New Approaches for Calculating Moran’s Index of Spatial Autocorrelation

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran’s index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran’s index. Moran’s scatterplot will be ameliorated, and new test methods will be proposed. The relationship between the global Moran’s index and Geary’s coefficient will be discussed from two different vantage points: spatial population and spatial sample. The sphere of applications for both Moran’s index and Geary’s coefficient will be clarified and defined. One of theoretical findings is that Moran’s index is a characteristic parameter of spatial weight matrices, so the selection of weight functions is very significant for autocorrelation analysis of geographical systems. A case study of 29 Chinese cities in 2000 will be employed to validate the innovatory models and methods. This work is a methodological study, which will simplify the process of autocorrelation analysis. The results of this study will lay the foundation for the scaling analysis of spatial autocorrelation.     

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test.     

Geographic Disparity in Chronic Obstructive Pulmonary Disease (COPD) Mortality Rates among the Taiwan Population

Chronic obstructive pulmonary disease (COPD) causes a high disease burden among the elderly worldwide. In Taiwan, the long-term temporal trend of COPD mortality is declining, but the geographical disparity of the disease is not yet known. Nationwide COPD age-adjusted mortality at the township level during 1999–2007 is used for elucidating the geographical distribution of the disease. With an ordinary least squares (OLS) model and geographically weighted regression (GWR), the ecologic risk factors such as smoking rate, area deprivation index, tuberculosis exposure, percentage of aborigines, density of health care facilities, air pollution and altitude are all considered in both models to evaluate their effects on mortality. Global and local Moran’s I are used for examining their spatial autocorrelation and identifying clusters. During the study period, the COPD age-adjusted mortality rates in males declined from 26.83 to 19.67 per 100,000 population, and those in females declined from 8.98 to 5.70 per 100,000 population. Overall, males’ COPD mortality rate was around three times higher than females’. In the results of GWR, the median coefficients of smoking rate, the percentage of aborigines, PM₁₀ and the altitude are positively correlated with COPD mortality in males and females. The median value of density of health care facilities is negatively correlated with COPD mortality. The overall adjusted R-squares are about 20% higher in the GWR model than in the OLS model. The local Moran’s I of the GWR’s residuals reflected the consistent high-high cluster in southern Taiwan. The findings indicate that geographical disparities in COPD mortality exist. Future epidemiological investigation is required to understand the specific risk factors within the clustering areas.     

Socio-Demographic Predictors and Distribution of Pulmonary Tuberculosis (TB) in Xinjiang,China: A Spatial Analysis

Objectives

Xinjiang is one of the high TB burden provinces of China. A spatial analysis was conducted using geographical information system (GIS) technology to improve the understanding of geographic variation of the pulmonary TB occurrence in Xinjiang, its predictors, and to search for targeted interventions.

Methods

Numbers of reported pulmonary TB cases were collected at county/district level from TB surveillance system database. Population data were extracted from Xinjiang Statistical Yearbook (2006~2014). Spatial autocorrelation (or dependency) was assessed using global Moran’s I statistic. Anselin’s local Moran’s I and local Getis-Ord statistics were used to detect local spatial clusters. Ordinary least squares (OLS) regression, spatial lag model (SLM) and geographically-weighted regression (GWR) models were used to explore the socio-demographic predictors of pulmonary TB incidence from global and local perspectives. SPSS17.0, ArcGIS10.2.2, and GeoDA software were used for data analysis.

