An estimating function approach to the inference of catch-effort models

A class of catch-effort models, which allows for heterogeneous removal probabilities, is proposed for closed populations. The model includes three types of removal probabilities: multiplicative, Poisson and logistic. The usual removal and generalized removal models then become special cases. The equivalence of the proposed model and a special type of capture-recapture model is discussed. A unified estimating function approach is used to estimate the initial population size. For the homogeneous model, the resulting population size estimator based on optimal estimating functions is asymptotically equivalent to the maximum likelihood estimator. One advantage for our approach is that it can be extended to handle the heterogeneous populations in which the maximum likelihood estimators do not exist. The bootstrap method is applied to construct variance estimators and confidence intervals. We illustrate the method by two real data examples. Results of a simulation study investigating the performance of the proposed estimation procedure are presented.     

Using global sensitivity analysis of demographic models for ecological impact assessment

Population viability analysis (PVA) is widely used to assess population‐level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input‐parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input‐parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea‐level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions.     

Modelling the multiple nutrient limitation of algal growth

The way in which simultaneously limiting nutrients are supposed to act upon the algal growth rate is an important aspect of aquatic ecosystem modelling and research. Three different relations between the multiple nutrient limitation and two single nutrient limitations are developed from different biochemical models: a “multiplicative” relation, used in most dynamic ecosystem models, a new “sequential” relation and a “threshold” relation, sensu Liebig. The characteristics and practical consequences of these relations are investigated. By means of three experiments, derived from the literature, it is shown that the multiplicative relation yields the statistically significant worst growth rate predictions.     

Relative stability of ecosystem linear models

A method to test the relative stability of ecosystem linear models is developed. This method uses the eigenvalue sensitivity to parameter perturbations to compute the relative stability of the model. The procedure is applied to the analysis of two models describing the ca;cium cycle in a forested watershed ecosystem and the magnesium cycle in a tropical rain forest respectively.     

Sensitivity of population viability to spatial and nonspatial parameters using GRIP.

Metapopulation dynamics are influenced by spatial parameters including the amount and arrangement of suitable habitat, yet these parameters may be uncertain when deciding how to manage species or their habitats. Sensitivity analyses of population viability analysis (PVA) models can help measure relative parameter influences on predictions, identify research priorities for reducing uncertainty, and evaluate management strategies. Few spatial PVAs, however, include sensitivity analyses of both spatial and nonspatial parameters, perhaps because computationally efficient tools for such analyses are lacking or inaccessible. We developed GRIP, a program to facilitate sensitivity analysis of spatial and nonspatial input parameters for PVAs created in RAMAS Metapop, a widely applied software program. GRIP creates random sets of input files by varying parameters specified in the PVA model including vital rates and their correlations among populations, the number and configuration of populations, dispersal rates, dispersal survival, initial population abundances, carrying capacities, and the probability, intensity, and spatial extent of catastrophes, while drawing on specified parameter distributions. We evaluated GRIP's performance as a tool for sensitivity analysis of spatial PVAs and explored the consequences of varying spatial input parameters for predictions of a published PVA model of the sand lizard (Lacerta agilis). We used GRIP output to generate standardized regression coefficients (SRCs) and nonparametric correlation coefficients as indices of the relative sensitivity of predicted conservation status to input parameters. GRIP performed well; with a single analysis we were able to rank the relative influence of input parameters identified as influential by the PVA's original author, S. A. Berglind, who used three separate forms of sensitivity analysis. Our analysis, however, also underscored the value of exploring the relative influence of spatial parameters on PVA predictions; both SRCs and correlation coefficients indicated that the most influential parameters in the sand lizard model were spatial in nature. We provide annotated code so that GRIP may be modified to reflect particular species biology, customized for more complex spatial PVA models, upgraded to incorporate features added in newer versions of RAMAS Metapop, used as a template to develop similar programs, or used as it is for computationally efficient sensitivity analyses in support of conservation planning.     

