Social network analysis and valid Markov chain Monte Carlo tests of null models

Analyses of animal social networks derived from group-based associations often rely on randomisation methods developed in ecology (Manly, Ecology 76:1109–1115, 1995) and made available to the animal behaviour community through implementation of a pair-wise swapping algorithm by Bejder et al. (Anim Behav 56:719–725, 1998). We report a correctable flaw in this method and point the reader to a wider literature on the subject of null models in the ecology literature. We illustrate the importance of correcting the method using a toy network and use it to make a preliminary analysis of a network of associations among eagle rays.

Quantifying parameter uncertainty in a coral reef model using Metropolis-Coupled Markov Chain Monte Carlo

Coral reefs are threatened ecosystems, so it is important to have predictive models of their dynamics. Most current models of coral reefs fall into two categories. The first is simple heuristic models which provide an abstract understanding of the possible behaviour of reefs in general, but do not describe real reefs. The second is complex simulations whose parameters are obtained from a range of sources such as literature estimates. We cannot estimate the parameters of these models from a single data set, and we have little idea of the uncertainty in their predictions.We have developed a compromise between these two extremes, which is complex enough to describe real reef data, but simple enough that we can estimate parameters for a specific reef from a time series. In previous work, we fitted this model to a long-term data set from Heron Island, Australia, using maximum likelihood methods. To evaluate predictions from this model, we need estimates of the uncertainty in our parameters. Here, we obtain such estimates using Bayesian Metropolis-Coupled Markov Chain Monte Carlo. We do this for versions of the model in which corals are aggregated into a single state variable (the three-state model), and in which corals are separated into four state variables (the six-state model), in order to determine the appropriate level of aggregation. We also estimate the posterior distribution of predicted trajectories in each case.In both cases, the fitted trajectories were close to the observed data, but we had doubts about the biological plausibility of some parameter estimates. We suggest that informative prior distributions incorporating expert knowledge may resolve this problem. In the six-state model, the posterior distribution of state frequencies after 40 years contained two divergent community types, one dominated by free space and soft corals, and one dominated by acroporid, pocilloporid, and massive corals. The three-state model predicts only a single community type. We conclude that the three-state model hides too much biological heterogeneity, but we need more data if we are to obtain reliable predictions from the six-state model. It is likely that there will be similarly large, but currently unevaluated, uncertainty in the predictions of other coral reef models, many of which are much more complex and harder to fit to real data.     

Nutrient criteria for lakes,ponds, and reservoirs: A Bayesian TREED model approach

We develop regional-scale eutrophication models for lakes, ponds, and reservoirs to investigate the link between nutrients and chlorophyll-a. The Bayesian TREED (BTREED) model approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the empirical water quality model. Nutrient data for lakes, ponds, and reservoirs across the United States were obtained from the Environmental Protection Agency (EPA) National Nutrient Criteria Database. The nutrient data consist of measurements for both stressor variables (such as total nitrogen and total phosphorus), and response variables (such as chlorophyll-a), used in the BTREED model. Markov chain Monte Carlo (McMC) posterior exploration guides a stochastic search through a rich suite of candidate trees toward models that better fit the data. The Bayes factor provides a goodness of fit criterion for comparison of resultant models. We randomly split the data into training and test sets; the training data were used in model estimation, and the test data were used to evaluate out-of-sample predictive performance of the model. An average relative efficiency of 1.02 between the training and test data for the four highest log-likelihood models suggests good out-of-sample predictive performance. Reduced model uncertainty relative to over-parameterized alternative models makes the BTREED models useful for nutrient criteria development, providing the link between nutrient stressors and meaningful eutrophication response.     

