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.     

The value of information for integrated assessment models of climate change

We estimate the value of information (VOI) for three key parameters of climate integrated assessment models (IAMs): marginal damages at low temperature anomalies, marginal damages at high temperature anomalies, and equilibrium climate sensitivity. Most empirical studies of climate damages have examined temperature anomalies up to 3 °C, while some recent theoretical studies emphasize the risks of “climate catastrophes,” which depend on climate sensitivity and on marginal damages at higher temperature anomalies. We use a new IAM to estimate the VOI for each parameter over a range of assumed levels of study precision based on prior probability distributions calibrated using results from previous studies. We measure the VOI as the maximum fixed fraction of consumption that a social planner would be willing to pay to conduct a new study before setting a carbon tax. Our central results suggest that the VOI is greatest for marginal damages at high temperature anomalies.     

Uncertainty propagation in vegetation distribution models based on ensemble classifiers

Ensemble learning techniques are increasingly applied for species and vegetation distribution modelling, often resulting in more accurate predictions. At the same time, uncertainty assessment of distribution models is gaining attention. In this study, Random Forests, an ensemble learning technique, is selected for vegetation distribution modelling based on environmental variables. The impact of two important sources of uncertainty, that is the uncertainty on spatial interpolation of environmental variables and the uncertainty on species clustering into vegetation types, is quantified based on sequential Gaussian simulation and pseudo-randomization tests, respectively. An empirical assessment of the uncertainty propagation to the distribution modelling results indicated a gradual decrease in performance with increasing input uncertainty. The test set error ranged from 30.83% to 52.63% and from 30.83% to 83.62%, when the uncertainty ranges on spatial interpolation and on vegetation clustering, respectively, were fully covered. Shannon’s entropy, which is proposed as a measure for uncertainty of ensemble predictions, revealed a similar increasing trend in prediction uncertainty. The implications of these results in an empirical distribution modelling framework are further discussed with respect to monitoring setup, spatial interpolation and species clustering.     

Spatial distribution of ecological security status assessment of West-Liaohe River based on geographic information system

Eco-security assessment is a hot research area in resource and environmental science, which involves data with much spatial, non-linear, and random features. Geographic information system (GIS), as a useful tool to analyze and manage spatial information, has a superior advantage in this field. A case study in the western part of the Liaohe River featuring a method of eco-security spatial differences (ESSD) based on GIS is developed in this paper. The method includes four steps: 1) developing the pressure-state-response (P-S-R) framework with site data; 2) digitizing West-Liaohe River and setting its GRID database of ecosecurity assessment indicators; 3) figuring out the relative membership degree (RMD) of eco-security indicators by using the analytical hierarchy process with the weight of indicator; 4) classifying the security zone and mapping the assessment result of eco-security status in grid by GIS method of assigning and clustering. The visual spatial differences of eco-security based on GIS enables decision makers to know the status of eco-security better in making policies for achieving sustainability.     

Prevalence-adjusted optimisation of fuzzy models for species distribution

Most performance criteria which have been applied to train ecological models focus on the accuracy of the model predictions. However, these criteria depend on the prevalence of the training set and often do not take into account ecological issues such as the distinction between omission and commission errors. Moreover, a previous study indicated that model training based on different performance criteria results in different optimised models. Therefore, model developers should train models based on different performance criteria and select the most appropriate model depending on the modelling objective. This paper presents a new approach to train fuzzy models based on an adjustable performance criterion, called the adjusted average deviation (aAD). This criterion was applied to develop a species distribution model for spawning grayling in the Aare River near Thun, Switzerland. To analyse the strengths and weaknesses of this approach, it was compared to model training based on other performance criteria. The results suggest that model training based on accuracy-based performance criteria may produce unrealistic models at extreme prevalences of the training set, whereas the aAD allows for the identification of more accurate and more reliable models. Moreover, the adjustable parameter in this criterion enables modellers to situate the optimised models in the search space and thus provides an indication of the ecological model relevance. Consequently, it may support modellers and river managers in the decision making process by improving model reliability and insight into the modelling process. Due to the universality and the flexibility of the approach, it could be applied to any other ecosystem or species, and may therefore be valuable to ecological modelling and ecosystem management in general.     

