A Hierarchical Bayesian Model for Spatial Prediction of Multivariate Non‐Gaussian Random Fields

Summary As most georeferenced data sets are multivariate and concern variables of different types, spatial mapping methods must be able to deal with such data. The main difficulties are the prediction of non‐Gaussian variables and the modeling of the dependence between processes. The aim of this article is to present a new hierarchical Bayesian approach that permits simultaneous modeling of dependent Gaussian, count, and ordinal spatial fields. This approach is based on spatial generalized linear mixed models. We use a moving average approach to model the spatial dependence between the processes. The method is first validated through a simulation study. We show that the multivariate model has better predictive abilities than the univariate one. Then the multivariate spatial hierarchical model is applied to a real data set collected in French Guiana to predict topsoil patterns.     

Hierarchical multivariate mixture generalized linear models for the analysis of spatial data: An application to disease mapping

Disease mapping of a single disease has been widely studied in the public health setup. Simultaneous modeling of related diseases can also be a valuable tool both from the epidemiological and from the statistical point of view. In particular, when we have several measurements recorded at each spatial location, we need to consider multivariate models in order to handle the dependence among the multivariate components as well as the spatial dependence between locations. It is then customary to use multivariate spatial models assuming the same distribution through the entire population density. However, in many circumstances, it is a very strong assumption to have the same distribution for all the areas of population density. To overcome this issue, we propose a hierarchical multivariate mixture generalized linear model to simultaneously analyze spatial Normal and non‐Normal outcomes. As an application of our proposed approach, esophageal and lung cancer deaths in Minnesota are used to show the outperformance of assuming different distributions for different counties of Minnesota rather than assuming a single distribution for the population density. Performance of the proposed approach is also evaluated through a simulation study.     

Estimating causal effects of air quality regulations using principal stratification for spatially correlated multivariate intermediate outcomes

Methods for causal inference regarding health effects of air quality regulations are met with unique challenges because (1) changes in air quality are intermediates on the causal pathway between regulation and health, (2) regulations typically affect multiple pollutants on the causal pathway towards health, and (3) regulating a given location can affect pollution at other locations, that is, there is interference between observations. We propose a principal stratification method designed to examine causal effects of a regulation on health that are and are not associated with causal effects of the regulation on air quality. A novel feature of our approach is the accommodation of a continuously scaled multivariate intermediate response vector representing multiple pollutants. Furthermore, we use a spatial hierarchical model for potential pollution concentrations and ultimately use estimates from this model to assess validity of assumptions regarding interference. We apply our method to estimate causal effects of the 1990 Clean Air Act Amendments among approximately 7 million Medicare enrollees living within 6 miles of a pollution monitor.     

Estimating occupancy dynamics for large‐scale monitoring networks: amphibian breeding occupancy across protected areas in the northeast United States

Regional monitoring strategies frequently employ a nested sampling design where a finite set of study areas from throughout a region are selected and intensive sampling occurs within a subset of sites within the individual study areas. This sampling protocol naturally lends itself to a hierarchical analysis to account for dependence among subsamples. Implementing such an analysis using a classic likelihood framework is computationally challenging when accounting for detection errors in species occurrence models. Bayesian methods offer an alternative approach for fitting models that readily allows for spatial structure to be incorporated. We demonstrate a general approach for estimating occupancy when data come from a nested sampling design. We analyzed data from a regional monitoring program of wood frogs (Lithobates sylvaticus) and spotted salamanders (Ambystoma maculatum) in vernal pools using static and dynamic occupancy models. We analyzed observations from 2004 to 2013 that were collected within 14 protected areas located throughout the northeast United States. We use the data set to estimate trends in occupancy at both the regional and individual protected area levels. We show that occupancy at the regional level was relatively stable for both species. However, substantial variation occurred among study areas, with some populations declining and some increasing for both species. In addition, When the hierarchical study design is not accounted for, one would conclude stronger support for latitudinal gradient in trends than when using our approach that accounts for the nested design. In contrast to the model that does not account for nesting, the nested model did not include an effect of latitude in the 95% credible interval. These results shed light on the range‐level population status of these pond‐breeding amphibians, and our approach provides a framework that can be used to examine drivers of local and regional occurrence dynamics.     

