Spatial autocorrelation

genalex is a user-friendly cross-platform package that runs within Microsoft Excel, enabling population genetic analyses of codominant, haploid and binary data. Allele frequency-based analyses include heterozygosity, F statistics, Nei's genetic distance, population assignment, probabilities of identity and pairwise relatedness. Distance-based calculations include amova, principal coordinates analysis (PCA), Mantel tests, multivariate and 2D spatial autocorrelation and twogener. More than 20 different graphs summarize data and aid exploration. Sequence and genotype data can be imported from automated sequencers, and exported to other software. Initially designed as tool for teaching, genalex 6 now offers features for researchers as well. Documentation and the program are available at http://www.anu.edu.au/BoZo/GenAlEx/

This paper presents an overview of GeoDa TM , a free software program intended to serve as a user-friendly and graphical introduction to spatial analysis for non-GIS specialists. It includes functionality ranging from simple mapping to exploratory data analysis, the visualization of global and local spatial autocorrelation, and spatial regression. A key feature of GeoDa is an interactive environment that combines maps with statistical graphics, using the technology of dynamically linked windows. A brief review of the software design is given, as well as some illustrative examples that highlight distinctive features of the program in applications dealing with public health, economic development, real estate analysis and criminology.

The spatial heterogeneity of populations and communities plays a central role in many ecological theories, for instance the theories of succession, adaptation, maintenance of species diversity, community stability, competition, predator-prey interactions, parasitism, epidemics and other natural catastrophes, ergoclines, and so on. This paper will review how the spatial structure of biological populations and communities can be studied. We first demonstrate that many of the basic statistical methods used in ecological studies are impaired by autocorrelated data. Most if not all environmental data fall in this category. We will look briefly at ways of performing valid statistical tests in the presence of spatial autocorrelation. Methods now available for analysing the spatial structure of biological populations are described, and illustrated by vegetation data. These include various methods to test for the presence of spatial autocorrelation in the data: univariate methods (all-directional and two-dimensional spatial correlograms, and two-dimensional spectral analysis), and the multivariate Mantel test and Mantel correlogram; other descriptive methods of spatial structure: the univariate variogram, and the multivariate methods of clustering with spatial contiguity constraint; the partial Mantel test, presented here as a way of studying causal models that include space as an explanatory variable; and finally, various methods for mapping ecological variables and producing either univariate maps (interpolation, trend surface analysis, kriging) or maps of truly multivariate data (produced by constrained clustering). A table shows the methods classified in terms of the ecological questions they allow to resolve. Reference is made to available computer programs.

In this paper we propose simple diagnostic tests, based on ordinary least-squares (OLS) residuals, for spatial error autocorrelation in the presence of a spatially lagged dependent variable and for spatial lag dependence in the presence of spatial error autocorrelation, applying the modified Lagrange multiplier (LM) test developed by Bera and Yoon (Econometric Theory, 1993, 9, 649-658). Our new tests may be viewed as computationally simple and robust alternatives to some existing procedures in spatial econometrics. We provide empirical illustrations to demonstrate the usefulness of the proposed tests. The finite sample size and power performance of the tests are also investigated through a Monte Carlo study. The results indicate that the adjusted LM tests have good finite sample properties. In addition, they prove to be more suitable for the identification of the source of dependence (lag or error) than their unadjusted counterparts.

When sampling locations are known, the association between genetic and geographic distances can be tested by spatial autocorrelation or regression methods. These tests give some clues to the possible shape of the genetic landscape. Nevertheless, correlation analyses fail when attempting to identify where genetic barriers exist, namely, the areas where a given variable shows an abrupt rate of change. To this end, a computational geometry approach is more suitable because it provides the locations and the directions of barriers and because it can show where geographic patterns of two or more variables are similar. In this frame we have implemented Monmonier's (1973) maximum difference algorithm in a new software package to identify genetic barriers. To provide a more realistic representation of the barriers in a genetic landscape, we implemented in the software a significance test by means of bootstrap matrices analysis. As a result, the noise associated with genetic markers can be visualized on a geographic map and the areas where genetic barriers are more robust can be identified. Moreover, this multiple matrices approach can visualize the patterns of variation associated with different markers in the same overall picture. This improved Monmonier's method is highly reliable and can be applied to nongenetic data whenever sampling locations and a distance matrix between corresponding data are available.

Recognition and analysis of spatial autocorrelation has defined a new paradigm in ecology. Attention to spatial pattern can lead to insights that would have been otherwise overlooked, while ignoring space may lead to false conclusions about ecological relationships. We used Gaussian spatial autoregressive models, fit with widely available software, to examine breeding habitat relationships for three common Neotropical migrant songbirds in the southern Appalachian Mountains of North Carolina and Tennessee, USA.

The distribution of plant species, the species compositions of different sites, and the factors that affect them in tropical rain forests are not well understood. The main hypotheses are that species composition is either (i) uniform over large areas, (ii) random but spatially autocorrelated ...

Molecular Ecology Notes (2007) 7, 15–17 ... A slightly more conservative test is also provided, which is based on estimates PGEN (f) and PSEX (f), of the same ... The frequency distribution of genetic distances can, for example, help to screen for scoring errors or somatic mutations ...

Because most macroecological and biodiversity data are spatially autocorrelated, special tools for describing spatial structures and dealing with hypothesis testing are usually required. Unfortunately, most of these methods have not been available in a single statistical package. Consequently, using these tools is still a challenge for most ecologists and biogeographers. In this paper, we present sam (Spatial Analysis in Macroecology), a new, easy-to-use, freeware package for spatial analysis in macroecology and biogeography. Through an intuitive, fully graphical interface, this package allows the user to describe spatial patterns in variables and provides an explicit spatial framework for standard techniques of regression and correlation. Moran's I autocorrelation coefficient can be calculated based on a range of matrices describing spatial relationships, for original variables as well as for residuals of regression models, which can also include filtering components (obtained by standard trend surface analysis or by principal coordinates of neighbour matrices). sam also offers tools for correcting the number of degrees of freedom when calculating the significance of correlation coefficients. Explicit spatial modelling using several forms of autoregression and generalized least-squares models are also available. We believe this new tool will provide researchers with the basic statistical tools to resolve autocorrelation problems and, simultaneously, to explore spatial components in macroecological and biogeographical data. Although the program was designed primarily for the applications in macroecology and biogeography, most of sam's statistical tools will be useful for all kinds of surface pattern spatial analysis. The program is freely available at http://www.ecoevol.ufg.br/sam (permanent URL at http://purl.oclc.org/sam/).

