network aggradation (AGG), network homogenization (HMG), and network amplification (AMP). Our results make two primary contributions. First, they demonstrate that five of the indicators – FCI, Indirect/Direct, IFI, AGG and HMG – are relatively robust to the flow and storage uncertainty in the Lake Lanier model. This stability lets us draw robust conclusions about the Lake Lanier ecosystem organization (e.g., phosphorus flux in the lake is dominated by internal processes) in spite of uncertainties in the model. Second, we show that the majority of the indicators co-vary and that most of their common variation could be mapped onto two latent factors, which we interpret as (1) system integration and (2) boundary influences.     

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.     

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.