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Statistical analysis of spatial pattern: a comparison of grid and hierarchical sampling approaches.

Previous studies have combined random-site hierarchical sampling designs with analysis of variance techniques, and grid sampling with spatial autocorrelation analysis. We illustrate that analysis techniques and sampling designs are interchangeable using densities of an infaunal bivalve from a study in Poverty Bay, New Zealand. Hierarchical designs allow the estimation of variances associated with each level, but high-level factors are imprecisely estimated, and they are inefficient for describing spatial pattern. Grid designs are efficient for describing spatial pattern, and are amenable to conventional analysis. Our example deals with a continuous spatial habitat, but our conclusions also apply in disjunct or patchy habitats. The influence of errors in positioning is also assessed. The advantages of systematic sampling are reviewed, and more efficient hierarchical approaches are identified. The distinction between biological and statistical significance in all analyses is emphasised.

Animals↗

Mitochondrial and nuclear DNA phylogeography of European grayling (Thymallus thymallus): evidence for secondary contact zones in central Europe.

Mitochondrial and microsatellite DNA markers were applied to infer the phylogeography, intraspecific diversity and dynamics of the distributional history of European grayling (Thymallus thymallus) with focus on its central and northern European distribution range. Phylogenetic and nested clade analyses revealed at least four major mtDNA lineages, which evolved in geographical isolation during the Pleistocene. These lineages should be recognized as the basic evolutionary significant units (ESUs) for grayling in central and northern Europe. In addition, and in contrast to previous work on grayling, the results of Bayesian analysis of individual admixture coefficients, two-dimensional scaling analysis and spatial analysis of molecular variance provided evidence for a high level of admixture among major lineages in contact zones between drainages (e.g. the low mountain range of Germany), most likely resulting from glacial perturbations and ancient river connections between drainages during the Pleistocene glaciations. Even within river systems, a high level of differentiation among populations was revealed as indicated by the microsatellite data. Grayling sampled from 29 sites displayed high levels of differentiation (overall F(ST) = 0.367), a high number of private alleles and high bootstrap support for the genetic distance-based population clusters across 12 loci. We specifically discuss our results in context of phylogeograpic studies on other European freshwater fish species with habitat preferences similar to those of grayling. Our study shows that both large-scale phylogeographical and detailed genetic analyses on a fine scale are mandatory for developing appropriate conservation guidelines of endangered species.

Animals↗

Epidemiologic analysis of spatial clustering of bovine ephemeral fever outbreaks. II. Principal component analysis.

The principal component analysis (PCA) was applied to analyze a correlation matrix of three variables on epidemic data of bovine ephemeral fever (BEF) outbreaks. These original data were summarized from the official outbreak report of Fukuoka Prefecture. The first and the second principal components of the PCA were interpreted as the infectious potency due to BEF virus and the prevention against BEF virus infection, respectively. The BEF outbreak areas were able to be classified epidemically into 4 groups by using the two principal components. The valuable epidemiological insights can be reasonably obtained from an application of the PCA. The results provided an important information for a further BEF vaccination campaign in the western part of Japan.

Animals↗

The use of geographical information systems in studies on environment and health.

Geographical information systems (GIS) provide a powerful technology for the spatial analysis of environmental and health data. Major areas of application include the assessment and mapping of environmental exposure, mapping of health outcome, and the analysis of spatial relationships between environment and health. The use of GIS nevertheless brings with it many potential problems and pitfalls. This article reviews some of the recent applications in relation to studies of environment and health, and examines some of the research issues involved.

Bias↗

[Characteristics of neonatal mortality in the State of Rio de Janeiro, Brazil, in the 1980's: a spatio-temporal analysis].

OBJECTIVE: The spatial distribution of neonatal mortality by age-group (0-23 hours, 1-6 days and 7-27 days) in the State of Rio de Janeiro, Brazil, for two periods of time 1979-81 and 1990-92, is analysed. METHODOLOGY: A methodology was used to perform the spatial analysis which took the counties of Rio de Janeiro as the spatial units and "first-nearest-neighbors" as the neighborhood criterion. For the purpose of detecting anisotropy, the connection matrix was defined through "first-nearest-neighbors" in a particular direction. To understand the spatial behavior of neonatal mortality, social and environmental indicators and indicators of medical assistance by county for both periods of time were constructed. RESULTS AND CONCLUSIONS: At the beginning of the 80's, the neonatal mortality for the age group 7-27 days showed the presence of clusters in the East and Southeast in direct association with the poorest conditions of life in the State, characteristics that had vanished by the next decade. Spatial dependence for the mortality rates for the first day of life, for 1991, was identified clusters in two different regions beings detected, followed by a positive correlation with "number of private hospital beds per inhabitant". Some of the cluster counties were, in particular, death receivers from neighboring counties and showed hospital case fatality rates much greater than the overall mean rate.