This paper discusses empirical and analytical rules to select a suitable grid resolution for output maps and based on the inherent properties of the input data. The choice of grid resolution was related with the cartographic and statistical concepts: scale, computer processing power, positional accuracy, size of delineations, inspection density, spatial autocorrelation structure and complexity of terrain. These were further related with the concepts from the general statistics and information theory such as Nyquist frequency concept from signal processing and equations to estimate the probability density function. Selection of grid resolution was demonstrated using four datasets: (1) GPS positioning datathe grid resolution was related to the area of circle described by the error radius, (2) map of agricultural plots-the grid resolution was related to the size of smallest and narrowest plots, (3) point dataset from soil mapping-the grid resolution was related to the inspection density, nugget variation and range of spatial autocorrelation and (4) contour map used for production of digital elevation model-the grid resolution was related with the spacing between the contour lines i.e. complexity of terrain. It was concluded that no ideal grid resolution exists, but rather a range of suitable resolutions. One should at least try to avoid using resolutions that do not comply with the effective scale or inherent properties of the input dataset. Three standard grid resolutions for output maps were finally recommended: (a) the coarsest legible grid resolution-this is the largest resolution that we should use in order to respect the scale of work and properties of a dataset; (b) the finest legible grid resolution-this is the smallest grid resolution that represents 95% of spatial objects or topography; and (c) recommended grid resolution-a compromise between the two. Objective procedures to derive the true optimal grid resolution that maximizes the predictive capabilities or information content of a map are further discussed. This methodology can now be integrated within a GIS package to help inexperienced users select a suitable grid resolution without doing extensive data preprocessing. r

Journal of Real Estate Finance and Economics, Vol. 17:1, 61±85 (1998) © 1998 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. ... Analysis of Spatial Autocorrelation in House Prices ... SABYASACHI BASU Statistics Department, Southern Methodist ...

Although clonal species are dominant in many habitats, from unicellular organisms to plants and animals, ecological and particularly evolutionary studies on clonal species have been strongly limited by the difficulty in assessing the number, size and longevity of genetic individuals within a population. The development of molecular markers has allowed progress in this area, and although allozymes remain of limited use due to their typically low level of polymorphism, more polymorphic markers have been discovered during the last decades, supplying powerful tools to overcome the problem of clonality assessment. However, population genetics studies on clonal organisms lack a standardized framework to assess clonality, and to adapt conventional data analyses to account for the potential bias due to the possible replication of the same individuals in the sampling. Moreover, existing studies used a variety of indices to describe clonal diversity and structure such that comparison among studies is difficult at best. We emphasize the need for standardizing studies on clonal organisms, and particularly on clonal plants, in order to clarify the way clonality is taken into account in sampling designs and data analysis, and to allow further comparison of results reported in distinct studies. In order to provide a first step towards a standardized framework to address clonality in population studies, we review, on the basis of a thorough revision of the literature on population structure of clonal plants and of a complementary revision on other clonal organisms, the indices and statistics used so far to estimate genotypic or clonal diversity and to describe clonal structure in plants. We examine their advantages and weaknesses as well as various conceptual issues associated with statistical analyses of population genetics data on clonal organisms. We do so by testing them on results from simulations, as well as on two empirical data sets of microsatellites of the seagrasses Posidonia oceanica and Cymodocea nodosa. Finally, we also propose a selection of new indices and methods to estimate clonal diversity and describe clonal structure in a way that should facilitate comparison between future studies on clonal plants, most of which may be of interest for clonal organisms in general.

Watershed land cover is widely used as a predictor of stream-ecosystem condition. However, numerous spatial factors can confound the interpretation of correlative analyses between land cover and stream indicators, particularly at broad spatial scales. We used a stream-monitoring data set collected from the Coastal Plain of Maryland, USA to address analytical challenges presented by (1) collinearity of land-cover class percentages, (2) spatial autocorrelation of land cover and stream data, (3) intercorrelations among and spatial autocorrelation within abiotic intermediaries that link land cover to stream biota, and (4) spatial arrangement of land cover within watersheds. We focused on two commonly measured stream indicators, nitrate-nitrogen (NO 3 -N) and macroinvertebrate assemblages, to evaluate how different spatial considerations may influence results. Partial correlation analysis of land-cover percentages revealed that simple correlations described relationships that could not be separated from the effects of other land-cover classes or relationships that changed substantially when the influences of other land-cover classes were taken into account. Partial Mantel tests showed that all land-cover percentages were spatially autocorrelated, and this spatial phenomenon accounted for much of the variation in macroinvertebrate assemblages that could naively be attributed to certain classes (e.g., percentage cropland). We extended our use of partial Mantel tests into a path-analytical framework and identified several independent pathways between percentage developed land and instream measurements after factoring out spatial autocorrelation and other confounding variables; however, under these conditions, percentage cropland was only linked to nitrate-N. Further analyses revealed that spatial arrangement of land cover, as measured by areal buffers and distance weighting, influenced the amount of developed land, resulting in a threshold change in macroinvertebrate-assemblage composition. Moreover, distanceweighted percentage cropland improved predictions of stream nitrate-N concentrations in small watersheds, but not in medium or large ones. Collectively, this series of analyses clarified the magnitude and critical scales of effects of different land-cover classes on Coastal Plain stream ecosystems and may serve as an analytical framework for other studies. Our results suggest that greater emphasis should be placed on these important spatial considerations; otherwise, we risk obscuring the relationships between watershed land cover and the condition of stream ecosystems.