Uncovering the drivers of host‐associated microbiota with joint species distribution modelling

In addition to the processes structuring free‐living communities, host‐associated microbiota are directly or indirectly shaped by the host. Therefore, microbiota data have a hierarchical structure where samples are nested under one or several variables representing host‐specific factors, often spanning multiple levels of biological organization. Current statistical methods do not accommodate this hierarchical data structure and therefore cannot explicitly account for the effect of the host in structuring the microbiota. We introduce a novel extension of joint species distribution models (JSDMs) which can straightforwardly accommodate and discern between effects such as host phylogeny and traits, recorded covariates such as diet and collection site, among other ecological processes. Our proposed methodology includes powerful yet familiar outputs seen in community ecology overall, including (a) model‐based ordination to visualize and quantify the main patterns in the data; (b) variance partitioning to assess how influential the included host‐specific factors are in structuring the microbiota; and (c) co‐occurrence networks to visualize microbe‐to‐microbe associations.     

A multilevel mixed effects varying coefficient model with multilevel predictors and random effects for modeling hospitalization risk in patients on dialysis

For patients on dialysis, hospitalizations remain a major risk factor for mortality and morbidity. We use data from a large national database, United States Renal Data System, to model time-varying effects of hospitalization risk factors as functions of time since initiation of dialysis. To account for the three-level hierarchical structure in the data where hospitalizations are nested in patients and patients are nested in dialysis facilities, we propose a multilevel mixed effects varying coefficient model (MME-VCM) where multilevel (patient- and facility-level) random effects are used to model the dependence structure of the data. The proposed MME-VCM also includes multilevel covariates, where baseline demographics and comorbidities are among the patient-level factors, and staffing composition and facility size are among the facility-level risk factors. To address the challenge of high-dimensional integrals due to the hierarchical structure of the random effects, we propose a novel two-step approximate EM algorithm based on the fully exponential Laplace approximation. Inference for the varying coefficient functions and variance components is achieved via derivation of the standard errors using score contributions. The finite sample performance of the proposed estimation procedure is studied through simulations.     

Spatial Modeling of Air Pollution in Studies of Its Short‐Term Health Effects

Summary In studies that estimate the short‐term effects of air pollution on health, daily measurements of pollution concentrations are often available from a number of monitoring locations within the study area. However, the health data are typically only available in the form of daily counts for the entire area, meaning that a corresponding single daily measure of pollution is required. The standard approach is to average the observed measurements at the monitoring locations, and use this in a log‐linear health model. However, as the pollution surface is spatially variable this simple summary is unlikely to be an accurate estimate of the average pollution concentration across the region, which may lead to bias in the resulting health effects. In this article, we propose an alternative approach that jointly models the pollution concentrations and their relationship with the health data using a Bayesian spatio‐temporal model. We compare this approach with the simple spatial average using a simulation study, by investigating the impact of spatial variation, monitor placement, and measurement error in the pollution data. An epidemiological study from Greater London is then presented, which estimates the relationship between respiratory mortality and four different pollutants.     

Generalized hierarchical multivariate CAR models for areal data

In the fields of medicine and public health, a common application of areal data models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, information on p>/= 2 diseases from the same population groups or regions), we need to consider multivariate areal data models in order to handle the dependence among the multivariate components as well as the spatial dependence between sites. In this article, we propose a flexible new class of generalized multivariate conditionally autoregressive (GMCAR) models for areal data, and show how it enriches the MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random field (MRF) through the specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo (MCMC). We compare our approach with existing MCAR models in the literature via simulation, using average mean square error (AMSE) and a convenient hierarchical model selection criterion, the deviance information criterion (DIC; Spiegelhalter et al., 2002, Journal of the Royal Statistical Society, Series B64, 583-639). Finally, we offer a real-data application of our proposed GMCAR approach that models lung and esophagus cancer death rates during 1991-1998 in Minnesota counties.     

