Hierarchical Bayesian space-time models

Space-time data are ubiquitous in the environmental sciences. Often, as is the case with atmo- spheric and oceanographic processes, these data contain many different scales of spatial and temporal variability. Such data are often non-stationary in space and time and may involve many observation/prediction locations. These factors can limit the effectiveness of traditional space- time statistical models and methods. In this article, we propose the use of hierarchical space-time models to achieve more flexible models and methods for the analysis of environmental data distributed in space and time. The first stage of the hierarchical model specifies a measurement- error process for the observational data in terms of some 'state' process. The second stage allows for site-specific time series models for this state variable. This stage includes large-scale (e.g. seasonal) variability plus a space-time dynamic process for the anomalies'. Much of our interest is with this anomaly proc ess. In the third stage, the parameters of these time series models, which are distributed in space, are themselves given a joint distribution with spatial dependence (Markov random fields). The Bayesian formulation is completed in the last two stages by speci- fying priors on parameters. We implement the model in a Markov chain Monte Carlo framework and apply it to an atmospheric data set of monthly maximum temperature.     

Solving multidimensional bioeconomic problems with singular-perturbation reduction methods: Application to managing pest resistance to pesticidal crops

We investigate the application of ‘singular-perturbation’ reduction methods from the dynamical-systems literature to solve continuous-time multidimensional bioeconomic models resulting from integrating economics with increasingly complex biological structures. These methods reduce multidimensional solution space to the lower-dimensional subspace confining long-term dynamics. They arise naturally in problems with state variables evolving on widely disparate time scales. In particular, we demonstrate how the methods reduce the solution space of a linear-control specification—characterized by two state variables adjusting at widely disparate rates—to a single differential equation in the slow variable. All other system variables are determined by algebraic equations. We apply singular-perturbation methods to investigate the optimal management of pest resistance to pesticidal crops. The pest population evolves on a fast-time scale, while the population's genetic composition evolves on a slow-time scale. In comparison with past work, we can more fully characterize the continuous-time dynamics associated with a complex genetic specification.     

When is a Life Too Costly to Save? The Evidence from U.S. Environmental Regulations

Under certain environmental statutes the EPA is required to balance costs and benefits in setting standards, whereas under others this is prohibited. This paper examines EPA regulatory decisions made under three statues, two of which require balancing and one of which does not. Using discrete choice models, we find that costs and benefits are significant explanatory variables for all three sets of decisions. This suggests that balancing occurred in each case; however, the value (implicit in these decisions) of avoiding a cancer case varies widely. We also find that a 1987 court ruling effectively curtailed whatever balancing occurred under the statute that prohibited it.     

3 forest simulation model

The 3 forest simulation model is a process model of tree growth, carbon and nitrogen dynamics in a single-species, even-aged forest stand. It is based on the model. Major changes include the computation of sun angle and radiation as a function of latitude and day of the year, the closed-form integration of canopy production as a function of day and hour, the introduction of tree number, height, and diameter as separate state variables, and different growth strategies, mortalities, and resulting self-thinning as function of crowding competition.The tree/soil system is described by a set of nonlinear ordinary differential equations for the state variables: tree number, base diameter, tree height, wood biomass, nitrogen in wood, leaf mass, fine root mass, fruit biomass, assimilate, carbon and nitrogen in litter, carbon and nitrogen in soil organic matter, and plant-available nitrogen. The model includes explicit formulations of all relevant ecophysiological processes such as: computation of radiation as a function of seasonal time, daytime and cloudiness, light attenuation in the canopy, and canopy photosynthesis as function of latitude, seasonal time, and daytime, respiration of all parts, assimilate allocation, increment formation, nitrogen fixation, mineralization, humification and leaching, forest management (thinning, felling, litter removal, fertilization etc.), temperature effects on respiration and decomposition, and environmental effects (pollution damage to photosynthesis, leaves, and fine roots). Only ecophysiological parameters which can be either directly measured or estimated with reasonable certainty are used. 3 is a generic process model which requires species- and site-specific parametrization. It can be applied to deciduous and coniferous forests under tropical, as well as temperate or boreal conditions.The paper presents a full documentation of the mathematical model as well as representative simulation results for spruce and acacia.     