Variation in forest canopy structure influences both understory light availability and its spatial distribution. Because light is a major environmental factor limiting growth and survival of many forest species, its distribution may affect stand-level regeneration patterns. We examined spatial patterning in light availability and seedling regeneration in old-growth, second-growth, and selectively logged stands of tropical moist forest in northeastern Costa Rica. Our objectives were to determine how the frequency distribution and spatial pattern of understory light ''microsites'' differ among tropical wet forests; whether patterns of seedling regeneration are linked to spatial patterning of light availability; and whether these relationships differ among old-growth, second-growth, and selectively logged forest stands. We used both sensor-based and hemispherical photograph-based methods to measure light availability along three 130-160 m long transects in each of eight stands (three old-growth, three second-growth, and two selectively logged). Woody seedling abundance was assessed at 4 m 2 , 25 m 2 , and full-stand scales (430 m 2 ), and species richness was computed at the 25-m 2 and full-stand levels. Data were analyzed using both conventional parametric approaches and spatial statistics. Mean light availability did not differ markedly among stand types, but variance and frequency distributions of light availability did. Second-growth stands had significantly higher unweighted canopy openness along solar tracks and a higher frequency of microsites at intermediate light levels. Old-growth stands had greater representation of both low-and high-light microsites, and greater overall variance in light availability. Old-growth stands also had slightly higher abundance and species richness of woody seedlings. Light availability was significantly spatially autocorrelated in all stand types, but patch size (analogous to gap size) was twice as large in old-growth stands, based on sensor data. Seedling abundance was also spatially autocorrelated over greater distances in old-growth than in second-growth stands, often at similar spatial scales to light distribution. The selectively logged stands demonstrated spatial autocorrelation of light and seedling abundance over distances intermediate to the other two stand types. Despite the similarities in patterns of light and seedling distributions, relationships between woody seedling abundance, species richness, and the three light availability measures were not strong or consistently positive, regardless of whether standard regressions or partial Mantel tests were applied. Although seedling abundance is likely to be affected by a wide variety of factors, the similarities in the scales of spatial autocorrelation of light and seedling abundance suggest that current seedling abundance distributions may reflect past patterns of light distribution within the stands. Our results confirm the importance of examining spatial dependence of resource availability in studies of forest dynamics, but they also underscore the limitations of a single period of data collection. Long-term studies as well as experimental manipulations of resource availability are needed to establish causal relationships between resource availability and stand-level patterns of seedling regeneration.

Cetacean-habitat modeling, although still in the early stages of development, represents a potentially powerful tool for predicting cetacean distributions and understanding the ecological processes determining these distributions. Marine ecosystems vary temporally on diel to decadal scales and spatially on scales from several meters to 1000s of kilometers. Many cetacean species are wideranging and respond to this variability by changes in distribution patterns. Cetacean-habitat models have already been used to incorporate this variability into management applications, including improvement of abundance estimates, development of marine protected areas, and understanding cetacean-fisheries interactions. We present a review of the development of cetacean-habitat models, organized according to the primary steps involved in the modeling process. Topics covered include purposes for which cetacean-habitat models are developed, scale issues in marine ecosystems, cetacean and habitat data collection, descriptive and statistical modeling techniques, model selection, and model evaluation. To date, descriptive statistical techniques have been used to explore cetacean-habitat relationships for selected species in specific areas; the numbers of species and geographic areas examined using computationally intensive statistic modeling techniques are considerably less, and the development of models to test specific hypotheses about the ecological processes determining cetacean distributions has just begun. Future directions in cetacean-habitat modeling span a wide range of possibilities, from development of basic modeling techniques to addressing important ecological questions.

The number of species in an area is critical to the development of evolutionary and ecological theory from mass extinctions to island biogeography. Still, the factors influencing the accuracy of estimators of species richness are poorly understood. We explored these factors by simulating landscapes that varied in species richness, relative abundances, and the spatial distribution. We compared the extrapolations of nine nonparametric estimators and two species accumulation curves under three sampling intensities. Community evenness of species' abundances, sampling intensity, and the level of true species richness significantly influenced bias, precision, and accuracy of the estimations. Perhaps most surprisingly, the effects of gradient strength and spatial autocorrelation type were generally insignificant. The nonparametric estimators were substantially less biased and more precise than the species accumulation curves. Observed species richness was most biased. Community evenness, sampling intensity, and the level of true species richness influenced the performance of the nonparametric estimators indirectly via the fraction of all species found in a sample or ''sample coverage.'' For each particular level of sample coverage, a single estimator was most accurate. Choice of estimator is confounded by a priori uncertainty about the sample coverage. Accordingly, researchers can extrapolate species richness by various estimators and base the estimator choice on the mean estimated sample coverage. Alternatively, the most reliable estimator with respect to community evenness can be chosen. These predictions from our simulations are confirmed in two field studies.

Many analytical techniques that assess resource selection focus on individual relocation points as the sample unit and classify resources as either used or available. Commonly, the relative use of each resource is quantified as the number of observations in each resource class or the proportional occurrence of a resource within a home range. We believe that a more accurate estimate can be summarized by a utilization distribution (UD). We present an analytical approach that explicitly incorporates a probabilistic measure of use, as defined by the UD. We used animal relocation points and fixed-kernel techniques to determine a UD within a home range. We related this probabilistic measure of use to categorical and continuous resource variables using multiple regression. Regression errors accounted for spatial autocorrelation so that the significance of regression coefficients could be appraised for each animal and averaged across animals. This allowed us to quantify the individualistic nature of resource selection and test for consistency in use of resources by a population. Sample sizes in population assessments correctly reflected the individual animal as the experimental unit. We used this technique in a geographic information system setting to examine the importance of local-scale (forest cover) and landscape-scale (degree of fragmentation, proximity to edges and human use areas) attributes to breeding season habitat selection by 25 radio-tagged Steller's Jays (Cyanocitta stelleri) in western Washington State, USA. Individual jays varied significantly in habitat use, but most (20) concentrated their use in areas with many vegetation patches or in areas with extensive edge between forest and nonforested land cover. This confirmed our prediction that jays prefer fragmented habitat and forest edges and helped to explain why jays are most abundant in fragmented landscapes. However, we refined our understanding of why they used such habitats by demonstrating that landscape attributes affected use of local habitat features: high-contrast edges were used most if they were associated with small human settlements and campgrounds. Use of patchy and edgy areas within home ranges may be reinforced by natural selection because jays that inhabited areas with complex-shaped patches and concentrated their activity in such areas were most likely to fledge young. Concentration of use along forest-human land use interfaces may explain the greater risk of nest predation to other birds in such settings.

