Modeling the Dynamics of Complex Spatial Systems Using GIS, Cellular Automata and Fuzzy Sets Applied to Invasive Plant Species Propagation

Geographic processes are embedded within complex spatial systems containing multiple interacting variables. These processes have spatial and temporal dynamics that are difficult to represent and model with the standard tools of geographic information systems (GIS) software. Consequently, representing the dynamics of geographic process and accounting for uncertainties in variable measurements are key considerations when developing realistic spatial models. This article discusses an integrated GIS-based cellular automata (CA) design that addresses spatial and temporal dynamics representation, and incorporates fuzzy sets for handling input spatial data uncertainties and errors. The integrated approach is demonstrated in the context of modeling the dynamics of invasive plant species in a simulated landscape. Using dynamic models as predictive tools can enable more targeted spatial decision making especially when resources are limited. In the case of invasive species, the GIS-CA model can be used to predict species locations for improved control and management strategies.

[1]  Michael Batty,et al.  Urban Systems as Cellular Automata , 1997 .

[2]  Miha Mraz,et al.  Intelligent bush fire spread prediction using fuzzy cellular automata , 1999, J. Intell. Fuzzy Syst..

[3]  Suzana Dragicevic,et al.  A fuzzy-constrained cellular automata model of forest insect infestations , 2006 .

[4]  Michael Batty,et al.  From Cells to Cities , 1994 .

[5]  Suzana Dragicevic,et al.  Modeling mountain pine beetle infestation with an agent-based approach at two spatial scales , 2010, Environ. Model. Softw..

[6]  Suzana Dragicevic,et al.  A fuzzy set approach for modelling time in GIS , 2000, Int. J. Geogr. Inf. Sci..

[7]  Fangju Wang,et al.  Fuzzy Representation of Geographical Boundaries in GIS , 1996, Int. J. Geogr. Inf. Sci..

[8]  K. Lowell.  A fuzzy surface cartographic representation for forestry based on Voronoi diagram area stealing , 1994 .

[9]  A. Heppenstall,et al.  A Fuzzy Cellular Automata Urban Growth Model (FCAUGM) for the City of Riyadh, Saudi Arabia. Part 1: Model Structure and Validation , 2009 .

[10]  Vincent B. Robinson,et al.  A probe mechanism to couple spatially explicit agents and landscape models in an integrated modelling framework , 2006, Int. J. Geogr. Inf. Sci..

[11]  F. Wu,et al.  Simulating urban encroachment on rural land with fuzzy-logic-controlled cellular automata in a geographical information system , 1998 .

[12]  Alex B. McBratney,et al.  Application of fuzzy sets to climatic classification , 1985 .

[13]  Chris Webster,et al.  Simulation of natural land use zoning under free-market and incremental development control regimes , 1998 .

[14]  Y. Leung.  On the Imprecision of Boundaries , 2010 .

[15]  R. Solé,et al.  The DivGame Simulator: a stochastic cellular automata model of rainforest dynamics , 2000 .

[16]  Paolo D'Odorico,et al.  Space-time self-organization of mesoscale rainfall and soil moisture , 2000 .

[17]  Roger White,et al.  Cellular Automata and Fractal Urban Form: A Cellular Modelling Approach to the Evolution of Urban Land-Use Patterns , 1993 .

[18]  Donna Peuquet,et al.  Making Space for Time: Issues in Space-Time Data Representation , 2001, GeoInformatica.

[19]  T. Wilhelm,et al.  Goal functions for the development of natural systems , 2000 .

[20]  W. Weaver.  Science and complexity. , 1948, American scientist.

[21]  Juval Portugali,et al.  Sociospatial Residential Dynamics: Stability and Instability within a Self‐Organizing City , 2010 .

[22]  Stuart R. Phinn,et al.  Modelling urban development with cellular automata incorporating fuzzy-set approaches , 2003, Comput. Environ. Urban Syst..

[23]  Michael Batty,et al.  Cellular Automata and Urban Form: A Primer , 1997 .

[24]  Ioannis G. Karafyllidis,et al.  A model for predicting forest fire spreading using cellular automata , 1997 .

[25]  M. Phipps,et al.  Dynamical Behavior of Cellular Automata under the Constraint of Neighborhood Coherence , 2010 .

[26]  Richard A. Wadsworth,et al.  Simulating the spread and management of alien riparian weeds: are they out of control? , 2000 .

[27]  David O'Sullivan,et al.  Toward micro-scale spatial modeling of gentrification , 2002, J. Geogr. Syst..

[28]  Guy Engelen,et al.  Cellular Automata as the Basis of Integrated Dynamic Regional Modelling , 1997 .

[29]  P. Vitousek,et al.  INTRODUCED SPECIES: A SIGNIFICANT COMPONENT OF HUMAN-CAUSED GLOBAL CHANGE , 1997 .

[30]  Ferdinando Semboloni,et al.  An Urban and Regional Model Based on Cellular Automata , 1997 .

[31]  Hui Lin,et al.  Formalizing fuzzy objects from uncertain classification results , 2001, Int. J. Geogr. Inf. Sci..

[32]  Margaret J Eppstein,et al.  Invasiveness in plant communities with feedbacks. , 2007, Ecology letters.

[33]  Fangju Wang,et al.  Comparison of Boolean and Fuzzy Classification Methods in Land Suitability Analysis by Using Geographical Information Systems , 1992 .

[34]  M. Kirkby,et al.  A cellular model of Holocene upland river basin and alluvial fan evolution , 2002 .

[35]  S. Higgins,et al.  A review of models of alien plant spread. , 1996 .

[36]  M. Goodchild,et al.  Dealing with error in spatial databases: a simple case study , 1995 .

