Categorising Count Data into Ordinal Responses with Application to Ecological Communities

Count data sets may involve overdispersion from a set of species and underdispersion from another set which would require fitting different models (e.g. a negative binomial model for the overdispersed set and a binomial model for the underdispersed one). Additionally, many count data sets have very high counts and very low counts. Categorising these counts into ordinal categories makes the actual counts less influential in the model fitting, giving broad categories which enable us to detect major broadly based patterns of turnover or nestedness shown by groups of species. In this paper, a strategy of categorising count data into ordinal data was carried out and also we implemented measures to compare different cluster structures. The application of this categorising strategy and a comparison of clustering results between count and categorised ordinal data in two ecological community data sets are shown. A major advantage of using our ordinal approach is that it allows for the inclusion of all different levels of dispersion in the data in one methodology, without treating the data differently. This reduction of the parameters on modelling different levels of dispersion does not substantially change the results in clustering structure. In the two data sets used in this paper, we observed ordinal clustering structure up to 93.1 % similar to those from the count data approaches. This has the important implication of supporting simpler, faster data collection using ordinal scales only.Supplementary materials accompanying this paper appear on-line.     

Multilevel Latent Gaussian Process Model for Mixed Discrete and Continuous Multivariate Response Data

We propose a Bayesian model for mixed ordinal and continuous multivariate data to evaluate a latent spatial Gaussian process. Our proposed model can be used in many contexts where mixed continuous and discrete multivariate responses are observed in an effort to quantify an unobservable continuous measurement. In our example, the latent, or unobservable measurement is wetland condition. While predicted values of the latent wetland condition variable produced by the model at each location do not hold any intrinsic value, the relative magnitudes of the wetland condition values are of interest. In addition, by including point-referenced covariates in the model, we are able to make predictions at new locations for both the latent random variable and the multivariate response. Lastly, the model produces ranks of the multivariate responses in relation to the unobserved latent random field. This is an important result as it allows us to determine which response variables are most closely correlated with the latent variable. Our approach offers an alternative to traditional indices based on best professional judgment that are frequently used in ecology. We apply our model to assess wetland condition in the North Platte and Rio Grande River Basins in Colorado. The model facilitates a comparison of wetland condition at multiple locations and ranks the importance of in-field measurements.     

Bayesian Semiparametric Model for Pathway-Based Analysis with Zero-Inflated Clinical Outcomes

In this paper, we propose a semiparametric regression approach for identifying pathways related to zero-inflated clinical outcomes, where a pathway is a gene set derived from prior biological knowledge. Our approach is developed by using a Bayesian hierarchical framework. We model the pathway effect nonparametrically into a zero-inflated Poisson hierarchical regression model with an unknown link function. Nonparametric pathway effect was estimated via a kernel machine, and the unknown link function was estimated by transforming a mixture of the beta cumulative density function. Our approach provides flexible nonparametric settings to describe the complicated association between gene expressions and zero-inflated clinical outcomes. The Metropolis-within-Gibbs sampling algorithm and Bayes factor were adopted to make statistical inferences. Our simulation results support that our semiparametric approach is more accurate and flexible than zero-inflated Poisson regression with the canonical link function, which is especially true when the number of genes is large. The usefulness of our approach is demonstrated through its applications to the Canine data set from Enerson et al. (Toxicol Pathol 34:27–32, 2006). Our approach can also be applied to other settings where a large number of highly correlated predictors are present.Supplementary materials accompanying this paper appear on-line.     

Empirical reformulation of the universal soil loss equation for erosion risk assessment in a tropical watershed

Efficient intervention to control soil erosion in rural tropical landscapes requires accurate models for predicting the spatial location and intensity of degradation. The Universal Soil Loss Equation (USLE) has commonly been applied for spatial erosion risk assessment in the tropics, but has rarely been validated using ground observations of soil degradation. As with any empirical model, application in new regions requires calibration before results are used for decision support. We evaluated USLE effectiveness for predicting erosion in a small watershed in western Kenya based on 420 georeferenced ground observations of ordinal erosion class (three categories) systematically collected from throughout the basin. Relativized model factors were parameterized using standard remote assessment methods based on interpolated spatial data layers. Inference of degradation status at cultivated sites was estimated by calibration to near infrared diffuse reflectance spectra obtained from sampled soils; diagnostic models based on spectra produced validation accuracies of 78% for three categories. Association between USLE predicted risk and observed erosion, estimated using mixed effects logistic regression to control for within-site variability, correctly classified only 38% of sites into three degradation classes and model sensitivity for delineating regions of severe degradation was only 28%. Graphical modeling was used to identify those USLE risk factors that were conditionally associated with observed degradation, and an ordinal logistic regression model, employing only these factors was developed. This alternative model, which allowed statistical flexibility in estimating effect direction and strength, correctly predicted ordinal degradation class at 54% of field sites, with 55% sensitivity for the severe degradation class. This result suggests a critical need for efficient ground-based sampling schemes to be used in conjunction with flexible statistical models based on USLE factors for future investments in erosion risk assessment in the tropics.     

