A measure of spatial stratified heterogeneity

Abstract Spatial stratified heterogeneity, referring to the within-strata variance less than the between strata-variance, is ubiquitous in ecological phenomena, such as ecological zones and many ecological variables. Spatial stratified heterogeneity reflects the essence of nature, implies potential distinct mechanisms by strata, suggests possible determinants of the observed process, allows the representativeness of observations of the earth, and enforces the applicability of statistical inferences. In this paper, we propose a q -statistic method to measure the degree of spatial stratified heterogeneity and to test its significance. The q value is within [0,1] (0 if a spatial stratification of heterogeneity is not significant, and 1 if there is a perfect spatial stratification of heterogeneity). The exact probability density function is derived. The q -statistic is illustrated by two examples, wherein we assess the spatial stratified heterogeneities of a hand map and the distribution of the annual NDVI in China.

[1]  B. Husband,et al.  A METAPOPULATION PERSPECTIVE IN PLANT POPULATION BIOLOGY , 1996 .

[2]  R. Sokal,et al.  Detecting Regions of Abrupt Change in Maps of Biological Variables , 1989 .

[3]  Bradley P. Carlin,et al.  Bayesian areal wombling for geographical boundary analysis , 2005 .

[4]  Douglas Steinley,et al.  K-means clustering: a half-century synthesis. , 2006, The British journal of mathematical and statistical psychology.

[5]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[6]  Luc Anselin,et al.  Thirty years of spatial econometrics , 2010 .

[7]  Zev Naveh,et al.  LANDSCAPE ECOLOGY: THEORY AND APPLICATION , 1983, Landscape Journal.

[8]  Brian D. Inouye,et al.  SPATIAL HETEROGENEITY EXPLAINS THE SCALE DEPENDENCE OF THE NATIVE-EXOTIC DIVERSITY RELATIONSHIP , 2005 .

[9]  A. Getis.  The Analysis of Spatial Association by Use of Distance Statistics , 2010 .

[10]  L. Holdridge.  Determination of World Plant Formations From Simple Climatic Data. , 1947, Science.

[11]  T. Ferguson.  A Course in Large Sample Theory , 1996 .

[12]  Wei-Yin Loh,et al.  Classification and regression trees , 2011, WIREs Data Mining Knowl. Discov..

[13]  P. Atkinson,et al.  Spatial Scale Problems and Geostatistical Solutions: A Review , 2000 .

[14]  Robert Haining,et al.  Sample surveying to estimate the mean of a heterogeneous surface: reducing the error variance through zoning , 2010, Int. J. Geogr. Inf. Sci..

[15]  G. Matheron.  Principles of geostatistics , 1963 .

[16]  Ershun Zhong,et al.  An information-fusion method to identify pattern of spatial heterogeneity for improving the accuracy of estimation , 2008 .

[17]  June Luo,et al.  A Spatial Scan Statistic on Trends , 2014 .

[18]  L. Anselin.  Local Indicators of Spatial Association—LISA , 2010 .

[19]  Manfred M. Fischer,et al.  Spatial Data Analysis: Models, Methods and Techniques , 2011 .

[20]  C. Thomas,et al.  The spatial structure of populations , 1999 .

[21]  P. Gong,et al.  Object-based Detailed Vegetation Classification with Airborne High Spatial Resolution Remote Sensing Imagery , 2006 .

[22]  Anil K. Jain.  Data clustering: 50 years beyond K-means , 2008, Pattern Recognit. Lett..

[23]  Robert Haining,et al.  Spatial Data Analysis: Theory and Practice , 2003 .

[24]  F. Baret,et al.  Quantifying spatial heterogeneity at the landscape scale using variogram models , 2006 .

[25]  Anil K. Jain.  Data clustering: 50 years beyond K-means , 2010, Pattern Recognit. Lett..

[26]  J. Rao.  Small Area Estimation , 2003 .

[27]  B. Everitt.  The Cambridge Dictionary of Statistics , 1998 .

[28]  W. H. Womble,et al.  Differential systematics. , 1951, Science.

[29]  W. Tobler.  A Computer Movie Simulating Urban Growth in the Detroit Region , 1970 .

[30]  P. Moran.  Notes on continuous stochastic phenomena. , 1950, Biometrika.

[31]  Bin Zou,et al.  Self-organizing dual clustering considering spatial analysis and hybrid distance measures , 2011 .

[32]  M. Kulldorff.  A spatial scan statistic , 1997 .

[33]  P. Legendre.  Spatial Autocorrelation: Trouble or New Paradigm? , 1993 .

[34]  Measuring population densities in a heterogeneous world , 2008 .

[35]  Daniel A. Griffith,et al.  Non-standard Spatial Statistics and Spatial Econometrics , 2011 .

[36]  Pierre R. L. Dutilleul,et al.  Spatio-Temporal Heterogeneity: Concepts and Analyses , 2011 .

[37]  Geoffrey M. Jacquez,et al.  From fields to objects: A review of geographic boundary analysis , 2000, J. Geogr. Syst..

[38]  Eric J. Gustafson,et al.  Quantifying Landscape Spatial Pattern: What Is the State of the Art? , 1998, Ecosystems.

[39]  WILLIAM F. FAGAN,et al.  Integrating Edge Detection and Dynamic Modeling in Quantitative Analyses of Ecological Boundaries , 2003 .

[40]  C. Justice,et al.  Global land cover classification by remote sensing: present capabilities and future possibilities , 1991 .

[41]  Xiaoying Zheng,et al.  Geographical Detectors‐Based Health Risk Assessment and its Application in the Neural Tube Defects Study of the Heshun Region, China , 2010, Int. J. Geogr. Inf. Sci..

[42]  H. Tian,et al.  Spatial and temporal patterns of China's cropland during 1990¿2000: An analysis based on Landsat TM data , 2005 .

[43]  Russell G. Congalton,et al.  A review of assessing the accuracy of classifications of remotely sensed data , 1991 .

[44]  J. Gribbin.  The Encyclopaedia Britannica guide to the 100 most influential scientists : the most important scientists from ancient Greece to the present day , 2008 .

[45]  J. Keith Ord,et al.  Spatial Processes Models and Applications , 1981 .

[46]  L. Anselin.  Spatial Econometrics: Methods and Models , 1988 .

[47]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[48]  Sudipto Banerjee,et al.  Bayesian Wombling , 2006, Journal of the American Statistical Association.

[49]  T. Caliński,et al.  A dendrite method for cluster analysis , 1974 .

[50]  M. Goodchild,et al.  GIS and spatial data analysis: Converging perspectives , 2003 .

[51]  Robert Haining,et al.  Sandwich Estimation for Multi-Unit Reporting on a Stratified Heterogeneous Surface , 2013 .

[52]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .