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Functions to calculate measures of spatial association, especially measures of spatial autocorrelation, have been made available in many software applications. Measures may be global, applying to the whole data set under consideration, or local, applying to each observation in the data set. Methods of statistical inference may also be provided, but these will, like the measures themselves, depend on the support of the observations, chosen assumptions, and the way in which spatial association is represented; spatial weights are often used as a representational technique. In addition, assumptions may be made about the underlying mean model, and about error distributions. Different software implementations may choose to expose these choices to the analyst, but the sets of choices available may vary between these implementations, as may default settings. This comparison will consider the implementations of global Moran’s I, Getis–Ord G and Geary’s C, local \\[I_i\\] and \\[G_i\\], available in a range of software including Crimestat, GeoDa, ArcGIS, PySAL and R contributed packages.

Macroecologists and biogeographers continue to predict the distribution of species across space based on the relationship between biotic processes and environmental variables. This approach uses data related to, for example, species abundance or presence/absence, climate, geomorphology, and soils. Researchers have acknowledged in their statistical analyses the importance of accounting for the effects of spatial autocorrelation (SAC), which indicates a degree of dependence between pairs of nearby observations. It has been agreed that residual spatial autocorrelation (rSAC) can have a substantial impact on modeling processes and inferences. However, more attention should be paid to the sources of rSAC and the degree to which rSAC becomes problematic. Here, we review previous studies to identify diverse factors that potentially induce the presence of rSAC in macroecological and biogeographical models. Furthermore, an emphasis is put on the quantification of rSAC by seeking to unveil the magnitude to which the presence of SAC in model residuals becomes detrimental to the modeling process. It turned out that five categories of factors can drive the presence of SAC in model residuals: ecological data and processes, scale and distance, missing variables, sampling design, and assumptions and methodological approaches. Additionally, we noted that more explicit and elaborated discussion of rSAC should be presented in species distribution modeling. Future investigations involving the quantification of rSAC are recommended in order to understand when rSAC can have an adverse effect on the modeling process.

The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the p = 2 setting linkages already established for the p = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient p = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation.

Recently, all kinds of geological disasters happen frequently on the earth. In China, there are countless earthquakes every year, which greatly affect the country’s economic level and development as well as the people’s life and health. The analysis of seismic activity is becoming more and more significant. In this article, the spatial distribution of China’s seismic activities was analyzed by using the provincial seismic data from 1970 to 2013. On the basis of spatial autocorrelation analysis theory, Global Moran’s , Local Moran’s , and the Local Indicators of Spatial Association are used to measure the geospatial distribution characteristics of China’s seismic activities. The research results show that earthquakes in mainland China have significant global autocorrelation characteristics as a whole, and the global autocorrelation coefficients are all positive. And the -value test ( < 0.05) shows that earthquakes in mainland China present a spatial agglomeration pattern. Furthermore, we observed a reduction trend in disparities of seismic activity among regions in China.

Fractal geometry has provided a new perspective for urban road network morphology research. This study systematically verifies and analyzes the spatial heterogeneity of fractal characteristics and influencing factors of urban road networks using spatial analysis. Here, Tokyo Metropolis was selected as a case, and the fractal dimensions of road networks were calculated. To determine the spatial heterogeneity in the relationship between fractal dimensions and influencing factors, we examined the spatial distribution characteristics of fractal dimensions using spatial autocorrelation analysis, selected population, build-up area density, and road network density as the explanatory variables, and established the global regression model and local regression model using ordinary least squares (OLS) and geographically weighted regression (GWR), respectively. The results indicated that the spatial distribution of fractal dimensions of the urban road network exhibited an obvious tendency toward geographical dependency. Considering the spatial heterogeneity in the relationship between the fractal characteristics of the road network and the influencing factors not only improves the reliability of analysis but also helps planners and decision-makers grasp the morphological characteristics of the urban road network and estimate the evolution of the road network, thereby promoting the development of urban road networks in a more orderly, efficient, and sustainable direction.

The geographic distribution of lung cancer rates tends to vary across a geographic landscape, and covariates (e.g., smoking rates, demographic factors, socio-economic indicators) commonly are employed in spatial analysis to explain the spatial heterogeneity of these cancer rates. However, such cancer risk factors often are not available, and conventional statistical models are unable to fully capture hidden spatial effects in cancer rates. Introducing random effects in the model specifications can furnish an efficient approach to account for variations that are unexplained due to omitted variables. Especially, a random effects model can be effective for a phenomenon that is static over time. The goal of this paper is to investigate geographic variation in Florida lung cancer incidence data for the time period 2000–2011 using random effects models. In doing so, a Moran eigenvector spatial filtering technique is utilized, which can allow a decomposition of random effects into spatially structured (SSRE) and spatially unstructured (SURE) components. Analysis results confirm that random effects models capture a substantial amount of variation in the cancer data. Furthermore, the results suggest that spatial pattern in the cancer data displays a mixture of positive and negative spatial autocorrelation, although the global map pattern of the random effects term may appear random.

