Regression analysis of spatial data.

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

SPATIAL VARIABILITY AND VITALITY OF EPIGEOUS TERMITE MOUNDS IN PASTURES OF MATO GROSSO DO SUL, BRAZIL

Epigeous termite mounds are frequently observed in pasture areas, but the processes regulating their population dynamics are poorly known. This study evaluated epigeous termite mounds in cultivated grasslands used as pastures, assessing their spatial distribution by means of geostatistics and evaluating their vitality. The study was conducted in the Cerrado biome in the municipality of Rio Brilhante, Mato Grosso do Sul, Brazil. In two pasture areas (Pasture 1 and Pasture 2), epigeous mounds (nests) were georeferenced and analyzed for height, circumference and vitality (inhabited or not). The area occupied by the mounds was calculated and termite specimens were collected for taxonomic identification. The spatial distribution pattern of the mounds was analyzed with geostatistical procedures. In both pasture areas, all epigeous mounds were built by the same species, Cornitermes cumulans. The mean number of mounds per hectare was 68 in Pasture 1 and 127 in Pasture 2, representing 0.4 and 1 % of the entire area, respectively. A large majority of the mounds were active (vitality), 91 % in Pasture 1 and 84 % in Pasture 2. A “pure nugget effect” was observed in the semivariograms of height and nest circumference in both pastures reflecting randomized spatial distribution and confirming that the distribution of termite mounds in pastures had a non-standard distribution.

SPATIAL CORRELATION BETWEEN PHYSICAL PROPERTIES OF SOIL AND WEEDS IN TWO MANAGEMENT SYSTEMS

The spatial correlation between soil properties and weeds is relevant in agronomic and environmental terms. The analysis of this correlation is crucial for the interpretation of its meaning, for influencing factors such as dispersal mechanisms, seed production and survival, and the range of influence of soil management techniques. This study aimed to evaluate the spatial correlation between the physical properties of soil and weeds in no-tillage (NT) and conventional tillage (CT) systems. The following physical properties of soil and weeds were analyzed: soil bulk density, macroporosity, microporosity, total porosity, aeration capacity of soil matrix, soil water content at field capacity, weed shoot biomass, weed density, Commelina benghalensis density, and Bidens pilosa density. Generally, the ranges of the spatial correlations were higher in NT than in CT. The cross-variograms showed that many variables have a structure of combined spatial variation and can therefore be mapped from one another by co-kriging. This combined variation also allows inferences about the physical and biological meanings of the study variables. Results also showed that soil management systems influence the spatial dependence structure significantly.

Spatial analysis of erythrocyte membrane fluctuations by digital holographic microscopy.

Red blood cell (RBC) membrane fluctuations provide important insights into cell states. We present a spatial analysis of red blood cell membrane fluctuations by using digital holographic microscopy (DHM). This interferometric and dye-free technique, possessing nanometric axial and microsecond temporal sensitivities enables to measure cell membrane fluctuations (CMF) on the whole cell surface. DHM acquisition is combined with a model which allows extracting the membrane fluctuation amplitude, while taking into account cell membrane topology. Uneven distribution of CMF amplitudes over the RBC surface is observed, showing maximal values in a ring corresponding to the highest points on the RBC torus as well as in some scattered areas in the inner region of the RBC. CMF amplitudes of 35.9+/-8.9 nm and 4.7+/-0.5 nm (averaged over the cell surface) were determined for normal and ethanol-fixed RBCs, respectively.

SPATIAL DEPENDENCE OF ELECTRICAL CONDUCTIVITY AND CHEMICAL PROPERTIES OF THE SOIL BY ELECTROMAGNETIC INDUCTION

Brazilian soils have natural high chemical variability; thus, apparent electrical conductivity (ECa) can assist interpretation of crop yield variations. We aimed to select soil chemical properties with the best linear and spatial correlations to explain ECa variation in the soil using a Profiler sensor (EMP-400). The study was carried out in Sidrolândia, MS, Brazil. We analyzed the following variables: electrical conductivity - EC (2, 7, and 15 kHz), organic matter, available K, base saturation, and cation exchange capacity (CEC). Soil ECa was measured with the aid of an all-terrain vehicle, which crossed the entire area in strips spaced at 0.45 m. Soil samples were collected at the 0-20 cm depth with a total of 36 samples within about 70 ha. Classical descriptive analysis was applied to each property via SAS software, and GS+ for spatial dependence analysis. The equipment was able to simultaneously detect ECa at the different frequencies. It was also possible to establish site-specific management zones through analysis of correlation with chemical properties. We observed that CEC was the property that had the best correlation with ECa at 15 kHz.

