生态模型的灵敏度分析

灵敏度分析用于定性或定量地评价模型参数误差对模型结果产生的影响,是模型参数化过程和模型校正过程中的有用工具,具有重要的生态学意义．灵敏度分析包括局部灵敏度分析和全局灵敏度分析．局部灵敏度分析只检验单个参数的变化对模型结果的影响程度;全局灵敏度分析则检验多个参数的变化对模型运行结果总的影响,并分析每一个参数及其参数之间相互作用对模型结果的影响．目前,在对生态模型的灵敏度分析中,越来越倾向于使用全局灵敏度分析的方法．但国内仍多采用局部灵敏度分析方法,很少采用全局灵敏度分析方法．文中详细论述了局部灵敏分析和全局灵敏度分析的主要方法(一次变换法、多元回归法、Morris法、Sobol’法、傅里叶幅度灵敏度检验法和傅里叶幅度灵敏度检验扩展法),希望能为国内生态模型的发展提供一个比较完善的灵敏度分析方法库．结合国内外的灵敏度分析发展现状,指出联合灵敏度研究、灵敏度共性研究及空间直观景观模型的灵敏度分析将为生态模型灵敏度分析研究中的热点和难点．     

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low‐quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision‐making framework will result in better‐informed, more robust decisions.     

基于物质流分析方法的唐山市经济与环境关系的协整检验和分解

利用物质流分析方法(MFA)建立物质流账户,分析唐山市在经济 环境系统运行中物质投入量与产出量的阶段特征及物质投入和产出强度对经济发展的影响程度;使用计量经济学模型,分别对国内生产总值(GDP)、直接物质投入(DMI)和直接废弃物排放(DPO)进行单位根检验、Johansen协整检验、向量误差修正分析、脉冲响应和方差分解分析,探索了各指标之间的双向作用机制和长期关系.结果表明: 1992—2011年,唐山市DMI和DPO 均呈增长趋势,DMI的增幅高于DPO.DMI投入强度呈增长趋势,DPO产出强度呈波动下降趋势.GDP与DMI、DPO之间存在着长期稳定协整关系,指标间的作用关系经历了由波动到逐步平稳的过程.DMI与DPO在短期内会对经济发展起到较强的正向冲击作用,但是经济-环境系统会逐步消化这些影响,并对系统内外指标进行短期的动态调整,最终使系统表现出一种长期的均衡关系;经济发展受到经济规模效应的影响逐步增加.将各指标对GDP的贡献度予以分解,其中,DMI的贡献度上升,GDP的贡献度下降,DPO的贡献度变化不大.总体上,唐山市的经济发展遵循了资源型城市的传统生产轨迹,较大程度上依赖于物质投入,高能源消耗又加剧了环境污染.     

A Probabilistic Dynamic Material Flow Analysis Model for Chinese Urban Housing Stock

The stock‐driven dynamic material flow analysis (MFA) model is one of the prevalent tools to investigate the evolution and related material metabolism of the building stock. There exists substantial uncertainty inherent to input parameters of the stock‐driven dynamic building stock MFA model, which has not been comprehensively evaluated yet. In this study, a probabilistic, stock‐driven dynamic MFA model is established and China's urban housing stock is selected as the empirical case. This probabilistic dynamic MFA model has the ability to depict the future evolution pathway of China's housing stock and capture uncertainties in its material stock, inflow, and outflow. By means of probabilistic methods, a detailed and transparent estimation of China's housing stock and its material metabolism behavior is presented. Under a scenario with a saturation level of the population, urbanization, and living space, the median value of the urban housing stock area, newly completed area, and demolished area would peak at around 49, 2.2, and 2.2 billion square meters, respectively. The corresponding material stock and flows are 79, 3.5, and 3.3 billion tonnes, respectively. Uncertainties regarding housing stock and its material stock and flows are non‐negligible. Relative uncertainties of the material stock and flows are above 50%. The uncertainty importance analysis demonstrates that the material intensity and the total population are major contributions to the uncertainty. Policy makers in the housing sector should consider the material efficiency as an essential policy to mitigate material flows of the urban building stock and to lower the risk of policy failures.     

