Autocorrelation has been viewed as a problem in telemetry studies because sequential observations are not independent in time or space, therefore violating assumptions for statistical inference. Yet nearly all ecological and behavioural data are autocorrelated in both space and time. We argue that there is much to learn about the structure of ecological and behavioural data from patterns of autocorrelation. Such patterns include periodicity in movement and patchiness in spatial data, which can be characterized by an autocorrelogram, semivariogram or spectrum. We illustrate the utility of temporal autocorrelation functions (ACFs) for analysing step-length data from GPS telemetry of wolves (Canis lupus), cougars (Puma concolor), grizzly bears (Ursus arctos) and elk (Cervus elaphus) in western Alberta. ACFs often differ by season, reflecting differences in foraging behaviour. In wilderness landscapes, step-length ACFs for predators decay slowly to apparently random patterns, but sometimes display strong daily rhythms in areas of human disturbance. In contrast, step lengths of elk are consistently periodic, reflecting crepuscular activity.
Alberta; autocorrelation; GPS radiotelemetry; movement; periodicity; step length
Most evolutionary processes occur in a spatial context and several spatial analysis techniques have been employed in an exploratory context. However, the existence of autocorrelation can also perturb significance tests when data is analyzed using standard correlation and regression techniques on modeling genetic data as a function of explanatory variables. In this case, more complex models incorporating the effects of autocorrelation must be used. Here we review those models and compared their relative performances in a simple simulation, in which spatial patterns in allele frequencies were generated by a balance between random variation within populations and spatially-structured gene flow. Notwithstanding the somewhat idiosyncratic behavior of the techniques evaluated, it is clear that spatial autocorrelation affects Type I errors and that standard linear regression does not provide minimum variance estimators. Due to its flexibility, we stress that principal coordinate of neighbor matrices (PCNM) and related eigenvector mapping techniques seem to be the best approaches to spatial regression. In general, we hope that our review of commonly used spatial regression techniques in biology and ecology may aid population geneticists towards providing better explanations for population structures dealing with more complex regression problems throughout geographic space.
autocorrelation; geographical genetics; isolation-by-distance; landscape genetics; spatial regression
Despite the advances in the diagnosis and treatment of leishmaniasis, it is still considered as a severe public health problem particularly in developing countries and a great economic burden on the health resources. The present study was designed and conducted to determine the eco-environmental characteristics of the leishmaniasis disease by spatial analysis.
Materials and Methods:
In an ecological study, data were collected on eco-environmental factors of Fars province in Iran and on cutaneous leishmaniasis (CL) cases from 2002 to 2009. geographic weighted regression (GWR) was used to analyse the data and compare them with ordinary least square (OLS) regression model results. Moran's Index was applied for analysis of spatial autocorrelation in residual of OLS. P value less than 0.05 was considered as significant and adjusted R2 was used for model preferences.
There was a significant spatial autocorrelation in the residuals of OLS model (Z=2.45, P=0.014). GWR showed that rainy days, minimum temperature, wind velocity, maximum relative humidity and population density were the most important eco-environmental risk factors and explained 0.388 of the associated factors of CL.
Spatial analysis can be a good tool for detection and prediction of CL disease. In autocorrelated and non-stationary data, GWR model yields a better fitness than OLS regression model. Also, population density can be used as a surrogate variable of acquired immunity and increase the adjusted R2.
Ecological study; environmental factors; geographic information systems; geographic weighted regression; leishmaniasis; spatial analysis
Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature.
Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices) in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression). The eigenfunction values from the spatial configuration matrices were then used to define expectations for prior distributions using a Markov chain Monte Carlo (MCMC) algorithm. A set of posterior means were defined in WinBUGS 1.4.3®. After the model had converged, samples from the conditional distributions were used to summarize the posterior distribution of the parameters. Thereafter, a spatial residual trend analyses was used to evaluate variance uncertainty propagation in the model using an autocovariance error matrix.
By specifying coefficient estimates in a Bayesian framework, the covariate number of tillers was found to be a significant predictor, positively associated with An. arabiensis aquatic habitats. The spatial filter models accounted for approximately 19% redundant locational information in the ecological sampled An. arabiensis aquatic habitat data. In the residual error estimation model there was significant positive autocorrelation (i.e., clustering of habitats in geographic space) based on log-transformed larval/pupal data and the sampled covariate depth of habitat.