Revisiting Kappa to account for change in the accuracy assessment of land-use change models

Land-use change models are typically calibrated to reproduce known historic changes. Calibration results can then be assessed by comparing two datasets: the simulated land-use map and the actual land-use map at the same time. A common method for this is the Kappa statistic, which expresses the agreement between two categorical datasets corrected for the expected agreement. This expected agreement is based on a stochastic model of random allocation given the distribution of class sizes. However, when a model starts from an initial land-use map and makes changes to it, that stochastic model does not pose a meaningful reference level. This paper introduces K_Simulation, a statistic that is identical in form to the Kappa statistic but instead applies a more appropriate stochastic model of random allocation of class transitions relative to the initial map. The new method is illustrated on a simple example and then the results of the Kappa statistic and K_Simulation are compared using the results of a land-use model. It is found that only K_Simulation truly tests models in their capacity to explain land-use changes over time, and unlike Kappa it does not inflate results for simulations where little change takes place over time.     

Software for prioritizing conservation actions based on probabilistic information

Marxan is the most common decision-support tool used to inform the design of protected-area systems. The original version of Marxan does not consider risk and uncertainty associated with threatening processes affecting protected areas, including uncertainty about the location and condition of species’ populations and habitats now and in the future. We described and examined the functionality of a modified version of Marxan, Marxan with Probability. This software explicitly considers 4 types of uncertainty: probability that a feature exists in a particular place (estimated based on species distribution models or spatially explicit population models); probability that features in a site will be lost in the future due to a threatening process, such as climate change, natural catastrophes, and uncontrolled human interventions; probability that a feature will exist in the future due to natural successional processes, such as a fire or flood; and probability the feature exists but has been degraded by threatening processes, such as overfishing or pollution, and thus cannot contribute to conservation goals. We summarized the results of 5 studies that illustrate how each type of uncertainty can be used to inform protected area design. If there were uncertainty in species or habitat distribution, users could maximize the chance that these features were represented by including uncertainty using Marxan with Probability. Similarly, if threatening processes were considered, users minimized the chance that species or habitats were lost or degraded by using Marxan with Probability. Marxan with Probability opens up substantial new avenues for systematic conservation planning research and application by agencies.     

Modified Weibull multi-state models for the analysis of animal carcinogenicity data

The Peto test is the standard method of analysis used in carcinogenicity studies to compare tumor incidence in groups of animals. It assumes that tumors are either instantly fatal or have no effect on mortality and requires a judgement of the lethality of each tumor. To avoid this requirement, parametric multi-state models have been proposed. In addition these allow estimation of tumor onset and mortality rates. This paper considers two such models and presents a modification. It is shown that the modified models provide a better fit to carcinogenicity data and simulated data are used to show that the modified models provide a modest increase in test power relative to the Peto test.     

Ecological relevance of performance criteria for species distribution models

Species distribution models have often been developed based on ecological data. To develop reliable data-driven models, however, a sound model training and evaluation procedures are needed. A crucial step in these procedures is the assessment of the model performance, with as key component the applied performance criterion. Therefore, we reviewed seven performance criteria commonly applied in presence-absence modelling (the correctly classified instances, Kappa, sensitivity, specificity, the normalised mutual information statistic, the true skill statistic and the odds ratio) and analysed their application in both the model training and evaluation process. Although estimates of predictive performance have been used widely to assess final model quality, a systematic overview was missing because most analyses of performance criteria have been empirical and only focused on specific aspects of the performance criteria. This paper provides such an overview showing that different performance criteria evaluate a model differently and that this difference may be explained by the dependency of these criteria on the prevalence of the validation set. We showed theoretically that these prevalence effects only occur if the data are inseparable by an n-dimensional hyperplane, n being the number of input variables. Given this inseparability, different performance criteria focus on different aspects of model performance during model training, such as sensitivity, specificity or predictive accuracy. These findings have important consequences for ecological modelling because ecological data are mostly inseparable due to data noise and the complexity of the studied system. Consequently, it should be very clear which aspect of the model performance is evaluated, and models should be evaluated consistently, that is, independent of, or taking into account, species prevalence. The practical implications of these findings are clear. They provide further insight into the evaluation of ecological presence/absence models and attempt to assist modellers in their choice of suitable performance criteria.     

