Detection of Critical Densities Associated with Pinon‐Juniper Woodland Ecotones

The interfaces between pifion-juniper canopies and grasslands in the south- western USA present an opportunity to use the modern theory of spatial phase transitions as a formal characterization of ecotone structure. The theory requires an estimation of a critical value of tree cover at which the woodlands switch abruptly from a fragmented collection of small patches of trees to a network of connected canopies. Presumably, this transition is associated with critical environmental conditions that regulate the ecologies of trees vs. grasses. We developed and tested a new method to estimate the critical cover value of woodlands on complex terrain. The method was based on multiscale assessments of the associations between local tree coverage and two types of patch edge. Tests on artificial gradient percolation maps revealed an interaction between the type of edge used ("hull edge," which is based on only the orthogonal connections between canopy-occupied cells, vs. "accessible edge," which is based on both orthogonal and diagonal connections beween canopy-occupied cells) and the neighborhood rule used to define a cluster (von Neumann 5-cell or Moore 9-cell). When applied to digitized, geographically referenced aerial photographs, the method indicated that areas ?6.6 ha exhibited the theoretical critical value of 59.3% cover predicted for square lattices and the 5-cell neighborhood. Construction of both edge types on a given map can reveal locations of steep environmental gradients that may be buffered against modest climate fluctuations. The edges can be used in the calibration of independent variables to predict tree cover. The agreement between the ex- pected and observed critical densities will motivate extensions of phase transition theory to studies of ecotones in real landscapes.

[1]  Ricard V. Solé,et al.  Are rainforests self-organized in a critical state? , 1995 .

[2]  Rudolf H. Riedi,et al.  Application of multifractals to the analysis of vegetation pattern , 1994 .

[3]  D. Frank,et al.  Temporal variation in actual evapotranspiration of terrestrial ecosystems: patterns and ecological implications , 1994 .

[4]  Bradford P. Wilcox,et al.  Runoff and erosion in intercanopy zones of pinyon-juniper woodlands , 1994 .

[5]  Zhiliang Zhu,et al.  US forest types and predicted percent forest cover from AVHRR data , 1994 .

[6]  P. S. Eagleson,et al.  A water use model for locating the boreal/deciduous forest ecotone in eastern North America , 1994 .

[7]  I. Noble,et al.  A Model of the Responses of Ecotones to Climate Change. , 1993, Ecological applications : a publication of the Ecological Society of America.

[8]  William J. Ripple,et al.  Analysis of conifer forest regeneration using Landsat Thematic Mapper data , 1993 .

[9]  Alan R. Johnson,et al.  Diffusion in Fractcal Landscapes: Simulations and Experimental Studies of Tenebrionid Beetle Movements , 1992 .

[10]  K. Lajtha,et al.  Plant Spatial Pattern and Nutrient Distribution in Pinyon-Juniper Woodlands Along an Elevational Gradient in Northern New Mexico , 1992, International Journal of Plant Sciences.

[11]  M. Rosso,et al.  Illumination: a new method for studying 3D percolation fronts in a concentration gradient , 1992 .

[12]  James J. Kay,et al.  Thermodynamics and Measures of Ecological Integrity , 1992 .

[13]  R. Creswick,et al.  Introduction to Renormalization Group Methods in Physics , 1991 .

[14]  Carla S. Williams,et al.  An integrated data flow visual language and software development environment , 1991, J. Vis. Lang. Comput..

[15]  E. Guyon,et al.  Directed percolation front in a gradient , 1991 .

[16]  J. Gosz.  Fundamental Ecological Characteristics of Landscape Boundaries , 1991 .

[17]  Jerry F. Franklin,et al.  Contributions of the Long-Term Ecological Research Program , 1990 .

[18]  B Chopard,et al.  Cellular automata approach to non-equilibrium diffusion and gradient percolation , 1989 .

[19]  M. Turner,et al.  LANDSCAPE ECOLOGY : The Effect of Pattern on Process 1 , 2002 .

[20]  Heinz-Otto Peitgen,et al.  The science of fractal images , 2011 .

[21]  Harvey Gould,et al.  An Introduction to Computer Simulation Methods: Applications to Physical Systems , 2006 .

[22]  P. Legendre,et al.  Practical aspects of modelling ecological phenomena using the cusp catastrophe , 1988 .

[23]  Richard F. Voss,et al.  Fractals in nature: from characterization to simulation , 1988 .

[24]  M. Hill,et al.  Data analysis in community and landscape ecology , 1987 .

[25]  H. Kesten.  Scaling relations for 2D-percolation , 1987 .

[26]  F. Woodward.  Climate and plant distribution , 1987 .

[27]  T. Grossman,et al.  Structure and perimeters of percolation clusters , 1986 .

[28]  R. Neilson,et al.  High-Resolution Climatic Analysis and Southwest Biogeography , 1986, Science.

[29]  T. Keyes,et al.  Biased percolation: forest fires with wind , 1986 .

[30]  Ohtsuki,et al.  Kinetic growth percolation: Epidemic processes with immunization. , 1986, Physical review. A, General physics.

[31]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[32]  R. Peters,et al.  The Greenhouse Effect and Nature ReservesGlobal warming would diminish biological diversity by causing extinctions among reserve species , 1985 .

[33]  P. S. Eagleson,et al.  Water‐Limited Equilibrium of Savanna Vegetation Systems , 1985 .

[34]  J. Sheaffer,et al.  Influence of Pacific Sea surface temperatures on seasonal precipitation over the western plateau of the United States , 1985 .

[35]  Lee A. Segel,et al.  PATTERN GENERATION IN SPACE AND ASPECT. , 1985 .

[36]  Mike P. Austin,et al.  Continuum Concept, Ordination Methods, and Niche Theory , 1985 .

[37]  P. Meakin.  Diffusion-controlled deposition on fibers and surfaces , 1983 .

[38]  P. Grassberger.  On the critical behavior of the general epidemic process and dynamical percolation , 1983 .

[39]  Claude M. Penchina,et al.  The physics of amorphous solids , 1983 .

[40]  Peter Reynolds,et al.  Large-cell Monte Carlo renormalization group for percolation , 1980 .

[41]  M. Mimura,et al.  On a diffusive prey--predator model which exhibits patchiness. , 1978, Journal of theoretical biology.

[42]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[43]  René Thom,et al.  Structural stability and morphogenesis , 1977, Pattern Recognit..

[44]  Val L. Mitchell.  The Regionalization of Climate in the Western United States , 1976 .

[45]  N. Yamamura.  A mathematical approach to spatial distribution and temporal succession in plant communities , 1976 .

[46]  Julius T. Tou,et al.  Pattern Recognition Principles , 1974 .

[47]  J. R. Wallis,et al.  Some ecological consequences of a computer model of forest growth , 1972 .

[48]  James H. Brown.  Mechanisms of Competitive Exclusion Between Two Species of Chipmunks , 1971 .

[49]  R. Whittaker,et al.  GRADIENT ANALYSIS OF VEGETATION* , 1967, Biological reviews of the Cambridge Philosophical Society.

[50]  H. Odum,et al.  Fundamentals of ecology , 1954 .

[51]  M. Nice,et al.  The social life of animals , 1939 .