Nitrogen source apportionment—a comparison between a dynamic and a statistical model

A dynamic model, HBV-N, and a statistical model, MESAW, for nitrogen source apportionment were compared regarding model performance, model uncertainty and user applicability. The HBV-N model simulates continuous series of nitrogen concentrations with meteorological data and sub-basin characteristics as input. Diffuse nitrogen emissions are defined as regional model parameters which are calibrated by comparison of observed and simulated nitrogen data. The MESAW model uses nitrogen loads for a fixed time interval at each monitoring site as response variable and sub-basin characteristics as explanatory variables to estimate diffuse nitrogen emissions through non-linear regression analysis. The two models were applied in the Matsalu Bay watershed (3640 km²) in Estonia and the same land use and point sources data were used as input. Both models gave similar levels of diffuse total nitrogen emissions and retention rates, which also fit well with previous estimates made in Estonia and Scandinavia. A sensitivity analysis of the model parameters also showed similar uncertainty levels, which indicated that the model uncertainty was more dependent on the availability of nitrogen data and land cover distribution than the choice of model. Furthermore, the sensitivity analysis showed a parameter interdependency in both models, which implied the risk of compensation between estimated diffuse emissions and retention. In conclusion, however, the study showed that both models were capable of estimating nitrogen leakage from the dominating land classes and giving reliable source apportionment from the available input data. The study indicated that the HBV-N model has its advantage in assessments where detailed outputs are needed and when run-off data are limited, while the statistical MESAW model has its advantage in extensive studies since it is easily applied to large watersheds that have dense monitoring networks.     

Assessing the impact on groundwater safety of inter-basin water transfer using a coupled modeling approach

Surface water and groundwater always behave in a coupled manner and are major components of hydrologic cycle. However, surface water simulation models and groundwater simulation models are run separately most of the time. Few models focus on the impact of hydraulic changes in the surface water flows on the groundwater, or specifically, the impact of a water transfer project to fill a seasonally dry channel. In this study, a linked surface water and groundwater simulation model was developed to assess the impact of a trans-basin water diversion project on the groundwater. A typical plain area east of Beijing was selected as a case study, representing Beijing’s main source of groundwater used for drinking water. A surface water quality model of the Chaobai River was developed based on the Water Quality Analysis Simulation Program (WASP), and a groundwater model was developed based on the Modular Finite-Difference Groundwater Flow Model (MODFLOW) and the Modular 3-D transport model (MT3D). The results of the surface water simulation were used as input for the groundwater simulation. Water levels and four contaminants (NH₃-N, COD_Mn, F, As) were simulated. With the same initial and boundary conditions, scenario analyses were performed to quantify the impact of different quantities of diversion water on the groundwater environment. The results showed the water quality of the groundwater sources was not significantly affected.     

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.     

SWAT模型在国内外非点源污染研究中的应用进展

模型模拟是定量估算非点源污染负荷的有效工具,也是对其进行规划、控制和管理的前提.近年来SWAT模型在国内外得到了快速的发展和应用,是目前全球评价大范围和环境变化条件下非点源污染问题的一个有效工具.简介SWAT模型的发展历程及原理,概述了SWAT模型目前在国内外的水文评价、污染物流失模拟、输人参数、土地利用及气候变化对水文响应的影响等方面的研究现状,并对SWAT模型的发展方向提出了建议,为模型的进一步完善与应用提供参考.结果显示,SWAT模型对水文评价(如径流量、泥沙量)可得到较好的模拟和预测结果,能够模拟污染物(如农药和化肥)在农田和河网中的迁移过程,模拟与分析土地利用/覆被变化及气候变化对水文过程的影响.模型参数的确定及其对地下水流与溶质运移的模拟是模型的主要问题,需要进一步研究与完善.     

Accounting for system dynamics in reserve design.