treedyn3 forest simulation model

The treedyn3 forest simulation model is a process model of tree growth, carbon and nitrogen dynamics in a single-species, even-aged forest stand. It is based on the treedyn model. Major changes include the computation of sun angle and radiation as a function of latitude and day of the year, the closed-form integration of canopy production as a function of day and hour, the introduction of tree number, height, and diameter as separate state variables, and different growth strategies, mortalities, and resulting self-thinning as function of crowding competition.The tree/soil system is described by a set of nonlinear ordinary differential equations for the state variables: tree number, base diameter, tree height, wood biomass, nitrogen in wood, leaf mass, fine root mass, fruit biomass, assimilate, carbon and nitrogen in litter, carbon and nitrogen in soil organic matter, and plant-available nitrogen. The model includes explicit formulations of all relevant ecophysiological processes such as: computation of radiation as a function of seasonal time, daytime and cloudiness, light attenuation in the canopy, and canopy photosynthesis as function of latitude, seasonal time, and daytime, respiration of all parts, assimilate allocation, increment formation, nitrogen fixation, mineralization, humification and leaching, forest management (thinning, felling, litter removal, fertilization etc.), temperature effects on respiration and decomposition, and environmental effects (pollution damage to photosynthesis, leaves, and fine roots). Only ecophysiological parameters which can be either directly measured or estimated with reasonable certainty are used. treedyn3 is a generic process model which requires species- and site-specific parametrization. It can be applied to deciduous and coniferous forests under tropical, as well as temperate or boreal conditions.The paper presents a full documentation of the mathematical model as well as representative simulation results for spruce and acacia.     

Some stochastic differential equation models of an aquatic ecosystem

A set of stochastic differential equations has been used to model an aquatic ecosystem. The randomness in the system has been introduced through initial conditions of the state variables, parameters, and input variables (light and temperature). These models were analysed using Monte Carlo simulation procedures and the results were similar to those observed in the experimental and field data. They were different, however, from the results of a deterministic simulation. This approach allows us to incorporate the maximum degree of information in the model and to study the behavior of the system without arbitrarily manipulating the values of the parameters. Some possible refinements and generalizations of this approach are also discussed.     

Spatial and temporal hydrodynamic and water quality modeling analysis of a large reservoir on the South Carolina (USA) coastal plain

Two-dimensional, 31-segment, 61-channel hydrodynamic and water quality models of Lake Marion (surface area 330.7 km²; volume 1548.3×10⁶ m³) were developed using the WASP5 modeling system. Field data from 1985 to 1990 were used to parameterize the models. Phytoplankton kinetic rates and constants were obtained from a related in situ study; others from modeling literature. The hydrodynamic model was calibrated to estimates of daily lake volume; the water quality model was calibrated for ammonia, nitrate, ortho-phosphate, dissolved oxygen, chlorophyll-a, biochemical oxygen demand, organic nitrogen, and organic phosphorus. Water quality calibration suggested the model characterized phytoplankton and nutrient dynamics quite well. The model was validated (Kolmogorov–Smirnov two-sample goodness-of-fit test at P<0.05) by reparameterizing the nutrient loading functions using an independent set of field data. The models identified several factors that may contribute to the spatial variability previously reported from other research in the reservoir, despite the superficial absence of complex structure. Sensitivity analysis of the phytoplankton kinetic rates suggest that study site-specific estimates were important for obtaining model fit to field data. Sediment sources of ammonia (10–60 mg m⁻² day⁻¹) and phosphate (1–6 mg m⁻² day⁻¹) were important to achieve model calibration, especially during periods of high temperatures and low dissolved oxygen. This sediment flux accounted for 78% (nitrogen) and 50% (phosphorus) of the annual load. Spatial and temporal variability in the lake, reflected in the calibrated and validated models, suggest that ecological factors that influence phytoplankton productivity and nutrient dynamics are different in various parts of the lake. The WASP5 model as implemented here does not fully accommodate the ecological variability in Lake Marion due to model constraints on the specification of rate constants. This level of spatial detail may not be appropriate for an operational reservoir model, but as a research tool the models are both versatile and useful.     