The possibility that homicides can spread from one geographic area to another has been entertained for some time by social scientists, yet systematic efforts to demonstrate the existence, or estimate the strength, of such a diffusion process are just beginning. This paper uses exploratory spatial data analysis (ESDA) to examine the distribution of homicides in 78 counties in, or around, the St. Louis metropolitan area for two time periods: a period of relatively stable homicide (1984)(1985)(1986)(1987)(1988)) and a period of generally increasing homicide (1988)(1989)(1990)(1991)(1992)(1993). The findings reveal that homicides are distributed nonrandomly, suggestive of positive spatial autocorrelation. Moreover, changes over time in the distribution of homicides suggest the possible diffusion of lethal violence out of one county containing a medium-sized city (Macon County) into two nearby counties (Morgan and Sangamon Counties) located to the west. Although traditional correlates of homicide do not account for its nonrandom spatial distribution across counties, we find some evidence that more affluent areas, or those more rural or agricultural areas, serve as barriers against the diffusion of homicides. The patterns of spatial distribution revealed through ESDA provide an empirical foundation for the specification of multivariate models which can provide formal tests for diffusion processes.

1 Unravelling which factors affect where tropical trees grow is an important goal for ecologists and conservationists. At the landscape scale, debate is mostly focused on the degree to which the distributions of tree species are determined by soil conditions or by neutral, distance-dependent processes. Problems with spatial autocorrelation, sparse soil sampling, inclusion of species-poor sites with extreme edaphic conditions, and the difficulty of obtaining sufficient sample sizes have all complicated assessments for high diversity tropical forests. 2 We evaluated the extent and pervasiveness of habitat association of trees within a 10 000 km 2 species-rich lowland landscape of uniform climate in south-west Amazonia. Forests growing on two non-flooded landscape units were inventoried using 88 floristic plots and detailed soil analyses, sampling up to 849 tree species. We applied singlespecies and community-level analytical techniques (frequency-distributions of presence records, association analysis, indicator species analysis, ordination, Mantel correlations, and multiple regression of distance matrices) to quantify soil/floristic relationships while controlling for spatial autocorrelation. 3 Obligate habitat-restriction is very rare: among 230 tree species recorded in ≥ 10 localities only five (2.2%) were always restricted to one landscape unit or the other. 4 However, many species show a significant tendency to habitat association. For example, using Monte Carlo randomization tests, of the 34 most dominant species across the landscape the distributions of 26 (76.5%) are significantly related to habitat. We applied density-independent and frequency-independent estimates of habitat association and found that rarer species tend to score higher, suggesting that our full community estimates of habitat association are still underestimated due to the inadequate sampling of rarer species. 5 Community-level floristic variation across the whole landscape is related to the variation in 14 of 16 measured soil variables, and to the geographical distances between samples. 6 Multiple regression of distance matrices shows that 10% of the floristic variation can be attributed to spatial autocorrelation, but even after accounting for this at least 40% is attributable to measured environmental variation. 7 Our results suggest that substrate-mediated local processes play a much more important role than distance-dependent processes in structuring forest composition in Amazonian landscapes.

Genetic admixture of distinct gene pools is the consequence of complex spatiotemporal processes that could have involved massive migration and local mating during the history of a species. However, current methods for estimating individual admixture proportions lack the incorporation of such a piece of information. Here, we extend Bayesian clustering algorithms by including global trend surfaces and spatial autocorrelation in the prior distribution on individual admixture coefficients. We test our algorithm by using spatially explicit and realistic coalescent simulations of colonization followed by secondary contact. By coupling our multiscale spatial analyses with a Bayesian evaluation of model complexity and fit, we show that the algorithm provides a correct description of smooth clinal variation, while still detecting zones of sharp variation when they are present in the data. We also apply our approach to understand the population structure of the killifish, Fundulus heteroclitus, for which the algorithm uncovers a presumed contact zone in the Atlantic coast of North America.

Little information is available regarding the landscape-scale distribution of microbial communities and its environmental determinants. However, a landscape perspective is needed to understand the relative importance of local and regional factors and land management for the microbial communities and the ecosystem services they provide. In the most comprehensive analysis of spatial patterns of microbial communities to date, we investigated the distribution of functional microbial communities involved in N-cycling and of the total bacterial and crenarchaeal communities over 107 sites in Burgundy, a 31 500 km 2 region of France, using a 16 Â 16 km 2 sampling grid. At each sampling site, the abundance of total bacteria, crenarchaea, nitrate reducers, denitrifiers-and ammonia oxidizers were estimated by quantitative PCR and 42 soil physicochemical properties were measured. The relative contributions of land use, spatial distance, climatic conditions, time, and soil physico-chemical properties to the spatial distribution of the different communities were analyzed by canonical variation partitioning. Our results indicate that 43-85% of the spatial variation in community abundances could be explained by the measured environmental parameters, with soil chemical properties (mostly pH) being the main driver. We found spatial autocorrelation up to 739 km and used geostatistical modelling to generate predictive maps of the distribution of microbial communities at the landscape scale. The present study highlights the potential of a spatially explicit approach for microbial ecology to identify the overarching factors driving the spatial heterogeneity of microbial communities even at the landscape scale.

