Ecological network analysis of an urban energy metabolic system: Model development, and a case study of four Chinese cities

Urban metabolism research faces difficulties defining ecological trophic levels and analyzing relationships among the metabolic system's energy components. Here, we propose a new way to perform such research. By integrating throughflow analysis with ecological network utility analysis, we used network flows to analyze the metabolic system's network structure and the ecological relationships within the system. We developed an ecological network model for the system, and used four Chinese cities as examples of how this approach provides insights into the flows within the system at both high and low levels of detail. Using the weight distribution in the network flow matrix, we determined the structure of the urban energy metabolic system and the trophic levels; using the sign distribution in the network utility matrix, we determined the relationships between each pair of the system's compartments and their degrees of mutualism. The model uses compartments based on 17 sectors (energy exploitation; coal-fired power; heat supply; washed coal; coking; oil refinery; gas generation; coal products; agricultural; industrial; construction; communication, storage, and postal service; wholesale, retail, accommodation, and catering; household; other consuming; recovery; and energy stocks). Analyzing the structure and functioning of the urban energy metabolic system revealed ways to optimize its structure by adjusting the relationships among compartments, thereby demonstrating how ecological network analysis can be used in future urban system research.     

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.     

How complex do models need to be to predict dispersal of threatened species through matrix habitats?

Persistence of species in fragmented landscapes depends on dispersal among suitable breeding sites, and dispersal is often influenced by the "matrix" habitats that lie between breeding sites. However, measuring effects of different matrix habitats on movement and incorporating those differences into spatially explicit models to predict dispersal is costly in terms of time and financial resources. Hence a key question for conservation managers is: Do more costly, complex movement models yield more accurate dispersal predictions? We compared the abilities of a range of movement models, from simple to complex, to predict the dispersal of an endangered butterfly, the Saint Francis' satyr (Neonympha mitchellii francisci). The value of more complex models differed depending on how value was assessed. Although the most complex model, based on detailed movement behaviors, best predicted observed dispersal rates, it was only slightly better than the simplest model, which was based solely on distance between sites. Consequently, a parsimony approach using information criteria favors the simplest model we examined. However, when we applied the models to a larger landscape that included proposed habitat restoration sites, in which the composition of the matrix was different than the matrix surrounding extant breeding sites, the simplest model failed to identify a potentially important dispersal barrier, open habitat that butterflies rarely enter, which may completely isolate some of the proposed restoration sites from other breeding sites. Finally, we found that, although the gain in predicting dispersal with increasing model complexity was small, so was the increase in financial cost. Furthermore, a greater fit continued to accrue with greater financial cost, and more complex models made substantially different predictions than simple models when applied to a novel landscape in which butterflies are to be reintroduced to bolster their populations. This suggests that more complex models might be justifiable on financial grounds. Our results caution against a pure parsimony approach to deciding how complex movement models need to be to accurately predict dispersal through the matrix, especially if the models are to be applied to novel or modified landscapes.     

Imperfectly optimal animals

Summary We consider models of behavior that apply to two different problems: when a predator should leave a foraging site and how a female should choose the best available male. In each case we derive rules for an optimal solution to the problem. We also derive models based on very simple, plausible rules of behavior that we suspect animals may actually use. Although the expected payoffs from optimality models always exceed the expected payoffs from our simpler behavioral models, under certain conditions the difference is not large. When good foraging sites last but a short time and when females' mobility in their habitat is limited, the results of simple models and optimal models are very close indeed.Because of the difficulty of distinguishing between the results of each type of model and because natural selection will presumably provide a best mix of solutions to a range of problems rather than a best solution to any one problem, we suggest that behavioral ecologists expend more effort on simple, plausible models of animal behavior. Such models provide ready-made testable hypotheses about the animal's approximation to optimality and about the actual mechanisms of behavior.     