Using Gall Wasps on Oaks to Test Broad Ecological Concepts

Abstract:  Planning conservation of insect herbivores requires knowing what needs to be conserved and developing a set of predictor variables that aid management. We conducted a state-wide survey to examine the species richness of gall wasps (Hymenoptera: Cynipidae) on six oak species dominant in the threatened scrub-oak vegetation in peninsular Florida. Eighty-eight cynipid species were recorded; 23 were new species to Florida (a 35% increase), including 17 species new to science and 6 species newly recorded in the state. The cynipid species represented 68% of cynipids of Florida, on only 24% of oak species sampled. This fauna represents a hotspot of richness, justifying conservation initiatives in scrub-oak habitat and throughout the state. We derived predictor variables from general ecological concepts: (1) the theory of island biogeography that insect species richness increases as host plant geographic area increases and as local abundance increases, (2) the plant-architecture hypothesis that insect species richness increases with increased plant size, and (3) phytochemical patterns in leaves, including nutrients and digestibility reducers predicting suitability for insect herbivores. Concepts 1 and 2, developed for large scales and species numbers, were tested at smaller scales relevant to much conservation research and management. A stepwise multiple regression including all predictor variables accounted for 99% of the variance in cynipid species richness with three variables: foliar hemicellulose concentration (81%), host geographic area (16%), and tree height (2%). The trends were negative, however, and opposite to those predicted by concepts 1 and 2. Ecological theory was not applicable to discovery of predictors of cynipid species richness on six oak species. Thus, we promote caution in applying ecological theory to a narrow set of species without specific testing of how patterns conform to theoretical predictions.     

Univariate Bayesian nonparametric binary regression with application in environmental management

In environmental management, we often have to deal with binary response variables whose outcome dictates the course of action. This paper introduces a nonparametric Bayesian binary regression model with a single predictor variable that is more flexible than the commonly used logistic or probit models. Due to the Bayesian feature, the model can be easily used to combine observed data with our knowledge of the subject to produce site-specific results. By using three examples, this paper shows the potential application of the model in the environmental management, and its advantages in terms of flexibility in model specification, robustness to outliers, and realistic interpretation of data.     

K-select analysis: a new method to analyse habitat selection in radio-tracking studies

Two kinds of wildlife habitat studies can be distinguished in the literature: hindcasting and forecasting studies. Hindcasting studies aim to emphasize among a large set of habitat variables those that are of interest for the focus species, whereas forecasting studies are intended to predict habitat selection according to a small number of habitat variables for a given area. We provide here a new analytical tool which relies on the concept of ecological niche, the K-select analysis, for hindcasting studies of habitat selection by animals using radio-tracking data. Each habitat variable defines one dimension in the ecological space. For each animal, the difference between the vector of average available habitat conditions and the vector of average used conditions defines the marginality vector. Its size is proportional to the importance of habitat selection, and its direction indicates which variables are selected. By performing a non-centered principal component analysis of the table containing the coordinates of the marginality vectors of each animal (row) on the habitat variables (column), the K-select analysis returns a linear combination of habitat variables for which the average marginality is greatest. It is a synthesis of variables which contributes the most to the habitat selection. As with principal component analysis, the biological significance of the factorial axes is deduced from the loading of variables. An example is provided: habitat selection by wild boar is studied in a Mediterranean habitat using the K-select analysis. The numerous advantages of the analysis (a large number of variables that can be included, individual variability in habitat selection taken into account, a lack of too strict underlying hypotheses) make it a powerful approach in radio-tracking studies designed to identify habitat variables that are selected by animals.     

Testing ecological models: the meaning of validation

The ecological literature reveals considerable confusion about the meaning of validation in the context of simulation models. The confusion arises as much from semantic and philosophical considerations as from the selection of validation procedures. Validation is not a procedure for testing scientific theory or for certifying the ‘truth’ of current scientific understanding, nor is it a required activity of every modelling project. Validation means that a model is acceptable for its intended use because it meets specified performance requirements.Before validation is undertaken, (1) the purpose of the model, (2) the performance criteria, and (3) the model context must be specified. The validation process can be decomposed into several components: (1) operation, (2) theory, and (3) data. Important concepts needed to understand the model evaluation process are verification, calibration, validation, credibility, and qualification. These terms are defined in a limited technical sense applicable to the evaluation of simulation models, and not as general philosophical concepts. Different tests and standards are applied to the operational, theoretical, and data components. The operational and data components can be validated; the theoretical component cannot.The most common problem with ecological and environmental models is failure to state what the validation criteria are. Criteria must be explicitly stated because there are no universal standards for selecting what test procedures or criteria to use for validation. A test based on comparison of simulated versus observed data is generally included whenever possible. Because the objective and subjective components of validation are not mutually exclusive, disagreements over the meaning of validation can only be resolved by establishing a convention.     

