Structure of pathways in ecological networks: relationships between length and number

In ecosystems network, structure determines adjacent (direct) and non-adjacent (indirect) pathways over which energy, matter, and information can flow. The more pathways, the more possible ways the conservative substance can move in zero-sum transactions between network nodes that the pathways interconnect, and the more possible non-conservative, nonzero-sum relations can be secondarily derived from these. Structural analysis is a tool we employ, from a family of input–output methods for exploring zero- and nonzero-sum attributes of environmental networks, to count pathways of varying length between network nodes. In this paper, we examine the relationship between pathway length (k) and number (P_k) as determined by system size (n, number of nodes) and extent and pattern of connectance (C). We develop a measure (m_a) of pathway growth in numbers with increasing length, and then normalize this to the maximum rate possible (m_a/m_c) for a given system size. These measures apply to two pathway types—paths, m_a(0) and m_a(0)/m_c(0), which forbid adjacent node repetitions, and walks, m_a(1) and m_a(1)/m_c(1), which allow them. We find that network size has a curvilinear effect on the pathway number versus length relationship, and extent and pattern of connectance are convolved. Values computed for the paths and walks of three ecosystem models (oyster reef, freshwater marsh, and reservoir cove) are used to compare their pathway structure.     

Dynamic environ analysis of compartmental systems: A computational approach

Ecosystems are often modeled as stocks of matter or energy connected by flows. Network environ analysis (NEA) is a set of mathematical methods for using powers of matrices to trace energy and material flows through such models. NEA has revealed several interesting properties of flow–storage networks, including dominance of indirect effects and the tendency for networks to create mutually positive interactions between species. However, the applicability of NEA is greatly limited by the fact that it can only be applied to models at constant steady states. In this paper, we present a new, computationally oriented approach to environ analysis called dynamic environ approximation (DEA). As a test of DEA, we use it to compute compartment throughflow in two implementations of a model of energy flow through an oyster reef ecosystem. We use a newly derived equation to compute model throughflow and compare its output to that of DEA. We find that DEA approximates the exact results given by this equation quite closely – in this particular case, with a mean Euclidean error ranging between 0.0008 and 0.21 – which gives a sense of how closely it reproduces other NEA-related quantities that cannot be exactly computed and discuss how to reduce this error. An application to calculating indirect flows in ecosystems is also discussed and dominance of indirect effects in a nonlinear model is demonstrated.     

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.     

Justifying Sustainability

In the framework of ethical social choice theory, sustainability is justified by efficiency and equity as ethical axioms. These axioms correspond to the Suppes–Sen grading principle. In technologies that are productive in a certain sense, the set of Suppes–Sen maximal utility paths is shown to equal the set of non-decreasing and efficient paths. Since any such path is sustainable, efficiency and equity can thus be used to deem any unsustainable path as ethically unacceptable. This finding is contrasted with results that seem to indicate that an infinite number of generations cannot be treated equally.     

A Reliability and Risk Analysis System for Multipurpose Reservoir Operation

This paper proposes a reliability analysis system, which can be widely applied to the cases in which a reservoir is operated to meet several purposes such as flood control, energy generation, irrigation, domestic and industrial water supply, etc. The presented system has a structure of three levels.1. Decision-making.2. Tradeoff analysis.3. The third level that mainly consists of three subsystems:i – The reservoir flood risk analysis subsystem by flood control simulation.ii – The benefit promotion subsystem of reservoir operation using Stochastic Dynamic Programming. In this subsystem, the Lagrange multipliers are introduced into the objective function to take into account the water supply failures. This method guarantees that each run of the SDP will necessarily derive a non-inferior policy for reservoir operation.iii – The reservoir operation simulation subsystem to derive the performance indices associated with the reservoir operation policies. With the input and feedback between the second level and the subsystems of the third level, a great deal of efficient operation policies and the associated performance indices can be obtained. Then the tradeoff relationships between different performance indices can be derived for the decision makers. With application to Yudong Reservoir in Yunnan province of China, the presented analysis system is practically tested.     

A mixed Bentham–Rawls criterion for intergenerational equity: Theory and implications

This paper proposes a welfare criterion that balances the need for development and the concern for the least advantaged generations, and explores its implications. This criterion, called the mixed Bentham–Rawls criterion, moderates the effect of discounting, yet permits some degree of intertemporal trade-off. It is a weighted average of two terms: (a) the sum of discounted utilities and (b) the utility level of the least advantaged generation. We derive necessary conditions to characterize growth paths that satisfy our criterion, and show that in some models with familiar dynamic specifications, an optimal path exists and displays appealing characteristics.     

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.     