Systematic conservation plans have only recently considered the dynamic nature of ecosystems. Methods have been developed to incorporate climate change, population dynamics, and uncertainty in reserve design, but few studies have examined how to account for natural disturbance. Considering natural disturbance in reserve design may be especially important for the world's remaining intact areas, which still experience active natural disturbance regimes. We developed a spatially explicit, dynamic simulation model, CONSERV, which simulates patch dynamics and fire, and used it to evaluate the efficacy of hypothetical reserve networks in northern Canada. We designed six networks based on conventional reserve design methods, with different conservation targets for woodland caribou habitat, high-quality wetlands, vegetation, water bodies, and relative connectedness. We input the six reserve networks into CONSERV and tracked the ability of each to maintain initial conservation targets through time under an active natural disturbance regime. None of the reserve networks maintained all initial targets, and some over-represented certain features, suggesting that both effectiveness and efficiency of reserve design could be improved through use of spatially explicit dynamic simulation during the planning process. Spatial simulation models of landscape dynamics are commonly used in natural resource management, but we provide the first illustration of their potential use for reserve design. Spatial simulation models could be used iteratively to evaluate competing reserve designs and select targets that have a higher likelihood of being maintained through time. Such models could be combined with dynamic planning techniques to develop a general theory for reserve design in an uncertain world.     

Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions

A stochastic model is applied to describe the spatial structure of a forest stand. We aim at quantifying the strength of the competition process between the trees in terms of interaction within and between different size classes of trees using multivariate Gibbs point processes with hierarchical interactions introduced in [Högmander, H., Särkkä, A., 1999. Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 1051–1058]. The new model overcomes the main limitation of the traditional use of the Gibbs models allowing to describe systems with non-symmetric interactions between different objects. When analyzing interactions between neighbouring trees it is natural to assume that the size of a tree determines its hierarchical level: the largest trees are not influenced by any other trees than the trees in the same size class, while trees in the other size classes are influenced by the other trees in the same class as well as by all larger trees. In this paper, we describe a wide range of Gibbs models with both hierarchical and non-hierarchical interactions as well as a simulation algorithm and a parameter estimation procedure for the hierarchical models. We apply the hierarchical interaction model to the analysis of forest data consisting of locations and diameters of tree stems.     

Large scale parameter study of an individual-based model of clonal plant with volunteer computing

Understanding clonal strategies (i.e. the ability of plants to reproduce vegetatively) is particularly important to explain species persistence. A clonal individual may be considered as a network of interconnected ramets that colonizes space. Resources in this network can be shared and/or stored. We developed an individual-based model (IBM) to simulate the growth of an individual clonal plant. Typically a realistic IBM requires a large set of parameters to adequately represent the complexity of the clonal plant growth. Simulations in the literature are often limited to small subsets of the parameter space and are guided by the a priori knowledge and with heuristic aims of the researcher. The aim of this paper was to demonstrate the benefit of volunteer computing in computational ecology to systematically browse the parameter space and analyze the simulation results in order to draw rigorous conclusions. To be specific, we simulated clonal plant growth using nine growth rules related to the metabolic process, plant architecture, resource sharing and storage and nineteen input parameters. We chose 2-4 values per input parameter which corresponded to 20 millions of combinations tested through volunteer computing. We used three criteria to evaluate plant performance: plant total resource, ramet production and maximum length of one branch. The 1% top-performing plants were sorted according to these criteria. Plant total resource and ramet production were correlated while considering the top-performing plants. The maximum length of one branch was independent from the other two performance traits. We detected two processes promoting at least one of the plant performance traits: (i) a relatively high metabolic gain (high photosynthetic activity and low production cost for new growth units), a low resource storage and long integration distance for resource sharing; (ii) short spacer lengths and the predominance of elongation of existing branches over branching. Interactive effects between parameter values were demonstrated for more than half of the input parameters. Best performance was reached for plants with slightly different combinations of values for these parameters (i.e. different strategies) rather than a single one (i.e. unique strategy). This modeling approach with volunteer computing enabled us to proceed to large-scale virtual experiments which provided a new quality of insight into ecological processes linked with clonal plant growth.     

Multiple sources of predictive uncertainty in modeled estimates of net ecosystem CO2 exchange