An autocorrelation error covariance matrix and a spatial filter analyses can prioritize mosquito control strategies by providing a computationally attractive and feasible description of variance uncertainty estimates for correctly identifying clusters of prolific An. arabiensis aquatic habitats based on larval/pupal productivity.
It is an ecological truism that population persistence depends on a population's growth rate when rare. To understand the interplay between temporal correlations, spatial heterogeneity and dispersal on persistence, an analytic approximation for this growth rate is derived for partially mixing populations. Partial mixing has two effects on population growth. In the absence of temporal correlations in relative fitness, greater movement to patches with, on average, higher relative fitness increases population growth rates. In the absence of spatial heterogeneity in the average relative fitnesses, lower dispersal rates enhance population growth when temporal autocorrelations of relative fitness within a patch exceed temporal cross-correlations in relative fitness between patches. This approximation implies that metapopulations whose expected fitness in every patch is less than 1 can persist if there are positive temporal autocorrelations in relative fitness, sufficiently weak spatial correlations and the population disperses at intermediate rates. It also implies that movement into lower quality habitats increases the population growth rate whenever the net temporal variation in per capita growth rates is sufficiently larger than the difference in the means of these per capita growth rates. Moreover, temporal autocorrelations, whether they be negative or positive, can enhance population growth for optimal dispersal strategies.
metapopulation persistence; spatial heterogeneity; temporal correlations; source-sink dynamics
Dispersal affects both social behavior and population structure and is therefore a key determinant of long-term population persistence. However, dispersal strategies and responses to spatial habitat alteration may differ between sexes. Here we analyzed spatial and temporal variation in ten polymorphic microsatellite DNA loci of male and female Cabanis’s greenbuls (Phyllastrephuscabanisi), a cooperative breeder of Afrotropical rainforest, to quantify rates of gene flow and fine-grained genetic structuring within and among fragmented populations. We found genetic evidence for female-biased dispersal at small spatial scales, but not at the landscape level. Local autocorrelation analysis provided evidence of positive genetic structure within 300 m distance ranges, which is consistent with behavioral observations of short-distance natal dispersal. At a landscape scale, individual-based autocorrelation values decreased over time while levels of admixture increased, possibly indicating increased gene flow over the past decade.
Contemporary impacts of anthropogenic climate change on ecosystems are increasingly being recognized. Documenting the extent of these impacts requires quantitative tools for analyses of ecological observations to distinguish climate impacts in noisy data and to understand interactions between climate variability and other drivers of change. To assist the development of reliable statistical approaches, we review the marine climate change literature and provide suggestions for quantitative approaches in climate change ecology. We compiled 267 peer-reviewed articles that examined relationships between climate change and marine ecological variables. Of the articles with time series data (n = 186), 75% used statistics to test for a dependency of ecological variables on climate variables. We identified several common weaknesses in statistical approaches, including marginalizing other important non-climate drivers of change, ignoring temporal and spatial autocorrelation, averaging across spatial patterns and not reporting key metrics. We provide a list of issues that need to be addressed to make inferences more defensible, including the consideration of (i) data limitations and the comparability of data sets; (ii) alternative mechanisms for change; (iii) appropriate response variables; (iv) a suitable model for the process under study; (v) temporal autocorrelation; (vi) spatial autocorrelation and patterns; and (vii) the reporting of rates of change. While the focus of our review was marine studies, these suggestions are equally applicable to terrestrial studies. Consideration of these suggestions will help advance global knowledge of climate impacts and understanding of the processes driving ecological change.