Anisotropy↗

Local stability analysis of spatially homogeneous solutions of multi-patch systems.

Multi-patch systems, in which several species interact in patches connected by dispersal, offer a general framework for the description and analysis of spatial ecological systems. This paper describes how to analyse the local stability of spatially homogeneous solutions in such systems. The spatial arrangement of the patches and their coupling is described by a matrix. For a local stability analysis of spatially homogeneous solutions it turns out to be sufficient to know the eigenvalues of this matrix. This is shown for both continuous and discrete time systems. A bookkeeping scheme is presented that facilitates stability analyses by reducing the analysis of a k-species, n-patch system to that of n uncoupled k-dimensional single-patch systems. This is demonstrated in a worked example for a chain of patches. In two applications the method is then used to analyse the stability of the equilibrium of a predator-prey system with a pool of dispersers and of the periodic solutions of the spatial Lotka-Volterra model.

Animals↗

Linear filtering and nonlinear interactions in direction-selective visual cortex neurons: a noise correlation analysis.

Spatial and temporal properties related to direction selectivity of both simple and complex type visual cortex neurons were assessed by cross-correlation analysis of their responses to random ternary white noise. This stimulus consisted of multiple randomly placed bars, each colored white, black, or gray with equal probability, which were rerandomized every 5-10 ms. A first-order cross-correlation analysis of a neuron's spike train with the spatiotemporal history of the stimulus provided an estimate of the neuron's linear spatiotemporal filtering properties. A nonlinear correlation analysis measured the amount of interaction for pair-wise combinations of bars as a function of their relative spatial and temporal separations. The spatiotemporal orientation of each of these functions was quantified using a "motion energy index" (MEI), which was compared to the neurons' direction selectivity measured with drifting sinewave gratings. Both first-order and nonlinear correlation plots usually showed s-t orientation whose sign was consistent with the neuron's direction preference; however, in many cases the MEI for first-order analysis was weak compared to that seen in the nonlinear interactions. The structures of the nonlinear interaction functions were also compared with predictions from a conventional model of direction selectivity based on a simple spatiotemporally oriented linear filter, followed by an intensive nonlinearity ("LN model"). These comparisons showed that some neurons' data agreed reasonably well with such a model, while others agreed poorly or not at all. Simulations of an alternative model which combines signals from idealized lagged and nonlagged front-end linear filters produce noise correlation results more like those seen in the neurophysiological data.

Animals↗

The effect of exposure duration on the analysis of spatial structure in eccentric vision.

There is some evidence from grating experiments that the transient presentation of a stimulus pattern interferes with the encoding of positional relationships between pattern elements (i.e. the analysis of spatial structure) more in eccentric vision than in central vision. The present study investigated the effect of exposure duration on the analysis of spatial structure in eccentric vision using a task in which the observer discriminated between two mirror symmetric patterns consisting of short line segments. In each trial, the two patterns were flashed for 140 or 500 ms, and the observer had to decide whether the patterns were identical or mirror symmetric. Both constant-size and size-scaled patterns were used in eccentric vision. The longer exposure duration slightly increased the proportion of correct responses in eccentric vision but performance remained distinctly inferior to that in central vision.

Humans↗

Spatial data analysis by epidermal Langerhans cells reveals an elegant system.

Langerhans cells are dendritic cells situated in the mammalian epidermis. In human epidermis, the concentration is between 460 and 1000 mm(-2). Langerhans cells fulfill an essential role in skin immune responses. Numerous scientific reports on Langerhans cells have appeared, but with no systematic research on the pattern of the spatial distributions. On the contrary, in certain fields, a spatial distribution is an important theme, and spatial data analysis has a long history. We hypothesized that epidermal Langerhans cells were set in the best formation for their immuno-surveillance by a sophisticated mechanism. To prove this hypothesis, we have imported spatial data analysis into the study of epidermal Langerhans cells. Here, we show that the distribution is completely regular; the pattern of Voronoi divisions fits the territories; the random packing model simulates their bone marrow derivation; a repulsive interaction is demonstrated and a repulsive potential function is estimated. Spatial data analysis-based computer simulation will be a new method of Langerhans cell study. In addition, this procedure shows promise for future distribution research of certain cells.

Animals↗

A cluster of hypoplastic left heart malformation in Baltimore, Maryland.