Aims Empirical tests of relationships between alcohol outlets and violence are generally conducted with statistical controls for correlates related to characteristics of people and the places in which they live. Crime potentials theory asserts that certain subpopulations are disposed to participate in criminal activities (population potentials) and certain neighborhoods are more likely to be places where crimes occur (place potentials). The current study assesses the degree to which measures of the different geographic distributions of these potentials contribute to violent crime. Design Cross-sectional data on hospital discharges for violent assaults were obtained for residents of 1637 zip code areas in California. Assault rates were related to measures of population and place characteristics using spatial statistical models corrected for spatial autocorrelated error. Findings Rates of assault were related to population and place characteristics within zip code areas, and with characteristics of populations living in adjacent zip code areas. Assault rates were greater in densely populated, poor minority urban areas with greater residential instability. Assault rates were also greater in zip code areas adjacent to densely populated urban areas. Assault rates were related significantly to local densities of off-premise alcohol retail establishments, not bars. However, densities of bars moderated substantially effects related to local population characteristics. Bars were related significantly to violence in unstable poor minority areas and in rural middle-income areas of the state. Conclusion Population and place characteristics are associated with rates of violence across spatial areas. Alcohol outlets directly affect and moderate potentials for violence associated with socio-demographic groups.

Background: Most heat-related deaths occur in cities and future trends in global climate change and urbanization may amplify this trend. Understanding how neighborhoods affect heat mortality fills an important gap between studies of individual susceptibility to heat and broadly comparative studies of temperature-mortality relationships in cities.

Objectives: We estimated neighborhood effects of population characteristics and the built and natural environments on deaths due to heat exposure in Maricopa County, Arizona (2000-2008).

Methods: We used U.S. Census data and remotely sensed vegetation and land surface temperature to construct indicators of neighborhood vulnerability and a Geographic Information System to map vulnerability and residential addresses of people who died from heat exposure in 2,081 census block groups. Binary logistic regression and spatial analysis were used to associate deaths with neighborhoods.

Results: Neighborhood scores on three factors – Socioeconomic Vulnerability, Elderly/Isolation, and Unvegetated Area – varied widely throughout the study area. The preferred model (based on fit and parsimony) for predicting the odds of one or more deaths from heat exposure within a census block group included the first two factors and surface temperature in residential neighborhoods, holding constant population size. Spatial analysis identified clusters of neighborhoods with the highest heat vulnerability scores. A large proportion of deaths occurred among people, including homeless persons, who lived in the inner cores of the largest cities and an industrial corridor.

Conclusions: Place-based indicators of vulnerability complement analyses of person-level heat risk factors. Surface temperature might be used in Maricopa County to identify the most heat-vulnerable neighborhoods but more attention to the socio-ecological complexities of climate adaptation is needed.

Biological soil thin-sections and a combination of image analysis and geostatistical tools were used to conduct a detailed investigation into the distribution of bacteria in soil and their relationship with pores. The presence of spatial patterns in the distribution of bacteria was demonstrated at the microscale, with ranges of spatial autocorrelation of 1 mm and below. Bacterial density gradients were found within bacterial patches in topsoil samples and also in one subsoil sample. Bacterial density patches displayed a mosaic of high and low values in the remaining subsoil samples. Anisotropy was detected in the spatial structure of pores, but was not detected in relation to the distribution of bacteria. No marked trend as a function of distance to the nearest pore was observed in bacterial density values in the topsoil, but in the subsoil bacterial density was greatest close to pores and decreased thereafter. Bacterial aggregation was greatest in the cropped topsoil, though no consistent trends were found in the degree of bacterial aggregation as a function of distance to the nearest pore. The implications of the results presented for modelling and predicting bacterial activity in soil are discussed.

One approach to dealing with spatial autocorrelation in regression analysis involves the filtering of variables in order to separate spatial effects from the variables' total effects. In this paper we compare two filtering approaches, both of which allow spatial statistical analysts to use conventional linear regression models. Getis' filtering approach is based on the autocorrelation observed with the use of the Gi local statistic. Griffith's approach uses an eigenfunction decomposition based on the geographic connectivity matrix used to compute a Moran's I statistic. Economic data are used to compare the workings of the two approaches. Afinal comparison with an autoregressive model strengthens the conclusion that both techniques are effective filtering devices, and that they yield similar regression models. We do note, however, that each technique should be used in its appropriate context.

The quality of maps obtained by interpolation of observations of a target environmental variable at a restricted number of locations, is partly determined by the spatial pattern of the sample locations. A method is presented for optimization of the sample pattern when the environmental variable is interpolated with the help of exhaustively known covariates, which are assumed to be linearly related to the target variable. In this method the spatially averaged universal kriging variance (MUKV), which incorporates trend estimation error as well as spatial interpolation error, is minimized. The optimal pattern is obtained using simulated annealing. The method requires that the covariance function or variogram of the regression-residuals is known. The method is tested in a case study on the Mean Highest Water table in a coversand area in The Netherlands. The patterns of 25, 50 and 100 sample locations are optimized and compared with the patterns optimized with the ordinary kriging (OK) model (assuming no trend) and with the multiple linear regression (MLR) model (assuming no spatial autocorrelation of residuals). The results show that the UK-patterns are a good compromise between spreading in geographic space and feature space. The MUKV for the UK-patterns is 19% (n = 25), 7% (n = 50) and 3% (n = 100) smaller than for the OK-patterns. Compared with the MLR-patterns the reduction is 2%, 4% and 4%, respectively.

This study examined relationships between greenness exposure and free-living physical activity behavior of children in smart growth and conventionally designed communities. Normalized Difference Vegetation Index (NDVI) was used to quantify children's (n ¼208) greenness exposure at 30-s epoch accelerometer and GPS data points. A generalized linear mixed model with a kernel density smoothing term for addressing spatial autocorrelation was fit to analyze residential neighborhood activity data. Excluding activity at home and during school-hours, an epoch-level analysis found momentary greenness exposure was positively associated with the likelihood of contemporaneous moderate-tovigorous physical activity (MVPA). This association was stronger for smart growth residents who experienced a 39% increase in odds of MVPA for a 10th to 90th percentile increase in exposure to greenness (OR ¼ 1.39, 95% CI 1.36-1.44). An individual-level analysis found children who experienced 420 min of daily exposure to greener spaces (490th percentile) engaged in nearly 5 times the daily rate of MVPA of children with nearly zero daily exposure to greener spaces (95% CI 3.09-7.20).