Land use/land cover change has been attracting increasing attention in the field of global environmental change research because of its role in the social and ecological environment. To explore the ecological risk characteristics of land use change in the Poyang Lake Eco-economic Zone of China, an eco-risk index was established in this study by the combination of a landscape disturbance index with a landscape fragmentation index. Spatial distribution and gradient difference of land use eco-risk are analyzed by using the methods of spatial autocorrelation and semivariance. Results show that ecological risk in the study area has a positive correlation, and there is a decreasing trend with the increase of grain size both in 1995 and 2005. Because the area of high eco-risk value increased from 1995 to 2005, eco-environment quality declined slightly in the study area. There are distinct spatial changes in the concentrated areas with high land use eco-risk values from 1995 to 2005. The step length of spatial separation of land use eco-risk is comparatively long—58 km in 1995 and 11 km in 2005—respectively. There are still nonstructural factors affecting the quality of the regional ecological environment at some small-scales. Our research results can provide some useful information for land eco-management, eco-environmental harnessing and restoration. In the future, some measures should be put forward in the regions with high eco-risk value, which include strengthening land use management, avoiding unreasonable types of land use and reducing the degree of fragmentation and separation.
land use change; ecological risk assessment; land ecological management; landscape pattern; spatial statistics; Poyang Lake
In the context of ecological studies, the Bayesian hierarchical Poisson model is of prime interest when studying the association between environmental exposure and rare diseases. However, adding spatially structured extra-variability in the model fitted to the data when such extra-variability does not exist conditionally on the covariates included in the model (over-fitting) may bias the estimation of the ecological association between covariates and relative risks toward the null. In order to investigate that possibility, a simulation study of the impact of introducing unnecessary residual spatial structure in the estimation model was conducted.
In the case where no underlying extra-variability from the Poisson process exists, the simulation results show that models accounting for structured and unstructured residuals do not underestimate the ecological association, unless covariates have a very strong autocorrelation structure, i.e., 0.98 at 100 km on a territory of diameter 1000 km."
• Background and Aims For rare endemics or endangered plant species that reproduce both sexually and vegetatively it is critical to understand the extent of clonality because assessment of clonal extent and distribution has important ecological and evolutionary consequences with conservation implications. A survey was undertaken to understand clonal effects on fine-scale genetic structure (FSGS) in two populations (one from a disturbed and the other from an undisturbed locality) of Echinosophora koreensis, an endangered small shrub belonging to a monotypic genus in central Korea that reproduces both sexually and vegetatively via rhizomes.
• Methods Using inter-simple sequence repeats (ISSRs) as genetic markers, the spatial distribution of individuals was evaluated using Ripley's L(d)-statistics and quantified the spatial scale of clonal spread and spatial distribution of ISSR genotypes using spatial autocorrelation analysis techniques (join-count statistics and kinship coefficient, Fij) for total samples and samples excluding clones.
• Key Results A high degree of differentiation between populations was observed (ΦST(g) = 0·184, P < 0·001). Ripley's L(d)-statistics revealed a near random distribution of individuals in a disturbed population, whereas significant aggregation of individuals was found in an undisturbed site. The join-count statistics revealed that most clones significantly aggregate at ≤6-m interplant distance. The Sp statistic reflecting patterns of correlograms revealed a strong pattern of FSGS for all four data sets (Sp = 0·072–0·154), but these patterns were not significantly different from each other. At small interplant distances (≤2 m), however, jackknifed 95 % CIs revealed that the total samples exhibited significantly higher Fij values than the same samples excluding clones.
• Conclusion The strong FSGS from genets is consistent with two biological and ecological traits of E. koreensis: bee-pollination and limited seed dispersal. Furthermore, potential clone mates over repeated generations would contribute to the observed high Fij values among genets at short distance. To ensure long-term ex situ genetic variability of the endangered E. koreensis, individuals located at distances of 10−12 m should be collected across entire populations of E. koreensis.
Clonal structure; conservation; Echinosophora koreensis; monotypic genus; Fabaceae; fine-scale genetic structure; genets; ISSRs; sampling strategies
We provide a relatively non‐technical glossary of terms and a description of the tools used in spatial or geographical epidemiology and associated geographical information systems. Statistical topics included cover adjustment and standardisation to allow for demographic and other background differences, data structures, data smoothing, spatial autocorrelation and spatial regression. We also discuss the rationale for geographical epidemiology and specific techniques such as disease clustering, disease mapping, ecological analyses, geographical information systems and global positioning systems.
Tick-borne encephalitis (TBE) virus can cause severe symptoms in humans. The incidence of this vector-borne pathogen in humans is characterised by spatial and temporal heterogeneity. To explain the variation in reported human TBE cases per county in southern Germany, we designed a time-lagged, spatially-explicit model that incorporates ecological, environmental, and climatic factors.