Generalized Linear Latent Variable Models for Multivariate Count and Biomass Data in Ecology

In this paper we consider generalized linear latent variable models that can handle overdispersed counts and continuous but non-negative data. Such data are common in ecological studies when modelling multivariate abundances or biomass. By extending the standard generalized linear modelling framework to include latent variables, we can account for any covariation between species not accounted for by the predictors, notably species interactions and correlations driven by missing covariates. We show how estimation and inference for the considered models can be performed efficiently using the Laplace approximation method and use simulations to study the finite-sample properties of the resulting estimates. In the overdispersed count data case, the Laplace-approximated estimates perform similarly to the estimates based on variational approximation method, which is another method that provides a closed form approximation of the likelihood. In the biomass data case, we show that ignoring the correlation between taxa affects the regression estimates unfavourably. To illustrate how our methods can be used in unconstrained ordination and in making inference on environmental variables, we apply them to two ecological datasets: abundances of bacterial species in three arctic locations in Europe and abundances of coral reef species in Indonesia.Supplementary materials accompanying this paper appear on-line.     

Assessment of soil erosion indicators for maize-based agro-ecosystems in Kenya

Measuring soil loss is costly, must cover a range of field situations, is not standardized, and is season dependent. In addition, use of sparse soil loss data (from other studies) compromises the integrity of many erosion models. Easily assessable soil erosion indicators to monitor the cumulative effect of erosion between tillage/weeding and harvesting called eroding clods, flow surfaces, pre-rills, and rills were surveyed directly after the 1995 rainy season in the Taita Taveta district of Kenya, to assessed the utility of each indicator. Their incidences were modeled using CPA. In the area, 70 maize plots in 11 map units, having considerable variation in altitude, land cover, rainfall, and geomorphology, were surveyed. Soil loss was considered variable between plots due to differences in surface soil, land cover, infrastructure (trash lines, grass strips, and Fanya-juu), crop management, slope, and map unit. The eroding clods indicator proved of little significance because the initial clods cover was unknown; the indicator probably relates better to soil erodibility then to soil loss. Flow surfaces, formed during erosive showers, were less present on fields with a higher ground and canopy cover, if the area of eroding clods was high, and if the topsoil had no loam which reduces chances of sealing; no impact of infrastructure, tillage, and weeding were detected. Fewer pre-rills were present where the fraction of groundcover was high, where Pigeon Peas were not grown (they cause micro-relief and concentrated flows), where weeding ended late (time effect), where more flow surfaces occurred, where Fanya-juu was constructed (less steep slopes), where the top-soil contained little sand (less sediment entrainment), and where maize was intercropped with vegetables (positive canopy cover effects). The model was not map unit specific and had an Adjusted R² of 67%. The log-linear relationship indicates that combined positive conditions exponentially reduce the occurrence of pre-rills. The “pre-rill” indicator related best to management-affected site conditions and seems to reflect best the cumulative effects of soil loss over time. Rills were found at 18 sites located in drier areas on sandy–clay soils. The model suggested more rills if the topsoil contains no silt; this makes the soil susceptible to compaction, peptisation when wet, and rill formation.     