The structure, biomass, and activity of the microbial community in the humus layer of boreal coniferous forest stands of different fertility were studied. The Scots pine dominated CT (Calluna vulgaris type) represented the lowest fertility, while VT (Vaccinium vitis-idaéa type), MT (Vaccinium myrtillus type), and OMT (Oxalis acetocella-Vaccinium myrtillus type) following this order, were more fertile types. The microbial community was studied more closely by sampling a succession gradient (from a treeless area to a 180-years-old Norway spruce stand) at the MT type site. The phospholipid fatty acid (PLFA) analysis revealed a gradual shift in the structure of the microbial community along the fertility gradient even though the total microbial biomass and respiration rate remained unchanged. The relative abundance of fungi decreased and that of bacteria increased with increasing fertility. The structure of the bacterial community also changed along the fertility gradient. Irrespective of a decrease in fungal biomass and change in bacterial community structure after clear-cutting, the PLFA analysis did not show strong differences in the microbial communities in the stands of different age growing on the MT type site. The spatial variation in the structure of the microbial community was studied at a MT type site. Semivariograms indicated that the bacterial biomass, the ratio between the fungal and bacterial biomasses, and the relative amount of PLFA 16:15 were spatially autocorrelated within distances around 3 to 4 m. The total microbial and fungal biomasses were autocorrelated only up to 1 m. The spatial distribution of the humus microbial community was correlated mainly with the location of the trees, and consequently, with the forest floor vegetation.

Region-growing segmentation algorithms are useful for remote sensing image segmentation. These algorithms need the user to supply control parameters, which control the quality of the resulting segmentation. This letter proposes an objective function for selecting suitable parameters for region-growing algorithms to ensure best quality results. It considers that a segmentation has two desirable properties: each of the resulting segments should be internally homogeneous and should be distinguishable from its neighbourhood. The measure combines a spatial autocorrelation indicator that detects separability between regions and a variance indicator that expresses the overall homogeneity of the regions.

Extreme heat is an important weather hazard associated with excess mortality and morbidity. We determine the relative importance of heat exposure and the built environment, socioeconomic vulnerability, and neighborhood stability for heat mortality (Philadelphia, PA, USA) or heat distress (Phoenix, AZ, USA), using an ecologic study design. We use spatial Generalized Linear and Mixed Models to account for non-independence (spatial autocorrelation) between neighboring census block groups. Failing to account for spatial autocorrelation can provide misleading statistical results. Phoenix neighborhoods with more heat exposure, Black, Hispanic, linguistically and socially isolated residents, and vacant households made more heat distress calls. Philadelphia heat mortality neighborhoods were more likely to have low housing values and a higher proportion of Black residents. Our methodology can identify important risk factors and geographic areas to target interventions.

... OTIS W. GILLEY Department of Economics and Finance, College of Administration and Business, Louisiana Tech University, Ruston ... 334 PACE AND GILLEY ... areas (INDUS), property tax rate (TAX), pupil±teacher ratio (PTRATIO), location contiguous to the Charles River (CHAS ...

Disturbances such as fire, insect outbreaks, and blowdown are important in shaping subalpine forests in the Rocky Mountains, but quantitative studies of their interactions are rare. We investigated the combined effects of past disturbances, current vegetation, and topography on spatial variability of the severity of a fire that burned approximately 4500 ha of subalpine forest during the extreme drought of 2002 in northwestern Colorado. Ordinal logistic regression was used to spatially model fire severity in relation to late 1800s fires, a 1940s spruce beetle outbreak, forest cover type, stand structure, and topography. The late 1800s fires reduced the probability of burning in 2002, and the 1940s beetle outbreak slightly increased the probability of fire, particularly at high severity. Aspen (Populus tremuloides) and lodgepole pine (Pinus contorta) stands, which established after the late 1800s fires, were less likely to burn, whereas Engelmann spruce (Picea engelmannii)-subalpine fir (Abies lasiocarpa) stands were more likely to burn. The highest elevations (Ն3100 m) had the lowest probability of burning, whereas intermediate elevations (2900-3100 m) had an increased probability of burning at high severity. The influences of the late 1800s fires and 1940s beetle outbreak on stand structure and forest cover type may be more important than their direct effects on fuels. The most important predictors determining fire severity were stand structure, forest cover type, the late 1800s fires, and elevation. Although, in other studies, the effects of pre-burn stand conditions and topography declined with increasingly severe fire weather, in the case of the 2002 fire in Colorado, these predictors explained 42% of the variability of fire severity. Thus, these results suggest that pre-burn stand conditions are important influences on burn severity even for fires burning during extreme drought.

Spectral-based image endmember extraction methods hinge on the ability to discriminate between pixels based on spectral characteristics alone. Endmembers with distinct spectral features (high spectral contrast) are easy to select, whereas those with minimal unique spectral information (low spectral contrast) are more problematic. Spectral contrast, however, is dependent on the endmember assemblage, such that as the assemblage changes so does the "relative" spectral contrast of each endmember to all other endmembers. It is then possible for an endmember to have low spectral contrast with respect to the full image, but have high spectral contrast within a subset of the image. The spatial-spectral endmember extraction tool (SSEE) works by analyzing a scene in parts (subsets), such that we increase the spectral contrast of low contrast endmembers, thus improving the potential for these endmembers to be selected. The SSEE method comprises three main steps: 1) application of singular value decomposition (SVD) to determine a set of basis vectors that describe most of the spectral variance for subsets of the image; 2) projection of the full image data set onto the locally defined basis vectors to determine a set of candidate endmember pixels; and, 3) imposing spatial constraints for averaging spectrally similar endmembers, allowing for separation of endmembers that are spectrally similar, but spatially independent. The SSEE method is applied to two real hyperspectral data sets to demonstrate the effects of imposing spatial constraints on the selection of endmembers. The results show that the SSEE method is an effective approach to extracting image endmembers. Specific improvements include the extraction of physically meaningful, low contrast endmembers that occupy unique image regions.