The alpha–beta–regional relationship: providing new insights into local–regional patterns of species richness and scale dependence of diversity components

Ecologists frequently regress local species richness on regional species richness to draw inferences about the processes that structure local communities. A more promising approach is to quantify the contributions of alpha and beta diversity to regional diversity (the ABR approach) using additive partitioning. We applied this approach to four local–regional relationships based on data from 583 arboreal beetle species collected in a hierarchically nested sampling design. All four local–regional relationships exhibited proportional sampling, yet the ABR approach indicated that each was produced by a different combination of alpha and beta richness. Using the results of the ABR analysis, we also analysed the scale dependence of alpha and beta using a hierarchical linear model. Alpha diversity contributed less than expected to regional diversity at the finest spatial scale and more than expected at the broadest spatial scale. A switch in relative dominance from beta to alpha diversity with increasing spatial scale suggested scale transitions in ecological processes. Analysing the scale dependence of diversity components using the ABR approach furthers our understanding about the additivity of species diversity in biological communities.     

Bayesian Modeling of ChIP‐chip Data Through a High‐Order Ising Model

Summary ChIP‐chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein–DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP‐chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP‐chip data through an Ising model with high‐order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios.     

The importance of spatial scale for trait–abundance relations

The concept of community assembly through trait‐based environmental filtering has played a key role in our understanding of how communities change over space and time, however, the importance of spatial scale in the filtering process remains unclear. We propose that different environmental filters may operate at different spatial scales, and that filters at finer scales would be nested within those acting at coarser scales. We tested for the existence of spatially nested sets of trait‐based filters in a temperate native grassland by applying the recently proposed maximum entropy (MaxEnt) approach to trait‐based community assembly, which we extend through a trait selection procedure. We found that different traits were important in influencing the abundances of species at the three different spatial scales examined (micro‐habitat, habitat, landscape), supporting the idea that trait based filtering processes operating at coarse spatial scales can be quite distinct from those operating at fine scales. Despite this result, we identified several traits which were frequently related to abundance at all spatial scales. Taken together, our results support the proposition that trait‐based environmental filters at finer spatial scales are nested within those operating at coarser scales. We compared our results to those obtained using a simpler trait‐by‐trait analytical approach (correlation analysis and MaxEnt on individual traits). The capacity for MaxEnt to incorporate multiple traits simultaneously provided unique insights into the important traits at each spatial scale and presents significant advantages over existing univariate and multivariate approaches.     

Host plant associations and geography interact to shape diversification in a specialist insect herbivore

Disentangling the processes underlying geographic and environmental patterns of biodiversity challenges biologists as such patterns emerge from eco‐evolutionary processes confounded by spatial autocorrelation among sample units. The herbivorous insect, Belonocnema treatae (Hymenoptera: Cynipidae), exhibits regional specialization on three plant species whose geographic distributions range from sympatry through allopatry across the southern United States. Using range‐wide sampling spanning the geographic ranges of the three host plants and genotyping‐by‐sequencing of 1,217 individuals, we tested whether this insect herbivore exhibited host plant‐associated genomic differentiation while controlling for spatial autocorrelation among the 58 sample sites. Population genomic structure based on 40,699 SNPs was evaluated using the hierarchical Bayesian model entropy to assign individuals to genetic clusters and estimate admixture proportions. To control for spatial autocorrelation, distance‐based Moran's eigenvector mapping was used to construct regression variables summarizing spatial structure inherent among sample sites. Distance‐based redundancy analysis (dbRDA) incorporating the spatial variables was then applied to partition host plant‐associated differentiation (HAD) from spatial autocorrelation. By combining entropy and dbRDA to analyse SNP data, we unveiled a complex mosaic of highly structured differentiation within and among gall‐former populations finding evidence that geography, HAD and spatial autocorrelation all play significant roles in explaining patterns of genomic differentiation in B. treatae. While dbRDA confirmed host association as a significant predictor of patterns of genomic variation, spatial autocorrelation among sites explained the largest proportion of variation. Our results demonstrate the value of combining dbRDA with hierarchical structural analyses to partition spatial/environmental patterns of genomic variation.     

