Hypothesis Of Complete Spatial Randomness Research Articles

Spatial distribution of Urban land-use in Addis Ababa, Ethiopia

ABSTRACT This study underlines the critical function of efficient urban land use planning, recommending mixed land use for improved city sustainability. The research, which is rooted in the historical context of urban renewal, attempts to harmonize theoretical frameworks with actual implementation, giving critical insights for policymakers and urban planners in constructing sustainable urban areas. The study identifies a deficit in empirical research on the spatial distribution of urban mixed land use, as well as a gap between theory and real application. Using a mixed-methods approach, it explores mixed land use planning concerns by including stakeholder input and temporal dynamics. Using theoretical frameworks, the study explores land use trends in four Addis Ababa sub-cities. When the null hypothesis of Complete Spatial Randomness is rejected, there is a significant relationship between location and land use functions (statistical chi-square value of 47.763). Finally, the study makes crucial recommendations for purposeful land use distribution in a dynamic urban setting, shedding light on the constraints of mixed land use planning in African urban growth.

EVALUATION AND QUANTIFICATION OF HEAT HOTSPOTS IN THE CHAPADA DOS GUIMARÃES-MT NATIONAL PARK

The study aimed to analyze the spatial distribution of heat sources inside and outside the Chapada dos Guimarães National Park (PNCG) in the State of Mato Grosso. The analyzes were performed through the estimate of kernel density (KDE) and Ripley's K function from 2005 to 2014. The data related to the number of hot spots were obtained from the National Institute for Space Research (INPE) from 2005 to 2014, and the vector files were acquired from the cartographic base of the Brazilian Institute of Geography and Statistics (IBGE). In the 10 years of analysis, 579 hot spots were detected in the PNCG, where it was found that the months of August and September had the highest incidence of hot spots in the park. The kernel maps demonstrated that most hotspots were observed in the years 2007, 2010 and 2012. The years 2005 and 2013 presented average densities and the years 2006, 2008, 2009, 2011 and 2014 indicated low density of the hot spots. Ripley's K function, calculated to observe the spatial distribution of the hot spots, rejected the hypothesis of complete spatial randomness (CSR), indicating that they showed a tendency to cluster during the study time series at the PNCG.

Spatial and Temporal Patterns of Commercial Citrus Trees Affected by Phyllosticta citricarpa in Florida

Citrus black spot (CBS) caused by Phyllosticta citricarpa, is the most recent introduction of an exotic citrus pathogen into Florida and has been a challenge to control to date. Understanding the dispersal pattern of the disease within affected groves is vital in developing effective control strategies to limit the spread of the disease. The spatial pattern of CBS-affected trees was studied in two commercial ‘Valencia’ orange groves over three consecutive citrus seasons. Cluster analyses based on nearest-neighbor distance (F, G and J-functions) and pairwise distances between points (Ripley’s K function, Besag’s L function and the pair correlation function, g) were used to test the hypothesis of complete spatial randomness (CSR) of CBS infected trees within the groves. In both groves, the hypothesis of CSR was rejected for all tests performed including quadrats testing (2 × 2 trees up to 10 × 10 trees). The relationship between tree age and disease was assessed at one experimental site. Citrus trees bearing fruit for the first time accounted for approximately 13% of trees positive for disease and were located within areas of heavy disease pressure. These findings support short distance movement of inoculum as the main spread of disease in the groves studied.

Spatial distribution pattern of Mezilaurus itauba (Meins.) Taub. Ex mez. in a seasonal forest area of the southern Amazon, Brazil

Abstract: Spatial analysis of forest tree distribution is a powerful tool to respond to basic ecological questions, and represent a useful support to strategies of genetic conservation and sustainable management practices of forest resources. Spatial analysis techniques combined with the use of Geographical Information Systems have been commonly applied to the study of stochastic processes in order to determine the existence of clusters to be related to microenviromental conditions and/or genetic factors. The present study focused on the distribution patterns of individuals of Mezilaurus itauba in a seasonal forest of the southern Amazon, with the aim of providing information about the spatial arrangement of these species at the juvenile and adult stages. Ripley’s K function with radius of 10, 20 and 30 m was used to describe spatial distribution patterns. The hypothesis of complete spatial randomness (CSR) of individuals was tested by constructing confidence envelopes for the Ripley’s K function through Monte Carlo simulations using a Poisson homogeneous process. The results obtained suggest a general random distribution of individuals, though a tendency to clustering at close distances was detected for individuals classified as adults (DBH > 50 cm). Contrastingly, a completely randomized spatial pattern was found for juveniles trees (DBH < 50 cm). Our results provide a useful baseline for the development of sustainable management plans and conservation of Mezilaurus itauba, as well as for other economically-exploited, native tree species in the southern Amazon forest.