Comparing canopy leaf temperature of three Central European tree species based on simultaneous confidence bands for penalized splines

Temperature is an important physical factor that is known to strongly affect biodiversity as well as ecosystems and their functioning. However, research in this area is still relatively limited; this may also be attributed to the multitude of influencing factors and the complexity of the statistics involved. This study analyzes the differences between the surface temperature of three Central European broadleaf tree species. A better understanding of these differences may help to elucidate the role of microclimate in biodiversity. We consider a time series of high-resolution thermal images taken from a meteorological observation tower and calculate mean canopy leaf temperatures for beech, ash and maple (Fagus silvatica, Fraxinus excelsior and Acer pseudoplatanus). In a first step, comparable image areas are extracted from the thermal image sections of the crown of each tree species avoiding shadow areas, branches, etc. We used an automatic segmentation technique, the Otsu thresholding. Extracted canopy leaf temperature values were then processed and the resulting temperature profiles estimated by O’Sullivan penalized splines. For comparing the differences in canopy leaf temperature over time, we propose the construction of simultaneous confidence bands. The analyses show that there are significant—though small—differences in canopy surface temperature between the three tree species.     

The maximum likelihood based intensity estimate for circular point processes

Identifying the geometrical nature of spatial point patterns plays an important role in many areas of scientific research. Common types of spatial point processes involve random, regular, and cluster patterns. However, some point patterns suggest identifiable geometrical shapes such as a circular or other conic patterns. These patterns may be recognized as either a specific clustered shape or an inhomogeneous point pattern. Less noisy conic shapes, including circular patterns, are heavily discussed in the pattern recognition literature, but the goodness-of-fit of conic-fitting algorithms is rarely discussed for very noisy data. This study addresses a parameter estimation technique for noisy circular point patterns using the maximum likelihood principle. Additionally, a spatial statistical tool known as the L-function is used to investigate whether the fitted location pattern is reasonably attributable to a circular shape. A novel quantity named ‘relative log-error’ (\(\gamma \)) is introduced to quantify the goodness-of-fit for circular model fits. An iteratively re-weighted least squares procedure is introduced and robustness is evaluated under several error structures. Computational efficiency of the current and novel circle-fitting methods is also discussed. The findings are applied to two environmental science data sets.     

村落生态系统分布特征和模式的探讨

村落生态系统的分布是地表突出和普遍的现象。本文概括总结了区域性村落生态系统分布的一般性原则，其分布特征表现为景观性、分散集聚性、动态迁移性、梯度性、趋适性、界限性以及人文性等各个方面；对诸如平原、山区、湖区、盆地、丘陵台地、岛屿以及过渡区等各种地貌类型区提出相应的理论分布模式。     

Regression models for some solute distribution equilibria in the terrestrial environment

Sorption coefficients (K_p) of several organochlorine insecticides (OCs) in volcanic ash silt from Central Java are presented.

Selected experimental and estimated octanol‐water partition coefficient (P) values are used to study log‐log regressions with K_p data collected from the literature (PAHs, chlorophenols, phenylureas, chloro‐s‐triazines, carbamates and organophosphorus insecticides) and those of the OCs determined in the present study. Leaching distances and bioactivities in soil are correlated with the K_p values of the pesticides, and with the organic matter and the water content of the soil.     

Effects of sample survey design on the accuracy of classification tree models in species distribution models

We evaluated the effects of probabilistic (hereafter DESIGN) and non-probabilistic (PURPOSIVE) sample surveys on resultant classification tree models for predicting the presence of four lichen species in the Pacific Northwest, USA. Models derived from both survey forms were assessed using an independent data set (EVALUATION). Measures of accuracy as gauged by resubstitution rates were similar for each lichen species irrespective of the underlying sample survey form. Cross-validation estimates of prediction accuracies were lower than resubstitution accuracies for all species and both design types, and in all cases were closer to the true prediction accuracies based on the EVALUATION data set. We argue that greater emphasis should be placed on calculating and reporting cross-validation accuracy rates rather than simple resubstitution accuracy rates. Evaluation of the DESIGN and PURPOSIVE tree models on the EVALUATION data set shows significantly lower prediction accuracy for the PURPOSIVE tree models relative to the DESIGN models, indicating that non-probabilistic sample surveys may generate models with limited predictive capability. These differences were consistent across all four lichen species, with 11 of the 12 possible species and sample survey type comparisons having significantly lower accuracy rates. Some differences in accuracy were as large as 50%. The classification tree structures also differed considerably both among and within the modelled species, depending on the sample survey form. Overlap in the predictor variables selected by the DESIGN and PURPOSIVE tree models ranged from only 20% to 38%, indicating the classification trees fit the two evaluated survey forms on different sets of predictor variables. The magnitude of these differences in predictor variables throws doubt on ecological interpretation derived from prediction models based on non-probabilistic sample surveys.     

