GLM versus CCA spatial modeling of plant species distribution

Despite the variety of statistical methods available for static modeling of plant distribution, few studies directly compare methods on a common data set. In this paper, the predictive power of Generalized Linear Models (GLM) versus Canonical Correspondence Analysis (CCA) models of plant distribution in the Spring Mountains of Nevada, USA, are compared. Results show that GLM models give better predictions than CCA models because a species-specific subset of explanatory variables can be selected in GLM, while in CCA, all species are modeled using the same set of composite environmental variables (axes). Although both techniques can be readily ported to a Geographical Information System (GIS), CCA models are more readily implemented for many species at once. Predictions from both techniques rank the species models in the same order of quality; i.e. a species whose distribution is well modeled by GLM is also well modeled by CCA and vice-versa. In both cases, species for which model predictions have the poorest accuracy are either disturbance or fire related, or species for which too few observations were available to calibrate and evaluate the model. Each technique has its advantages and drawbacks. In general GLM will provide better species specific-models, but CCA will provide a broader overview of multiple species, diversity, and plant communities.     

Model evaluation and spatial interpolation by Bayesian combination of observations with outputs from numerical models

Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information for dry deposition levels in the United States: one is pollution measurements at a sparse set of about 50 monitoring stations called CASTNet, and the other is the output of the regional scale air quality models, called Models-3. A related problem is the evaluation of these numerical models for air quality applications, which is crucial for control strategy selection. We develop formal methods for combining sources of information with different spatial resolutions and for the evaluation of numerical models. We specify a simple model for both the Models-3 output and the CASTNet observations in terms of the unobserved ground truth, and we estimate the model in a Bayesian way. This provides improved spatial prediction via the posterior distribution of the ground truth, allows us to validate Models-3 via the posterior predictive distribution of the CASTNet observations, and enables us to remove the bias in the Models-3 output. We apply our methods to data on SO2 concentrations, and we obtain high-resolution SO2 distributions by combining observed data with model output. We also conclude that the numerical models perform worse in areas closer to power plants, where the SO2 values are overestimated by the models.     

Spatial association between speciated fine particles and mortality

Particulate matter (PM) has been linked to a range of serious cardiovascular and respiratory health problems, including premature mortality. The main objective of our research is to quantify uncertainties about the impacts of fine PM exposure on mortality. We develop a multivariate spatial regression model for the estimation of the risk of mortality associated with fine PM and its components across all counties in the conterminous United States. We characterize different sources of uncertainty in the data and model the spatial structure of the mortality data and the speciated fine PM. We consider a flexible Bayesian hierarchical model for a space-time series of counts (mortality) by constructing a likelihood-based version of a generalized Poisson regression model that combines methods for point-level misaligned data and change of support regression. Our results seem to suggest an increase by a factor of two in the risk of mortality due to fine particles with respect to coarse particles. Our study also shows that in the Western United States, the nitrate and crustal components of the speciated fine PM seem to have more impact on mortality than the other components. On the other hand, in the Eastern United States, sulfate and ammonium explain most of the fine PM effect.     

Hierarchical spatial modeling of additive and dominance genetic variance for large spatial trial datasets

Summary .  This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein–Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine ( Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability.     

Comparison of Bayesian methods for flexible modeling of spatial risk surfaces in disease mapping

Bayesian hierarchical models usually model the risk surface on the same arbitrary geographical units for all data sources. Poisson/gamma random field models overcome this restriction as the underlying risk surface can be specified independently to the resolution of the data. Moreover, covariates may be considered as either excess or relative risk factors. We compare the performance of the Poisson/gamma random field model to the Markov random field (MRF)‐based ecologic regression model and the Bayesian Detection of Clusters and Discontinuities (BDCD) model, in both a simulation study and a real data example. We find the BDCD model to have advantages in situations dominated by abruptly changing risk while the Poisson/gamma random field model convinces by its flexibility in the estimation of random field structures and by its flexibility incorporating covariates. The MRF‐based ecologic regression model is inferior. WinBUGS code for Poisson/gamma random field models is provided.     

Bayesian detection and modeling of spatial disease clustering

Many current statistical methods for disease clustering studies are based on a hypothesis testing paradigm. These methods typically do not produce useful estimates of disease rates or cluster risks. In this paper, we develop a Bayesian procedure for drawing inferences about specific models for spatial clustering. The proposed methodology incorporates ideas from image analysis, from Bayesian model averaging, and from model selection. With our approach, we obtain estimates for disease rates and allow for greater flexibility in both the type of clusters and the number of clusters that may be considered. We illustrate the proposed procedure through simulation studies and an analysis of the well-known New York leukemia data.     