Net ecosystem CO₂ exchange (NEE) is typically measured directly by eddy covariance towers or is estimated by ecosystem process models, yet comparisons between the data obtained by these two methods can show poor correspondence. There are three potential explanations for this discrepancy. First, estimates of NEE as measured by the eddy-covariance technique are laden with uncertainty and can potentially provide a poor baseline for models to be tested against. Second, there could be fundamental problems in model structure that prevent an accurate simulation of NEE. Third, ecosystem process models are dependent on ecophysiological parameter sets derived from field measurements in which a single parameter for a given species can vary considerably. The latter problem suggests that with such broad variation among multiple inputs, any ecosystem modeling scheme must account for the possibility that many combinations of apparently feasible parameter values might not allow the model to emulate the observed NEE dynamics of a terrestrial ecosystem, as well as the possibility that there may be many parameter sets within a particular model structure that can successfully reproduce the observed data. We examined the extent to which these three issues influence estimates of NEE in a widely used ecosystem process model, Biome-BGC, by adapting the generalized likelihood uncertainty estimation (GLUE) methodology. This procedure involved 400,000 model runs, each with randomly generated parameter values from a uniform distribution based on published parameter ranges, resulting in estimates of NEE that were compared to daily NEE data from young and mature Ponderosa pine stands at Metolius, Oregon. Of the 400,000 simulations run with different parameter sets for each age class (800,000 total), over 99% of the simulations underestimated the magnitude of net ecosystem CO₂ exchange, with only 4.07% and 0.045% of all simulations providing satisfactory simulations of the field data for the young and mature stands, even when uncertainties in eddy-covariance measurements are accounted for. Results indicate fundamental shortcomings in the ability of this model to produce realistic carbon flux data over the course of forest development, and we suspect that much of the mismatch derives from an inability to realistically model ecosystem respiration. However, difficulties in estimating historic climate data are also a cause for model-data mismatch, particularly in a highly ecotonal region such as central Oregon. This latter difficulty may be less prevalent in other ecosystems, but it nonetheless highlights a challenge in trying to develop a dynamic representation of the terrestrial biosphere.     

An integrated modeling framework for performing environmental assessments: Application to ecosystem services in the Albemarle-Pamlico basins (NC and VA, USA)

The U.S. Environmental Protection Agency uses environmental models to inform rulemaking and policy decisions at multiple spatial and temporal scales. As decision-making has moved towards integrated thinking and assessment (e.g. media, site, region, services), the increasing complexity and interdisciplinary nature of modern environmental problems has necessitated a new generation of integrated modeling technologies. Environmental modelers are now faced with the challenge of determining how data from manifold sources, types of process-based and empirical models, and hardware/software computing infrastructure can be reliably integrated and applied to protect human health and the environment.In this study, we demonstrate an Integrated Modeling Framework that allows us to predict the state of freshwater ecosystem services within and across the Albemarle-Pamlico Watershed, North Carolina and Virginia (USA). The Framework consists of three facilitating technologies: Data for Environmental Modeling automates the collection and standardization of input data; the Framework for Risk Assessment of Multimedia Environmental Systems manages the flow of information between linked models; and the Supercomputer for Model Uncertainty and Sensitivity Evaluation is a hardware and software parallel-computing interface with pre/post-processing analysis tools, including parameter estimation, uncertainty and sensitivity analysis. In this application, five environmental models are linked within the Framework to provide multimedia simulation capabilities: the Soil Water Assessment Tool predicts watershed runoff; the Watershed Mercury Model simulates mercury runoff and loading to streams; the Water quality Analysis and Simulation Program predicts water quality within the stream channel; the Habitat Suitability Index model predicts physicochemical habitat quality for individual fish species; and the Bioaccumulation and Aquatic System Simulator predicts fish growth and production, as well as exposure and bioaccumulation of toxic substances (e.g., mercury).Using this Framework, we present a baseline assessment of two freshwater ecosystem services-water quality and fisheries resources-in headwater streams throughout the Albemarle-Pamlico. A stratified random sample of 50 headwater streams is used to draw inferences about the target population of headwater streams across the region. Input data is developed for a twenty-year baseline simulation in each sampled stream using current land use and climate conditions. Monte Carlo sampling (n = 100 iterations per stream) is also used to demonstrate some of the Framework's experimental design and data analysis features. To evaluate model performance and accuracy, we compare initial (i.e., uncalibrated) model predictions (water temperature, dissolved oxygen, fish density, and methylmercury concentration within fish tissue) against empirical field data. Finally, we ‘roll-up’ the results from individual streams, to assess freshwater ecosystem services at the regional scale.     