Geostatistical model averaging based on conditional information criteria

Variable selection in geostatistical regression is an important problem, but has not been well studied in the literature. In this paper, we focus on spatial prediction and consider a class of conditional information criteria indexed by a penalty parameter. Instead of applying a fixed criterion, which leads to an unstable predictor in the sense that it is discontinuous with respect to the response variables due to that a small change in the response may cause a different model to be selected, we further stabilize the predictor by local model averaging, resulting in a predictor that is not only continuous but also differentiable even after plugging-in estimated model parameters. Then Stein’s unbiased risk estimate is applied to select the penalty parameter, leading to a data-dependent penalty that is adaptive to the underlying model. Some numerical experiments show superiority of the proposed model averaging method over some commonly used variable selection methods. In addition, the proposed method is applied to a mercury data set for lakes in Maine.     

基于生态系统管理的湿地概念生态模型研究

湿地是地球上的一种重要生态系统,基于生态系统管理理念,进行湿地保护与管理,既是湿地科学发展的必然结果.也是当前湿地保护与管理的客观需求.湿地生态模型是以湿地生态系统作为研究对象的模型,是对湿地生态系统组成、结构、过程和功能进行简化、类比或抽象,是用来反映湿地生态系统各种过程和关系的定性或定量化工具.湿地概念生态模型是各类湿地生态模型中最基本的类型,是对湿地生态系统组成及其相互关系的一种简约的定性表达,特别是指人类活动影响下湿地生态系统因子变化及其相互关系的概念性表达.湿地概念生态模型构建的主要目的是旨在识别人类活动对湿地生态系统的驱动与胁迫,这些驱动与胁迫产生的一系列生态效应,以及湿地生态系统对此所表现出来的特征.湿地生态系统是一个多层次、多因子组成的,结构复杂、功能多样、具有多向反馈和调节机制的复杂大系统或巨系统.影响系统状态或驱动系统变化的因子众多,既有来自系统内部的、也有来自系统外部的,它们对系统造成的影响往往具有联动关系和因果效应.湿地概念生态模型就是在生态系统管理理论指导下,将这些系统因子及其关系抽象并提取出来,以"驱动-胁迫-效应-表征"为主线,判断系统变化与演化背后存在的因果关系,构建能够反映系统变化与演化特征和规律的结构性关系网络模型.湿地概念生态模型研究的意义在于在科学与决策之间架起一座桥梁,为实施湿地生态保护与管理提供指导,同时为建立湿地数量化模型奠定基础.     

基于GIS的中国API指数时空分布规律研究

以2009年1月至2012年12月的中国120个重点城市的API监测数据为基础,通过选取最优的空间插值方法获得各月及各季节的API空间分布图,并运用剖面线分析等空间数据分析方法研究其空间分布规律。结果表明,API在不同时段的变化较大;存在着明显的季节变化趋势,总体上冬季最高、春季次之、夏季最低,且夏秋季基本均分布在100以内;中国空气质量状况总体良好,API主要分布在51~100之间,但有较多地区分布在80~100间,空气环境质量仍不容乐观;API分布着以兰州和西宁为中心、陕西省西安市为中心及乌鲁木齐市和吐鲁番市为中心的几个空气质量较差的高值集聚的＂热点＂区域及海南省、广东省及福建省的沿海区域、西藏自治区等几个空气质量较好的低值集聚的＂冷点＂区域;在N-S、WE、NW-SE、NE-SW四个剖面线方向上相同季节的分布趋势基本一致,且同一方向上春夏秋冬四季的分布也大致相同,基本呈现＂低-高-低＂的分布趋势且北方地区明显高于南方地区。     

Potential effects of climate change on ecosystem and tree species distribution in British Columbia

A new ecosystem-based climate envelope modeling approach was applied to assess potential climate change impacts on forest communities and tree species. Four orthogonal canonical discriminant functions were used to describe the realized climate space for British Columbia's ecosystems and to model portions of the realized niche space for tree species under current and predicted future climates. This conceptually simple model is capable of predicting species ranges at high spatial resolutions far beyond the study area, including outlying populations and southern range limits for many species. We analyzed how the realized climate space of current ecosystems changes in extent, elevation, and spatial distribution under climate change scenarios and evaluated the implications for potential tree species habitat. Tree species with their northern range limit in British Columbia gain potential habitat at a pace of at least 100 km per decade, common hardwoods appear to be generally unaffected by climate change, and some of the most important conifer species in British Columbia are expected to lose a large portion of their suitable habitat. The extent of spatial redistribution of realized climate space for ecosystems is considerable, with currently important sub-boreal and montane climate regions rapidly disappearing. Local predictions of changes to tree species frequencies were generated as a basis for systematic surveys of biological response to climate change.