Spatial Point Pattern Analysis and Industry Concentration

Traditional measures of spatial industry concentration are restricted to given areal units. They do not make allowance for the fact that concentration may be differently pronounced at various geographical levels. Methods of spatial point pattern analysis allow to measure industry concentration at a continuum of spatial scales. While common distancebased methods are well applicable for sub-national study areas, they become inefficient in measuring concentration at various levels within industrial countries. This particularly applies in testing for conditional concentration where overall manufacturing is used as a reference population. Using Ripley’s K function approach to second-order analysis, we propose a subsample similarity test as a feasible testing approach for establishing conditional clustering or dispersion at different spatial scales. For measuring the extent of clustering and dispersion, we introduce a concentration index of the style of Besag’s (1977) L function. By contrast to Besag’s L function, the new index can be employed to measure deviations of observed from general spatial point patterns. The K function approach is illustratively applied to measuring and testing industry concentration in Germany.Spatial concentration, clustering, dispersion, spatial point pattern analysis, K function

Hierarchical second-order analysis of replicated spatial point patterns with non-spatial covariates

In this paper we propose a method for incorporating the effect of non-spatial covariates into the spatial second-order analysis of replicated point patterns. The variance stabilizing transformation of Ripley’s K function is used to summarize the spatial arrangement of points, and the relationship between this summary function and covariates is modelled by hierarchical Gaussian process regression. In particular, we investigate how disease status and some other covariates affect the level and scale of clustering of epidermal nerve fibres. The data are point patterns with replicates extracted from skin blister samples taken from 47 subjects.Peer reviewe

Identifying directional properties of spatial point patterns an investigation of two methods

Analyses of spatial point patterns tend to focus on deviations from randomness by either clustering or regularity. One assumption of these analyses implies that the point generating process is equal in all directions. However, the association of the location of points with a process biased in one or more directions is widely neglected due to a lack of appropriate statistical procedures. This is surprising, since patterns generated by directional processes are important in Geography. The purpose of this thesis is to investigate the blunt-triangle method and the third moment method for their potential of identifying directionality in spatial point patterns. A point process model is presented that combines the properties of both clustering and directionality. Realizations of this model are used with the objective of evaluating the two spatial analytical procedures. The blunt-triangle method is based on the comparison of blunt angles between triplets of points to theoretical blunt-triangle statistics. The failure of these statistics to find the characteristics given in the model can be explained by the dependence of the blunt-triangle method on assumptions of randomness. The third moment method examines the distributions of distances and angles between points, and is thus expected to be sensitive to a directional bias in spatial point patterns. It is shown that if the parameters of the procedure are chosen properly, different levels of directionality can be identified. The third moment method can thus be recommended for empirical applications in Geography

A class of spatial econometric methods in the empirical analysis of clusters of firms in the space

In this paper we aim at identifying stylized facts in order to suggest adequate models of spatial co–agglomeration of industries. We describe a class of spatial statistical methods to be used in the empirical analysis of spatial clusters. Compared to previous contributions using point pattern methods, the main innovation of the present paper is to consider clustering for bivariate (rather than univariate) distributions, which allows uncovering co–agglomeration and repulsion phenomena between the different industrial sectors. Furthermore we present the results of an empirical application of such methods to a set of European Patent Office (EPO) data and we produce a series of empirical evidences referred to the the pair–wise intra–sectoral spatial distribution of patents in Italy in the nineties. In this analysis we are able to identify some distinctive joint patterns of location between patents of different sectors and to propose some possible economic interpretations

Identifying a spatial scale for the analysis of residential burglary: An empirical framework based on point pattern analysis

A key issue in the spatial and temporal analysis of residential burglary is the choice of scale: spatial patterns might differ appreciably for different time periods and vary across geographic units of analysis. Based on point pattern analysis of burglary incidents in Columbus, Ohio during a 9-year period, this study develops an empirical framework to identify a useful spatial scale and its dependence on temporal aggregation. Our analysis reveals that residential burglary in Columbus clusters at a characteristic scale of 2.2 km. An ANOVA test shows no significant impact of temporal aggregation on spatial scale of clustering. This study demonstrates the value of point pattern analysis in identifying a scale for the analysis of crime patterns. Furthermore, the characteristic scale of clustering determined using our method has great potential applications: (1) it can reflect the spatial environment of criminogenic processes and thus be used to define the spatial boundary for place-based policing; (2) it can serve as a candidate for the bandwidth (search radius) for hot spot policing; (3) its independence of temporal aggregation implies that police officials need not be concerned about the shifting sizes of risk-areas depending on the time of the year

A class of spatial econometric methods in the empirical analysis of clusters of firms in the space