中国区域多源土地覆被遥感产品类别精度探索性分析

分析了GLOBCOVER,MODIS COLLECTION5,GLCNMO和GLC2000四种数据在中国区域的类别精度、空间一致性及类别均质性空间分布特征,结果表明:四种全球土地覆被遥感数据与参考数据存在一定的混淆现象,混淆主要发生于林地、草地、灌木和耕地之间,其中灌木与其他地类的混淆程度最为严重;四种数据完全空间一致性区域主要位于以林地、耕地、草地为主的光谱特征较为显著区域,其总面积约占研究区域总面积的39.03%;较为一致区域主要分布于完全一致区域周围,该区域的面积约占研究区总面积的40.67%,该区域主要地表类型为草地和裸地以及耕地为主;不一致区域的面积约占研究区总面积的18.56%,该区域地表类型较为复杂,地表景观呈现明显的破碎现象,耕地、林地、灌木、草地交错分布;完全不一致区域约占研究区总面积的1.74%,并且集中分布于胡焕庸地理分界线两侧,成典型的带状分布特征;四种土地覆被遥感数据的空间均质性谱图整体上趋于一致,主要分布于中国的华北平原、西北沙漠地区和东南地区。图谱表明,各地表土地覆被类别在中国西南地区的均质性区域几乎消失,这主要是因为该区域地表景观过于复杂,表现出强烈的景观异质性。本文为用户合理利用这些数据提供科学合理的依据,为多源土地覆被数据融合提供了必要的先验知识。     

土壤侵蚀模型研究进展

国内外土壤侵蚀模型的发展过程,可以大致划分为经验统计模型、物理过程模型与分布式模型三个阶段.就这三个阶段,介绍了国内外土壤侵蚀模型的研究成果.并将地理信息系统(GIS)在土壤侵蚀模型中的应用分为三类,一是以GIS为工具,利用GIS提取模型所需因子,然后按照模型要求利用GIS的图形运算和地图代数运算,最后得到计算结果.二是将GIS与土壤侵蚀模型作为两个不同的系统,考虑结合方法的问题.三是利用GIS开发新的模型或改善已有模型.     

ASSESSING LANDSLIDE SUSCEPTIBILITY BY INCORPORATING THE SURFACE COVER INDEX AS A MEASUREMENT OF VEGETATIVE COVER

Local environmental conditions are known to be the most influential in landslide dynamics. Some variables, such as slope, elevation, lithology, vegetative cover, and soil type, are more common and influential than others. Every variable, except for vegetative cover, has been incorporated into many different statistical models as a continuous variable showing nuances and differentiation among the data. In regions where vegetative cover is the single most important variable in determining slope stability, a land cover classification cannot provide the level of information required for efficient modeling of landslide events. It is hoped that the surface cover index (SCI) can be used to numerically assess vegetative cover by using Landsat imagery and sub‐pixel analysis. Two models utilizing simple raster calculations involving slope and the SCI were created. Each model was then assessed and validated for accuracy by using a user‐created multi‐temporal landslide inventory of the Dominical, Costa Rica area. Results determined that normalized inputs of slope and SCI can produce an algorithm with a high degree of accuracy and proved that the SCI can be used in assessing landslide hazard in a tropical forest environment. Copyright © 2011 John Wiley & Sons, Ltd.     

A comprehensive approach to soil‐atmosphere trace‐gas flux estimation with static chambers

A new procedure (HMR) for soil‐atmosphere trace‐gas flux estimation with static chambers is presented. It classifies data series into three categories according to criteria based on the application of a particular non‐linear model and provides statistical data analyses for all categories. The two main categories are non‐linear and linear concentration data, for which data are analysed by, respectively, the non‐linear model and linear regression. The third category is represented by concentration data within the range of experimental error, or noise, from sites with no significant flux. Data in this category may be analysed by linear regression or simply classified as no flux. The particular non‐linear model has been selected among alternatives because its exponential curvature generally fits non‐linear static chamber concentration data well, and because it can be proven, mathematically, to be robust against horizontal gas transport through the soil or leaks in the chamber. The application of the HMR procedure is demonstrated on 244 data series of nitrous oxide accumulation over time. On average, 47% of these data were non‐linear, with an average flux increase over linear regression of 52%. The classification and analysis of data with a small signal‐to‐noise ratio requires special attention, and it is demonstrated how diagnostic graphical plots may be used to select the appropriate data analysis. The HMR procedure has been implemented as a free add‐on package for the free software R and is available for download through CRAN ( http://www.r‐project.org ).     

Imputation Approaches for Animal Movement Modeling

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.     

棉花动态模拟模型研究进展

该文对棉花生理生态模型、棉花形态结构模型以及棉花结构功能模型的研究动态进行了综述，提出将形态结构和生理生态过程紧密结合的棉花结构功能模型的研究应是今后棉花模拟研究的重点，指出了目前生理生态模型和结构模型结合遇到的关键理论和技术问题：未能实现冠层微环境的精确模拟；物质分配和植株结构的结合研究还处于初步阶段；地上部分和根系耦合模拟还未实现。最后对该领域今后的研究趋势和内容进行了探讨：应基于形态结构模型进行冠层微环境的精确模拟；地上部分的物质分配可基于源－汇模型；地上部分和根系进行耦合模拟时，可将地上部分看作是“源”，根据根系各部分的“汇强”模拟物质分配和根的生长。     

A Non-Gaussian Spatial Generalized Linear Latent Variable Model

We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents.     

