A practical approach to the study of spatial structure in simple cases of heterogeneous vegetation

. Spatial heterogeneity is a characteristic of most natural ecosystems which is difficult to handle analytically, particularly in the absence of knowledge about the exogenous factors responsible for this heterogeneity. While classical methods for analysis of spatial point patterns usually require the hypothesis of homogeneity, we present a practical approach for partitioning heterogeneous vegetation plots into homogeneous subplots in simple cases of heterogeneity without drastically reducing the data. It is based on the detection of endogenous variations of the pattern using local density and second-order local neighbour density functions that allow delineation of irregularly shaped subplots that could be considered as internally homogeneous. Spatial statistics, such as Ripley's K-function adapted to analyse plots of irregular shape, can then be computed for each of the homogeneous subplots. Two applications to forest ecological field data demonstrate that the method, addressed to ecologists, can avoid misinterpretations of the spatial structure of heterogeneous vegetation stands.

[1]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[2]  Raphaël Pélissier,et al.  On explicit formulas of edge effect correction for Ripley's K‐function , 1999 .

[3]  J. Franklin,et al.  Second-Order Neighborhood Analysis of Mapped Point Patterns , 1987 .

[4]  J. Proctor,et al.  Ecological studies in four contrasting lowland rain forests in Gunung Mulu National Park, Sarawak. IV: Associations between tree distribution and soil factors , 1984 .

[5]  Dietrich Stoyan,et al.  Anisotropy analysis for particle systems , 1991 .

[6]  J. Wiens Spatial Scaling in Ecology , 1989 .

[7]  Dietrich Stoyan,et al.  Marked Point Processes in Forest Statistics , 1992, Forest Science.

[8]  Robert Haining,et al.  Statistics for spatial data: by Noel Cressie, 1991, John Wiley & Sons, New York, 900 p., ISBN 0-471-84336-9, US $89.95 , 1993 .

[9]  Peter Haase,et al.  Spatial patterns in a two‐tiered semi‐arid shrubland in southeastern Spain , 1996 .

[10]  G. Vázquez,et al.  The relationship between vegetation dynamics and water table in tropical dune slacks , 1999 .

[11]  Raphaël Pélissier,et al.  Structure and floristic composition of a tropical evergreen forest in south-west India , 1996, Journal of Tropical Ecology.

[12]  S. Pickett,et al.  Microsite and elevational influences on early forest regeneration after catastrophic windthrow , 1990 .

[13]  N. C. Kenkel,et al.  Pattern of Self‐Thinning in Jack Pine: Testing the Random Mortality Hypothesis , 1988 .

[14]  Peter J. Diggle,et al.  Simple Monte Carlo Tests for Spatial Pattern , 1977 .

[15]  D. Peart,et al.  Post-dispersal predation on isolated seeds : a comparative study of 40 tree species in a Southeast Asian rainforest , 1998 .

[16]  P. Forget,et al.  Spatial patterns of two rodent-dispersed rain forest trees Carapa procera (Meliaceae) and Vouacapoua americana (Caesalpiniaceae) at Paracou, French Guiana , 1999, Journal of Tropical Ecology.

[17]  Bernard W. Silverman,et al.  Methods for Analysing Spatial Processes of Several Types of Points , 1982 .

[18]  P J Diggle,et al.  Second-order analysis of spatial clustering for inhomogeneous populations. , 1991, Biometrics.

[19]  Richard P. Duncan,et al.  COMPETITION AND THE COEXISTENCE OF SPECIES IN A MIXED PODOCARP STAND , 1991 .

[20]  J. Pardé De 1882 à 1976/80, les places d'expérience de sylviculture du Hêtre en forêt domaniale de Haye (Meurthe-et-Moselle) , 1981 .

[21]  C. Skarpe Spatial patterns and dynamics of woody vegetation in an arid savanna , 1991 .

[22]  D. DeAngelis,et al.  Competition and Coexistence: The Effects of Resource Transport and Supply Rates , 1994, The American Naturalist.

[23]  G. J. G. Upton,et al.  Spatial data Analysis by Example , 1985 .

[24]  Raphaël Pélissier,et al.  Tree spatial patterns in three contrasting plots of a southern Indian tropical moist evergreen forest , 1998 .

[25]  T. Mattfeldt Stochastic Geometry and Its Applications , 1996 .

[26]  Sébastien Barot,et al.  DEMOGRAPHY OF A SAVANNA PALM TREE: PREDICTIONS FROM COMPREHENSIVE SPATIAL PATTERN ANALYSES , 1999 .

[27]  Christine A. Ribic,et al.  Testing for life historical changes in spatial patterns of four tropical tree species. , 1986 .

[28]  W. Cleveland Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[29]  Jean Thioulouse,et al.  ADE-4: a multivariate analysis and graphical display software , 1997, Stat. Comput..

[30]  C. S. Holling Cross-Scale Morphology, Geometry, and Dynamics of Ecosystems , 1992 .

[31]  Michel Goulard,et al.  Marked point process : using correlation functions to explore a spatial data set , 1995 .

[32]  D. Tilman Species Richness of Experimental Productivity Gradients: How Important is Colonization Limitation? , 1993 .

[33]  J. Kolasa,et al.  Introduction: The Heterogeneity of Heterogeneity: A Glossary , 1991 .

[34]  W. Cleveland,et al.  Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting , 1988 .

[35]  Friedel Hartmann,et al.  Second-Order Analysis , 1985 .

[36]  E. J. S.,et al.  Quantitative Plant Ecology , 1934, Nature.

[37]  P. Forget Recruitment Pattern of Vouacapoua americana (Caesalpiniaceae), a Rodent-dispersed Tree Species in French Guiana1 , 1994 .

[38]  Pierre Dutilleul,et al.  Spatial Heterogeneity and the Design of Ecological Field Experiments , 1993 .

[39]  Douglas A. Maguire,et al.  Modeling the spatial structure of topical forests , 1998 .

[40]  B. Ripley The Second-Order Analysis of Stationary Point Processes , 1976 .

[41]  S. Pickett,et al.  Ecology: Individuals, populations and communities , 1987 .

[42]  Eric Renshaw,et al.  A practical guide to the spectral analysis of spatial point processes , 1996 .

[43]  B. Ripley Modelling Spatial Patterns , 1977 .

[44]  Melinda Moeur,et al.  Characterizing Spatial Patterns of Trees Using Stem-Mapped Data , 1993, Forest Science.

[45]  Jerzy Szwagrzyk,et al.  Spatial patterns of trees in natural forests of East‐Central Europe , 1993 .

[46]  E. Desouhant,et al.  Oviposition pattern of phytophagous insects: on the importance of host population heterogeneity , 1998, Oecologia.