[37]  Stephen J. Walsh,et al.  2.5D Morphogenesis: modeling landuse and landcover dynamics in the Ecuadorian Amazon , 2001, Plant Ecology.

[38]  A. Rossman.  A Special Issue on Global Movement of Invasive Plants and Fungi , 2001 .

[39]  A. McBratney,et al.  Application of fuzzy sets in soil science: fuzzy logic, fuzzy measurements and fuzzy decisions , 1997 .

[40]  Claes Andersson,et al.  Assessing the impact of temporal dynamics on land-use change modeling , 2004, Comput. Environ. Urban Syst..

[41]  V. Robinson.  Some implications of fuzzy set theory applied to geographic databases , 1988 .

[42]  D F Wagner,et al.  Cellular Automata and Geographic Information Systems , 1997 .

[43]  Keith C. Clarke,et al.  A Self-Modifying Cellular Automaton Model of Historical Urbanization in the San Francisco Bay Area , 1997 .

[44]  Bertram Ostendorf,et al.  The effect of climate change on tropical rainforest vegetation pattern , 2001 .

[45]  Peter Deadman,et al.  Modelling Rural Residential Settlement Patterns with Cellular Automata , 1993 .

[46]  R. Coulson,et al.  Simulation Modeling as a Tool for Understanding the Landscape Ecology of Southern Pine Beetle Infestations in Southern Appalachian Forests , 2008 .

[47]  R. White,et al.  High-resolution integrated modelling of the spatial dynamics of urban and regional systems , 2000 .

[48]  Suzana Dragicevic,et al.  Assessing cellular automata model behaviour using a sensitivity analysis approach , 2006, Comput. Environ. Urban Syst..

[49]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[50]  F. Wang.  Improving remote sensing image analysis through fuzzy information representation , 1990 .

[51]  B. Huntley,et al.  Predicting the spatial distribution of non‐indigenous riparian weeds: issues of spatial scale and extent , 2000 .

[52]  Peter A. Burrough,et al.  Fuzzy mathematical methods for soil survey and land evaluation , 1989 .

[53]  Roger Smith,et al.  The application of cellular automata to the erosion of landforms , 1991 .

[54]  K. Clarke,et al.  A Cellular Automaton Model of Wildfire Propagation and Extinction , 1994 .

[55]  P. Davy,et al.  A stochastic precipiton model for simulating erosion/sedimentation dynamics , 2001 .

[56]  H. Balzter,et al.  Cellular automata models for vegetation dynamics , 1998 .

[57]  Danielle J. Marceau,et al.  Exploration of Spatial Scale Sensitivity in Geographic Cellular Automata , 2005 .

[58]  Thomas C. Schelling,et al.  Dynamic models of segregation , 1971 .

[59]  Peter M. Allen,et al.  Cities And Regions as Evolutionary, Complex Systems , 1997 .

[60]  Helen Couclelis,et al.  Cellular Worlds: A Framework for Modeling Micro—Macro Dynamics , 1985 .

[61]  Linda See,et al.  Calibration of a fuzzy cellular automata model of urban dynamics in Saudi Arabia , 2009 .

[62]  Xia Li,et al.  Errors and uncertainties in urban cellular automata , 2006, Comput. Environ. Urban Syst..

[63]  Fulong Wu.  A linguistic cellular automata simulation approach for sustainable land development in a fast growing region , 1996 .

[64]  Tara Sharma,et al.  Integrated modeling for exploring sustainable agriculture futures , 2006 .

[65]  Alex B. McBratney,et al.  The application of fuzzy classification to soil pH profiles in the Lockyer Valley, Queensland, Australia , 1991 .

[66]  Robert M. Itami,et al.  Simulating spatial dynamics: cellular automata theory , 1994 .

[67]  Vincent B. Robinson,et al.  A Perspective on the Fundamentals of Fuzzy Sets and their Use in Geographic Information Systems , 2003, Trans. GIS.

[68]  Anthony Gar-On Yeh,et al.  Zoning land for agricultural protection by the integration of remote sensing, GIS, and cellular automata , 2001 .

[69]  Suzana Dragicevic,et al.  Fuzzy Sets for Representing the Spatial and Temporal Dimensions in GIS Databases , 2004 .

[70]  Xia Li,et al.  Sustainable Land Development Model for Rapid Growth Areas Using GIS , 1998, Int. J. Geogr. Inf. Sci..

[71]  A Ratz,et al.  Long-Term Spatial Patterns Created by Fire: a Model Oriented Towards Boreal Forests , 1995 .

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

[73]  Debra P. C. Peters,et al.  Modeling invasive weeds in grasslands: the role of allelopathy in Acroptilon repens invasion , 2001 .

[74]  Daniel G. Brown,et al.  Classification and Boundary Vagueness in Mapping Presettlement Forest Types , 1998, Int. J. Geogr. Inf. Sci..

[75]  Michael F. Goodchild,et al.  Geographical information science , 1992, Int. J. Geogr. Inf. Sci..

[76]  A. Clerici,et al.  Simulation of the Parma River blockage by the Corniglio landslide (Northern Italy) , 2000 .

[77]  Xia Li,et al.  Modelling sustainable urban development by the integration of constrained cellular automata and GIS , 2000, Int. J. Geogr. Inf. Sci..

[78]  Daniel Z. Sui,et al.  A FUZZY GIS MODELING APPROACH FOR URBAN LAND EVALUATION , 1992 .

[79]  May Yuan,et al.  Understanding Dynamics of Geographic Domains , 2008 .

[80]  Stephen Wolfram,et al.  Cellular automata as models of complexity , 1984, Nature.