A Bayesian Solution to the Modifiable Areal Unit Problem

The Modifiable Areal Unit Problem (MAUP) prevails in the analysis of spatially aggregated data and influences pattern recognition. It describes the sensitivity of the measurement of spatial phenomena to the size (the scale problem) and the shape (the aggregation problem) of the mapping unit. Much attention has been recieved from fields as diverse as statistical physics, image processing, human geography, landscape ecology, and biodiversity conservation. Recently, in the field of spatial ecology, a Bayesian estimation was proposed to grasp how our description of species distribution (described by range size and spatial autocorrelation) changes with the size and the shape of grain. This Bayesian estimation (BYE), called the scaling pattern of occupancy, is derived from the comparison of pair approximation (in the spatial analysis of cellular automata) and join-count statistics (in the spatial autocorrelation analysis) and has been tested using various sources of data. This chapter explores how the MAUP can be described and potentially solved by the BYE. Specifically, the scale and the aggregation problems are analyzed using simulated data from an individual-based model. The BYE will thus help to finalize a comprehensive solution to the MAUP.

[1]  Lenore Fahrig,et al.  Population Ecology in Spatially Heterogeneous Environments , 2005 .

[2]  C. Hui,et al.  Does the self-similar species distribution model lead to unrealistic predictions? , 2008, Ecology.

[3]  Jianguo Wu,et al.  The modifiable areal unit problem and implications for landscape ecology , 1996, Landscape Ecology.

[4]  S. Levin,et al.  Mathematical and Computational Challenges in Population Biology and Ecosystems Science , 1997, Science.

[5]  Brian D. Ripley,et al.  Spatial Statistics: Ripley/Spatial Statistics , 2005 .

[6]  John L. Adgate,et al.  The Importance of Spatial Effects for Environmental Health Policy and Research , 2002 .

[7]  A S Fotheringham,et al.  The Modifiable Areal Unit Problem in Multivariate Statistical Analysis , 1991 .

[8]  Cang Hui,et al.  Niche construction and polymorphism maintenance in metapopulations , 2005, Ecological Research.

[9]  Richard Fox,et al.  Spatial patterns in species distributions reveal biodiversity change , 2004, Nature.

[10]  Bridgette Lery,et al.  A Comparison of Foster Care Entry Risk at Three Spatial Scales , 2008, Substance use & misuse.

[11]  Graham Bell,et al.  THE CO‐DISTRIBUTION OF SPECIES IN RELATION TO THE NEUTRAL THEORY OF COMMUNITY ECOLOGY , 2005 .

[12]  J. A. Harrison,et al.  The atlas of southern African birds , 1997 .

[13]  J. Downing.  Biological Heterogeneity in Aquatic Ecosystems , 1991 .

[14]  William E. Kunin,et al.  Scale Dependency of Rarity, Extinction Risk, and Conservation Priority , 2003 .

[15]  Alan J. A. Stewart,et al.  The Ecological Consequences of Environmental Heterogeneity , 2000 .

[16]  Kei-ichi Tainaka,et al.  Paradoxical effect in a three-candidate voter model , 1993 .

[17]  S. Dark,et al.  The modifiable areal unit problem (MAUP) in physical geography , 2007 .

[18]  C. Amrhein.  Searching for the Elusive Aggregation Effect: Evidence from Statistical Simulations , 1995 .

[19]  Stewart Fotheringham,et al.  Scale-independent spatial analysis , 1989 .

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

[21]  S. Hubbell,et al.  Percolation theory for the distribution and abundance of species. , 2003, Physical review letters.

[22]  Cang Hui,et al.  A spatially explicit approach to estimating species occupancy and spatial correlation. , 2006, The Journal of animal ecology.

[23]  R. Levins.  Some Demographic and Genetic Consequences of Environmental Heterogeneity for Biological Control , 1969 .

[24]  C. Hui,et al.  Capturing the “droopy-tail” in the occupancy–abundance relationship , 2007 .

[25]  C. Meynard,et al.  Predicting species distributions: a critical comparison of the most common statistical models using artificial species , 2007 .

[26]  C. E. Gehlke,et al.  Certain Effects of Grouping upon the Size of the Correlation Coefficient in Census Tract Material , 1934 .

[27]  Y. Iwasa,et al.  Population persistence and spatially limited social interaction. , 1995, Theoretical population biology.

[28]  C. Hui,et al.  Distribution patterns of metapopulation determined by Allee effects , 2004, Population Ecology.

[29]  Jennifer L. Dungan,et al.  Illustrations and guidelines for selecting statistical methods for quantifying spatial pattern in ecological data , 2002 .

[30]  J. Reynolds,et al.  On definition and quantification of heterogeneity , 1995 .

[31]  N. Gotelli,et al.  NULL MODELS IN ECOLOGY , 1996 .

[32]  Danny Dorling,et al.  The Visualization of Local Urban Change across Britain , 1995 .

[33]  David J. Unwin,et al.  GIS, spatial analysis and spatial statistics , 1996 .

[34]  P. Burrough,et al.  Principles of geographical information systems , 1998 .