We studied amphibian populations in a human-dominated landscape, in Northern Italy, to evaluate the effects of patch quality and isolation on each species distribution and community structure. We used logistic and linear multiple regression to relate amphibian presence during the breeding season in 84 wetlands to wetland features and isolation. Jackknife procedure was used to evaluate predictive capability of the models. Again, we tested the response of each species to habitat features related to the richest communities. Amphibian presence depends strongly on habitat quality and isolation: the richest communities live in fish-free, sunny wetlands near to occupied wetlands. The negative effects of isolation do not seem to be biased by spatial autocorrelation of habitat features. The system shows strong nestedness: amphibian persistence depends on the contemporary effects of species adaptability and mobility. The commonest species, the pool frog (Rana synklepton esculenta) and the Italian tree frog (Hyla intermedia), are able to move through the matrix using canals and hedgerows, and can maintain metapopulations across the landscape; the rarest species (newts and toads) are more sensitive to habitat alteration, and they are strongly affected by isolation effects. If human exploitation of the landscape continues, only few species, mobile and opportunistic, will persist in this landscape.

Revealing spatially varying relationships between urban growth patterns and underlying determinants is important for better understanding local dimensions of urban development. Through a case study of Nanjing, China, we employ both global and local logistic regressions to model the probability of urban land expansion against a set of spatial variables. We found that compared with other fast growing coastal cities, Nanjing remains a relatively compact city. The orthodox logistic regression found the significance of proximity, neighborhood conditions, and urban agglomeration in urban land change. The logistic GWR significantly improves the global logistic regression model in terms of better model goodness-of-fit and lower level of spatial autocorrelation of residuals. More importantly, the local estimates of parameters of spatial variables enable us to investigate spatial variations of the influences of spatial variables on urban growth. We have found distinctive local patterns and effects of urban growth in Nanjing, shaped by local urban spatial and institutional structures. A probability surface of urban growth, which is generated from raster calculations among the parameter and variable surfaces, provides a clear scenario of urban growth patterns and can be useful for decision making. This study also shows the importance of policy studies and fieldwork in the interpretation of results generated from statistical and GIS modeling.

The estimation of the predictive power of transfer functions assumes that the test sites are independent of the modelling sites. Cross-validation in the presence of spatial autocorrelation seriously violates this assumption. This assumption and the consequences of its violation have not been discussed before. We show, by simulation, that the expected r2 of a transfer function model from an autocorrelated environment can be high, and is not near zero as commonly assumed. We investigate a foraminiferal sea surface temperature training set for the North Atlantic, for which, with cross-validation, the modern analogue technique (MAT) and artificial neural networks (ANN) outperform transfer function methods based on a unimodal species-environment response model. However, when a spatially independent test set, the South Atlantic, is used, all models have a similar predictive power. We show that there is a spatial structure in the foraminiferal assemblages even after accounting for temperature, presumably due to autocorrelations in other environmental variables. Since the residuals from MAT show little spatial structure, in contrast to the residuals of unimodal response models, we contend that MAT has inappropriately internalized the non-temperature spatial structure to improve its performance. We argue that most, if not all, estimates of the predictive power of MAT and ANN models for sea surface temperatures hitherto published are over-optimistic and misleading.

This article considers critically how one of the oldest and most widely applied statistical methods, principal components analysis (PCA), is employed with spatial data. We first provide a brief guide to how PCA works: This includes robust and compositional PCA variants, links to factor analysis, latent variable modeling, and multilevel PCA. We then present two different approaches to using PCA with spatial data. First we look at the nonspatial approach, which avoids challenges posed by spatial data by using a standard PCA on attribute space only. Within this approach we identify four main methodologies, which we define as (1) PCA applied to spatial objects, (2) PCA applied to raster data, (3) atmospheric science PCA, and (4) PCA on flows. In the second approach, we look at PCA adapted for effects in geographical space by looking at PCA methods adapted for first-order nonstationary effects (spatial heterogeneity) and second-order stationary effects (spatial autocorrelation). We also describe how PCA can be used to investigate multiple scales of spatial autocorrelation. Furthermore, we attempt to disambiguate a terminology confusion by clarifying which methods are specifically termed “spatial PCA” in the literature and how this term has different meanings in different areas. Finally, we look at a further three variations of PCA that have not been used in a spatial context but show considerable potential in this respect: simple PCA, sparse PCA, and multilinear PCA. Este artículo considera críticamente la manera de utilizar con datos espaciales uno de los métodos estadísticos más viejos y de aplicación generalizada, el análisis de componentes principales (ACP). Antes de todo, suministramos una breve guía sobre cómo trabaja el ACP: Esto incluye variantes del ACP robustas y composicionales, vínculos con el análisis factorial, modelización de variable latente, y ACP de nivel múltiple. Luego presentamos dos enfoques diferentes para utilizar el ACP con datos espaciales. Primero, dirigimos nuestra atención al enfoque no espacial, que evita los problemas que surgen cuando los datos espaciales se utilizan con un ACP estándar de solo el espacio como atributo. Dentro de este enfoque identificamos cuatro metodologías principales, las cuales definimos como (1) el ACP aplicado a objetos espaciales, (2) el ACP aplicado a datos raster, (3) el ACP para ciencia atmosférica, y (4) el ACP para flujos. En el segundo enfoque, tratamos al ACP adaptado para efectos en el espacio geográfico, examinando métodos de ACP adaptados para efectos no estacionarios de primer orden (heterogeneidad espacial) y efectos estacionarios de segundo orden (autocorrelación espacial). También describimos la manera de utilizar el ACP para investigar múltiples escalas de autocorrelación espacial. Adicionalmente, intentamos desambiguar una confusión de terminología aclarando qué métodos son específicamente denominados “ACP espacial” en la literatura y cómo esta expresión tiene significados diferentes en áreas distintas. Por último, dirigimos nuestra atención a tres variaciones adicionales del ACP que no han sido usadas en un contexto espacial pero que muestran considerable potencial en este respecto: ACP simple, ACP ralo y ACP multilineal.