苏南地区典型作物冠层阻力参数及潜热通量的模拟

准确测算和模拟农田潜热通量对农业生产有着重要意义。该研究基于波文比能量观测系统对苏南地区夏玉米和冬小麦生育期内潜热通量进行连续观测,采用Katerji-Perrier（KP）和Todorovic（TD）两种方法来确定Penman-Monteith（P-M）模型中冠层阻力参数,探究两种冠层阻力参数子模型的估算误差及成因。结果表明：冬小麦生育期内主要气象因子呈现相似变化趋势,净辐射日均值呈现出波动上升趋势。两种冠层阻力参数子模型对冬小麦潜热通量模拟均取得良好的模拟效果,模拟R2不小于0.84,纳什系数不小于0.86,但KP模型精度稍高于TD模型。KP模型对冬小麦和夏玉米潜热通量均有高估,而TD模型高估了夏玉米潜热通量,饱和水汽压差是影响KP和TD两种冠层阻力参数子模型误差的主要因素,且饱和水汽压差越大绝对误差越大。研究为当地农业用水管理提供科学依据。     

Multi-scale Modeling of Animal Movement and General Behavior Data Using Hidden Markov Models with Hierarchical Structures

Hidden Markov models (HMMs) are commonly used to model animal movement data and infer aspects of animal behavior. An HMM assumes that each data point from a time series of observations stems from one of N possible states. The states are loosely connected to behavioral modes that manifest themselves at the temporal resolution at which observations are made. Due to advances in tag technology and tracking with digital video recordings, data can be collected at increasingly fine temporal resolutions. Yet, inferences at time scales cruder than those at which data are collected and, which correspond to larger-scale behavioral processes, are not yet answered via HMMs. We include additional hierarchical structures to the basic HMM framework, incorporating multiple Markov chains at various time scales. The hierarchically structured HMMs allow for behavioral inferences at multiple time scales and can also serve as a means to avoid coarsening data. Our proposed framework is one of the first that models animal behavior simultaneously at multiple time scales, opening new possibilities in the area of animal movement and behavior modeling. We illustrate the application of hierarchically structured HMMs in two real-data examples: (i) vertical movements of harbor porpoises observed in the field, and (ii) garter snake movement data collected as part of an experimental design. Supplementary materials accompanying this paper appear online.     

Another Look at Bayesian Analysis of AMMI Models for Genotype-Environment Data

Linear–bilinear models are frequently used to analyze two-way data such as genotype-by-environment data. A well-known example of this class of models is the additive main effects and multiplicative interaction effects model (AMMI). We propose a new Bayesian treatment of such models offering a proper way to deal with the major problem of overparameterization. The rationale is to ignore the issue at the prior level and apply an appropriate processing at the posterior level to be able to arrive at easily interpretable inferences. Compared to previous attempts, this new strategy has the great advantage of being directly implementable in standard software packages devoted to Bayesian statistics such as WinBUGS/OpenBUGS/JAGS. The method is assessed using simulated datasets and a real dataset from plant breeding. We discuss the benefits of a Bayesian perspective to the analysis of genotype-by-environment interactions, focusing on practical questions related to general and local adaptation and stability of genotypes. We also suggest a new solution to the estimation of the risk of a genotype not exceeding a given threshold.     

Development and evaluation of predictive habitat models to assist the conservation planning of a threatened lucanid beetle, Hoplogonus simsoni, in north-east Tasmania