A Procedure for Making Optimal Selection of Input Variables for Multivariate Environmental Classifications

Abstract:  Multivariate classifications of environmental factors are used as frameworks for conservation management. Although classification performance is likely to be sensitive to choice of input variables, these choices have been subjective in most previous studies. We used the Mantel test on a limited set of sites for which biological data were available to iteratively seek a definition of environmental space (i.e., intersite distances calculated with a set of appropriately transformed and weighted environmental variables) that had maximal correlation with the same sites described in a biological space. The procedure was used to select input variables for a classification of New Zealand's rivers that discriminates variation in fish communities for biodiversity management. The classification performed (i.e., discriminated biological variation) better than classifications with subjectively chosen variables. The inherently linear measures of environmental distance that underlie multivariate environmental classifications mean that they will perform best if they are defined based on variables for which there is a linear variation in the biological community throughout the entire range of the variable. Classification performance will therefore be improved when variables that have nonlinear relationships with biological variation are transformed to make their relationship with biological turnover more linear and when the contributions of environmental factors that have particularly strong relationships with biological variation are increased by weighting. Our results indicate that attention to the manner in which environmental space is defined improves the efficacy of multivariate classification and other techniques in which the environment is used as a surrogate for biological variation.     

中国农业非点源污染控制的经济措施探讨--以北京密云水库为例

针对我国农业非点源污染特征,提出污染控制经济政策体系,包括基于限制和约束功能的税费政策,基于引导和鼓励功能的补贴、补偿等优惠政策,以及创建基于流域的使污染削减总成本最小化的排污权交易市场。选择北京市重要水源地———密云水库的2大汇水流域之一的潮河流域(密云县境内)为政策设计示范区,从经济、技术及制度方面分析了各经济政策的功能和适用情况,提出本区以鼓励扶持引导为主、收费惩罚为辅控制削减农业非点源污染的经济政策构想,并估算了对农民环保行为给予补贴和补偿的额度。     

ICZM in the Black Sea region: experience and perspectives

Sustainable development of the Black Sea countries is aimed at increase of living standards of population together with maintenance of the unique ecosystems in the region. This process is impossible without development of an efficient system of Integrated Coastal Zone Management (ICZM) in every state and at the regional level. Presence of similar social, economic, and ecological problems, most of them of transboundary character, calls for the necessity of close cooperation of all Black Sea states in creating and improving their national ICZM systems, and in finding also regional solutions. The ICZM activities in the Black Sea region date back to the signing of the Convention on the Protection of the Black Sea Against Pollution (Bucharest Convention) in 1992. The first steps and achievements in ICZM within the Black Sea region for 15 years are presented in this paper and further steps are outlined.     

Interaction structures analysed from water-quality data

Fortnightly observations of water quality parameters, discharge and water temperature along the River Elbe have been subjected to a multivariate data analysis. In a previous study [Petersen, W., Bertino, L., Callies, U., Zorita, E., 2001. Process identification by principal component analysis of river-quality data. Ecol. Model. 138, 193–213] applied principal component analysis (PCA) to show that 60% of variability in the data set can be explained through just two linear combinations of eight original variables. In the present paper more advanced multivariate methods are applied to the same data set, which are supposed to suit better interpretations in terms of the underlying system dynamics.The first method, graphical modelling, represents interaction structures in terms of a set of conditional independence constraints between pairs of variables given the values of all other variables. Assuming data from a multinormal distribution conditional independence constraints are expressed by zero partial correlations. Different graphical structures with nodes for each variable and connecting edges between them can be assessed with regard to their likelihood. The second method, canonical correlation analysis (CCA), is applied for studying the correlation structures of external forcing and water quality parameters.Results of CCA turn out to be consistent with the dominant patterns of variability obtained from PCA. The percentages of variability explained by external forcing, however, are estimated to be smaller. Fitting graphical models allows a more detailed representation of interaction structures. For instance, for given discharge and temperature correlated variations of the concentrations of oxygen and nitrate, respectively, can be modelled as being mediated by variations of pH, which is a representer for algal activity. Considerably simplified graphical models do not much affect the outcomes of both PCA and CCA, and hence it is concluded that these graphical models successfully represent the main interaction structures represented by the covariance matrix of the data. The analysed conditional independence patterns provide constraints to be satisfied by directed probabilistic networks, for instance.     

Coregionalization analysis with a drift for multi-scale assessment of spatial relationships between ecological variables 1. Estimation of drift and random components