We fitted a logistic regression model to the annual counts of reported human TBE cases in each of 140 counties over an eight year period. The model controlled for spatial autocorrelation and unexplained temporal variation. The occurrence of human TBE was found to be positively correlated with the proportions of broad-leafed, mixed and coniferous forest cover. An index of forest fragmentation was negatively correlated with TBE incidence, suggesting that infection risk is higher in fragmented landscapes. The results contradict previous evidence regarding the relevance of a specific spring-time temperature regime for TBE epidemiology. Hunting bag data of roe deer (Capreolus capreolus) in the previous year was positively correlated with human TBE incidence, and hunting bag density of red fox (Vulpes vulpes) and red deer (Cervus elaphus) in the previous year were negatively correlated with human TBE incidence.
Our approach suggests that a combination of landscape and climatic variables as well as host-species dynamics influence TBE infection risk in humans. The model was unable to explain some of the temporal variation, specifically the high counts in 2005 and 2006. Factors such as the exposure of humans to infected ticks and forest rodent population dynamics, for which we have no data, are likely to be explanatory factors. Such information is required to identify the determinants of TBE more reliably. Having records of TBE infection sites at a finer scale would also be necessary.
Ecological and epidemiological invasions occur in a spatial context. We investigated how these processes correlate to the distance dependence of spread or dispersal between spatial entities such as habitat patches or epidemiological units. Distance dependence is described by a spatial kernel, characterized by its shape (kurtosis) and width (variance). We also developed a novel method to analyse and generate point-pattern landscapes based on spectral representation. This involves two measures: continuity, which is related to autocorrelation and contrast, which refers to variation in patch density. We also analysed some empirical data where our results are expected to have implications, namely distributions of trees (Quercus and Ulmus) and farms in Sweden. Through a simulation study, we found that kernel shape was not important for predicting the invasion speed in randomly distributed patches. However, the shape may be essential when the distribution of patches deviates from randomness, particularly when the contrast is high. We conclude that the speed of invasions depends on the spatial context and the effect of the spatial kernel is intertwined with the spatial structure. This implies substantial demands on the empirical data, because it requires knowledge of shape and width of the spatial kernel, and spatial structure.
kurtosis; spread of disease; point patterns; spectral density; dispersal; invasion
One of the central issues in ecology is the question what allows sympatric occurrence of closely related species in the same general area? The non-biting midges Chironomus riparius and C. piger, interbreeding in the laboratory, have been shown to coexist frequently despite of their close relatedness, similar ecology and high morphological similarity.
In order to investigate factors shaping niche partitioning of these cryptic sister species, we explored the actual degree of reproductive isolation in the field. Congruent results from nuclear microsatellite and mitochondrial haplotype analyses indicated complete absence of interspecific gene-flow. Autocorrelation analysis showed a non-random spatial distribution of the two species. Though not dispersal limited at the scale of the study area, the sister species occurred less often than expected at the same site, indicating past or present competition. Correlation and multiple regression analyses suggested the repartition of the available habitat along water chemistry gradients (nitrite, conductivity, CaCO3), ultimately governed by differences in summer precipitation regime.
We show that these morphologically cryptic sister species partition their niches due to a certain degree of ecological distinctness and total reproductive isolation in the field. The coexistence of these species provides a suitable model system for the investigation of factors shaping the distribution of closely related, cryptic species.
A major goal of ecology is to determine the causes of the latitudinal gradient in global distribution of species richness. Current evidence points to either energy availability or habitat heterogeneity as the most likely environmental drivers in terrestrial systems, but their relative importance is controversial in the absence of analyses of global (rather than continental or regional) extent. Here we use data on the global distribution of extant continental and continental island bird species to test the explanatory power of energy availability and habitat heterogeneity while simultaneously addressing issues of spatial resolution, spatial autocorrelation, geometric constraints upon species' range dynamics, and the impact of human populations and historical glacial ice-cover. At the finest resolution (1°), topographical variability and temperature are identified as the most important global predictors of avian species richness in multi-predictor models. Topographical variability is most important in single-predictor models, followed by productive energy. Adjusting for null expectations based on geometric constraints on species richness improves overall model fit but has negligible impact on tests of environmental predictors. Conclusions concerning the relative importance of environmental predictors of species richness cannot be extrapolated from one biogeographic realm to others or the globe. Rather a global perspective confirms the primary importance of mountain ranges in high-energy areas.
geometric constraints; global biodiversity; habitat heterogeneity; species richness; species-energy theory; topography
Child maltreatment and its consequences are a persistent problem throughout the world. Public health workers, human services officials, and others are interested in new and efficient ways to determine which geographic areas to target for intervention programs and resources. To improve assessment efforts, selected perinatal factors were examined, both individually and in various combinations, to determine if they are associated with increased risk of infant maltreatment. State of Georgia birth records and abuse and neglect data were analyzed using an area-based, ecological approach with the census tract as a surrogate for the community. Cartographic visualization suggested some correlation exists between risk factors and child maltreatment, so bivariate and multivariate regression were performed. The presence of spatial autocorrelation precluded the use of traditional ordinary least squares regression, therefore a spatial regression model coupled with maximum likelihood estimation was employed.
Results indicate that all individual factors or their combinations are significantly associated with increased risk of infant maltreatment. The set of perinatal risk factors that best predicts infant maltreatment rates are: mother smoked during pregnancy, families with three or more siblings, maternal age less than 20 years, births to unmarried mothers, Medicaid beneficiaries, and inadequate prenatal care.
This model enables public health to take a proactive stance, to reasonably predict areas where poor outcomes are likely to occur, and to therefore more efficiently allocate resources. U.S. states that routinely collect the variables the National Center for Health Statistics (NCHS) defines for birth certificates can easily identify areas that are at high risk for infant maltreatment. The authors recommend that agencies charged with reducing child maltreatment target communities that demonstrate the perinatal risks identified in this study.
This paper describes how the quantitative analytical tools of CMEIAS image analysis software can be used to investigate in situ microbial interactions involving cell-to-cell communication within biofilms. Various spatial pattern analyses applied to the data extracted from the 2-dimensional coordinate positioning of individual bacterial cells at single-cell resolution indicate that microbial colonization within natural biofilms is not a spatially random process, but rather involves strong positive interactions between communicating cells that influence their neighbors' aggregated colonization behavior. Geostatistical analysis of the data provide statistically defendable estimates of the micrometer scale and interpolation maps of the spatial heterogeneity and local intensity at which these microbial interactions autocorrelate with their spatial patterns of distribution. Including in situ image analysis in cell communication studies fills an important gap in understanding the spatially dependent microbial ecophysiology that governs the intensity of biofilm colonization and its unique architecture.
bacterial cell-to-cell communication; biofilm; calling distance; CMEIAS; colonization behavior; ecophysiology; geostatistics; image analysis; spatial pattern analysis
As the intermediate layer between the muscle and skin, the subcutaneous tissue frequently experiences shear and lateral stresses whenever the body is in motion. However, quantifying such stresses in vivo is difficult. The lack of such measures is partly responsible for our poor understanding of the biomechanical behaviors of subcutaneous tissue. In this study, we employ both ultrasound imaging and a novel spatial anisotropy measure - incorporating Moran’s I spatial autocorrelation calculations - to investigate the structuromechanical features of subcutaneous tissues within the extremities of sixteen healthy volunteers. This approach is based on the understanding that spatial anisotropy can be an effective surrogate for the summative, tensile forces experienced by biological tissue. We found that spatial anisotropy in the arm, thigh, and calf was attributed to the echogenic bands spanning the width of the ultrasound images. In both univariable and multivariable analyses, the calf was significantly associated with greater anisotropy compared to the thigh and arm. Spatial anisotropy was inversely related to subcutaneous thickness and was significantly increased with longitudinally oriented probe images compared to transversely orientated images. Maximum peaks in spatial anisotropy were frequently observed when the longitudinally oriented ultrasound probe was swept across the extremity suggesting that longitudinal channels with greater tension exist in the subcutaneous layer. These results suggest that subcutaneous biomechanical tension is mediated by collagenous/echogenic bands, greater in the calf compared to the thigh and arm, increased in thinner individuals, and maximal along longitudinal trajectories parallel to the underlying muscle. Spatial anisotropy analysis of ultrasound images has yielded meaningful patterns and may be an effective means to understand the biomechanical strain patterns within the subcutaneous tissue of the extremities.