MARS Approach for Global Sensitivity Analysis of Differential Equation Models with Applications to Dynamics of Influenza Infection

Differential equation models are widely used for the study of natural phenomena in many fields. The study usually involves unknown factors such as initial conditions and/or parameters. It is important to investigate the impact of unknown factors (parameters and initial conditions) on model outputs in order to better understand the system the model represents. Apportioning the uncertainty (variation) of output variables of a model according to the input factors is referred to as sensitivity analysis. In this paper, we focus on the global sensitivity analysis of ordinary differential equation (ODE) models over a time period using the multivariate adaptive regression spline (MARS) as a meta model based on the concept of the variance of conditional expectation (VCE). We suggest to evaluate the VCE analytically using the MARS model structure of univariate tensor-product functions which is more computationally efficient. Our simulation studies show that the MARS model approach performs very well and helps to significantly reduce the computational cost. We present an application example of sensitivity analysis of ODE models for influenza infection to further illustrate the usefulness of the proposed method.     

Good modeling practice for PAT applications: Propagation of input uncertainty and sensitivity analysis

The uncertainty and sensitivity analysis are evaluated for their usefulness as part of the model‐building within Process Analytical Technology applications. A mechanistic model describing a batch cultivation of Streptomyces coelicolor for antibiotic production was used as case study. The input uncertainty resulting from assumptions of the model was propagated using the Monte Carlo procedure to estimate the output uncertainty. The results showed that significant uncertainty exists in the model outputs. Moreover the uncertainty in the biomass, glucose, ammonium and base‐consumption were found low compared to the large uncertainty observed in the antibiotic and off‐gas CO₂ predictions. The output uncertainty was observed to be lower during the exponential growth phase, while higher in the stationary and death phases ‐ meaning the model describes some periods better than others. To understand which input parameters are responsible for the output uncertainty, three sensitivity methods (Standardized Regression Coefficients, Morris and differential analysis) were evaluated and compared. The results from these methods were mostly in agreement with each other and revealed that only few parameters (about 10) out of a total 56 were mainly responsible for the output uncertainty. Among these significant parameters, one finds parameters related to fermentation characteristics such as biomass metabolism, chemical equilibria and mass‐transfer. Overall the uncertainty and sensitivity analysis are found promising for helping to build reliable mechanistic models and to interpret the model outputs properly. These tools make part of good modeling practice, which can contribute to successful PAT applications for increased process understanding, operation and control purposes. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

区域生态经济系统的物质输入与输出分析——以常州市武进区为例

运用物质流分析（MFA）方法,对江苏省常州市武进区生态经济系统中物质输入与输出进行了系统的分析,结果表明：（1）随着社会经济发展和人口增长,武进区物质输入总量及人均物质输入量也在增加,但递增速率均远小于GDP增长速率,而物质输出总量及人均物质输出量则呈现递减趋势;（2）在不考虑水的因素情况下,武进区物质输入量保持较快的上升速度,其中固体物质的增长速率远远大于气体物质的增长速率;物质输出量则呈总体下降趋势,其中以气体物质输出量的贡献最大,对环境造成污染的物质以气体特别是以化石燃料燃烧排放的废气和工业废气为主;（3）排除占大部分比例农业用水的上升,工业用水、城镇生活用水和地下水总量及人均利用强度都在减少;同时,总的废水排放量及人均排放量在减少,其中又以生活废水排放量的减少最快,其次是工业废水;（4）单位GDP物质输入量的变化处于波动状态,同期的单位GDP物质输出量则呈递减趋势,单位GDP用水量和单位GDP废水排放量则有相同的递减趋势,表征了武进区资源利用效率的稳步提高,区域经济增长和环境压力也在逐步脱钩。上述结果体现了武进区近年来循环经济发展模式的优势,但还存在较多问题,说明武进区在调整物质利用强度和提高资源利用效率方面还需下更大的功夫,并采取相关措施,以期提高实施循环经济战略与建设节约型社会的地位和意义。文章最后结合研究区实际情况就区域环境一经济的协调发展进行了展望,指出了物质流分析方法在应用中的一些缺陷,为今后该领域的进一步研究提供了借鉴。     