Rapid urban growth has increased concerns about spatial equity in access to Primary Healthcare Facilities (PHCs), particularly in contexts where proximity-based assessments may overestimate effective access by overlooking population demand and service capacity. This study evaluates district-level accessibility and equity of PHCs in Jeddah, Saudi Arabia using a capacity-sensitive Modified Two-Step Floating Catchment Area (M2SFCA) framework incorporating population weighting, distance decay and bed capacity. Network-based service area analysis was used to define catchment thresholds, while origin–destination cost matrices supported accessibility indexing. Spatial patterns were examined using Global Moran’s I, and distributional equity was assessed through coefficient of variation, percentile ratio, accessibility shares, Gini coefficient and Lorenz curves. A planning-oriented location–allocation model evaluated a scenario-based PHC expansion. Results show that although approximately 69% of the urban area lies within nominal PHC catchments, baseline accessibility exhibits noticeable spatial inequities, with near-zero access in several peripheral districts and significant spatial clustering (Moran’s I = 0.398). The proposed scenario introducing four PHCs with varied capacity produced systematic improvements in underserved areas. The percentage ratio declined sharply from 81.34 to 9.13, demonstrating substantial disparities between the highest and lowest-access districts. This increased the accessibility share of the bottom 40% of the population, and lowered overall inequality from 0.191 to 0.172 while slightly weakening spatial clustering. The findings demonstrate that capacity-aware accessibility modelling integrated with planning scenarios provides policy-relevant insights for improving spatial equity in PHC provision and is transferable to other rapidly urbanizing urban contexts.

The research of Art Getis has had many positive direct effects on the fields of regional science and spatial statistics. There already have been, and will continue to be, many indirect effects as well, as the repercussions of his work ripple through the field. With his contributions to spatial statistics, Art Getis laid out a rich research agenda for future work in the field. In this presentation, I describe several research problems inspired by his work. These include (a) the multiple testing problem, (b) the effects of global spatial autocorrelation on the power and use of local statistics, (c) the effects of weight misspecification on the power of local statistics, and (d) the statistical distribution of his local spatial heterogeneity (LOSH) statistic. In addition, there are a number of connections between the local statistics he developed and other statistics. These include the relationships between (a) the Getis-Ord statistic and the two-sample t statistic, (b) the Getis-Ord statistic and the maximum of Gaussian random fields, and (c) the LOSH statistic and the well-known Geary statistic.

Dispersal is a fundamental process that influences the response of species to landscape change and habitat fragmentation. In an attempt to better understand dispersal in the Australian bush rat, Rattusfuscipes, we have combined a new multilocus autocorrelation method with hypervariable microsatellite genetic markers to investigate fine‐scale (<1 km) patterns of spatial distribution and spatial genetic structure. The study was conducted across eight trapping transects at four sites, with a total of 270 animals sampled. Spatial autocorrelation analysis of bush rat distribution revealed that, in general, animals occurred in groups or clusters of higher density (<200 m across), with intervening gaps or lower density areas. Spatial genetic autocorrelation analysis, based on seven hypervariable microsatellite loci (He= 0.8) with a total of 80 alleles, revealed a consistent pattern of significant positive local genetic structure. This genetic pattern was consistent for all transects, and for adults and sub‐adults, males and females. By testing for autocorrelation at multiple scales from 10 to 800 m we found that the extent of detectable positive spatial genetic structure exceeded 500 m. Further analyses detected significantly weaker spatial genetic structure in males compared with females, but no significant differences were detected between adults and sub adults. Results from Mantel tests and hierarchical AMOVA further support the conclusion that the distribution of bush rat genotypes is not random at the scale of our study. Instead, proximate bush rats are more genetically alike than more distant animals. We conclude that in bush rats, gene flow per generation is sufficiently restricted to generate the strong positive signal of local spatial genetic structure. Although our results are consistent with field data on animal movement, including the reported tendency for males to move further than females, we provide the first evidence for restricted gene flow in bush rats. Our study appears to be the first microsatellite‐based study of fine‐scale genetic variation in small mammals and the first to report consistent positive local genetic structure across sites, age‐classes, and sexes. The combination of new forms of autocorrelation analyses, hypervariable genetic markers and fine‐scale analysis (<1 km) may thus offer new evolutionary insights that are overlooked by more traditional larger scaled (>10 km) population genetic studies.

Genotypic distributions affect the persistence of coral populations, and mapping these distributions is important for population management. Many studies have examined genetic connectivity among sites, but within-site spatial genotypic patterns based on clonal distribution and kinship are poorly understood. Such patterns are an important index for understanding the potential for population recovery at small spatial scales. Here, we studied within-reef spatial genotypic distributions and clonality of a broadcast-spawning coral, Galaxea fascicularis, by using mitochondrial DNA (mtDNA) and 15 nuclear microsatellite markers. Specimens were collected at shallow reefs (< 3 m) at four sites in the Ryukyu Archipelago, Japan. Among 289 colonies analyzed, we detected two common mtDNA types (mt-L, 174 colonies; mt-S, 113 colonies) and one rare type (mt-L + , 2 colonies). The proportion of duplicate clonal colonies differed across sites and reef topographies; the maximum distance between clonemates was approximately 120 m. Pairwise kinship among colonies tended to decrease with distance at the ramet level (i.e., including clonal replicates), but not at the genet level. Ramet-level kinship varied among sites rather than between mtDNA types. Genet-level kinship (i.e., excluding clonal replicates) was similar among sites. These results for clonality and kinship suggest that both sexual and asexual reproduction contribute to population recovery after disturbances and maintain genetic diversity in local populations. However, the extent of sexual and asexual reproduction differs across sites. Our results will contribute to more effective management of marine reserves by emphasizing the importance of clonal distributions and genetic kinship at each reef site.