Subcutaneous tissue; spatial anisotropy; autocorrelation; biomechanic; mechanical; ultrasound
The concept of a metapopulation acknowledges local extinctions as a natural part of the dynamics of a patchily distributed population. However, if extinctions are not balanced by recolonizations or if there is a high degree of spatial synchrony of local extinctions, this poses a threat to and will reduce the metapopulation persistence time. Here we show that, in a metapopulation network of 378 pond patches used by the tree frog (Hyla arborea), even though extinctions are frequent (mean extinction probability p(e) = 0.24) they pose no threat to the metapopulation as they are balanced by recolonizations (p(c) = 0.33). In any one year there was a pattern of large populations tending to persist while small populations became extinct. The total number of individuals belonging to populations that went extinct was small (< 5%) compared with those populations that persisted. A spatial autocorrelation analysis indicated no clustering of local extinctions. The tree frog metapopulation studied consisted of a set of larger, persistent populations mixed with smaller populations characterized by high turnover dynamics.
Background and Aims
The botanic gardens of the world are now unmatched ex situ collections of plant biodiversity. They mirror two biogeographical patterns (positive diversity–area and diversity–age relationships) but differ from nature with a positive latitudinal gradient in their richness. Whether these relationships can be explained by socio-economic factors is unknown.
Species and taxa richness of a comprehensive sample of botanic gardens were analysed as a function of key ecological and socio-economic factors using (a) multivariate models controlling for spatial autocorrelation and (b) structural equation modelling.
The number of plant species in botanic gardens increases with town human population size and country Gross Domestic Product (GDP) per person. The country flora richness is not related to the species richness of botanic gardens. Botanic gardens in more populous towns tend to have a larger area and can thus host richer living collections. Botanic gardens in richer countries have more species, and this explains the positive latitudinal gradient in botanic gardens' species richness.
Socio-economic factors contribute to shaping patterns in the species richness of the living collections of the world's botanic gardens.
Biodiversity loss; global priorities; hotspots conservation; large-scale patterns; local and regional diversity; macroecology; plant biogeography; rarity; species–people correlation; species–time relationship; tropical ecosystems; urban ecology
A common goal in ecology and wildlife management is to determine the causes of variation in population dynamics over long periods of time and across large spatial scales. Many assumptions must nevertheless be overcome to make appropriate inference about spatio-temporal variation in population dynamics, such as autocorrelation among data points, excess zeros, and observation error in count data. To address these issues, many scientists and statisticians have recommended the use of Bayesian hierarchical models. Unfortunately, hierarchical statistical models remain somewhat difficult to use because of the necessary quantitative background needed to implement them, or because of the computational demands of using Markov Chain Monte Carlo algorithms to estimate parameters. Fortunately, new tools have recently been developed that make it more feasible for wildlife biologists to fit sophisticated hierarchical Bayesian models (i.e., Integrated Nested Laplace Approximation, ‘INLA’). We present a case study using two important game species in North America, the lesser and greater scaup, to demonstrate how INLA can be used to estimate the parameters in a hierarchical model that decouples observation error from process variation, and accounts for unknown sources of excess zeros as well as spatial and temporal dependence in the data. Ultimately, our goal was to make unbiased inference about spatial variation in population trends over time.
Understanding interactions between mobile species distributions and landcover characteristics remains an outstanding challenge in ecology. Multiple factors could explain species distributions including endogenous evolutionary traits leading to conspecific clustering and endogenous habitat features that support life history requirements. Birds are a useful taxon for examining hypotheses about the relative importance of these factors among species in a community. We developed a hierarchical Bayes approach to model the relationships between bird species occupancy and local landcover variables accounting for spatial autocorrelation, species similarities, and partial observability. We fit alternative occupancy models to detections of 90 bird species observed during repeat visits to 316 point-counts forming a 400-m grid throughout the Patuxent Wildlife Research Refuge in Maryland, USA. Models with landcover variables performed significantly better than our autologistic and null models, supporting the hypothesis that local landcover heterogeneity is important as an exogenous driver for species distributions. Conspecific clustering alone was a comparatively poor descriptor of local community composition, but there was evidence for spatial autocorrelation in all species. Considerable uncertainty remains whether landcover combined with spatial autocorrelation is most parsimonious for describing bird species distributions at a local scale. Spatial structuring may be weaker at intermediate scales within which dispersal is less frequent, information flows are localized, and landcover types become spatially diversified and therefore exhibit little aggregation. Examining such hypotheses across species assemblages contributes to our understanding of community-level associations with conspecifics and landscape composition.