Animal social networks: an introduction

Network analysis has a long history in the mathematical and social sciences and the aim of this introduction is to provide a brief overview of the potential that it holds for the study of animal behaviour. One of the most attractive features of the network paradigm is that it provides a single conceptual framework with which we can study the social organisation of animals at all levels (individual, dyad, group, population) and for all types of interaction (aggressive, cooperative, sexual etc.). Graphical tools allow a visual inspection of networks which often helps inspire ideas for testable hypotheses. Network analysis itself provides a multitude of novel statistical tools that can be used to characterise social patterns in animal populations. Among the important insights that networks have facilitated is that indirect social connections matter. Interactions between individuals generate a social environment at the population level which in turn selects for behavioural strategies at the individual level. A social network is often a perfect means by which to represent heterogeneous relationships in a population. Probing the biological drivers for these heterogeneities, often as a function of time, forms the basis of many of the current uses of network analysis in the behavioural sciences. This special issue on social networks brings together a diverse group of practitioners whose study systems range from social insects over reptiles to birds, cetaceans, ungulates and primates in order to illustrate the wide-ranging applications of network analysis. This contribution is part of the special issue “Social Networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James).     

Estimation of total sediment load concentration obtained by experimental study using artificial neural networks

Estimation of sediment concentration in rivers is very important for water resources projects planning and managements. The sediment concentration is generally determined from the direct measurement of sediment concentration of river or from sediment transport equations. Direct measurement is very expensive and cannot be conducted for all river gauge stations. However, sediment transport equations do not agree with each other and require many detailed data on the flow and sediment characteristics. The main purpose of the study is to establish an effective model which includes nonlinear relations between dependent (total sediment load concentration) and independent (bed slope, flow discharge, and sediment particle size) variables. In the present study, by performing 60 experiments for various independent data, dependent variables were obtained, because of the complexity of the phenomena, as a soft computing method artificial neural networks (ANNs) which is the powerful tool for input–output mapping is used. However, ANN model was compared with total sediment transport equations. The results show that ANN model is found to be significantly superior to total sediment transport equations.     

Combining state and transition models with dynamic Bayesian networks

Bashari et al. (2009) propose combining state and transition models (STMs) with Bayesian networks for decision support tools where the focus is on modelling the system dynamics. There is already an extension of Bayesian networks - so-called dynamic Bayesian networks (DBNs) - for explicitly modelling systems that change over time, that has also been applied in ecological modelling. In this paper we propose a combination of STMs and DBNs that overcome some of the limitations of Bashari et al.’s approach including providing an explicit representation of the next state, while retaining its advantages, such an the explicit representation of transitions. We then show that the new model can be applied iteratively to predict into the future consistently with different time frames. We use Bashari et al.’s rangeland management problem as an illustrative case study. We present a comparative complexity analysis of the different approaches, based on the structure inherent in the problem being modelled. This analysis showed that any models that explicitly represent all the transitions only remain tractable when there are natural constraints in the domain. Thus we recommend modellers should analyse these aspects of their problem before deciding whether to use the framework.     

A global Bayesian sensitivity analysis of the 1d SimSphere soil–vegetation–atmospheric transfer (SVAT) model using Gaussian model emulation

Sensitivity analysis consists of an integral and important validatory check of a computer simulation model before the code is used in performing any kind of analysis operation. The present paper demonstrates the use of a relatively new method and tool for conducting global sensitivity analysis (GSA) for environmental models, providing simultaneously the first GSA study of the widely used 1d soil–vegetation–atmospheric transfer (SVAT) model named SimSphere. A software platform called the Gaussian emulation machine for sensitivity analysis (GEM SA), which has been developed for performing a GSA via Bayesian theory, is applied to SimSphere model in order to identify the most responsive model inputs to the simulation of key model outputs, detect their interactions and derive absolute sensitivity measures concerning the model structure. This study is also very timely in that, use of this particular SVAT model is currently being considered to be used in a scheme being developed for the operational retrieval of the soil surface moisture content by National Polar-orbiting Operational Environmental Satellite System (NPOESS), in a series of satellite platforms that are due to be launched in the next 12 years starting from 2016.The employed GSA method was found capable of identifying the most responsive SimSphere inputs and also of capturing their key interactions for each of the simulated target quantities on which the GSA was conducted. The most sensitive model inputs were the topography parameters (slope, aspect) as well as the fractional vegetation cover and soil surface moisture availability. The implications of these findings for the future use of SimSphere are discussed.     

Strategic environmental policy; eco-dumping or a green strategy?