How do simple energy activities comprise complex behavior of life systems?: A conceptual synthesis and decomposition of the energy structure of life systems

Reduction and synthesis has always been Science’s way to learn about complex systems. The problem is, of course, that after studying the behavior of the system components, the reconstruction of system behavior cannot be any simple summation of the behavior of the individual components. How should we go about with the reconstruction is an umbrella question addressed in the paper. In particular, one should ask what is the contribution of each component to the system, and what kind and quantitative relations do the connections among the components signify in the total system? Answering these questions is necessary to understand the internal mechanism of a life system, the regularity of its dynamics, and the nature of the control mechanisms.The general approach of the paper is based on the assumption that the life energy transmission structure of the system is the fundamental principle of reduction and synthesis.The paper generalizes the energy transmission in terms of two basic types, based upon the mode of linkage in energy activities, such as sequential or parallel. The basic mathematical concept is an eigenparameter analysis in a model called Life Energy System Model (LESM). Simple examples illustrate the models application. It is true that the energy transmission structure of a natural life system is usually very complex, in which case the analysis has to incorporate more details than shown in the paper. Yet, the analysis still follows the same fundamental principle as outlined.     

Implications of different population model structures for management of threatened plants

Population viability analysis (PVA) is a reliable tool for ranking management options for a range of species despite parameter uncertainty. No one has yet investigated whether this holds true for model uncertainty for species with complex life histories and for responses to multiple threats. We tested whether a range of model structures yielded similar rankings of management and threat scenarios for 2 plant species with complex postfire responses. We examined 2 contrasting species from different plant functional types: an obligate seeding shrub and a facultative resprouting shrub. We exposed each to altered fire regimes and an additional, species‐specific threat. Long‐term demographic data sets were used to construct an individual‐based model (IBM), a complex stage‐based model, and a simple matrix model that subsumes all life stages into 2 or 3 stages. Agreement across models was good under some scenarios and poor under others. Results from the simple and complex matrix models were more similar to each other than to the IBM. Results were robust across models when dominant threats are considered but were less so for smaller effects. Robustness also broke down as the scenarios deviated from baseline conditions, likely the result of a number of factors related to the complexity of the species’ life history and how it was represented in a model. Although PVA can be an invaluable tool for integrating data and understanding species’ responses to threats and management strategies, this is best achieved in the context of decision support for adaptive management alongside multiple lines of evidence and expert critique of model construction and output.     

A note on the sufficiency of low resolution ecosystem models

Analysis of a system of non-linear differential equations illustrates the effects of interactions between biotic and abiotic components of a complex aquatic ecosystem model. A stochastic analysis shows that the variance of the abiotic variables is related in a simple manner to the autocorrelation function of the biotic variables. The results suggest that for oligotrophic and eutrophic conditions, relatively simple ecosystem models may be sufficient for studies of an aquatic environment. Under mesotrophic conditions, the high state variable resolution of a complex model may be necessary.     

Assessment of uncertainties in expert knowledge, illustrated in fuzzy rule-based models

The coherence between different aspects in the environmental system leads to a demand for comprehensive models of this system to explore the effects of different management alternatives. Fuzzy logic has been suggested as a means to extend the application domain of environmental modelling from physical relations to expert knowledge. In such applications the expert describes the system in terms of fuzzy variables and inference rules. The result of the fuzzy reasoning process is a numerical output value. In such a model, as in any other, the model context, structure, technical aspects, parameters and inputs may contribute uncertainties to the model output. Analysis of these contributions in a simplified model for agriculture suitability shows how important information about the accuracy of the expert knowledge in relation to the other uncertainties can be provided. A method for the extensive assessment of uncertainties in compositional fuzzy rule-based models is proposed, combining the evaluation of model structure, input and parameter uncertainties. In an example model, each of these three appear to have the potential to dominate aggregated uncertainty, supporting the relevance of an ample uncertainty approach.     

Flexible hierarchical mark-recapture modeling for open populations using WinBUGS

Hierarchical mark-recapture models offer three advantages over classical mark-recapture models: (i) they allow expression of complicated models in terms of simple components; (ii) they provide a convenient way of modeling missing data and latent variables in a way that allows expression of relationships involving latent variables in the model; (iii) they provide a convenient way of introducing parsimony into models involving many nuisance parameters. Expressing models using the complete data likelihood we show how many of the standard mark-recapture models for open populations can be readily fitted using the software WinBUGS. We include examples that illustrate fitting the Cormack–Jolly–Seber model, multi-state and multi-event models, models including auxiliary data, and models including density dependence.