Results

Incidence of sputum smear positive (SS+) TB and new SS+TB showed a declining trend from 2005 to 2013. Pulmonary TB incidence showed a declining trend from 2005 to 2010 and a rising trend since 2011 mainly caused by the rising trend of sputum smear negative (SS-) TB incidence (p<0.0001). Spatial autocorrelation analysis showed the presence of positive spatial autocorrelation for pulmonary TB incidence, SS+TB incidence and SS-TB incidence from 2005 to 2013 (P <0.0001). The Anselin’s Local Moran’s I identified the “hotspots” which were consistently located in the southwest regions composed of 20 to 28 districts, and the “coldspots” which were consistently located in the north central regions consisting of 21 to 27 districts. Analysis with the Getis-Ord Gi* statistic expanded the scope of “hotspots” and “coldspots” with different intensity; 30 county/districts clustered as “hotspots”, while 47 county/districts clustered as “coldspots”. OLS regression model included the “proportion of minorities” and the “per capita GDP” as explanatory variables that explained 64% the variation in pulmonary TB incidence (adjR² = 0.64). The SLM model improved the fit of the OLS model with a decrease in AIC value from 883 to 864, suggesting “proportion of minorities” to be the only statistically significant predictor. GWR model also improved the fitness of regression (adj R² = 0.68, AIC = 871), which revealed that “proportion of minorities” was a strong predictor in the south central regions while “per capita GDP” was a strong predictor for the southwest regions.

Conclusion

The SS+TB incidence of Xinjiang had a decreasing trend during 2005–2013, but it still remained higher than the national average in China. Spatial analysis showed significant spatial autocorrelation in pulmonary TB incidence. Cluster analysis detected two clusters—the “hotspots”, which were consistently located in the southwest regions, and the “coldspots”, which were consistently located in the north central regions. The exploration of socio-demographic predictors identified the “proportion of minorities” and the “per capita GDP” as predictors and may help to guide TB control programs and targeting intervention.     

A comparison of metrics for estimating phylogenetic signal under alternative evolutionary models

Several metrics have been developed for estimating phylogenetic signal in comparative data. These may be important both in guiding future studies on correlated evolution and for inferring broad-scale evolutionary and ecological processes (e.g., phylogenetic niche conservatism). Notwithstanding, the validity of some of these metrics is under debate, especially after the development of more sophisticated model-based approaches that estimate departure from particular evolutionary models (i.e., Brownian motion). Here, two of these model-based metrics (Blomberg’s K-statistics and Pagel’s λ) are compared with three statistical approaches [Moran’s I autocorrelation coefficient, coefficients of determination from the autoregressive method (ARM), and phylogenetic eigenvector regression (PVR)]. Based on simulations of a trait evolving under Brownian motion for a phylogeny with 209 species, we showed that all metrics are strongly, although non-linearly, correlated to each other. Our analyses revealed that statistical approaches provide valid results and may be still particularly useful when detailed phylogenies are unavailable or when trait variation among species is difficult to describe by more standard Brownian or O-U evolutionary models.     

Red herrings revisited: spatial autocorrelation and parameter estimation in geographical ecology

There have been numerous claims in the ecological literature that spatial autocorrelation in the residuals of ordinary least squares (OLS) regression models results in shifts in the partial coefficients, which bias the interpretation of factors influencing geographical patterns. We evaluate the validity of these claims using gridded species richness data for the birds of North America, South America, Europe, Africa, the ex‐USSR, and Australia. We used richness in 110×110 km cells and environmental predictor variables to generate OLS and simultaneous autoregressive (SAR) multiple regression models for each region. Spatial correlograms of the residuals from each OLS model were then used to identify the minimum distance between cells necessary to avoid short‐distance residual spatial autocorrelation in each data set. This distance was used to subsample cells to generate spatially independent data. The partial OLS coefficients estimated with the full dataset were then compared to the distributions of coefficients created with the subsamples. We found that OLS coefficients generated from data containing residual spatial autocorrelation were statistically indistinguishable from coefficients generated from the same data sets in which short‐distance spatial autocorrelation was not present in all 22 coefficients tested. Consistent with the statistical literature on this subject, we conclude that coefficients estimated from OLS regression are not seriously affected by the presence of spatial autocorrelation in gridded geographical data. Further, shifts in coefficients that occurred when using SAR tended to be correlated with levels of uncertainty in the OLS coefficients. Thus, shifts in the relative importance of the predictors between OLS and SAR models are expected when small‐scale patterns for these predictors create weaker and more unstable broad‐scale coefficients. Our results indicate both that OLS regression is unbiased and that differences between spatial and nonspatial regression models should be interpreted with an explicit awareness of spatial scale.     