The Porter hypothesis claims that a strong environmental policy best serves the interests of a nation's export industry. While this hypothesis seems to be based on some form of bounded rationality, this paper argues that governments may have good reasons for setting an especially strong environmental policy even though firms are fully rational. If the available abatement technology turns the environment into an “inferior input”, competitiveness is spurred by a strong environmental policy. The government should take advantage of this, and set an especially strict emission quota or an especially high emission tax. The findings in the paper also has consequences for the desirability of international cooperation with respect to national environmental policy. If a strict environmental policy spurs competitiveness, the environment is better protected without cooperation.     

Potential banana skins in animal social network analysis

Social network analysis is an increasingly popular tool for the study of the fine-scale and global social structure of animals. It has attracted particular attention by those attempting to unravel social structure in fission–fusion populations. It is clear that the social network approach offers some exciting opportunities for gaining new insights into social systems. However, some of the practices which are currently being used in the animal social networks literature are at worst questionable and at best over-enthusiastic. We highlight some of the areas of method, analysis and interpretation in which greater care may be needed in order to ensure that the biology we extract from our networks is robust. In particular, we suggest that more attention should be given to whether relational data are representative, the potential effect of observational errors and the choice and use of statistical tests. The importance of replication and manipulation must not be forgotten, and the interpretation of results requires care. This contribution is part of the special issue “Social Networks: new perspectives” (Guest Editors: J. Krause, D. Lusseau and R. James).     

Radial basis function networks with partially classified data

The problem of estimating a classification rule with partially classified observations, which often occurs in biological and ecological modelling, and which is of major interest in pattern recognition, is discussed. Radial basis function networks for classification problems are presented and compared with the discriminant analysis with partially classified data, in situations where some observations in the training set are unclassified. An application on a set of morphometric data obtained from the skulls of 288 specimens of Microtus subterraneus and Microtus multiplex is performed. This example illustrates how the use of both classified and unclassified observations in the estimate of the hidden layer parameters has the potential to greatly improve the network performances.     

Control system approaches to ecological systems analysis: Invariants and frequency response

The steady-state assumption is a mainstay for the analysis of ecological systems with more than three or four states. However, it is well accepted in ecology that inputs to large systems come in pulses assumed to have a reasonably constant magnitude and frequency. Steady pulse inputs and the use of electro-chemical–mechanical control systems methodology enables limited short term dynamic responses of ecological systems of a scale often occurring in systems of potential engineering importance to be analyzed. This paper explores and presents a survey of multi-input–multi-output (MIMO) control systems analysis of ecosystem network models to better understand pulse frequency issues and further develop experimentally verifiable approaches to testing the MIMO concept. The analysis process is demonstrated using two network model exemplars. Two aspects of MIMO analyses appear relevant to understanding ecological systems: (1) Eigenvalue invariant analyses and singular value decomposition (SVD) analyses enable assessment of stability and relative strength of states. Eigenvalues reflect time constants and provide a check on experimentally determined system matrices. (2) Analysis of SVD versus frequency for each output indicates maximum pulse frequencies that allow system components to benefit from pulsing. As a group, MIMO analyses complement other analytical methods and provide a theoretical systems focus convenient for analyzing ecosystems from an engineering perspective.     

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.     

Urban ecosystem health assessment based on emergy and set pair analysis—A comparative study of typical Chinese cities

Regarding various energy and materials flowing in the urban ecosystem and the merit of emergy as an embodied energetic equivalent for integrated ecological economic evaluation, an evaluation framework of emergy-based urban ecosystem health indicators (UEHI_em) was established in view of five aspects including vigor, structure, resilience, ecosystem service function maintenance and environmental impact to depict the urban ecosystem health states. Further, set pair analysis (SPA) was employed to assess the urban ecosystem health level based on the UEHI_em, by which the approximate degree of real index set to the optimal one was defined and evaluated to describe the relative health state of the concerned urban ecosystems. Choosing twenty typical Chinese cities in 2005 as cases, we evaluated and compared their urban ecosystem health levels based on UEHI_em and SPA. The results showed that health levels of Xiamen, Qingdao, Shenzhen and Shanghai are pretty well, while those of Wuhan, Harbin, Yinchuan, Beijing and Urumchi are relatively weak. Moreover, the relative health levels were analyzed by SPA to discern the influences of the mentioned five aspects on the UEHI_em. It is concluded that emergy synthesis combined with SPA can serve as an effective relative-measure to compare different ecosystem health levels of urban ecosystems.     

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.     

An analysis of joint costs in a managed forest ecosystem

This paper analyzes the tenability of line item budgeting and independently determined output costs for a managed forest ecosystem. The general problem of cost allocation in a joint production system is discussed as one of choosing paths of integration. A production structure is hypothesized for describing a managed forest ecosystem and its characteristics of “jointness” are discussed. Finally, an empirical case example is presented which indicates that cost estimates and associated means of production which result from single output costing procedures and from joint costing procedures may be significantly different in a managed forest ecosystem.