SPATIAL UNCERTAINTY OF NUTRIENT LOSS BY EROSION IN SUGARCANE HARVESTING SCENARIOS

The assessment of spatial uncertainty in the prediction of nutrient losses by erosion associated with landscape models is an important tool for soil conservation planning. The purpose of this study was to evaluate the spatial and local uncertainty in predicting depletion rates of soil nutrients (P, K, Ca, and Mg) by soil erosion from green and burnt sugarcane harvesting scenarios, using sequential Gaussian simulation (SGS). A regular grid with equidistant intervals of 50 m (626 points) was established in the 200-ha study area, in Tabapuã, São Paulo, Brazil. The rate of soil depletion (SD) was calculated from the relation between the nutrient concentration in the sediments and the chemical properties in the original soil for all grid points. The data were subjected to descriptive statistical and geostatistical analysis. The mean SD rate for all nutrients was higher in the slash-and-burn than the green cane harvest scenario (Student’s t-test, p<0.05). In both scenarios, nutrient loss followed the order: Ca>Mg>K>P. The SD rate was highest in areas with greater slope. Lower uncertainties were associated to the areas with higher SD and steeper slopes. Spatial uncertainties were highest for areas of transition between concave and convex landforms.

SPATIAL VARIABILITY OF SOIL PROPERTIES IN AN AGRARIAN REFORM SETTLEMENT

ABSTRACT The study of soil chemical and physical properties variability is important for suitable management practices. The aim of this study was to evaluate the spatial variability of soil properties in the Malhada do Meio settlement to subsidize soil use planning. The settlement is located in Chapadinha, MA, Brazil, and has an area of 630.86 ha. The vegetation is seasonal submontane deciduous forest and steppe savanna. The geology is formed of sandstones and siltstones of theItapecuru Formation and by colluvial and alluvial deposits. The relief consists of hills with rounded and flat tops with an average altitude of 67 m, and frequently covered over by ferruginous duricrusts. A total of 183 georeferenced soil samples were collected at the depth of 0.00-0.20 m inPlintossolos, Neossolo andGleissolo. The following chemical variables were analyzed: pH(CaCl2), H+Al, Al, SB, V, CEC, P, K, OM, Ca, Mg, SiO2, Al2O3, and Fe2O3; along with particle size variables: clay, silt, and sand. Descriptive statistical and geostatistical analyses were carried out. The coefficient of variation (CV) was high for most of the variables, with the exception of pH with a low CV, and of sand with a medium CV. The models fitted to the experimental semivariograms of these variables were the exponential and the spherical. The range values were from 999 m to 3,690 m. For the variables pH(CaCl2), SB, and clay, there are three specific areas for land use planning. The central part of the area (zone III), where thePlintossolos Pétricos and Neossolos Flúvicos occur, is the most suitable for crops due to higher macronutrient content, organic matter and pH. Zones I and II are indicated for environmental preservation.

A spatial accommodation by neighboring cells is required for organ initiation in Arabidopsis.

Lateral root formation in plants can be studied as the process of interaction between chemical signals and physical forces during development. Lateral root primordia grow through overlying cell layers that must accommodate this incursion. Here, we analyze responses of the endodermis, the immediate neighbor to an initiating lateral root. Endodermal cells overlying lateral root primordia lose volume, change shape, and relinquish their tight junction-like diffusion barrier to make way for the emerging lateral root primordium. Endodermal feedback is absolutely required for initiation and growth of lateral roots, and we provide evidence that this is mediated by controlled volume loss in the endodermis. We propose that turgidity and rigid cell walls, typical of plants, impose constraints that are specifically modified for a given developmental process.