Multiple-pattern parameter identification and uncertainty analysis approach for water quality modeling

This paper presents a multiple-pattern parameter identification and uncertainty analysis approach for robust water quality modeling using a neural network (NN) embedded genetic algorithm (GA). The modeling approach uses an adaptive NN–GA framework to inversely solve the governing equations in a water quality model for multiple parameter patterns, along with an alternating fitness method to maintain solution diversity. The procedure was demonstrated through a coupled 2D hydrodynamic and eutrophication model for Loch Raven Reservoir in Maryland. The inverse problem was formulated as a nonlinear optimization problem minimizing the degree of misfit (DOM) between model results and observed data. A set of NN models was developed to approximate the input-output response relationship of the Loch Raven Reservoir model and was incorporated into a GA framework in an adaptive fashion to search for near-optimal solutions minimizing the DOM. The numerical example showed that the adaptive NN–GA approach is capable of identifying multiple parameter patterns that reproduce the observed data equally well. The resulting parameter patterns were incorporated into the numerical model, and a multiple-pattern robust water quality modeling analysis, along with a compound margin of safety (CMOS) method, was proposed and applied to analyze the parameter pattern uncertainty.     

RIVPACS models for predicting the expected macroinvertebrate fauna and assessing the ecological quality of rivers

The European Union Water Framework Directive recognises the need for and value of biological monitoring. This paper reviews the modelling approach known as River Invertebrate Prediction and Classification System (RIVPACS for assessing the ecological quality of river sites using macroinvertebrate sampling. The RIVPACS philosophy is to develop statistical relationships between the fauna and the environmental characteristics of a large set of high quality reference sites which can be used to predict the macroinvertebrate fauna to be expected at any site in the absence of pollution or other environmental stress. The observed fauna at new test sites can then be compared with their site-specific expected fauna to derive indices of ecological quality. All methodological decisions in any such model development have implications for the reliability, precision and robustness of any resulting indices for assessing the ecological quality and ecological grade (‘status’) of individual river stretches. The choice of reference sites and environmental predictor variables, the site classification and discrimination methods, the estimation of the expected fauna, and indices for comparing the agreement, or lack of it, between the observed and expected fauna, are all discussed. The indices are assessed on the reference sites and on a separate test set of 340 sites, which are subject to a wide range of types and degrees of impairment.     

Proposing an information criterion for individual-based models developed in a pattern-oriented modelling framework

Individual-based models (IBMs) have been improved in quality and reliability in recent years with an approach called pattern-oriented modelling (POM). POM proposes guidelines to develop models reproducing multiple patterns observed on the field and to test systematically how well the IBMs reproduce them. POM studies used generally traditional methods of goodness of fit such as the sum of squares evaluation or ad hoc comparisons of fitting errors and variations. Model selection, however, can be a rigorous statistical approach based on information theory and information criteria such as the Akaike's information criterion (AIC) or the deviance information criterion (DIC). So far, it has not been tried to link POM to these rigorous techniques. The main problems to achieve that are: (a) the difficulty to have likelihood functions for IBMs’ parameters and (b) the possibility to obtain posterior distributions of IBMs’ parameters given the patterns to reproduce. In a first part, this paper answers problem (a) by proposing and explaining how to calculate a deviance measure (POMDEV) for models developed in a context of POM. And while answering the second problem, a second part of the paper proposes an information criterion for model selection in a POM context (the pattern-oriented modelling information criterion: POMIC). This criterion does not yet have the same theoretical foundation as, e.g., AIC, but uses formal analogies to the DIC. In a third part POMIC is tested with a modelling exercise. This exercise shows the potential of POMIC to use multiple patterns for selecting among multiple potential submodels and eventually select the most parsimonious and well fitting model version. We conclude that POMIC, although being a heuristically derived approach, can greatly improve the POM framework.     

Methods for estimating the uncertainty in emergy table-form models

Emergy studies have suffered criticism due to the lack of uncertainty analysis and this shortcoming may have directly hindered the wider application and acceptance of this methodology. Recently, to fill this gap, the sources of uncertainty in emergy analysis were described and analytical and stochastic methods were put forward to estimate the uncertainty in unit emergy values (UEVs). However, the most common method used to determine UEVs is the emergy table-form model, and only a stochastic method (i.e., the Monte Carlo method) was provided to estimate the uncertainty of values calculated in this way. To simplify the determination of uncertainties in emergy analysis using table-form calculations, we introduced two analytical methods provided by the Guide to the Expression of Uncertainty in Measurement (GUM), i.e., the Variance method and the Taylor method, to estimate the uncertainty of emergy table-form calculations for two different types of data, and compared them with the stochastic method in two case studies. The results showed that, when replicate data are available at the system level, i.e., the same data on inputs and output are measured repeatedly in several independent systems, the Variance method is the simplest and most reliable method for determining the uncertainty of the model output, since it considers the underlying covariance of the inputs and requires no assumptions about the probability distributions of the inputs. However, when replicate data are only available at the subsystem level, i.e., repeat samples are measured on subsystems without specific correspondence between an output and a certain suite of inputs, the Taylor method will be a better option for calculating uncertainty, since it requires less information and is easier to understand and perform than the Monte Carlo method.     