Parameterising competing zooplankton for survival in plankton functional type models

Marine plankton ecosystems are an important component of biogeochemical cycling in the oceans. Operational plankton functional type (PFT) models, that group plankton according to their biogeochemical properties, are currently being developed to resolve biogenic gas exchange between the ocean and atmosphere, and to model the lowest trophic levels in fisheries models. A fundamental problem with these models is that PFTs often go extinct in computer simulations, effectively removing the biogeochemical processes from the models. Cropp and Norbury [Cropp, R., Norbury, J., 2009a. Parameterizing plankton functional type models: insights from a dynamical systems perspective. J. Plankton Res. 31, 939-963] demonstrated that parameter combinations that allowed all PFTs to stay extant for all time in stable, homogeneous environments were rare in a PFT model with two competing phytoplankton and one zooplankton (NP₁P₂Z). In this paper, we examine the dynamical properties of a generic predator-predator-prey PFT model, and apply the analysis techniques developed by Cropp and Norbury to a simple example PFT model with one phytoplankton and two zooplankton (NPZ₁Z₂) in order to explore its properties and parameter space. We find that the properties of predator-predator-prey PFT systems are fundamentally different from those of predator-prey-prey PFT systems. The likelihood of parameter combinations for which all PFTs stay extant for all time in predator-predator-prey PFT systems depends critically on the process formulations used, and the properties of co-existing zooplankton (as defined by their parameter values) are quite different to those of co-existing phytoplankton.     

Estimating the critical phosphorus loading of shallow lakes with the ecosystem model PCLake: Sensitivity, calibration and uncertainty

There is a vast body of knowledge that eutrophication of lakes may cause algal blooms. Among lakes, shallow lakes are peculiar systems in that they typically can be in one of two contrasting (equilibrium) states that are self-stabilizing: a ‘clear’ state with submerged macrophytes or a ‘turbid’ state dominated by phytoplankton. Eutrophication may cause a switch from the clear to the turbid state, if the P loading exceeds a critical value. The ecological processes governing this switch are covered by the ecosystem model PCLake, a dynamic model of nutrient cycling and the biota in shallow lakes. Here we present an extensive analysis of the model, using a three-step procedure. (1) A sensitivity analysis revealed the key parameters for the model output. (2) These parameters were calibrated on the combined data on total phosphorus, chlorophyll-a, macrophytes cover and Secchi depth in over 40 lakes. This was done by a Bayesian procedure, giving a weight to each parameter setting based on its likelihood. (3) These weights were used for an uncertainty analysis, applied to the switchpoints (critical phosphorus loading levels) calculated by the model. The model was most sensitive to changes in water depth, P and N loading, retention time and lake size as external input factors, and to zooplankton growth rate, settling rates and maximum growth rates of phytoplankton and macrophytes as process parameters. The results for the ‘best run’ showed an acceptable agreement between model and data and classified nearly all lakes to which the model was applied correctly as either ‘clear’ (macrophyte-dominated) or ‘turbid’ (phytoplankton-dominated). The critical loading levels for a standard lake showed about a factor two uncertainty due to the variation in the posterior parameter distribution. This study calculates in one coherent analysis uncertainties in critical phosphorus loading, a parameter that is of great importance to water quality managers.     

Composite likelihood approach to the regression analysis of spatial multivariate ordinal data and spatial compositional data with exact zero values

In many environmental and ecological studies, it is of interest to model compositional data. One approach is to consider positive random vectors that are subject to a unit-sum constraint. In landscape ecological studies, it is common that compositional data are also sampled in space with some elements of the composition absent at certain sampling sites. In this paper, we first propose a practical spatial multivariate ordered probit model for multivariate ordinal data, where the response variables can be viewed as the discretized non-negative compositions without the unit-sum constraint. We then propose a novel two-stage spatial mixture Dirichlet regression model. The first stage models the spatial dependence and the presence of exact zero values, and the second stage models all the non-zero compositional data. A maximum composite likelihood approach is developed for parameter estimation and inference in both the spatial multivariate ordered probit model and the two-stage spatial mixture Dirichlet regression model. The standard errors of the parameter estimates are computed by an estimate of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods. A land cover data example in landscape ecology further illustrates that accounting for spatial dependence can improve the accuracy in the prediction of presence/absence of different land covers as well as the magnitude of land cover compositions.