Spatial Analysis of Schistosomiasis in Hubei Province,China: A GIS-Based Analysis of Schistosomiasis from 2009 to 2013

Background

Schistosomiasis remains a major public health problem in China. The major endemic areas are located in the lake and marshland regions of southern China, particularly in areas along the middle and low reach of the Yangtze River. Spatial analytical techniques are often used in epidemiology to identify spatial clusters in disease regions. This study assesses the spatial distribution of schistosomiasis and explores high-risk regions in Hubei Province, China to provide guidance on schistosomiasis control in marshland regions.

Methods

In this study, spatial autocorrelation methodologies, including global Moran’s I and local Getis–Ord statistics, were utilized to describe and map spatial clusters and areas where human Schistosoma japonicum infection is prevalent at the county level in Hubei province. In addition, linear logistic regression model was used to determine the characteristics of spatial autocorrelation with time.

Results

The infection rates of S. japonicum decreased from 2009 to 2013. The global autocorrelation analysis results on the infection rate of S. japonicum for five years showed statistical significance (Moran’s I > 0, P < 0.01), which suggested that spatial clusters were present in the distribution of S. japonicum infection from 2009 to 2013. Local autocorrelation analysis results showed that the number of highly aggregated areas ranged from eight to eleven within the five-year analysis period. The highly aggregated areas were mainly distributed in eight counties.

Conclusions

The spatial distribution of human S. japonicum infections did not exhibit a temporal change at the county level in Hubei Province. The risk factors that influence human S. japonicum transmission may not have changed after achieving the national criterion of infection control. The findings indicated that spatial–temporal surveillance of S. japonicum transmission plays a significant role on schistosomiasis control. Timely and integrated prevention should be continued, especially in the Yangtze River Basin of Jianghan Plain area.     

The consequences of spatial structure for the design and analysis of ecological field surveys

In ecological field surveys, observations are gathered at different spatial locations. The purpose may be to relate biological response variables (e.g., species abundances) to explanatory environmental variables (e.g., soil characteristics). In the absence of prior knowledge, ecologists have been taught to rely on systematic or random sampling designs. If there is prior knowledge about the spatial patterning of the explanatory variables, obtained from either previous surveys or a pilot study, can we use this information to optimize the sampling design in order to maximize our ability to detect the relationships between the response and explanatory variables?
The specific questions addressed in this paper are: a) What is the effect (type I error) of spatial autocorrelation on the statistical tests commonly used by ecologists to analyse field survey data? b) Can we eliminate, or at least minimize, the effect of spatial autocorrelation by the design of the survey? Are there designs that provide greater power for surveys, at least under certain circumstances? c) Can we eliminate or control for the effect of spatial autocorrelation during the analysis? To answer the last question, we compared regular regression analysis to a modified t‐test developed by Dutilleul for correlation coefficients in the presence of spatial autocorrelation.
Replicated surfaces (typically, 1000 of them) were simulated using different spatial parameters, and these surfaces were subjected to different sampling designs and methods of statistical analysis. The simulated surfaces may represent, for example, vegetation response to underlying environmental variation. This allowed us 1) to measure the frequency of type I error (the failure to reject the null hypothesis when in fact there is no effect of the environment on the response variable) and 2) to estimate the power of the different combinations of sampling designs and methods of statistical analysis (power is measured by the rate of rejection of the null hypothesis when an effect of the environment on the response variable has been created).
Our results indicate that: 1) Spatial autocorrelation in both the response and environmental variables affects the classical tests of significance of correlation or regression coefficients. Spatial autocorrelation in only one of the two variables does not affect the test of significance. 2) A broad‐scale spatial structure present in data has the same effect on the tests as spatial autocorrelation. When such a structure is present in one of the variables and autocorrelation is found in the other, or in both, the tests of significance have inflated rates of type I error. 3) Dutilleul's modified t‐test for the correlation coefficient, corrected for spatial autocorrelation, effectively corrects for spatial autocorrelation in the data. It also effectively corrects for the presence of deterministic structures, with or without spatial autocorrelation.
The presence of a broad‐scale deterministic structure may, in some cases, reduce the power of the modified t‐test.     