Dynamic Bayesian sensitivity analysis of a myocardial metabolic model

Dynamic compartmentalized metabolic models are identified by a large number of parameters, several of which are either non-physical or extremely difficult to measure. Typically, the available data and prior information is insufficient to fully identify the system. Since the models are used to predict the behavior of unobserved quantities, it is important to understand how sensitive the output of the system is to perturbations in the poorly identifiable parameters. Classically, it is the goal of sensitivity analysis to asses how much the output changes as a function of the parameters. In the case of dynamic models, the output is a function of time and therefore its sensitivity is a time dependent function. If the output is a differentiable function of the parameters, the sensitivity at one time instance can be computed from its partial derivatives with respect to the parameters. The time course of these partial derivatives describes how the sensitivity varies in time.When the model is not uniquely identifiable, or if the solution of the parameter identification problem is known only approximately, we may have not one, but a distribution of possible parameter values. This is always the case when the parameter identification problem is solved in a statistical framework. In that setting, the proper way to perform sensitivity analysis is to not rely on the values of the sensitivity functions corresponding to a single model, but to consider the distributed nature of the sensitivity functions, inherited from the distribution of the vector of the model parameters.In this paper we propose a methodology for analyzing the sensitivity of dynamic metabolic models which takes into account the variability of the sensitivity over time and across a sample. More specifically, we draw a representative sample from the posterior density of the vector of model parameters, viewed as a random variable. To interpret the output of this doubly varying sensitivity analysis, we propose visualization modalities particularly effective at displaying simultaneously variations over time and across a sample. We perform an analysis of the sensitivity of the concentrations of lactate and glycogen in cytosol, and of ATP, ADP, NAD⁺ and NADH in cytosol and mitochondria, to the parameters identifying a three compartment model for myocardial metabolism during ischemia.     

A Novel Approach to Characterize Data Uncertainty in Material Flow Analysis and its Application to Plastics Flows in Austria

Material flow analysis (MFA) is widely used to investigate flows and stocks of resources or pollutants in a defined system. Data availability to quantify material flows on a national or global level is often limited owing to data scarcity or lacking data. MFA input data are therefore considered inherently uncertain. In this work, an approach to characterize the uncertainty of MFA input data is presented and applied to a case study on plastics flows in major Austrian consumption sectors in the year 2010. The developed approach consists of data quality assessment as a basis for estimating the uncertainty of input data. Four different implementations of the approach with respect to the translation of indicator scores to uncertainty ranges (linear‐ vs. exponential‐type functions) and underlying probability distributions (normal vs. log‐normal) are examined. The case study results indicate that the way of deriving uncertainty estimates for material flows has a stronger effect on the uncertainty ranges of the resulting plastics flows than the assumptions about the underlying probability distributions. Because these uncertainty estimates originate from data quality evaluation as well as uncertainty characterization, it is crucial to use a well‐defined approach, building on several steps to ensure the consistent translation of the data quality underlying material flow calculations into their associated uncertainties. Although subjectivity is inherent in uncertainty assessment in MFA, the proposed approach is consistent and provides a comprehensive documentation of the choices underlying the uncertainty analysis, which is essential to interpret the results and use MFA as a decision support tool.     

Consumption‐based Material Flow Accounting

In 2007, imports accounted for approximately 34% of the material input (domestic extraction and imports) into the Austrian economy and almost 60% of the GDP stemmed from exports. Upstream material inputs into the production of traded goods, however, are not yet included in the standard framework of material flow accounting (MFA). We have reviewed different approaches accounting for these upstream material inputs, or raw material equivalents (RME), positioning them in a wider debate about consumption‐based perspectives in environmental accounting. For the period 1995–2007, we calculated annual RME of Austria's trade and consumption applying a hybrid approach. For exports and competitive imports, we used an environmentally extended input‐output model of the Austrian economy, based on annual supply and use tables and MFA data. For noncompetitive imports, coefficients for upstream material inputs were extracted from life cycle inventories. The RME of Austria's imports and exports were approximately three times larger than the trade flows themselves. In 2007, Austria's raw material consumption was 30 million tonnes or 15% higher than its domestic material consumption. We discuss the material composition of these flows and their temporal dynamics. Our results demonstrate the need for a consumption‐based perspective in MFA to provide robust indicators for dematerialization and resource efficiency analysis of open economies.     