Congenital cardiovascular malformations (CCVMs) of the left side of the heart show familial recurrence of various forms of obstructive malformations, including hypoplastic left heart (HLH), interrupted aortic arch, coarctation of the aorta, and aortic stenosis. In a previous population-based study in the Baltimore-Washington region, these malformations were associated with parental reports of occupational or leisure solvent exposure, overt diabetes, and family history of CCVM in first-degree relatives. Spatial analysis in this well-characterized study population may augment self-reported data by revealing additional associations with potential environmental risk factors. We used spatial analysis to identify clusters of HLH as a group. The study population included all live-born cases of hypoplastic left heart syndrome diagnosed in the first year of life between 1981 and 1989 and a random sample of unaffected infant controls matched by year and hospital of birth. The nested case-control cohort in this spatial analysis included 77 HLH cases and 1894 controls in Maryland and the District of Columbia. Nonparametric and regression analyses included personal variables from the interview data set as well as spatial variables. A region of Baltimore was identified that contained HLH at twice the expected frequency based on the distribution of population younger than 5 years of age. The region included 30 of 77 geocoded cases of HLH in the cohort and is significant by spatial scanning at p = 0.056. Within this region, male cases of HLH were disproportionately present compared to females. This cluster is in a region of Baltimore with industrial release of solvents, dioxin, and polychlorinated biphenyls in air. Outside the cluster, HLH is associated with family history of CCVM in a first-degree relative, maternal exposure to miscellaneous solvents, paternal anesthesia, maternal art painting, aspirin ingestion, and maternal diabetes. Inside the cluster, father's painting and exposure to sympathomimetic drugs were associated risk factors. Spatial analysis of HLH cases delineated an urban region with increased prevalence of this left heart malformation. Within this region, excess male cases of HLH occurred, and industrial release to air of solvents, dioxin, and polychlorinated biphenyl compounds was documented. We propose that both genetic and environmental factors contribute to the phenotype of HLH.

Air Pollution↗

Spatial correlation analysis of the pharmacological conversion of sustained atrial fibrillation in conscious goats by cibenzoline.

The nonlinear spatial redundancy and the linear spatial correlation function were used to investigate to what extent non-linearity was involved in the coupling of atrial regions and how organization in activation patterns of sustained atrial fibrillation (AF) had been modified by administration of the class IC agent cibenzoline in the experimental model of sustained AF in instrumented conscious goats. Electrograms were measured in five goats during sustained AF and when the fibrillation interval had been prolonged to about 25%, 50% and 85% (CIB25, CIB50, CIB85) with respect to control. The nonlinear association length and linear correlation length were estimated along the principal axes of two-dimensional correlation maps estimated from the spatial redundancy and the spatial correlation function, respectively. The estimated short axis association length in the right atrium increased already shortly after the start of infusion (CIB25, +61%), and remained significantly different from control during the experiment, including the effects of non-simultaneous interaction. At CIB85 the association length had almost become twice as long with respect to control (increase from 16 to 29 mm, 89%), while in the left atrium changes were less pronounced (increase from 9 to 12 mm, +32%). The linearized association length which was estimated using multivariate surrogate data increased more gradually and was less sensitive to changes in spatial organization. The results of the spatial correlation analysis suggest that the drug-induced nonlinearity in the spatio-temporal dynamics of sustained AF is related to activation patterns which are characterized by extended uniformly propagating fibrillation wavefronts (AF type I). We conclude that cibenzoline enhanced the spatial organization of sustained AF associated with a transition from type II to type I AF activation patterns. This may destabilize the perpetuation of AF since an increase in association length is equivalent to a reduction of atrial tissue mass available to support reentrant circuits. The results are consistent with the hypothesis that larger association lengths result from fewer and larger reentrant circuits. It is argued that effects of diminished curvature of fibrillation wavefronts are anti-arrhythmic under conditions of suppressed excitability imposed by cibenzoline. Termination of AF may be mediated by a mechanism resembling a bifurcation of the dynamics which sets in when the ends of fractionated wavefronts cannot sufficiently curve anymore to maintain a positive balance of newly generated wavelets needed to sustain AF.

Animals↗

Remote sensing and spatial statistical analysis to predict the distribution of Oncomelania hupensis in the marshlands of China.

Remote sensing and spatial statistical analysis were employed to predict the distribution of Oncomelania hupensis, the intermediate host snail of Schistosoma japonicum, in the marshlands of Jiangning county in China. Surrogate indices related to environmental factors in the marshlands were derived from a Landsat 7 ETM+ image, and the relationship between environmental covariates and the density of O. hupensis was analyzed by stepwise regression models and ordinary kriging. Although stepwise regression demonstrated that O. hupensis densities of live snails in the marshlands related significantly to the modified soil-adjusted vegetation index, wetness and land surface temperature, the correlation coefficient was low (0.282). Therefore, spatial patterns of the regression residual were investigated by the semi-variogram method, and the spatial variation of O. hupensis density attributed to the spatial autocorrelation was estimated by ordinary kriging. The regression model of the snail density and ordinary kriging of its spatial variation were then combined with the aim of improving the prediction of O. hupensis. Following this approach, the prediction indeed improved considerably (0.852). Our results show that it is possible to predict the distribution of O. hupensis in these marshlands by using remotely sensed environmental indices, and that spatial statistical analyses are capable of improving prediction accuracy. These findings are of relevance for mapping and prediction of schistosomiasis japonica in China, and hence the national control programme.