Spatial autocorrelation as a tool for identifying the geographical patterns of aphid annual abundance

Abstract 1 A spatial autocorrelation analysis was undertaken to investigate the spatial structure of annual abundance for the pest aphid Myzus persicae collected in suction traps distributed across north‐west Europe. 2 The analysis was applied at two different scales. The Moran index was used to estimate the degree of spatial autocorrelation at all sites within the study area (global level). The contributions of each site to the global index were identified by the use of a local indicator of spatial autocorrelation (LISA). A hierarchical cluster analysis was undertaken to highlight differences between groups of resulting correlograms. 3 Similarity between traps was shown to occur over large geographical distances, suggesting an impact of phenomena such as climatic gradients or land use types. 4 The presence of outliers and zones of similarity (hot‐spots) and of dissimilarity (cold‐spots) were identified indicating a strong impact of local effects. 5 Several groups of traps characterized by similarities in their local spatial structure (correlograms, value of Moran's I_i) also had similar values for land use variables (the area occupied by agricultural zones, forest and sea). 6 It is concluded that trap data can provide information about Myzus persicae that is representative of large geographical areas. Thus, trap data can be used to estimate the aerial abundance of this species, even if the suction traps are not regularly and densely distributed.     

Spatial autocorrelation of allozyme and quantitative markers within a natural population of Centaurea jacea (Asteraceae)

This paper compares the fine‐scale genetic structure of quantitative traits and allozyme markers within a natural population of Centaurea jacea s.l. To that end, a spatial autocorrelation approach is developed based on pairwise correlation coefficients between individuals and using sib families. Statistical properties of the proposed statistics are investigated with numerical simulations. Our results show that most quantitative traits have a significant spatial structure for their genetic component. On average, allozyme markers and the genetic component of quantitative traits have similar patterns of spatial autocorrelation that are consistent with a neutral model of isolation by distance. We also show evidence that environmental heterogeneity generates a spatial structure for the environmental component of quantitative traits. Results are discussed in terms of mechanisms generating spatial structure and are compared with those obtained on a large geographical scale.     

Joint Effects of Habitat Heterogeneity and Species’ Life-History Traits on Population Dynamics in Spatially Structured Landscapes

Both habitat heterogeneity and species’ life-history traits play important roles in driving population dynamics, yet there is little scientific consensus around the combined effect of these two factors on populations in complex landscapes. Using a spatially explicit agent-based model, we explored how interactions between habitat spatial structure (defined here as the scale of spatial autocorrelation in habitat quality) and species life-history strategies (defined here by species environmental tolerance and movement capacity) affect population dynamics in spatially heterogeneous landscapes. We compared the responses of four hypothetical species with different life-history traits to four landscape scenarios differing in the scale of spatial autocorrelation in habitat quality. The results showed that the population size of all hypothetical species exhibited a substantial increase as the scale of spatial autocorrelation in habitat quality increased, yet the pattern of population increase was shaped by species’ movement capacity. The increasing scale of spatial autocorrelation in habitat quality promoted the resource share of individuals, but had little effect on the mean mortality rate of individuals. Species’ movement capacity also determined the proportion of individuals in high-quality cells as well as the proportion of individuals experiencing competition in response to increased spatial autocorrelation in habitat quality. Positive correlations between the resource share of individuals and the proportion of individuals experiencing competition indicate that large-scale spatial autocorrelation in habitat quality may mask the density-dependent effect on populations through increasing the resource share of individuals, especially for species with low mobility. These findings suggest that low-mobility species may be more sensitive to habitat spatial heterogeneity in spatially structured landscapes. In addition, localized movement in combination with spatial autocorrelation may increase the population size, despite increased density effects.     