In two articles, we present ‘coregionalization analysis with a drift’ (CRAD), a method to assess the multi-scale variability of and relationships between ecological variables from a multivariate spatial data set. In phase I of CRAD (the first article), a deterministic drift component representing the large-scale pattern and a random component modeled as a second-order stationary process are estimated for each variable separately. In phase II (this article), a linear model of coregionalization (LMC) is fitted by estimated generalized least squares to the direct and cross experimental variograms of residuals (i.e., after the removal of estimated drifts). Structural correlations and coefficients of determination at smaller scales are then computed from the estimated coregionalization matrices, while the estimated drifts are used to calculate pseudo coefficients at large scale. The performance of five procedures in estimating correlations and coefficients of determination was compared using a Monte Carlo study. In four CRAD procedures, drift estimation was based on local polynomials of order 0, 1, 2 (L₀, L₁, L₂) or a global polynomial with forward selection of the basis functions; the fifth procedure was coregionalization analysis (CRA), in which large-scale patterns were modeled as a supplemental component in the LMC. In bivariate and multivariate analyses, the uncertainty in the estimation of correlations and coefficients of determination could be related to the interference between spatial components within a bounded sampling domain. In the bivariate case, most procedures provided acceptable estimates of correlations. In regionalized redundancy analysis, uncertainty was highest for CRA, while L₁ provided the best results overall. In a forest ecology example, the identification of scale-specific correlations between plant species diversity and soil and topographical variables illustrated the potential of CRAD to provide unique insight into the functioning of complex ecosystems.     

Application of a Random Forest algorithm to predict spatial distribution of the potential yield of Ruditapes philippinarum in the Venice lagoon, Italy

We present a modelling framework that combines machine learning techniques and Geographic Information Systems to support the management of an important aquaculture species, Manila clam (Ruditapes philippinarum). We use the Venice lagoon (Italy), the first site in Europe for the production of R. philippinarum, to illustrate the potential of this modelling approach. To investigate the relationship between the yield of R. philippinarum and a set of environmental factors, we used a Random Forest (RF) algorithm. The RF model was tuned with a large data set (n = 1698) and validated by an independent data set (n = 841). Overall, the model provided good predictions of site-specific yields and the analysis of marginal effect of predictors showed substantial agreement among the modelled responses and available ecological knowledge for R. philippinarum. The most influent environmental factors for yield estimation were percentage of sand in the sediment, salinity, and water depth. Our results agree with findings from other North Adriatic lagoons. The application of the fitted RF model to continuous maps of all the environmental variables allowed estimates of the potential yield for the whole basin. Such a spatial representation enabled site-specific estimates of yield in different farming areas within the lagoon. We present a possible management application of our model by estimating the potential yield under the current farming distribution and comparing it to a proposed re-organization of the farming areas. Our analysis suggests a reduction of total yield is likely to result from the proposed re-organization.     

Using structural equation modeling to investigate relationships among ecological variables

Structural equation modeling is an advanced multivariate statistical process with which a researcher can construct theoretical concepts, test their measurement reliability, hypothesize and test a theory about their relationships, take into account measurement errors, and consider both direct and indirect effects of variables on one another. Latent variables are theoretical concepts that unite phenomena under a single term, e.g., ecosystem health, environmental condition, and pollution (Bollen, 1989). Latent variables are not measured directly but can be expressed in terms of one or more directly measurable variables called indicators. For some researchers, defining, constructing, and examining the validity of latent variables may be the end task of itself. For others, testing hypothesized relationships of latent variables may be of interest. We analyzed the correlation matrix of eleven environmental variables from the U.S. Environmental Protection Agency's (USEPA) Environmental Monitoring and Assessment Program for Estuaries (EMAP-E) using methods of structural equation modeling. We hypothesized and tested a conceptual model to characterize the interdependencies between four latent variables-sediment contamination, natural variability, biodiversity, and growth potential. In particular, we were interested in measuring the direct, indirect, and total effects of sediment contamination and natural variability on biodiversity and growth potential. The model fit the data well and accounted for 81% of the variability in biodiversity and 69% of the variability in growth potential. It revealed a positive total effect of natural variability on growth potential that otherwise would have been judged negative had we not considered indirect effects. That is, natural variability had a negative direct effect on growth potential of magnitude –0.3251 and a positive indirect effect mediated through biodiversity of magnitude 0.4509, yielding a net positive total effect of 0.1258. Natural variability had a positive direct effect on biodiversity of magnitude 0.5347 and a negative indirect effect mediated through growth potential of magnitude –0.1105 yielding a positive total effects of magnitude 0.4242. Sediment contamination had a negative direct effect on biodiversity of magnitude –0.1956 and a negative indirect effect on growth potential via biodiversity of magnitude –0.067. Biodiversity had a positive effect on growth potential of magnitude 0.8432, and growth potential had a positive effect on biodiversity of magnitude 0.3398. The correlation between biodiversity and growth potential was estimated at 0.7658 and that between sediment contamination and natural variability at –0.3769.     

美国大气污染物排放标准体系综述

介绍了美国大气固定源排放标准的体系、标准内容、标准制定程序与标准实施的有关规定。并分析了其特点。