On the scaling patterns of species spatial distribution and association

Understanding how species distribution (occupancy and spatial autocorrelation) and association (that is, multi-species co-distribution) change across scales is fundamental to unlocking the pattern formation in population ecology and macroecology. Based on the Bayesian rule and join-count statistics, I present here a mathematical model that can demonstrate the effect of spatial scale on the observation of species distribution and association. Results showed that the intensity of spatial autocorrelation and species association declines when the grain in the spatial analysis increases, although the category of species distribution (aggregated or segregated) and association (positive or negative) remains the same. Random distribution and species independence were proved to be scale-free. Regardless of the possible patterns of species distribution and association, species tend to be randomly distributed and independent from each other when scaling-up (an increasing grain), reflecting a percolation process. This model, thus, grasps the statistical essence of species scaling pattern and presents a step forward for unveiling mechanisms behind species distributional and macroecological patterns.     

Multiscale modeling of lipids and lipid bilayers

A multiscale modeling approach is applied for simulations of lipids and lipid assemblies on mesoscale. First, molecular dynamics simulation of initially disordered system of lipid molecules in water within all-atomic model was carried out. On the next stage, structural data obtained from the molecular dynamics (MD) simulation were used to build a coarse-grained (ten sites) lipid model, with effective interaction potentials computed by the inverse Monte Carlo method. Finally, several simulations of the coarse-grained model on longer length- and time-scale were performed, both within Monte Carlo and molecular dynamics simulations: a periodical sample of lipid molecules ordered in bilayer, a free sheet of such bilayer without periodic boundary conditions, formation of vesicle from a plain membrane, process of self-assembly of lipids randomly dispersed in volume. It was shown that the coarse-grained model, developed exclusively from all-atomic simulation data, reproduces well all the basic features of lipids in water solution.     

Explaining variation in tropical plant community composition: influence of environmental and spatial data quality

The degree to which variation in plant community composition (beta-diversity) is predictable from environmental variation, relative to other spatial processes, is of considerable current interest. We addressed this question in Costa Rican rain forest pteridophytes (1,045 plots, 127 species). We also tested the effect of data quality on the results, which has largely been overlooked in earlier studies. To do so, we compared two alternative spatial models [polynomial vs. principal coordinates of neighbour matrices (PCNM)] and ten alternative environmental models (all available environmental variables vs. four subsets, and including their polynomials vs. not). Of the environmental data types, soil chemistry contributed most to explaining pteridophyte community variation, followed in decreasing order of contribution by topography, soil type and forest structure. Environmentally explained variation increased moderately when polynomials of the environmental variables were included. Spatially explained variation increased substantially when the multi-scale PCNM spatial model was used instead of the traditional, broad-scale polynomial spatial model. The best model combination (PCNM spatial model and full environmental model including polynomials) explained 32% of pteridophyte community variation, after correcting for the number of sampling sites and explanatory variables. Overall evidence for environmental control of beta-diversity was strong, and the main floristic gradients detected were correlated with environmental variation at all scales encompassed by the study (c. 100–2,000 m). Depending on model choice, however, total explained variation differed more than fourfold, and the apparent relative importance of space and environment could be reversed. Therefore, we advocate a broader recognition of the impacts that data quality has on analysis results. A general understanding of the relative contributions of spatial and environmental processes to species distributions and beta-diversity requires that methodological artefacts are separated from real ecological differences.     

Molecular modeling study of sulfonated SIBS triblock copolymers

An important class of thermoplastic elastomers involves polystyrene and polyisobutylene blocks (SIBS). Sulfonated SIBS Triblock Copolymers (S-SIBS) are of particular interest because of potential applications for fuel cell and textile applications, where breathable, protective clothing is required. We have used multiscale modeling to gain an understanding of the static and dynamic properties of these polymer systems at detailed atomistic levels. Quantum chemistry tools were used to elucidate the bonding of water molecules and sulfonate groups. In addition, molecular dynamics was applied to calculate the polymer density at various levels of sulfonation. The structures of polymer with hydronium ions and also water were studied and the mechanism of water self-diffusion was proposed. It was found that with increase of water content the hydronium ions move further away from sulfonate groups. The self-diffusion coefficients of water were found to reproduce well experimental trends. Two different distributions of sulfonate groups were studied: one blocky and another perfectly dispersed. In the case of the blocky architecture, the water clusters are connected at a lower sulfonation level, leading to increased water diffusion coefficients as compared to the dispersed architecture.     

Bayesian modeling of skewed X inactivation in genetically diverse mice identifies a novel Xce allele associated with copy number changes

Female mammals are functional mosaics of their parental X-linked gene expression due to X chromosome inactivation (XCI). This process inactivates one copy of the X chromosome in each cell during embryogenesis and that state is maintained clonally through mitosis. In mice, the choice of which parental X chromosome remains active is determined by the X chromosome controlling element (Xce), which has been mapped to a 176-kb candidate interval. A series of functional Xce alleles has been characterized or inferred for classical inbred strains based on biased, or skewed, inactivation of the parental X chromosomes in crosses between strains. To further explore the function structure basis and location of the Xce, we measured allele-specific expression of X-linked genes in a large population of F1 females generated from Collaborative Cross (CC) strains. Using published sequence data and applying a Bayesian “Pólya urn” model of XCI skew, we report two major findings. First, inter-individual variability in XCI suggests mouse epiblasts contain on average 20–30 cells contributing to brain. Second, CC founder strain NOD/ShiLtJ has a novel and unique functional allele, Xce^g, that is the weakest in the Xce allelic series. Despite phylogenetic analysis confirming that NOD/ShiLtJ carries a haplotype almost identical to the well-characterized C57BL/6J (Xce^b), we observed unexpected patterns of XCI skewing in females carrying the NOD/ShiLtJ haplotype within the Xce. Copy number variation is common at the Xce locus and we conclude that the observed allelic series is a product of independent and recurring duplications shared between weak Xce alleles.     

Geospatial analysis of population-based incidence of multiple myeloma in the United States

BackgroundWe investigated the spatial patterns of multiple myeloma (MM) incidence in the United States (US) between 2013 and 2017 to improve understanding of potential environmental risk factors for MM.MethodsWe analyzed the average county-level age-adjusted incidence rates (“ASR”) of MM between 2013 and 2017 in 50 states and the District of Columbia using the U.S. Cancer Statistics Public Use Databases. We firstly divided the ASR into quintiles and described spatial patterns using a choropleth map. To identify global and local clusters of the ASR, we performed the Spatial Autocorrelation (Global Moran’s I) analysis and the Anselin’s Local Indicator of Spatial Autocorrelation (LISA) analysis. We compared the means of selected demographic and socioeconomic factors between the clusters and counties of the whole US using Welch one-sided t-test.ResultsWe identified distinct spatial dichotomy of the ASR across counties. High ASR were observed in counties in the Southeast of the US as well as the Capital District (metropolitan areas surrounding Albany) and New York City in the state of New York, while low ASR were observed in counties in the Southwest and West of the US. The ASR showed a significant positive spatial autocorrelation. We identified two major high-high local clusters of the ASR in Georgia and Southern Carolina and five major low-low local clusters of the ASR in Alabama, Arizona, New Hampshire, Ohio, Oregon, and Tennessee. The racial population distribution may partly explain the spatial distribution of MM incidence in the US.ConclusionFindings from this study showed distinct spatial distribution of MM in the US and two high-high and five low-low local clusters. The non-random distribution of MM suggests that environmental exposures in certain regions may be important for the risk of MM.     

The spatial structure of the physical environment

There is substantial environmental variance at small spatial scales (1 m or less) in both natural and disturbed environments. We have investigated the spatial structure of physical variables at larger scales (up to 10⁶ m). We analysed surveys of edaphic properties of Wisconsin forest soils, of the water chemistry of lakes in Ontario and Labrador, and of temperature and precipitation in northeastern North America. We found no clear indication that the variance among sites approaches some maximal value as the distance between them increases. We suggest instead that the variance of the physical environment tends to increase continually with distance. The slope of the log-log regression of variance on distance provides a means of comparing the heterogeneity of different environments with respect to a given factor, or of comparing different factors within a given environment. This slope provides a useful measure of environmental structure that can be related to the biodiversity or plasticity of native organisms.     

Metabolic modeling of spatial heterogeneity of biofilms in microbial fuel cells reveals substrate limitations in electrical current generation

Microbial fuel cells (MFCs) have been proposed as an alternative energy resource for the conversion of organic compounds to electricity. In an MFC, microorganisms such as Geobacter sulfurreducens form an anode‐associated biofilm that can completely oxidize organic matter (electron donor) to carbon dioxide with direct electron transfer to the anode (electron acceptor). Mathematical models are useful in analyzing biofilm processes; however, existing models rely on Nernst–Monod type expressions, and evaluate extracellular processes separated from the intracellular metabolism of the microorganism. Thus, models that combine both extracellular and intracellular components, while addressing spatial heterogeneity, are essential for improved representation of biofilm processes. The goal of this work is to develop a model that integrates genome‐scale metabolic models with the model of biofilm environment. This integrated model shows the variations of electrical current production and biofilm thickness under the presence/absence of NH₄ in the bulk solution, and under varying maintenance energy demands. Further, sensitivity analysis suggested that conductivity is not limiting electrical current generation and that increasing cell density can lead to enhanced current generation. In addition, the modeling results also highlight instances such as the transformation into respiring cells, where the mechanism of electrical current generation during biofilm development is not yet clearly understood.     

Bayesian modeling of air pollution extremes using nested multivariate max‐stable processes

Capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks. In order to investigate the multivariate spatial dependence properties of air pollution extremes, we introduce a new class of multivariate max‐stable processes. Our proposed model admits a hierarchical tree‐based formulation, in which the data are conditionally independent given some latent nested positive stable random factors. The hierarchical structure facilitates Bayesian inference and offers a convenient and interpretable characterization. We fit this nested multivariate max‐stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the Los Angeles area, showing that the proposed model succeeds in capturing their complex tail dependence structure.