Reliability and Validity of Quantifying Absolute Muscle Hardness Using Ultrasound Elastography

Muscle hardness is a mechanical property that represents transverse muscle stiffness. A quantitative method that uses ultrasound elastography for quantifying absolute human muscle hardness has been previously devised; however, its reliability and validity have not been completely verified. This study aimed to verify the reliability and validity of this quantitative method. The Young’s moduli of seven tissue-mimicking materials (in vitro; Young’s modulus range, 20–80 kPa; increments of 10 kPa) and the human medial gastrocnemius muscle (in vivo) were quantified using ultrasound elastography. On the basis of the strain/Young’s modulus ratio of two reference materials, one hard and one soft (Young’s moduli of 7 and 30 kPa, respectively), the Young’s moduli of the tissue-mimicking materials and medial gastrocnemius muscle were calculated. The intra- and inter-investigator reliability of the method was confirmed on the basis of acceptably low coefficient of variations (≤6.9%) and substantially high intraclass correlation coefficients (≥0.77) obtained from all measurements. The correlation coefficient between the Young’s moduli of the tissue-mimicking materials obtained using a mechanical method and ultrasound elastography was 0.996, which was equivalent to values previously obtained using magnetic resonance elastography. The Young’s moduli of the medial gastrocnemius muscle obtained using ultrasound elastography were within the range of values previously obtained using magnetic resonance elastography. The reliability and validity of the quantitative method for measuring absolute muscle hardness using ultrasound elastography were thus verified.     

Non-stationarity and local approaches to modelling the distributions of wildlife

Despite a growing interest in species distribution modelling, relatively little attention has been paid to spatial autocorrelation and non-stationarity. Both spatial autocorrelation (the tendency for adjacent locations to be more similar than distant ones) and non-stationarity (the variation in modelled relationships over space) are likely to be common properties of ecological systems. This paper focuses on non-stationarity and uses two local techniques, geographically weighted regression (GWR) and varying coefficient modelling (VCM), to assess its impact on model predictions. We extend two published studies, one on the presence–absence of calandra larks in Spain and the other on bird species richness in Britain, to compare GWR and VCM with the more usual global generalized linear modelling (GLM) and generalized additive modelling (GAM). For the calandra lark data, GWR and VCM produced better-fitting models than GLM or GAM. VCM in particular gave significantly reduced spatial autocorrelation in the model residuals. GWR showed that individual predictors became stationary at different spatial scales, indicating that distributions are influenced by ecological processes operating over multiple scales. VCM was able to predict occurrence accurately on independent data from the same geographical area as the training data but not beyond, whereas the GAM produced good results on all areas. Individual predictions from the local methods often differed substantially from the global models. For the species richness data, VCM and GWR produced far better predictions than ordinary regression. Our analyses suggest that modellers interpolating data to produce maps for practical actions (e.g. conservation) should consider local methods, whereas they should not be used for extrapolation to new areas. We argue that local methods are complementary to global methods, revealing details of habitat associations and data properties which global methods average out and miss.     