Blood‐Capillary‐Inspired,Free‐Standing,Flexible, and Low‐Cost Super‐Hydrophobic N‐CNTs@SS Cathodes for High‐Capacity,High‐Rate,and Stable Li‐Air Batteries

With the rising demand for flexible and wearable electronic devices, flexible power sources with high energy densities are required to provide a sustainable energy supply. Theoretically, rechargeable, flexible Li‐O₂/air batteries can provide extremely high specific energy densities; however, the high costs, complex synthetic methods, and inferior mechanical properties of the available flexible cathodes severely limit their practical applications. Herein, inspired by the structure of human blood capillary tissue, this study demonstrates for the first time the in situ growth of interpenetrative hierarchical N‐doped carbon nanotubes on the surface of stainless‐steel mesh (N‐CNTs@SS) for the fabrication of a self‐supporting, flexible electrode with excellent physicochemical properties via a facile and scalable one‐step strategy. Benefitting from the synergistic effects of the high electronic conductivity and stable 3D interconnected conductive network structure, the Li‐O₂ batteries obtained with the N‐CNTs@SS cathode exhibit superior electrochemical performance, including a high specific capacity (9299 mA h g^?1 at 500 mA g^?1), an excellent rate capability, and an exceptional cycle stability (up to 232 cycles). Furthermore, as‐fabricated flexible Li‐air batteries containing the as‐prepared flexible super‐hydrophobic cathode show excellent mechanical properties, stable electrochemical performance, and superior H₂O resistibility, which enhance their potential to power flexible and wearable electronic devices.     

Population genetic structure reveals terrestrial affinities for a headwater stream insect

1. The spatial distribution of stream‐dwelling organisms is often considered to be limited primarily according to the hierarchical structure of the hydrologic network, and previous conceptual models of population genetic structure have reflected this generality. Headwater specialists, however, are confined to short upstream sections of the network, and therefore are unlikely to respond in the same way as species with a broader range of habitat tolerance. 2. Here, we propose a model to describe spatial patterns of genetic diversity in headwater specialists with a limited ability for among‐stream dispersal. The headwater model predicts a partitioning of genetic variance according to higher‐elevation ‘islands’ of terrestrial habitat that provide required headwater stream conditions. The model therefore expects a geographic pattern of genetic variance similar to that expected for low‐dispersal terrestrial species occupying the adjacent habitat. 3. Using a 1032‐bp mitochondrial DNA fragment encompassing parts of the COI and COII genes, we demonstrate that Madrean Sky Islands populations of the giant water bug Abedus herberti conform to the proposed headwater model. Furthermore, they exhibit phylogeographic patterns broadly concordant with those shown for several terrestrial species in the region, including a major zone of discontinuity in the Chiricahua mountain range. 4. Overall, populations are highly isolated from one another, and a nested clade analysis suggested that A. herberti population structure, similarly to terrestrial Sky Islands species studied previously, has been influenced by Pleistocene climatic cycles causing expansion and contraction of temperate woodland habitat. 5. Because they have no ability to disperse among present‐day mountaintop habitat islands, A. herberti and other headwater species with limited dispersal ability are vulnerable to the projected increasing rate of climatic warming in this region.     