Lumbar and thoracic perforators: vascular anatomy and clinical implications.

Pedicled perforator flaps in the thoracic and lumbar regions allow reconstruction of the posterior trunk. They enable reconstruction of various local defects without microvascular anastomoses and with minimal donor-site morbidity and excellent cosmesis. The authors examined the locations of perforators in the lumbar and thoracic regions. Ten cadaver hemithoraces and lumbar regions were freshly harvested and dissected. Intraarterial injections were performed with colored latex, followed by dissection in the suprafascial plane. Perforators with a diameter larger than 0.5 cm were located and measured from the midline and from C7 (thoracic) and coccygeal (lumbar) reference points. The most dominant perforators were injected with radiopaque dye and scanned with high-resolution computed tomography. The patterns were analyzed by the quadrat counting test (based on chi-square statistics) for the null hypothesis of complete spatial randomness. A total of 164 thoracic and 216 lumbar perforators were identified. These were clustered in highest density in two major areas within 10 to 20 cm of the C7 and coccygeal reference points and 10 cm from the midline; this pattern was not a random distribution (p < 0.001). Perforasomes of lumbar perforators in some instances crossed the midline, joining adjacent contralateral lumbar perforators by means of direct and indirect linking vessels. Lumbar and thoracic pedicled perforator flaps provide useful options for reconstructing complex defects. Use of these flaps is aided by anatomical knowledge of the location of major clusters of perforators.

Spatial pattern analysis of fire events in Central India – A case study

The impact of fires on environment can have adverse effects. To fully understand the synoptic behaviour of fire events, information on the spatial distributions and their pattern are highly important. In this study, we used 9-year (1997–2005) integrated fire count datasets derived from Along Track Scanning Radiometer (ATSR) satellite to geographically map the distribution of fire events in the Madhya Pradesh state, central India. We then used robust spatial metrics to test the spatial pattern of fire events against the hypothesis of complete spatial randomness (CSR). Specifically, we used the index of dispersion, Green's index, in addition to nearest neighbour statistic for testing CSR. Also, quantification of clustering is carried out using Ripley's K-function. To spatially map the fire events, we used Kernel density estimation that relies on bi-variate probability density functions. Results from using different spatial pattern metrics and nearest neighbour statistics suggested relatively high clustering of fire events in the study area. In addition, results from Ripley's K-function suggested the fire events to be clustered at a lag-distance of ∼60 mile radius. By converting original fire ignition locations that are based on historical records to continuous density surfaces, the probability of fire events could be mapped effectively using kernel density estimation. As each fire event is the result of certain spatial process including biophysical and anthropogenic attributes, results from this study can provide useful information on fire management at a local district level. Also, the analysis presented in this study illustrates how spatial patterns in the point datasets can be quantified using different dispersion indices, clustering and density estimation techniques.

Detecting Randomness in Spatial Point Patterns: A “Stat-Geometrical” Alternative

There are several methods to test the hypothesis of complete spatial randomness of point patterns. This work involves a new geometrical-based strategy to detect spatial arrangements, which takes into account both Euclidean and angular distances, defining a triangle-based network. An asymptotic test based on the Kolmogorov–Smirnov statistic is proposed to accommodate this situation. To assess the usefulness of this method (Stat-Geo), simulations based on Monte Carlo procedures, conducted using SPLUS™, give satisfactory results with a high degree of accuracy. As expected, the new technique proposed in this paper, performs better than traditional ones like distance-based or angle-based, since more information (combining distance and angle) is introduced in the decision-making system. This approach is a very simple way to offer high efficiency results for a low computational cost. Furthermore, this alternative method allows barycentric interpolation of the unsampled points into a two-dimensional simplex (triangular) framework.