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).     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

From meso- to macro-scale dynamic water quality modelling for the assessment of land use change scenarios

The implementation of the European Water Framework Directive requires reliable tools to predict the water quality situations in streams caused by planned land use changes at the scale of large regional river basins. This paper presents the results of modelling the in-stream nitrogen load and concentration within the macro-scale basin of the Saale river (24,167 km²) using a semi-distributed process-based ecohydrological dynamic model SWIM (Soil and Water Integrated Model). The simulated load and concentration at the last gauge of the basin show that SWIM is capable to provide a satisfactory result for a large basin. The uncertainty analysis indicates the importance of realistic input data for agricultural management, and that the calibration of parameters can compensate the uncertainty in the input data to a certain extent. A hypothesis about the distributed nutrient retention parameters for macro-scale basins was tested aimed in improvement of the simulation results at the intermediate gauges and the outlet. To verify the hypothesis, the retention parameters were firstly proved to have a reasonable representation of the denitrification conditions in six meso-scale catchments. The area of the Saale region was classified depending on denitrification conditions in soil and groundwater into three classes (poor, neutral and good), and the distributed parameters were applied. However, the hypothesis about the usefulness of distributed retention parameters for macro-scale basins was not confirmed. Since the agricultural management is different in the sub-regions of the Saale basin, land use change scenarios were evaluated for two meso-scale subbasins of the Saale. The scenario results show that the optimal agricultural land use and management are essential for the reduction in nutrient load and improvement of water quality to meet the objectives of the European Water Framework Directive and in view of the regional development plans for future.     

Local calibration of coliforms parameters of water quality problem at Igapó I Lake, Londrina, Paraná, Brazil

This article presents results concerning the local calibration of the transport parameters (longitudinal and transversal diffusions and decay coefficient) for a two-dimensional problem of water quality at Igapó I Lake, located in Londrina, Paraná, Brazil, using fecal coliforms as an indicator of water quality. The simulation of fecal coliforms concentrations all over the water body is conducted by means of a structured discretization of the geometry of Igapó I Lake, together with the finite difference and finite element methods. By using the velocity field, modeled by the Navier-Stokes and Poisson equations, the flow of fecal coliforms is described by means of a transport model, which considers advective and diffusive processes, as well as a process of fecal coliforms decay. In the checkpoint, the longitudinal and transversal diffusion coefficients and the coliforms decay coefficient that best fitted the value of the fecal coliforms concentration were D_x = D_y = 0.001 m²/h and k = 0.5 d⁻¹ = 0.02083 h⁻¹. A qualitative and quantitative analysis of the numerical simulations conducted in function of the diffusion coefficients and of the coliforms decay parameter provided a better understanding of the local water quality at Igapó I Lake.     

Environmental indicators as tools for the management of estuaries—Methodology and case study of the Tejo estuary

The need for a better management of estuaries requires an environmental characterization following a methodology that allows the comparison of distinct estuarine systems and the assessment of their evolution. The peculiar characteristics of estuaries, in particular their intrinsic variability, make this characterization difficult and there is no commonly accepted general methodology available. The approach followed in freshwater ecosystems is generally based on the concept of environmental indicators, but such a concept has not been developed for estuaries. Indeed, a different approach is needed here, due to the spatial heterogeneity and the different time scales associated with the processes that control water quality. This paper presents a proposal for a methodology that starts with observed values and uses a procedure to integrate these values in time and space in order to calculatesignificant values, upon whichnormalized indicators are built which take into account criteria based either on legal, scientific or heuristic concentration limits. A normalization is carried out in two steps: (1) application of a mathematical operator to theignificant values, (2) transformation using the concept ofpenalty curves. This methodology may be complemented with the definition ofquality classes, particularly appealing and useful, as tools to communicate with decision makers and the public in general. Water quality data pertaining to the Tejo estuary are used to test the methodology.     

Artificial neural network modeling of the river water quality—A case study

The paper describes the training, validation and application of artificial neural network (ANN) models for computing the dissolved oxygen (DO) and biochemical oxygen demand (BOD) levels in the Gomti river (India). Two ANN models were identified, validated and tested for the computation of DO and BOD concentrations in the Gomti river water. Both the models employed eleven input water quality variables measured in river water over a period of 10 years each month at eight different sites. The performance of the ANN models was assessed through the coefficient of determination (R²) (square of the correlation coefficient), root mean square error (RMSE) and bias computed from the measured and model computed values of the dependent variables. Goodness of the model fit to the data was also evaluated through the relationship between the residuals and model computed values of DO and BOD. The model computed values of DO and BOD by both the ANN models were in close agreement with their respective measured values in the river water. Relative importance and contribution of the input variables to the model output was evaluated through the partitioning approach. The identified ANN models can be used as tools for the computation of water quality parameters.     

The Extended Kalman Filter (EKF) as a tool for the assimilation of high frequency water quality data

The Extended Kalman Filter (EKF) was applied to the analysis of high frequency field measurements of dissolved oxygen (DO), water temperature, salinity, collected by multiparametric sensors in the lagoon of Venice. This paper focuses on the practical aspects of the implementation of the EKF as a data assimilation technique and does not deal with the problems associated with the identification of the model. In this regard, the EKF has proved to be a useful tool for the updating of the estimates of the parameters of a simple DO-chlorophyll model, which can be used for linking the high frequency data to meteorological forcings, such as solar radiation and wind, and to other low frequency measurements of water quality parameters, such as the concentrations of Chlorophyll a and nutrients. The model can subsequently be used as a tool for checking the consistency of all this data, and may also be employed for controlling the quality of the data collected by the multiparametric sensors.     

Design of a water quality monitoring network in a large river system using the genetic algorithm

Despite several decades of operations and the increasing importance of water quality monitoring networks, the authorities still rely on experiential insights and subjective judgments in siting water quality monitoring stations. This study proposes an integrated technique which uses a genetic algorithm (GA) and a geographic information system (GIS) for the design of an effective water quality monitoring network in a large river system. In order to develop a design scheme, planning objectives were identified for water quality monitoring networks and corresponding fitness functions were defined using linear combinations of five selection criteria that are critical for developing a monitoring system. The criteria include the representativeness of a river system, compliance with water quality standards, supervision of water use, surveillance of pollution sources and examination of water quality changes. The fitness levels were obtained through a series of calculations of the fitness functions using GIS data. A sensitivity analysis was performed for major parameters such as the numbers of generations, population sizes and probability of crossover and mutation, in order to determine a good fitness level and convergence for optimum solutions. The proposed methodology was applied to the design of water quality monitoring networks in the Nakdong River system, in Korea. The results showed that only 35 out of 110 stations currently in operation coincide with those in the new network design, therefore indicating that the effectiveness of the current monitoring network should be carefully re-examined. From this study, it was concluded that the proposed methodology could be a useful decision support tool for the optimized design of water quality monitoring networks.     

Study of the water quality close to urban sewers in eastern Ligurian coast by means of bioluminescence tests and conventional analyses

Five municipal sewers with small flow rates (Manarola, Riomaggiore, Portovenere, Tellaro, Bocca di Magra) were studied using the Microtox^® test and a bacterial luminescence bioassay in order to evaluate the water quality in these areas of the eastern Ligurian coast. The work was performed including chemical analysis, microbiological and ecotoxicological assays. Analyses were carried out on both the effluents and the water body close to the pipe discharge. None of the measured chemical parameters exceeded the permitted limits, both in the effluents and in the seawater samples, even if some slightly critical situations were highlighted by the Microtox^® test on the effluents. On the other hand, the Microtox^® appeared to be less effective than another ecotoxicological assay based on the luminescent fraction of epibacteria for the evaluation of seawater quality. The good water quality of the considered areas was assessed although a slightly worse condition was encountered in Bocca di Magra.     