Multi-Scale Identification of Urban Landscape Structure Based on Two-Dimensional Wavelet Analysis: The Case of Metropolitan Beijing,China

Scale dependence is one of the major characteristics of landscape. Urban landscape is highly affected by human activities with a multi-scale structure, which makes the multi-scale identification of urban structure an obligation for urban spatial studies. Although there have been many previous studies on urban landscape structure, most of them have been conducted on a single scale, and the multi-scale effects of landscape patterns were rarely involved. Two-dimensional wavelet transforms can link spatial structures to scale and spatial locations, and maybe an effective method for the multi-scale analysis of landscape. In this paper, we applied two-dimensional discrete wavelet transform and wavelet variance to analyze the multi-scale spatial structure characteristics and the nested hierarchical structure of the metropolitan Beijing area. The results indicated that the spatial distribution and configuration of the patches were highly scattered at small scales, and the urban landscape exhibited a relatively complicated structure. At medium scales, a combination of the polycentric and sectorial structure was identified due to the prominence of dominant patches within each administrative district. At larger scales, the urban landscape pattern exhibits typical concentric ring characteristics. Two characteristic scales were detected by the wavelet variance in the south-north direction of the main urban zones, scale 4 (112m) and 8 (1792m) in Dongcheng District, scale 3 (56m) and 6 (448m) in Xicheng District, which were corresponding to the extent of middle-small blocks and large blocks respectively. One characteristic scale was detected in each of the suburb areas (Chaoyang, Haidian, and Fengtai District). The spatial structure of the main urban zones is more complex than that of the suburb areas, and it presents a typical hierarchical structure in the south-north direction. In general, the spatial structure of Beijing metropolitan area appears polycentric and concentric ring structure at large scales, the main urban area has nested hierarchies at different characteristic scales, and the wavelet method can effectively identify multi-scale characteristics of urban spatial structure.     

Modeling the Spatial and Temporal Dependence in fMRI Data

Summary Functional magnetic resonance imaging (fMRI) data sets are large and characterized by complex dependence structures driven by highly sophisticated neurophysiology and aspects of the experimental designs. Typical analyses investigating task‐related changes in measured brain activity use a two‐stage procedure in which the first stage involves subject‐specific models and the second‐stage specifies group (or population) level parameters. Customarily, the first‐level accounts for temporal correlations between the serial scans acquired during one scanning session. Despite accounting for these correlations, fMRI studies often include multiple sessions and temporal dependencies may persist between the corresponding estimates of mean neural activity. Further, spatial correlations between brain activity measurements in different locations are often unaccounted for in statistical modeling and estimation. We propose a two‐stage, spatio‐temporal, autoregressive model that simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We develop an algorithm that leverages the special structure of our covariance model, enabling relatively fast and efficient estimation. Using our proposed method, we analyze fMRI data from a study of inhibitory control in cocaine addicts.     

A general production model with dependence between data from multiple surveys

A fishery‐independent survey for stock assessments is made sometimes more than once per year to detect a difference in relative sizes of fish populations (e.g., catch‐per‐unit‐effort [CPUE]) in response to a seasonal change in fish spatial distributions. Many managers tended to treat such data independently instead of systematically synthesizing them. A primary objective of this study was to synthesize all survey data via a simple hierarchical structure. I used the general (Pella‐Tomlinson) surplus production model for the illustration, because the purpose of this study was not a stock assessment, and the model was simpler than an age‐structured model. The surplus production model has about an eight decade history (since Graham's paper in 1935) and has been prominent in fish population dynamics. The logistic (Graham‐Schaefer) version was useful in the sense of simplifying the dynamics of a fish population in relation to its intrinsic growth, natural mortality, recruitment, density‐dependence, and fishery catch, but it was criticized because of its unrealistic limitations. Subsequently, the general version was suggested to accommodate flexibility and be realistic. In this study, I inferred parameters in the general surplus production model, simultaneously synthesizing all available data even from different temporal ranges. I used Georges Bank yellowtail flounder (Limanda ferruginea) data for demonstration.     