Small-angle X-ray scattering (SAXS) is a technique for obtaining low-resolution structural information about biological macromolecules, by exposing a dilute solution to a high-intensity X-ray beam and capturing the resulting scattering pattern on a two-dimensional detector. The two-dimensional pattern is reduced to a one-dimensional curve through radial averaging; that is, by averaging across annuli on the detector plane. Subsequent analysis of structure relies on these one-dimensional data. This paper reviews the technique of SAXS and investigates autocorrelation structure in the detector plane and in the radial averages. Across a range of experimental conditions and molecular types, spatial autocorrelation in the detector plane is present and is well-described by a stationary kernel convolution model. The corresponding autocorrelation structure for the radial averages is non-stationary. Implications of the autocorrelation structure for inference about macromolecular structure are discussed.
Gaussian process; Kernel convolution; Spatial autocorrelation
Past studies of associations between measures of the built environment, particularly street connectivity, and active transportation (AT) or leisure walking/bicycling have largely failed to account for spatial autocorrelation of connectivity variables and have seldom examined both the propensity for AT and its duration in a coherent fashion. Such efforts could improve our understanding of the spatial and behavioral aspects of AT. We analyzed spatially identified data from Los Angeles and San Diego Counties collected as part of the 2001 California Health Interview Survey.
Principal components analysis indicated that ~85% of the variance in nine measures of street connectivity are accounted for by two components representing buffers with short blocks and dense nodes (PRIN1) or buffers with longer blocks that still maintain a grid like structure (PRIN2). PRIN1 and PRIN2 were positively associated with active transportation (AT) after adjustment for diverse demographic and health related variables. Propensity and duration of AT were correlated in both Los Angeles (r = 0.14) and San Diego (r = 0.49) at the zip code level. Multivariate analysis could account for the correlation between the two outcomes.
After controlling for demography, measures of the built environment and other factors, no spatial autocorrelation remained for propensity to report AT (i.e., report of AT appeared to be independent among neighborhood residents). However, very localized correlation was evident in duration of AT, particularly in San Diego, where the variance of duration, after accounting for spatial autocorrelation, was 5% smaller within small neighborhoods (~0.01 square latitude/longitude degrees = 0.6 mile diameter) compared to within larger zip code areas. Thus a finer spatial scale of analysis seems to be more appropriate for explaining variation in connectivity and AT.
Joint analysis of the propensity and duration of AT behavior and an explicitly geographic approach can strengthen studies of the built environment and physical activity (PA), specifically AT. More rigorous analytical work on cross-sectional data, such as in the present study, continues to support the need for experimental and longitudinal study designs including the analysis of natural experiments to evaluate the utility of environmental interventions aimed at increasing PA.
A spatial autocorrelation analysis method is adopted to process the spatial dynamic change of industrial Chemical Oxygen Demand (COD) discharge in China over the past 15 years. Studies show that amount and intensity of industrial COD discharges are on a decrease, and the tendency is more remarkable for discharge intensity. There are large differences between inter-provincial discharge amount and intensity, and with different spatial differentiation features. Global spatial autocorrelation analysis reveals that Global Moran’s I of discharge amount and intensity is on the decrease. In space, there is an evolution from an agglomeration pattern to a discretization pattern. Local spatial autocorrelation analysis shows that the agglomeration area of industrial COD discharge amount and intensity varies greatly in space with time. Stringent environmental regulations and increased funding for environmental protections are the crucial factors to cut down industrial COD discharge amount and intensity.
industrial COD discharge; spatial autocorrelation; Moran’s I; spatial pattern