厦门市生态经济系统物质流分析

运用物质流分析(MFA)方法和STIRPAT模型,对1996～2007年厦门生态经济系统物质输入与输出进行分析,结果表明:(1)在不考虑水的情况下,物质输入与输出不断增加(年均增长率分别为11.48%、11.41%),但均小于GDP增长速度(15.94%),二者成正比;物质流增长集中表现在对金属、非金属矿物的需求及化石燃料燃烧废气、工业废气的排放.(2)用水量和废水排放量均不断增加,尤以生活污水排放量增长速度较快,加重了区域环境的压力.(3)物质输入与GDP、物质输出与GDP呈良好线性关系.厦门经济发展很大程度上依赖资源消耗.(4)单位GDP物质输入与输出均不断减小,表明资源利用率、处置率明显提高,区域逐步走向生态环境与社会经济的协调发展.(5)构建了厦门物质输入驱动机制的STIRPAT模型,得出人口数量、富裕程度、技术水平或经济结构每分别发生1%的变化,将引起输入量相应发生0.99%、0.98%、0.17%、0.31%的变化.提升技术水平和优化经济结构具有较大调控空间,将是厦门物质减量化战略的实施重点.     

基于过程模型CROBAS的全局灵敏度分析方法比较

过程机理模型在开发过程中常受限于生理学参数无法直接或准确测量.全局灵敏度分析可以评估模型预测结果对于生理学参数变化的响应,为模型结构改进、数据收集和参数校准提供参考.本研究基于过程模型CROBAS,以华山松为例,选取模型中描述树木结构关系的10个参数,以树高和各器官生物量的Nash-Sutcliffe效率(NSE)为目...     

Unified Materials Information System (UMIS): An Integrated Material Stocks and Flows Data Structure

Modern society depends on the use of many diverse materials. Effectively managing these materials is becoming increasingly important and complex, from the analysis of supply chains, to quantifying their environmental impacts, to understanding future resource availability. Material stocks and flows data enable such analyses, but currently exist mainly as discrete packages, with highly varied type, scope, and structure. These factors constitute a powerful barrier to holistic integration and thus universal analysis of existing and yet to be published material stocks and flows data. We present the Unified Materials Information System (UMIS) to overcome this barrier by enabling material stocks and flows data to be comprehensively integrated across space, time, materials, and data type independent of their disaggregation, without loss of information, and avoiding double counting. UMIS can therefore be applied to structure diverse material stocks and flows data and their metadata across material systems analysis methods such as material flow analysis (MFA), input‐output analysis, and life cycle assessment. UMIS uniquely labels and visualizes processes and flows in UMIS diagrams; therefore, material stocks and flows data visualized in UMIS diagrams can be individually referenced in databases and computational models. Applications of UMIS to restructure existing material stocks and flows data represented by block flow diagrams, system dynamics diagrams, Sankey diagrams, matrices, and derived using the economy‐wide MFA classification system are presented to exemplify use. UMIS advances the capabilities with which complex quantitative material systems analysis, archiving, and computation of material stocks and flows data can be performed.     

Parameter optimization and sensitivity analysis for large kinetic models using a real-coded genetic algorithm

Dynamic modeling is a powerful tool for predicting changes in metabolic regulation. However, a large number of input parameters, including kinetic constants and initial metabolite concentrations, are required to construct a kinetic model. Therefore, it is important not only to optimize the kinetic parameters, but also to investigate the effects of their perturbations on the overall system. We investigated the efficiency of the use of a real-coded genetic algorithm (RCGA) for parameter optimization and sensitivity analysis in the case of a large kinetic model involving glycolysis and the pentose phosphate pathway in Escherichia coli K-12. Sensitivity analysis of the kinetic model using an RCGA demonstrated that the input parameter values had different effects on model outputs. The results showed highly influential parameters in the model and their allowable ranges for maintaining metabolite-level stability. Furthermore, it was revealed that changes in these influential parameters may complement one another. This study presents an efficient approach based on the use of an RCGA for optimizing and analyzing parameters in large kinetic models.     