[35]  D. Wong,et al.  Spatial Decomposition of Segregation Indices: A Framework Toward Measuring Segregation at Multiple Levels , 2003 .

[36]  L. Downey.  Using Geographic Information Systems to Reconceptualize Spatial Relationships and Ecological Context 1 , 2006, American Journal of Sociology.

[37]  C. Hui,et al.  Evolution of body size, range size, and food composition in a predator–prey metapopulation , 2006 .

[38]  L. R. Taylor,et al.  Aggregation, Variance and the Mean , 1961, Nature.

[39]  Jay M. Ver Hoef,et al.  Spatial Analysis in Ecology , 2006 .

[40]  C. Hui,et al.  Spatial Patterns of Prisoner’s Dilemma Game in Metapopulations , 2007, Bulletin of mathematical biology.

[41]  Stan Openshaw,et al.  Modifiable Areal Unit Problem , 2008, Encyclopedia of GIS.

[42]  Y. Iwasa,et al.  Dynamic modeling of wave regeneration (Shimagare) in subalpine Abies forests , 1991 .

[43]  Lawrence Todd,et al.  Grain, Extent, and Intensity: The Components of Scale in Archaeological Survey , 2006 .

[44]  W. Kunin,et al.  Extrapolating species abundance across spatial scales , 1998, Science.

[45]  Simon A. Levin,et al.  Biologically generated spatial pattern and the coexistence of competing species , 1997 .

[46]  Peter Kareiva,et al.  Spatial ecology : the role of space in population dynamics and interspecific interactions , 1998 .

[47]  M. Fortin,et al.  Spatial Analysis: A Guide for Ecologists 1st edition , 2005 .

[48]  Cang Hui,et al.  Metapopulation dynamics and distribution, and environmental heterogeneity induced by niche construction , 2004 .

[49]  S. Levin.  The problem of pattern and scale in ecology , 1992 .

[50]  John Bell,et al.  A review of methods for the assessment of prediction errors in conservation presence/absence models , 1997, Environmental Conservation.

[51]  K. Gaston,et al.  Occupancy-abundance relationships and spatial distribution: A review , 2002 .

[52]  K. Gaston,et al.  Occupancy frequency distributions: patterns, artefacts and mechanisms , 2002, Biological reviews of the Cambridge Philosophical Society.

[53]  Yoh Iwasa,et al.  The Geometry of Ecological Interactions: Pair Approximations for Lattice-based Ecological Models , 2000 .

[54]  C. Hui,et al.  A self-similarity model for the occupancy frequency distribution. , 2007, Theoretical population biology.

[55]  Norio Konno,et al.  Upper bounds for survival probability of the contact process , 1991 .

[56]  Philippe C. Baveye,et al.  Use of spatial SQL to assess the practical significance of the Modifiable Areal Unit Problem , 2006, Comput. Geosci..

[57]  Joe N. Perry,et al.  Spatial analysis by distance indices , 1995 .

[58]  Joe N. Perry,et al.  MEASURES OF SPATIAL PATTERN FOR COUNTS , 1998 .

[59]  Yoh Iwasa,et al.  Lattice population dynamics for plants with dispersing seeds and Vegetative propagation , 1994, Researches on Population Ecology.

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

[61]  R. Geary,et al.  The Contiguity Ratio and Statistical Mapping , 1954 .

[62]  C. Hui,et al.  Modeling species distributions by breaking the assumption of self‐similarity , 2007 .

[63]  M. Morisita,et al.  I σ-Index, a measure of dispersion of individuals , 1962, Researches on Population Ecology.

[64]  R. Kadmon,et al.  A SYSTEMATIC ANALYSIS OF FACTORS AFFECTING THE PERFORMANCE OF CLIMATIC ENVELOPE MODELS , 2003 .

[65]  David Manley,et al.  Scales, levels and processes: Studying spatial patterns of British census variables , 2006, Comput. Environ. Urban Syst..

[66]  Ulf Dieckmann,et al.  The Geometry of Ecological Interactions: Simplifying Spatial Complexity , 2000 .

[67]  R. Whittaker.  Evolution and measurement of species diversity , 1972 .

[68]  J. H. Ratcliffe,et al.  Hotbeds of crime and the search for spatial accuracy , 1999, J. Geogr. Syst..

[69]  C. I. Bliss,et al.  FITTING THE NEGATIVE BINOMIAL DISTRIBUTION TO BIOLOGICAL DATA AND NOTE ON THE EFFICIENT FITTING OF THE NEGATIVE BINOMIAL , 1953 .

[70]  Jennifer L. Dungan,et al.  A balanced view of scale in spatial statistical analysis , 2002 .

[71]  Monica G. Turner,et al.  Ecosystem Function in Heterogeneous Landscapes , 2005 .

[72]  On species–area and species accumulation curves: A comment on Chong and Stohlgren's index , 2008 .

[73]  Akira Sasaki,et al.  Statistical Mechanics of Population: The Lattice Lotka-Volterra Model , 1992 .

[74]  C. Hui,et al.  Dynamical complexity and metapopulation persistence , 2003 .

[75]  S. Scheiner.  Six types of species‐area curves , 2003 .