A probabilistic approach to niche-based community models for spatial forecasts of assemblage properties and their uncertainties

Aim Conservation strategies are in need of predictions that capture spatial community composition and structure. Currently, the methods used to generate these predictions generally focus on deterministic processes and omit important stochastic processes and other unexplained variation in model outputs. Here we test a novel approach of community models that accounts for this variation and determine how well it reproduces observed properties of alpine butterfly communities. Location The western Swiss Alps. Methods We propose a new approach to process probabilistic predictions derived from stacked species distribution models (S-SDMs) in order to predict and assess the uncertainty in the predictions of community properties. We test the utility of our novel approach against a traditional threshold-based approach. We used mountain butterfly communities spanning a large elevation gradient as a case study and evaluated the ability of our approach to model species richness and phylogenetic diversity of communities. Results S-SDMs reproduced the observed decrease in phylogenetic diversity and species richness with elevation, syndromes of environmental filtering. The prediction accuracy of community properties vary along environmental gradient: variability in predictions of species richness was higher at low elevation, while it was lower for phylogenetic diversity. Our approach allowed mapping the variability in species richness and phylogenetic diversity projections. Main conclusion Using our probabilistic approach to process species distribution models outputs to reconstruct communities furnishes an improved picture of the range of possible assemblage realisations under similar environmental conditions given stochastic processes and help inform manager of the uncertainty in the modelling results

Spatial correlations and cross sections of clusters in the A + B -> 0 reaction

We consider the distribution of cross sections of clusters and the density-density correlation functions for the A+B¿0 reaction. We solve the reaction-diffusion equations numerically for random initial distributions of reactants. When both reactant species have the same diffusion coefficients the distribution of cross sections and the correlation functions scale with the diffusion length and obey superuniversal laws (independent of dimension). For different diffusion coefficients the correlation functions still scale, but the scaling functions depend on the dimension and on the diffusion coefficients. Furthermore, we display explicitly the peculiarities of the cluster-size distribution in one dimension.

Spatial patterns mediated by subcritical and supercritical thermal fluctuations in the splay Fréedericksz transition

The magnetically induced splay Fréedericksz transition is reexamined to look for pattern forming phenomena slightly above or below criticality. By using our traditional scheme of stochastic nematodynamic equations, situations are, respectively, found of transient and permanent predominance of transversal periodicities (wave numbers) along the direction perpendicular to the initial orientation within the sample. The relevance of these predictions in relation with recent observations in the electrically driven splay Fréedericksz transition, and in general with other pattern forming phenomena, is stressed.

Public health expenditure and spatial interactions in a decentralized national health system

One of the limitations of cross-country health expenditure analysis refers to the fact that the financing, the internal organization and political restraints of health care decision-making are country-specific and heterogeneous. Yet, a potential solution is to examine the influence of such effects in those countries that have undertaken decentralization processes. In such a setting, it is possible to examine potential expenditure spillovers across the geography of a country as well as the influence of the political ideology of regional incumbents on public health expenditure. This paper examines the determinants of public health expenditure within Spanish region-states (Autonomous Communities, ACs), most of them subject to similar financing structures although exhibiting significant heterogeneity as a result of the increasing decentralization, region-specific political factors along with different use of health care inputs, economic dimension and spatial interactions

Influence of bedrock structures on the spatial pattern of erosional landforms in small alpine catchments

Structural settings and lithological characteristics are traditionally assumed to influence the development of erosional landforms, such as gully networks and rock couloirs, in steep mountain rock basins. The structural control of erosion of two small alpine catchments of distinctive rock types is evaluated by comparing the correspondences between the orientations of their gullies and rock couloirs with (1) the sliding orientations of potential slope failures mechanisms, and (2) the orientation of the maximum joint frequency, this latter being considered as the direction exploited primarily by erosion and mass wasting processes. These characteristic orientations can be interpreted as structural weaknesses contributing to the initiation and propagation of erosion. The morphostructural analysis was performed using digital elevation models and field observations. The catchment comprised of magmatic intrusive rocks shows a clear structural control, mostly expressed through potential wedges failure. Such joint configurations have a particular geometry that encourages the development of gullies in hard rock, e.g. through enhanced gravitational and hydrological erosional processes. In the catchment underlain by sedimentary rocks, penetrative joints that act as structural weaknesses seem to be exploited by gullies and rock couloirs. However, the lithological setting and bedding configuration prominently control the development of erosional landforms, and influence not only the local pattern of geomorphic features, but the general morphology of the catchment. The orientations of the maximum joint frequency are clearly associated with the gully network, suggesting that its development is governed by anisotropy in rock strength. These two catchments are typical of bedrock-dominated basins prone to intense processes of debris supply. This study suggests a quantitative approach for describing the relationship between bedrock jointing and geomorphic features geometry. Incorporation of bedrock structure can be relevant when studying processes governing the transfer of clastic material, for the assessment of sediment yields and in landforms evolution models.