Animals↗

Spatial autocorrelation analysis reveals that A, B and O allele frequency surfaces on the Indian subcontinent are highly fractured.

Spatial autocorrelation analysis performed on published data pertaining to caste and tribal populations of the Indian subcontinent has revealed that the surfaces of A, B and O allele frequencies are highly fractured. The only significant spatial autocorrelation was observed in respect of the A allele frequency among caste populations.

ABO Blood-Group System↗

Diversity of some gene frequencies in European and Asian populations. III. Spatial correlogram analysis.

The gene frequencies at eight loci in some European and Asian human populations have been subjected to spatial autocorrelation analysis, using Geary's c coefficient. Contrary to what is expected for markers affected only by gene flow and genetic drift, the spatial correlograms show distinct modes of gene frequency variation: there are significant clinal patterns (at the GLO and ESD loci), significant non-clinal patterns (AK, ADA, 6-PGD and GPT) and marginally significant patterns (PGP and SOD). Any hypothesis on the evolution of these polymorphisms should account for the observed heterogeneity of their geographical distributions.

Asia↗

The boundary value problem in spatial statistical analysis.

"The primary objective of this paper is to investigate procedures for detecting and handling existing border biasing in spatial statistical analysis." Six conventional solutions to the boundary value problem are criticized, and three alternate statistical solutions are proposed.

Demography↗

Distance and risk measures for the analysis of spatial data: a study of childhood cancers.

Three statistical approaches, used to detect spatial clusters of disease associated with a point source exposure, are applied to childhood cancer data for the city of San Francisco (1973-88). The distributions of incident cases of leukemia (51 cases), brain cancer (35 cases), and lymphatic cancer (37 cases) among individuals less than 21 years of age are described using three measures of clustering: distance on a geopolitical map, distance on a density equalized transformed map, and relative risk. The point source of exposure investigated is a large microwave tower located southwest of the center of the city (Sutro Tower). The three analytic approaches indicate that the patterns of the major childhood cancers are essentially random with respect to the point source. These results and a statistical model for spatial clustering are used to explore distance and risk measures in the analysis of spatial data. Both types of measures of spatial clustering are shown to perform similarly when a specific area of exposure can be defined.

Adolescent↗

New double-tracer digital radiography for analysis of spatial and temporal myocardial flow heterogeneity.

A new high-resolution digital radiographic technique based on the deposition of (125)I- and (3)H-labeled desmethylimipramine (IDMI and HDMI, respectively) was developed for the assessment of spatial and temporal myocardial flow heterogeneity at a microvascular level. The density distributions of two tracers, or relative flow distributions, were determined by subtraction digital radiography using two imaging plates of different sensitivity. The regions resolved are comparable in size to vascular regulatory units (400 x 400 microm(2)). This method was applied to the measurement of within-layer myocardial flow distributions in Langendorff-perfused rabbit hearts. The validity of this method was confirmed by the strong correlation between regional densities of two tracers injected simultaneously (r = 0.89 +/- 0.03, n = 8). The temporal flow stability was evaluated by a 90-s continuous IDMI injection and subsequent bolus HDMI injection (n = 8). Regional densities of the two tracers were fairly correlated (r = 0.86 +/- 0.03), indicating that the spatial pattern of flow distribution was stable even at a microvascular level over a 90-s period. The effect of microsphere embolization on the flow distribution was also investigated by the sequential injections of IDMI, 15-microm microspheres, and HDMI at 20-s intervals (n = 8). Microembolization increased the coefficient of variation of tracer density from 19 to 25% (P < 0.05), whereas the regional densities of two tracers were still correlated substantially, as in the case of no embolization (r = 0.84 +/- 0.06). Thus the microsphere embolization enhanced flow heterogeneity with increasing flow differences between control high-flow and control low-flow regions but rather maintained the pattern of flow distribution. In conclusion, double-tracer digital radiography will be a promising method for the spatial and temporal myocardial flow analysis at microvascular levels.

Animals↗

Spatial autocorrelation analysis offers new insights into gene flow in the Australian bush rat, Rattus fuscipes.

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, Rattus fuscipes, we have combined a new multilocus autocorrelation method with hypervariable microsatellite genetic markers to investigate fine-scale (< or = 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 (< or = 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.

Animals↗