A spectral theory for Wright’s inbreeding coefficients and related quantities

Wright’s inbreeding coefficient, F_ST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principal component analysis (PCA) have, however, become prominent in recent analyses of population structure. In this study, we describe the relationships between Wright’s inbreeding coefficients and PCA for a model of K discrete populations. Our theory provides an equivalent definition of F_ST based on the decomposition of the genotype matrix into between and within-population matrices. The average value of Wright’s F_ST over all loci included in the genotype matrix can be obtained from the PCA of the between-population matrix. Assuming that a separation condition is fulfilled and for reasonably large data sets, this value of F_ST approximates the proportion of genetic variation explained by the first (K − 1) principal components accurately. The new definition of F_ST is useful for computing inbreeding coefficients from surrogate genotypes, for example, obtained after correction of experimental artifacts or after removing adaptive genetic variation associated with environmental variables. The relationships between inbreeding coefficients and the spectrum of the genotype matrix not only allow interpretations of PCA results in terms of population genetic concepts but extend those concepts to population genetic analyses accounting for temporal, geographical and environmental contexts.     

Incorporating spatial autocorrelation into species distribution models alters forecasts of climate‐mediated range shifts

Species distribution models (SDMs) are widely used to forecast changes in the spatial distributions of species and communities in response to climate change. However, spatial autocorrelation (SA) is rarely accounted for in these models, despite its ubiquity in broad‐scale ecological data. While spatial autocorrelation in model residuals is known to result in biased parameter estimates and the inflation of type I errors, the influence of unmodeled SA on species' range forecasts is poorly understood. Here we quantify how accounting for SA in SDMs influences the magnitude of range shift forecasts produced by SDMs for multiple climate change scenarios. SDMs were fitted to simulated data with a known autocorrelation structure, and to field observations of three mangrove communities from northern Australia displaying strong spatial autocorrelation. Three modeling approaches were implemented: environment‐only models (most frequently applied in species' range forecasts), and two approaches that incorporate SA; autologistic models and residuals autocovariate (RAC) models. Differences in forecasts among modeling approaches and climate scenarios were quantified. While all model predictions at the current time closely matched that of the actual current distribution of the mangrove communities, under the climate change scenarios environment‐only models forecast substantially greater range shifts than models incorporating SA. Furthermore, the magnitude of these differences intensified with increasing increments of climate change across the scenarios. When models do not account for SA, forecasts of species' range shifts indicate more extreme impacts of climate change, compared to models that explicitly account for SA. Therefore, where biological or population processes induce substantial autocorrelation in the distribution of organisms, and this is not modeled, model predictions will be inaccurate. These results have global importance for conservation efforts as inaccurate forecasts lead to ineffective prioritization of conservation activities and potentially to avoidable species extinctions.     

中国省际灰水足迹测度及荷载系数的空间关联分析

借鉴Hoekstra等提出的灰水足迹计算公式,从农业、工业及生活三方面计算了1998—2012年中国31个省市(自治区)的灰水足迹及其灰水足迹荷载系数。结果表明:1研究期间全国灰水足迹呈现波动趋势,1998年至2006年的灰水足迹呈现波动上升趋势;2007年开始,全国灰水足迹呈现下降趋势;农业在总灰水足迹的贡献率最高、工业最低;231个省市(自治区)15a灰水足迹荷载系数整体呈现小幅波动趋势。在全国内部也存在着明显的地区差异,大体分为5类,分别为高荷载地区、较高荷载区、中度荷载区、较低荷载区、低荷载区。3借助全局与局部空间自相关对全国31个省市(自治区)灰水足迹荷载系数进行空间关联格局分析可知,中国省级灰水足迹存在空间集聚现象且集聚现象逐渐减弱,其中H-H集聚区主要集中在华北地区,L-L集聚区主要集中在南方与青藏地区。通过全国灰水足迹测度与灰水足迹荷载系数空间关联格局分析为灰水足迹分析提供新的研究思路同时为区域可持续发展提供理论支持。     

Investigating associations between COVID-19 mortality and population-level health and socioeconomic indicators in the United States: A modeling study