The use of predictive habitat distribution models by land managers in the conservation management of threatened species is increasing. Few models, however, are subsequently field-checked and evaluated. This study evaluates the statistical strength and usefulness for conservation purposes of three predictive habitat models developed for a threatened stag beetle, Hoplogonus simsoni, found in the wet eucalypt forests and mixed/rainforests of north-east Tasmania. The relationship between various environmental variables for which spatial (GIS) information was available and the density, frequency of occurrence and presence/absence of the species was investigated using generalised linear modelling. Models developed were coupled with the GIS data to develop maps of predicted occurrence within the species’ range, grouped into categories of habitat quality. The models found that altitude, aspect, slope, distance to nearest stream and overstorey tree height were significantly associated with the occurrence of the species. Evaluation of the statistical strength of the models with independent data of species’ occurrence collected at 95 sites found that the density model performed poorly with little correlation between predicted and observed densities of the species. The frequency of occurrence model, however, showed a moderate ability to predict both species’ abundance and presence/absence. The presence/absence model had a similar discriminatory ability in predicting presence or absence of H. simsoni, but also showed some potential as an indirect predictor of species’ abundance. Assuming a correlation between relative abundance and habitat quality, the frequency of occurrence predictive model appeared to be the better and more direct discriminator of high quality habitat relative to the other models. The value of species’ habitat models and the need to evaluate their utility in the development of conservation strategies are discussed.     

Non-homogeneity of variance components from spatially nested sampling of the soil

Spatially nested sampling and the associated nested analysis of variance by spatial scale is a well-established methodology for the exploratory investigation of soil variation over multiple, disparate scales. The variance components that can be estimated this way can be accumulated to approximate the variogram. This allows us to identify the important scales of variation, and the general form of the spatial dependence, in order to plan more detailed sampling by design-based or model-based methods. Implicit in the standard analyses of nested sample data is the assumption of homogeneity in the variance, i.e. that all variations from sub-station means at some scale represent a random variable of uniform variance. If this assumption fails then the comparable assumption of stationarity in the variance, which is an important assumption in geostatistics, will also be implausible. However, data from nested sampling may be analysed with a linear mixed model in which the variance components are parameters which can be estimated by residual maximum likelihood (REML). Within this framework it is possible to propose an alternative variance parameterization in which the variance depends on some auxiliary variable, and so is not generally homogeneous. In this paper we demonstrate this approach, using data from nested sampling of chemical and biogeochemical soil properties across a region in central England, and use land use as our auxiliary variable to model non-homogeneous variance components. We show how the REML analysis allows us to make inferences about the need for a non-homogeneous model. Variances of soil pH and cation exchange capacity at different scales differ between these land uses, but a homogeneous variance model is preferable to such non-homogeneous models for the variance of soil urease activity at standard concentrations of urea.     

Risk Assessment for Toxicity Experiments with Discrete and Continuous Outcomes: A Bayesian Nonparametric Approach

We present a Bayesian nonparametric modeling approach to inference and risk assessment for developmental toxicity studies. The primary objective of these studies is to determine the relationship between the level of exposure to a toxic chemical and the probability of a physiological or biochemical response. We consider a general data setting involving clustered categorical responses on the number of prenatal deaths, the number of live pups, and the number of live malformed pups from each laboratory animal, as well as continuous outcomes (e.g., body weight) on each of the live pups. We utilize mixture modeling to provide flexibility in the functional form of both the multivariate response distribution and the various dose–response curves of interest. The nonparametric model is built from a structured mixture kernel and a dose-dependent Dirichlet process prior for the mixing distribution. The modeling framework enables general inference for the implied dose–response relationships and for dose-dependent correlations between the different endpoints, features which provide practical advances relative to traditional parametric models for developmental toxicology. We use data from a toxicity experiment that investigated the toxic effects of an organic solvent (diethylene glycol dimethyl ether) to demonstrate the range of inferences obtained from the nonparametric mixture model, including comparison with a parametric hierarchical model.Supplementary materials accompanying this paper appear on-line.     

基于证据理论的多源遥感产品土地覆被分类精度优化

针对现有土地覆被遥感产品及融合方法存在的不足,该文提出了一种新的分类体系转换方法,实现了证据理论(Dempster-Shafer)框架下多源产品的集成,并以GEOWIKI、林业调查数据为参考,通过绝对及交叉验证方法对融合结果精度进行了评价。研究结果表明:无论总体精度还是类别精度,融合结果与原始数据相比均有一定提高,说明在融合过程中,吸收了多源数据的类别分布特征,做到了多源数据间的互补。通过融合结果的不确定性分析,总体上融合结果的不确定性较小,但在景观异质性较强区域,融合结果的不确定性显著,不确定性值集中于0.4~0.7之间,这说明如何提高景观异质性区域的土地覆被类别精度,实现该区域数据重构是未来亟需解决的问题。该文所得成果为未来全球或区域尺度土地覆被遥感产品的研制及产品精度验证提供了参考。