Exploring Spatial and Multitype Assemblages of Species Abundances

The ecological theory of the existence of multiple stable states between species, or the spatial heterogeneity of some unobserved environmental factor, supports the idea of multitype interactions between species. These multitype interactions can lead to different assemblages of species abundances. An exploratory tool for the detection of these species assemblages and for their spatial analysis is presented in this article. A two‐stage analysis is proposed. First, a classification into types of species assemblages using only the species abundances at each site, regardless of their spatial location, is performed. The clustering procedure is based on multivariate normal mixtures and provides a measure of the classification uncertainty. Second, some tools for the study of the spatial structure of these types of assemblages are presented. We transfer the classification uncertainty to the spatial analysis of the classes in order to draw more accurate conclusions. This classification and spatial analysis method is used to point out a spatial gradient of infection in a host–pathogen system in the Åland Islands in Finland. It can be a useful preliminary tool for ecological studies involving the spatial distributions of several species.     

Identifying the spatial effects and driving factors of urban PM2.5 pollution in China

Exploring exactly where air pollution comes from, and identifying the key factors that influence it, can provide a scientific basis for the rational formulation and effective implementation of air pollution policies in China. Based on the data from 2001 to 2012 covering PM_2.5 concentrations in 285 Chinese cities, we use dynamic spatial panel models to empirically analyze the key driving factors of this air pollution. Results show that China’s urban smog demonstrates both obvious global spatial autocorrelation and local spatial agglomeration. There is a significant inverted “U-shaped” curve between economic development level and air pollution, and most cities are in the phase in which pollution is increasing in conjunction with improvements to the economy. Due to a rapid increase in population in built up areas, a high-proportion of secondary industry, a coal-dominated energy structure and increasing traffic intensity, China’s smog problem is becoming more and more serious. FDI probably will not play a future role in mitigating the air pollution. Central heating in winter in northern China further aggravates local smog to a certain extent. Because China’s haze pollution presents path-dependent characteristics and spatial spillover effects in the time dimension and in the space dimension respectively, so smog alleviation policies should be implemented based both on the strategies of maximizing effort and regional joint prevention and control.     

Metacommunity analysis of Mexican bats: environmentally mediated structure in an area of high geographic and environmental complexity

Aim We tested the hypothesis that distributions of Mexican bats are defined by shared responses to environmental gradients for the entire Mexican bat metacommunity and for each of four metaensembles (frugivores, nectarivores, gleaning insectivores, and aerial insectivores). Further, we identified the main environmental factors to which bats respond for multiple spatial extents. Location Mexico. Methods Using bat presence–absence data, as well as vegetation composition for each of 31 sites, we analysed metacommunity structure via a comprehensive, hierarchical approach that uses reciprocal averaging (RA) to detect latent environmental gradients corresponding to each metacommunity structure (e.g. Clementsian, Gleasonian, nested, random). Canonical correspondence analysis (CCA) was used to relate such gradients to variation in vegetation composition. Results For all bat species and for each ensemble, the primary gradient of ordination from RA, which is based on species data only, recovered an axis of humidity that matched that obtained for the first axis of the CCA ordination, which is based both on vegetation attributes and on species composition of sites. For the complete assemblage as well as for aerial and gleaning insectivores, analyses revealed Clementsian or quasi‐Clementsian structures with discrete compartments (distinctive groups of species along portions of an environmental gradient) coincident with the humidity gradient and with the Nearctic–Neotropical divide. Within‐compartment analysis further revealed Clementsian or quasi‐Clementsian structures corresponding to a gradient of elevational complexity that matched the second ordination axis in CCA. Frugivores had quasi‐nested structure, whereas nectarivores had Gleasonian structure. Main conclusions Our hierarchical approach to metacommunity analysis detected complex metacommunity structures associated with multiple environmental gradients at different spatial extents. More importantly, the resulting structures and their extent along environmental gradients are determined by ensemble‐specific characteristics and not by arbitrarily circumscribed study areas. This property renders compartment‐level analyses particularly useful for large‐scale ecological analyses in areas where more than one gradient may exist and species sorting may occur at multiple scales.