BackgroundWith the availability of multiple Coronavirus Disease 2019 (COVID-19) vaccines and the predicted shortages in supply for the near future, it is necessary to allocate vaccines in a manner that minimizes severe outcomes, particularly deaths. To date, vaccination strategies in the United States have focused on individual characteristics such as age and occupation. Here, we assess the utility of population-level health and socioeconomic indicators as additional criteria for geographical allocation of vaccines.Methods and findingsCounty-level estimates of 14 indicators associated with COVID-19 mortality were extracted from public data sources. Effect estimates of the individual indicators were calculated with univariate models. Presence of spatial autocorrelation was established using Moran’s I statistic. Spatial simultaneous autoregressive (SAR) models that account for spatial autocorrelation in response and predictors were used to assess (i) the proportion of variance in county-level COVID-19 mortality that can explained by identified health/socioeconomic indicators (R²); and (ii) effect estimates of each predictor.Adjusting for case rates, the selected indicators individually explain 24%–29% of the variability in mortality. Prevalence of chronic kidney disease and proportion of population residing in nursing homes have the highest R². Mortality is estimated to increase by 43 per thousand residents (95% CI: 37–49; p < 0.001) with a 1% increase in the prevalence of chronic kidney disease and by 39 deaths per thousand (95% CI: 34–44; p < 0.001) with 1% increase in population living in nursing homes. SAR models using multiple health/socioeconomic indicators explain 43% of the variability in COVID-19 mortality in US counties, adjusting for case rates. R² was found to be not sensitive to the choice of SAR model form. Study limitations include the use of mortality rates that are not age standardized, a spatial adjacency matrix that does not capture human flows among counties, and insufficient accounting for interaction among predictors.ConclusionsSignificant spatial autocorrelation exists in COVID-19 mortality in the US, and population health/socioeconomic indicators account for a considerable variability in county-level mortality. In the context of vaccine rollout in the US and globally, national and subnational estimates of burden of disease could inform optimal geographical allocation of vaccines.

Sasikiran Kandula and Jeffrey Shaman study population health and COVID-19 mortality in the United States.     

Fine‐scale foraging habitat selection by two diving central place foragers in the Northeast Atlantic

Habitat selection and spatial usage are important components of animal behavior influencing fitness and population dynamic. Understanding the animal–habitat relationship is crucial in ecology, particularly in developing strategies for wildlife management and conservation. As this relationship is governed by environmental features and intra‐ and interspecific interactions, habitat selection of a population may vary locally between its core and edges. This is particularly true for central place foragers such as gray and harbor seals, where, in the Northeast Atlantic, the availability of habitat and prey around colonies vary at local scale. Here, we study how foraging habitat selection may vary locally under the influence of physical habitat features. Using GPS/GSM tags deployed at different gray and harbor seals’ colonies, we investigated spatial patterns and foraging habitat selection by comparing trip characteristics and home‐range similarities and fitting GAMMs to seal foraging locations and environmental data. To highlight the importance of modeling habitat selection at local scale, we fitted individual models to colonies as well as a global model. The global model suffered from issues of homogenization, while colony models showed that foraging habitat selection differed markedly between regions for both species. Despite being capable of undertaking far‐ranging trips, both gray and harbor seals selected their foraging habitat depending on local availability, mainly based on distance from the last haul‐out and bathymetry. Distance from shore and tidal current also influenced habitat preferences. Results suggest that local conditions have a strong influence on population spatial ecology, highlighting the relevance of processes occurring at fine geographical scale consistent with management within regional units.     