Mortality and predation in ecosystem models: is it important how these are expressed?

The effects of the form of the grazing and mortality terms used in plankton models are well known. The same cannot be said for ecosystem models. As ecosystem models become more popular more needs to be known about the effects of model formulation on model behaviour and performance. The impact of the form of the grazing response function and mortality terms used in a biogeochemical ecosystem model are considered here. We show that in the large and inter-linked webs used in ecosystem models, model behaviour is far more sensitive to the form of the grazing term than to that of the mortality terms that close the modelled food web.When using biogeochemical ecosystem models in shallow marine ecosystems, the most dynamic and sophisticated functional responses describing grazing require more parameters and validation than the simpler Holling disk equation, but usually still lead to the same general conclusions about the system state and the effects of changes in forcing functions. Thus, the use of more complex functional responses is not necessarily warranted in many cases. Similarly, the extra effort and data required to explicitly represent the top predators (sharks, mammals and birds) is not necessary if they are not the focus of the study. A quadratic mortality term applied to intermediate predators (such as piscivores) is sufficient to achieve plausible model behaviour. It should be noted, however, that some degree of sophistication is required in the grazing and mortality terms. Use of simple linear functional responses and mortality terms is unsuitable for models used to consider a range of nutrient loading or harvesting scenarios.     

Linking male qualities to multiple display traits: an example in a fish with exclusive male care

Recent theoretical models predict that the relative allocation to advertisement and parental care depends on whether paternal care is necessary for offspring survival: In species with exclusive male care, male investment in attraction is expected to reliably indicate paternal care effort and male phenotypic quality. Previous research, yielding contrasting results, has considered how one trait involved in mate attraction interacts with parental care or a specific aspect of male quality. In the blenny Salaria pavo, we perform a comprehensive analysis of the interplay between overall male attractiveness and male quality, the latter in terms of fertility, condition, and parental care. In this fish, males are larger than females, exhibit two sexually dimorphic traits (head crest and anal glands), and solely care for eggs. We generated a male attractiveness index through principal component analyses of morphological traits and quantified parental effort as the total time spent in egg care. In addition, we analyzed the relationships between specific components of attractiveness and male qualities. In agreement with theory predictions, we found that male overall attractiveness is a reliable indicator of fertility, in terms of sperm number, but is unrelated to body condition and parental care effort, with males able to perform high levels of care regardless of their level of advertisement. However, the relative expression of head crest area appears positively related to sperm number but is traded-off with parental care effort. These findings underline the need, in addressing real patterns, to consider interactions between multiple aspects of male display and quality.     

Developing shared qualitative models for complex systems

Understanding complex systems is essential to ensure their conservation and effective management. Models commonly support understanding of complex ecological systems and, by extension, their conservation. Modeling, however, is largely a social process constrained by individuals’ mental models (i.e., a small-scale internal model of how a part of the world works based on knowledge, experience, values, beliefs, and assumptions) and system complexity. To account for both system complexity and the diversity of knowledge of complex systems, we devised a novel way to develop a shared qualitative complex system model. We disaggregated a system (carbonate coral reefs) into smaller subsystem modules that each represented a functioning unit, about which an individual is likely to have more comprehensive knowledge. This modular approach allowed us to elicit an individual mental model of a defined subsystem for which the individuals had a higher level of confidence in their knowledge of the relationships between variables. The challenge then was to bring these subsystem models together to form a complete, shared model of the entire system, which we attempted through 4 phases: develop the system framework and subsystem modules; develop the individual mental model elicitation methods; elicit the mental models; and identify and isolate differences for exploration and identify similarities to cocreate a shared qualitative model. The shared qualitative model provides opportunities to develop a quantitative model to understand and predict complex system change.     

A state-dependent model for the optimal management of an invasive metapopulation.