In this paper we aim at identifying stylized facts in order to suggest adequate models of spatial co–agglomeration of industries. We describe a class of spatial statistical methods to be used in the empirical analysis of spatial clusters. Compared to previous contributions using point pattern methods, the main innovation of the present paper is to consider clustering for bivariate (rather than univariate) distributions, which allows uncovering co–agglomeration and repulsion phenomena between the different industrial sectors. Furthermore we present the results of an empirical application of such methods to a set of European Patent Office (EPO) data and we produce a series of empirical evidences referred to the the pair–wise intra–sectoral spatial distribution of patents in Italy in the nineties. In this analysis we are able to identify some distinctive joint patterns of location between patents of different sectors and to propose some possible economic interpretations.Agglomeration, Bivariate K–functions, co–agglomeration, Non parametric concentration measures, Spatial clusters, Spatial econometrics

Spatial patterns of an endemic Mediterranean palm recolonizing old fields

Throughout Europe, increased levels of land abandonment lead to (re)colonization of old lands by forests and shrublands. Very little is known about the spatial pattern of plants recolonizing such old fields. We mapped in two 21–22-ha plots, located in the Doñana National Park (Spain), all adult individuals of the endozoochorous dwarf palm Chamaerops humilis L. and determined their sex and sizes. We used techniques of spatial point pattern analysis (SPPA) to precisely quantify the spatial structure of these C. humilis populations. The objective was to identify potential processes generating the patterns and their likely consequences on palm reproductive success. We used (1) Thomas point process models to describe the clustering of the populations, (2) random labeling to test the sexual spatial segregation, and (3) mark correlation functions to assess spatial structure in plant sizes. Plants in both plots showed two critical scales of clustering, with small clusters of a radius of 2.8–4 m nested within large clusters with 38–44 m radius. Additional to the clustered individuals, 11% and 27% of all C. humilis individuals belonged to a random pattern that was independently superimposed to the clustered pattern. The complex spatial pattern of C. humilis could be explained by the effect of different seed-dispersers and predators’ behavior and their relative abundances. Plant sexes had no spatial segregation. Plant sizes showed a spatial aggregation inside the clusters, with a decreasing correlation with distance. Clustering of C. humilis is strongly reliant on its seed dispersers and stressful environmental conditions. However, it seems that the spatial patterns and dispersal strategies of the dwarf palm make it a successful plant for new habitat colonization. Our results provide new information on the colonization ability of C. humilis and can help to develop management strategies to recover plant populationsPeer reviewe

A Spatially Explicit Census Reveals Population Structure and Recruitment Patterns for a Narrowly Endemic Pine, Pinus torreyana

We conducted a census of the rare pine, Pinus torreyana ssp.  torreyana, in order to determine: a) what is the population size and is it stable, growing or declining; b) what is the spatial variation in population structure; c) what is the spatial patterning of trees in different life stages; and, d) what environmental factors are related to seedling recruitment?  Trees were classified into four stages classes: adult (160 cm tall with cones); sub-adult (160 cm without cones); saplings (30-160 cm), and seedlings (30 cm).  Stem diameter was measured for adults and sub-adults, and height for saplings and seedlings.  Stands were defined by spatial clustering of the tree map.  Univariate and bivariate point pattern analyses were used to explore spatial patterns for adult and juvenile trees and identify potential stand development processes such as density dependence, dispersal limitations, and patchy recruitment.  Logistic regression was used to analyze seedling establishment and survival in relation to environmental variables derived from digital maps.  We expected to find little or no recruitment based on earlier studies.  Instead, 5422 trees were mapped and measured, and tree size had “reverse J-shaped†distribution suggestive of a recruiting population.  However, population structure was variable among stands.  The predominant spatial pattern detected for adult and juvenile trees was clustering at lag distances 10 m.  Bivariate pattern analysis did not suggest repulsion between adult and juvenile size classes.  Seedlings tended to be found close to adults and on certain soil types.  Taken together, this suggests that the clustered patterns resulting from patchy recruitment and survival of juveniles persist over time.

A global descriptor of spatial pattern interaction in the galaxy distribution

We present the function J as a morphological descriptor for point patterns formed by the distribution of galaxies in the Universe. This function was recently introduced in the field of spatial statistics, and is based on the nearest neighbor distribution and the void probability function. The J descriptor allows to distinguish clustered (i.e. correlated) from ``regular'' (i.e. anti-correlated) point distributions. We outline the theoretical foundations of the method, perform tests with a Matern cluster process as an idealised model of galaxy clustering, and apply the descriptor to galaxies and loose groups in the Perseus-Pisces Survey. A comparison with mock-samples extracted from a mixed dark matter simulation shows that the J descriptor can be profitably used to constrain (in this case reject) viable models of cosmic structure formation.Comment: Significantly enhanced version, 14 pages, LaTeX using epsf, aaspp4, 7 eps-figures, accepted for publication in the Astrophysical Journa