Using a spatial econometric perspective, the speed of convergence for a sample of 163 regions of the European Union (EU) over the period 1981–1996 is estimated. For this purpose, we use a specification strategy which allows an explicit modeling of both spatial heterogeneity and spatial autocorrelation found in the analyzed sample. The estimated final model combines groupwise heterocedasticity, the identification of two spatial regimes and spatial dependence. Our results show how an appropriate consideration of the role of spatial effects can shed new insights into the European convergence process. We find that regions in the EU cohesion-fund countries (Ireland, Greece, Portugal and Spain) are converging separately from the rest of regions of the EU. Our estimations indicate that over the analyzed period, there was a faster conditional convergence in relative income levels of the regions belonging to Cohesion countries (5.3%) than in the rest of the regions of the EU (3.3%). Therefore, our results contrast with other evidence that points to the fact that the convergence process in Europe has weakened or even has stopped at the beginning of the 1980s. Moreover, our work shows clear evidence of separate spatial convergence clubs among EU regions.

In developing red data books of threatened species, the World Conservation Union uses measures of rarity, rates of decline, and population fragmentation to categorize species according to their risk of extinction. However, most quantitative measures of these three concepts are sensitive to the scale at which they are made.

Distributions of species, animals or plants, terrestrial or aquatic, are influenced by numerous factors such as physical and biogeographical gradients. Dominant wind and current directions cause the appearance of gradients in physical conditions whereas biogeographical gradients can be the result of historical events (e.g. glaciations). No spatial modelling technique has been developed to this day that considers the direction of an asymmetric process controlling species distributions along a gradient or network. This paper presents a new method that can model species spatial distributions generated by a hypothesized asymmetric, directional physical process. This method is an eigenfunction-based spatial filtering technique that offers as much flexibility as the Moran's eigenvector maps (MEM) framework; it is called asymmetric eigenvector maps (AEM) modelling. Information needed to construct eigenfunctions through the AEM framework are the spatial coordinates of the sampling or experimental sites, a connexion diagram linking the sites to one another, prior information about the direction of the hypothesized asymmetric process influencing the response variable(s), and optionally, weights attached to the edges (links). To illustrate how this new method works, AEM is compared to MEM analysis through simulations and in the analysis of an ecological example where a known asymmetric forcing is present. The ecological example reanalyses the dietary habits of brook trout (Salvelinus fontinalis) sampled in 42 lakes of the Mastigouche Reserve, Québec.

Greenhouse gas inventories and emissions reduction programs require robust methods to quantify carbon sequestration in forests. We compare forest carbon estimates from Light Detection and Ranging (Lidar) data and QuickBird high-resolution satellite images, calibrated and validated by field measurements of individual trees. We conducted the tests at two sites in California: (1) 59 km 2 of secondary and old-growth coast redwood (Sequoia sempervirens) forest (Garcia-Mailliard area) and (2) 58 km 2 of old-growth Sierra Nevada forest (North Yuba area). Regression of aboveground live tree carbon density, calculated from field measurements, against Lidar height metrics and against QuickBird-derived tree crown diameter generated equations of carbon density as a function of the remote sensing parameters. Employing Monte Carlo methods, we quantified uncertainties of forest carbon estimates from uncertainties in field measurements, remote sensing accuracy, biomass regression equations, and spatial autocorrelation. Validation of QuickBird crown diameters against field measurements of the same trees showed significant correlation (r =0.82, P b 0.05). Comparison of stand-level Lidar height metrics with field-derived Lorey's mean height showed significant correlation (Garcia-Mailliard r =0.94, P b 0.0001; North Yuba R =0.89, P b 0.0001). Field measurements of five aboveground carbon pools (live trees, dead trees, shrubs, coarse woody debris, and litter) yielded aboveground carbon densities (mean ± standard error without Monte Carlo) as high as 320±35 Mg ha − 1 (old-growth coast redwood) and 510 ± 120 Mg ha − 1 (red fir [Abies magnifica] forest), as great or greater than tropical rainforest. Lidar and QuickBird detected aboveground carbon in live trees, 70-97% of the total. Large sample sizes in the Monte Carlo analyses of remote sensing data generated low estimates of uncertainty. Lidar showed lower uncertainty and higher accuracy than QuickBird, due to high correlation of biomass to height and undercounting of trees by the crown detection algorithm. Lidar achieved uncertainties of b1%, providing estimates of aboveground live tree carbon density (mean ± 95% confidence interval with Monte Carlo) of 82± 0.7 Mg ha − 1 in Garcia-Mailliard and 140 ± 0.9 Mg ha − 1 in North Yuba. The method that we tested, combining field measurements, Lidar, and Monte Carlo, can produce robust wall-to-wall spatial data on forest carbon.

Microbial ecologists often obtain data from sampling a piece of geographic space. These are likely to be spatially autocorrelated. Autocorrelation removes degrees of freedom from the usual tests of inferential statistics and can generate spurious correlations among variables, with the consequence that suspected causal relations may not hold. This paper describes methods that can be used to explore the spatial structure of ecological data and to include spatial location as a variable in the study of relationships and models. The relationship between environmental heterotrophic bacteria and phytoplankton, well established in aquatic environments, is reexamined in the Thau brackish lagoon (Mediterranean coast of France). It did not hold for the bacteria growing on bioMCrieux nutrient agar (BNA), which are presumably of continental origin; their spatial gradient can only partly be explained by the particulate organic carbon variable (POC) and not at all by phytoplankton biomass (CHL A), despite the existence of a spurious correlation between BNA and CHL A. The spatial gradient of abundance of heterotrophs growing on marine agar (MA), expected to bc mostly of marine origin, can be entirely explained by POC and CHL A. Different segments of the bacterial community, both reacting positively to variations ofthe particulate organic carbon, may follow partly, or not, variations of phytoplankton biomass. The mode of analysis developed here extends to many other spatially distributed processes in ecology and other fields. Contribution 1 of the ECOTHAU program, Laboratoire d'Hydrobiologie marine, Universite des Sciences et Techniques du Languedoc, and contribution 336 of the Groupe d'Ecologie des Eaux deuces, Univcrsite de Montreal. We thank G. Cauwet and G. Jacques for the use of their organic carbon and chlorophyll data obtained during the ECOTHAU sampling program.