Management of invasive species involves choosing between different management strategy options, but often the best strategy for a particular scenario is not obvious. We illustrate the use of optimization methods to determine the most efficient management strategy using one of the most devastating invasive forest pests in North America, the gypsy moth (Lymantria dispar), as a case study. The optimization approach involves the application of stochastic dynamic programming (SDP) to a metapopulation framework with different infestation patch sizes, with the goal of minimizing infestation spread. We use a novel "moving window" approach as a way to address a spatially explicit problem without being explicitly spatial. We examine results for two cases in order to develop general rules of thumb for management. We explore a model with limited parameter information and then assess how strategies change with specific parameterization for the gypsy moth. The model results in a complex but stable, state-dependent management strategy for a multiyear management program that is robust even under situations of uncertainty. The general rule of thumb for the basic model consists of three strategies: eradicating medium-density infestations, reducing large-density infestations, and reducing the colonization rate from the main infestation, depending on the state of the system. With specific gypsy moth parameterization, reducing colonization decreases in importance relative to the other two strategies. The application of this model to gypsy moth management emphasizes the importance of managing based on the state of the system, and if applied to a specific geographic area, has the potential to substantially improve the efficiency and cost-effectiveness of current gypsy moth eradication programs, helping to slow the spread of this pest. Additionally, the approach used for this particular invasive species can be extended to the optimization of management programs for the spread of other invasive and problem species exhibiting metapopulation dynamics.     

State-of-the-art of ecological modelling with emphasis on development of structural dynamic models

The paper deals with two major problems in ecological modelling today, namely how to get reliable parameters? and how to build ecosystem properties into our models? The use of new mathematical tools to answer these questions is mentioned briefly, but the main focus of the paper is on development of structural dynamic models which are models using goal functions to reflect a current change of the properties of the biological components in the models. These changes of the properties are due to the enormous adaptability of the biological components to the prevailing conditions. All species in an ecosystem attempt to obtain most biomass, i.e. to move as far away as possible from thermodynamic equilibrium which can be measured by the thermodynamic concept exergy. Consequently, exergy has been proposed as a goal function in ecological models with dynamic structure, meaning currently changed properties of the biological components and in model language currently changed parameters. An equation to compute an exergy index of a model is presented. The theoretical considerations leading to this equation are not presented here but references to literature where the basis theory can be found are given. Two case studies of structural dynamic modelling are presented: a shallow lake where the structural dynamic changes have been determined before the model was developed, and the application of biomanipulation in lake management, where the structural dynamic changes are generally known. Moreover. it is also discussed how the same idea of using exergy as a goal function in ecological modelling may be applied to facilitate the estimation of parameters.     

Two-goal regional environmental policy: The case of the Santa Ana river basin

In determining public policy measures, the value of information about the functional relationships between targets and instruments can hardly be understated. In the present paper these macrorelations are obtained for a competitive industry by way of aggregation over many individual firms following simple behavioristic patterns. With the exact knowledge of the macrorelations, obtaining the numerical values of the instruments becomes a simple mathematical programming problem. These principles are applied in examination of the water pollution problems generated by the dairy industry in the Santa Ana River Basin where local governments face the problem of controlling environmental quality with minimum opportunity costs in terms of output.     

Uncertainty in epidemiology and health risk and impact assessment

Environmental epidemiology and health risk and impact assessment have long grappled with problems of uncertainty in data and their relationships. These uncertainties have become more challenging because of the complex, systemic nature of many of the risks. A clear framework defining and quantifying uncertainty is needed. Three dimensions characterise uncertainty: its nature, its location and its level. In terms of its nature, uncertainty can be both intrinsic and extrinsic. The former reflects the effects of complexity, sparseness and nonlinearity; the latter arises through inadequacies in available observational data, measurement methods, sampling regimes and models. Uncertainty occurs in three locations: conceptualising the problem, analysis and communicating the results. Most attention has been devoted to characterising and quantifying the analysis—a wide range of statistical methods has been developed to estimate analytical uncertainties and model their propagation through the analysis. In complex systemic risks, larger uncertainties may be associated with conceptualisation of the problem and communication of the analytical results, both of which depend on the perspective and viewpoint of the observer. These imply using more participatory approaches to investigation, and more qualitative measures of uncertainty, not only to define uncertainty more inclusively and completely, but also to help those involved better understand the nature of the uncertainties and their practical implications.