Sensitivity analysis to identify key parameters influencing Salmonella infection dynamics in a pig batch

In the context of managed herds, epidemiological models usually take into account relatively complex interactions involving a high number of parameters. Some parameters may be uncertain and/or highly variable, especially epidemiological parameters. Their impact on the model outputs must then be assessed by a sensitivity analysis, allowing to identify key parameters. The prevalence over time is an output of particular interest in epidemiological models, so sensitivity analysis methods adapted to such dynamic output are needed.In this paper, such a sensitivity analysis method, based on a principal component analysis and on analysis of variance, is presented. It allows to compute a generalised sensitivity index for each parameter of a model representing Salmonella spread within a pig batch. The model is a stochastic discrete-time model describing the batch dynamics and movements between rearing rooms, from birth to slaughterhouse delivery. Four health states were introduced: Salmonella-free, seronegative shedder, seropositive shedder and seropositive carrier. The indirect transmission was modelled via an infection probability function depending on the quantity of Salmonella in the rearing room.Simulations were run according to a fractional factorial design enabling the estimation of main effects and two-factor interactions. For each of the 18 epidemiological parameters, four values were chosen, leading to 4096 scenarios. For each scenario, 15 replications were performed, leading to 61 440 simulations. The sensitivity analysis was then conducted on the seroprevalence output.The parameters governing the infection probability function and residual room contaminations were identified as key parameters. To control the Salmonella seroprevalence, efficient measures should therefore aim at these parameters. Moreover, the shedding rate and maternal protective factor also had a major impact. Therefore, further investigation on the protective effect of maternal or post-infection antibodies would be needed.     

Uncertainty analysis of the productivity of cattle populations in tropical drylands

This article presents an uncertainty analysis of the productivity of cattle herds in traditional farming systems of West and Central African drylands. The study focused on productivity rates in animal numbers (RN) and meat weights (RW) estimated from a herd growth model, which were compared with FAOSTAT-based estimates. The uncertainty analysis contained the following two steps: uncertainty propagation and a global sensitivity analysis. The analysis was based on a state-of-the-art of the current knowledge and a set of available data on the herd performances. The calculations used Monte Carlo simulations to estimate the 95% confidence intervals (CI) of RN and RW and the standardized regression coefficients method to estimate the contribution of the input variables to the outputs variances. The mean rate RN was estimated to 0.127 animal/animal-year with a 95% CI of (0.091, 0.163) and the mean rate RW to 11.7 kg/animal-year with a 95% CI of (8.8, 14.7), corresponding to relative variation around the mean of about ±29% and ±25%, respectively. The input variables that contributed most to the variance of RN (almost 76% of the output variance) were the calving rate, the adult female mortality rate and the female proportion in the population (determined by the pattern of the male offtake in the herds). The input variables that contributed most to the variance of RW were the same as those for RN plus the adult live weights. The CI ranges that were estimated in this article indicate that productivity rates based on literature data or expert estimations of the herd performances should be considered with caution. Research efforts based on gold-standard herd monitoring protocols accounting for temporal and spatial variations should be undertaken in future to decrease the knowledge gaps on the input variables that contribute most to these ranges.     

A Data Characterization Framework for Material Flow Analysis

The validity of material flow analyses (MFAs) depends on the available information base, that is, the quality and quantity of available data. MFA data are cross‐disciplinary, can have varying formats and qualities, and originate from heterogeneous sources, such as official statistics, scientific models, or expert estimations. Statistical methods for data evaluation are most often inadequate, because MFA data are typically isolated values rather than extensive data sets. In consideration of the properties of MFA data, a data characterization framework for MFA is presented. It consists of an MFA data terminology, a data characterization matrix, and a procedure for database analysis. The framework facilitates systematic data characterization by cell‐level tagging of data with data attributes. Data attributes represent data characteristics and metainformation regarding statistical properties, meaning, origination, and application of the data. The data characterization framework is illustrated in a case study of a national phosphorus budget. This work furthers understanding of the information basis of material flow systems, promotes the transparent documentation and precise communication of MFA input data, and can be the foundation for better data interpretation and comprehensive data quality evaluation.