Spectral tests of randomness for spatial point patterns

We develop a spectral framework for testing the hypothesis of complete spatial randomness (CSR) for a spatial point pattern. Five formal tests based on the periodogram (sample spectrum) proposed in Mugglestone (1990) are considered. A simulation study is used to evaluate and compare the power of the tests against clustered, regular and inhomogeneous alternatives to CSR. A subset of the tests is shown to be uniformly more powerful than the others against the alternatives considered. The spectral tests are also compared with three widely used space-domain tests that are based on the mean nearest-neighbor distance, the reduced second-order moment function (K-function), and a bivariate Cramer-von Mises statistic. The test based on the scaled cumulative R-spectrum is more powerful than the space-domain tests for detecting clustered alternatives to CSR, especially when the number of events is small.

Venus: Crater distribution and plains resurfacing models

Detailed analysis of the distribution of craters on Venus using Mth nearest neighbor analysis, coupled with models based upon surface morphology constraints, indicates that the hypothesis of complete spatial randomness (CSR) cannot be rejected, but is not a unique model of the observed crater distribution. Based on morphologic mapping, the extensive volcanic plains can be divided into four units that have a spread in age of the order of 0.5T (the mean surface age of the planet). This four‐unit plains model, along with its derivatives, produce test statistics that indicate such models also cannot be rejected. Further, the probability of obtaining a result at least as extreme as the observed test statistic given that the null hypothesis (model corresponds to Venus) is true is lowest for the CSR model. There is no particular reason to pick a CSR model (along with its implications for catastrophic resurfacing) as a constraint on the evolution of Venus, and there are geological reasons to choose the multiage models. We find that we cannot distinguish statistically among models that have two, three, or four distinct production ages within the plains. However, the hypothesis that the variation in crater density within all of the plains is due to a single random process can be rejected for two reasons. First, the binomial probability that such a process could exist within each of the plains units is ≤0.05 except the smallest and youngest unit, PL1. Second, using a chi‐squared statistic to test the hypothesis that four plains units have the same age gives a p value of 10−4, indicating confident rejection of the hypothesis. Thus CSR cannot be used as a constraint on models of resurfacing or planetary evolution of Venus because of the non‐uniqueness in matching such a model to the observed crater distribution and the strong indication of distinct ages within the plains with a significant spread in age. Geological and geophysical constraints provide our best clues for understanding Venus.

The spatial pattern of a forest ecosystem

Statistical analysis of stands of trees as a whole need suitable methods of spatial statistics. Obviously, trees within a stand affect development and survival of their neighbours. They interact and therefore have to be considered as a system of dependent random variates from an unknown stochastic process. One such statistical model which considers the spatial dependence among trees in a forest and their characteristics is a marked point process. The `points', called events in spatial statistics, are the tree positions and the `marks' are tree characteristics such as crown lengths or tree species. A minimal prerequisite for any serious attempt to model an observed pattern is to test the hypothesis of complete spatial randomness (CSR). Concerning the fitting of parametric models to spatial point patterns, a class of models which seems potentially useful for describing the present type of data is the class of marked Gibbs (pairwise interaction) point processes. Essentially, these processes characterise the interaction between events by some parametrically specified function of distance. In this paper several statistical methods to test CSR are described and marked Gibbs processes are used to fit a model in two different forest ecosystems.

Spectral techniques in spatial analysis

This paper shows how spectral analysis can be used as a tool for the exploratory analysis of spatial patterns. The emphasis is on relating periodogram structure to the type of biological generating mechanism that could have produced the observed pattern; examples include the spatial distributions of a Scots pine forest canopy and a developing stand of willow herb in a recently thinned woodland. Three statistical tests are presented for examining the null hypothesis of complete spatial randomness against specific alternatives, and these are then applied to spatial data on Japanese black pine saplings, redwood seedlings, and biological cells.

Spatial pattern analysis in ecology based on Ripley's K‐function: Introduction and methods of edge correction

Abstract. Spatial pattern analysis based on Ripley's K‐function is a second‐order analysis of point patterns in a twodimensional space. The method is increasingly used in studies of spatial distribution patterns of plant communities, but the statistical methods involved are sometimes poorly understood or have been modified without evaluating the effects on results. The procedures of field data acquisition, statistical analysis, and the test for the null hypothesis of complete spatial randomness are described and the presentation of results is discussed. Different methods of edge correction were tested on a computer‐generated random pattern and a mapped distribution of a Mediterranean shrubland. The inclusion of buffer zones around mapped plots describes the spatial pattern most accurately, but may not warrant the additional labour involved. Three variations of the weighted edge correction yielded comparable results for the distribution patterns tested. The toroidal edge correction may give biased results for non‐random patterns. Recommendations for standardisation of the statistical procedures and data presentation are given.