An antibiotic composite electrode for improving the sensitivity of electrochemically active biofilm biosensor

• Antibiotic azithromycin employed in graphite electrode for EAB biosensor. • Azithromycin at 0.5% dosage increased the sensitivity for toxic formaldehyde. • Azithromycin increased the relative abundance of Geobacter. • Azithromycin regulated thickness of electroactive biofilm. Extensive research has been carried out for improved sensitivity of electroactive biofilm-based sensor (EAB-sensor), which is recognized as a useful tool in water quality early-warning. Antibiotic that is employed widely to treat infection has been proved feasible in this study to regulate the EAB and to increase the EAB-biosensor’s sensitivity. A novel composite electrode was prepared using azithromycin (AZM) and graphite powder (GP), namely AZM@GP electrode, and was employed as the anode in EAB-biosensor. Different dosages of AZM, i.e., 2 mg, 4 mg, and 8 mg, referred to as 0.25%, 0.5% and 1% AZM@GP were under examination. Results showed that EAB-biosensor was greatly benefited from appropriate dosage of AZM (0.5% AZM@GP) with reduced start-up time period, comparatively higher voltage output, more readable electrical signal and increased inhibition rate (30%-65% higher than control sensor with GP electrode) when exposing to toxic formaldehyde. This may be attributed to the fact that AZM inhibited the growth of non-EAM without much influence on the physiologic or metabolism activities of EAM under proper dosage. Further investigation of the biofilm morphology and microbial community analysis suggested that the biofilm formation was optimized with reduced thickness and enriched Geobacter with 0.5% AZM@GP dosage. This novel electrode is easily fabricated and equipped, and therefore would be a promising way to facilitate the practical application of EAB-sensors.     

Using a fisheries ecosystem model with a water quality model to explore trophic and habitat impacts on a fisheries stock: A case study of the blue crab population in the Chesapeake Bay

Recent calls for the development of ecosystem-based fisheries management compel the development of resource management tools and linkages between existing fisheries management tools and other resource tools to enable assessment and management of multiple impacts on fisheries resources. In this paper, we describe the use of the Chesapeake Bay Fisheries Ecosystem Model (CBFEM), developed using the Ecopath with Ecosim (EwE) software, and the Chesapeake Bay Water Quality Model (WQM) to demonstrate how linkages between available modeling tools can be used to inform ecosystem-based natural resource management. The CBFEM was developed to provide strategic ecosystem information in support of fisheries management. The WQM was developed to assess impacts on water quality. The CBFEM was indirectly coupled with the WQM to assess the effects of water quality and submerged aquatic vegetation (SAV) on blue crabs. The output from two WQM scenarios (1985-1994), a baseline scenario representing actual nutrient inputs and another with reduced inputs based on a tributary management strategy, was incorporated into the CBFEM. The results suggested that blue crab biomass could be enhanced under management strategies (reduced nutrient input) when the effective search rate of blue crab young-of-the-year's (YOY's) predators or the vulnerability of blue crab YOY to its predators was adjusted by SAV. Such model linkages are important for incorporating physical and biological components of ecosystems in order to explore ecosystem-based fisheries management options.     

Using algal biomass-phosphorus (P) relationships and nutrient limitation theory to evaluate the adequacy of P water quality criteria for regulated monsoon rivers and reservoirs

Different P criteria have been set for lotic and lentic waters where the latter had stricter criteria than the former. The binary P criteria have been developed due to differences in limnological features and this helps avoid unneeded costs with stricter criteria for flowing waters that normally have lower potential of algal blooms. However, if different criteria are warranted, the responses of Chl a to TP and TN:TP ratio should vary distinctively between rivers and reservoirs. Contrary to these predictions, inconsistent and statistically indistinguishable variations have been observed between the two types of waterbody in Chl a yield per unit TP. Additionally, there was no significant difference in the strength of relationship between Chl a and TN:TP ratio between waterbody types, although the mass ratio of TN to TP was significantly higher in reservoirs than in rivers. Hence, the data suggest that there is no scientifically defensible reason that lotic and lentic waters require different TP standards and specifically that lentic waters do not necessarily require stricter P criteria. A more holistic and nuanced approach would aid in developing revised or new TP criteria in which water quality issues can be addressed scientifically as well as pragmatically.