Evaluating,partitioning, and mapping the spatial autocorrelation component in ecological niche modeling: a new approach based on environmentally equidistant records

Most species data display spatial autocorrelation that can affect ecological niche models (ENMs) accuracy‐statistics, affecting its ability to infer geographic distributions. Here we evaluate whether the spatial autocorrelation underlying species data affects accuracy‐statistics and map the uncertainties due to spatial autocorrelation effects on species range predictions under past and future climate models. As an example, ENMs were fitted to Qualea grandiflora (Vochysiaceae), a widely distributed plant from Brazilian Cerrado. We corrected for spatial autocorrelation in ENMs by selecting sampling sites equidistant in geographical (GEO) and environmental (ENV) spaces. Distributions were modelled using 13 ENMs evaluated by two accuracy‐statistics (TSS and AUC), which were compared with uncorrected ENMs. Null models and the similarity statistics I were used to evaluate the effects of spatial autocorrelation. Moreover, we applied a hierarchical ANOVA to partition and map the uncertainties from the time (across last glacial maximum, pre‐insustrial, and 2080 time periods) and methodological components (ENMs and autocorrelation corrections). The GEO and ENV models had the highest accuracy‐statistics values, although only the ENV model had values higher than expected by chance alone for most of the 13 ENMs. Uncertainties from time component were higher in the core region of the Brazilian Cerrado where Q. grandiflora occurs, whereas methodological components presented higher uncertainties in the extreme northern and southern regions of South America (i.e. outside of Brazilian Cerrado). Our findings show that accounting for autocorrelation in environmental space is more efficient than doing so in geographical space. Methodological uncertainties were concentrated in outside the core region of Q. grandiflora's habitat. Conversely, uncertainty due to time component in the Brazilian Cerrado reveals that ENMs were able to capture climate change effects on Q. grandiflora distributions.     

Environmental and geographical constraints on common swift and barn swallow spring arrival patterns throughout the Iberian Peninsula

Aim Still poorly understood, the main migratory pathways for most trans‐Saharan species pass through the Iberian Peninsula, which acts as a gateway to the European–African migratory system. Arrival patterns in this region for the common swift (Apus apus) and barn swallow (Hirundo rustica), of similar morphology and flight capabilities, were described, and the environmental and geographical factors best explaining them were examined, in a search for common ecological constraints on these two migratory species. Location Latitude ranged from 36.02 to 43.68°N, longitude from 9.05°W to 3.17°E, and altitude from 0 to 1595 m a.s.l. for 482 common swift and 812 barn swallow Spanish localities spread widely over the Iberian breeding grounds of the two species. Methods Our data set, covering the years 1960–1990, consisted of 3206 first‐arrival dates for common swifts and 6036 for barn swallows. Forty topographical, climatic, river basin, geographical and spatial variables were used as explanatory variables in general regression models (GRMs). GRMs included polynomial terms up to cubic functions in all variables when they were significant. A backward stepwise selection procedure was applied in all models until only significant terms remained. GRMs were applied in two steps. First, we searched for the best model in each one of the five types of variables (topographical, climatic, river basin, geographical and spatial). To cope with the unavoidable correlation between explanatory variables, the relative importance of each type of variable was assessed by hierarchical variance partitioning. Secondly, we searched for that model able to explain the maximum amount of the observed variability in arrival date. To obtain this model all significant explanatory variables were subjected jointly to a GRM. Spatial variables were then added to this model to take any remaining spatial structure in the data into account. Moran's I autocorrelation coefficient was used to check for spatial autocorrelation. Results Both species arrived earlier in the south‐western Iberian Peninsula, where summers are warmer and drier. From there, both species followed the main southern Iberian river basins towards the north‐east; however, several mountainous regions impede the colonization of eastern Iberia. The best models for each type of variable explained 19–47% of the variability in common swift arrival dates and 14–44% in barn swallow arrival dates. Variance partitioning indicated that climatic and geographical variables best explained variability. The best predictive models built with all variables accounted for 52% of the variability in common swift arrival dates and 50% for the barn swallow. Residuals from both models were not spatially autocorrelated, an indication that all major spatially structured variation had been accounted for. Main conclusions Spring arrival patterns are highly dependent on the geographical configuration of the Iberian Peninsula. This spatial constraint forces both species to converge very closely in their spring migration, because common swifts and barn swallows are subject to a trade‐off between optimum migratory pathways and territories ecologically suitable for breeding.