In January I posted a request for information about programs to analyze spatial patterns of trees (e.g. Ripley's K(d) and Nearest Neighbour Method). I received several responses, all of which refer to programs unavailable commercially (with one exception). Please note that in general, Ripley's K gives a more complete description of a spatial pattern than nearest-neighbour methods because it takes into account all the inter-tree distances and not just the minimum distance. Also, be aware that the analysis of spatial patterns involves some assumptions and specificity related to one's project and objectives. It is a good idea to read on the subject before using someone else's program: see list of references below. Here is a summary of the responses: 1) Mark. R. Fulton <mrfulton@delphi.com> has written a FORTRAN program to do a 'standard' (univariate) Ripley's K analysis of mapped point locations in a rectangular plot. 2) Phil LePage <plepage@mfor01.for.gov.bc.ca> has a SAS macro for analyzing spatial patterns of trees. The macro performs either the Nearest Neigbhbour (NN) method, or Ripley's (RK) method. The macro can be used for univariate or bivariate analyses. 3) Catherine B. Statland <cbstatland@galaxy.gov.bc.ca> and a colleague have both written algorithms for Ripley's K(d): one can be used for both square and circular plots (written in PASCAL); the other one for rectangular plots (written in C). 4) Mark Hanus <hanusm@ccmail.orst.edu> has written a small program to calculate both K(d) and L(d) for some Douglas-fir stands in western Oregon. It takes as input the x,y coordinates in a text file, one coordinate pair per line 5) Norm Kenkel <kenkel@mail.cc.umanitoba.ca> has a Microsoft BASIC program to perform Ripley K analysis. Works only for square study areas. Runs on a Macintosh: please note that the compiled program may only work with Mac OS version 6.0). Other programs (?): S. Imfeld <simfeld@wild.unizh.ch> suggested to look at the GSTAT module of GRASS developed by Marc J. MacLennan, in: National Center for Geographic Information Analysis (NCGIA): Technical Paper 91-19, Aug. 1991. It has G and L functions. J. den ouden <Jan=den=Ouden%BTBO%BOSB.WAU@Vines2.WAU.NL> mentioned that P. Alaback <palaback@selway.umt.edu> used a macro (EXCEL) to calculate nearest neighbors for shrubs. R. Knox <knox@spruce.gsfc.nasa.gov> suggested that, if you access to the S language (e.g., S-plus), you can try ftp files to perform spatial analyses from <markov.stats.ox.ac.uk>. If you don't have access to the S language, the FORTRAN subroutines ought to be useful. Someone mentioned that Melinda Moeur (Intermountain Res. Station, USDA For. Serv., Moscow, ID 83843, USA) has a FORTRAN program to perform both K(d) and L(d). Also, someone referred to R. P. Duncan (School of Forestry, University of Canterbury, Christchurch, New Zealand) who has a program to compute both univariate and bivariate Ripley's K(d) on IBM-Dos. Thanks to all who responded! ¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨' Daniel Mailly, Ph.D. Candidate mailly@unixg.ubc.ca Faculty of Forestry, University of British Columbia 270-2357 Main Mall, Vancouver, BC Canada V6T 1Z4 ¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨'¨' Useful references: __________________ Berg, E. and J. L. Hamrick. 1994. Spatial and genetic structure of two sandhills oaks: Quercus laevis and Quercus margaretta (Fagaceae). Amer. J. Bot., 81(1): 7-14. Diggle, P.J. 1983. Statistical analysis of spatial point patterns. Academic Press. 148 pp. (see pp. 71-72 for univariate K(t) analysis, pp. 107-108 for bivariate K(t) analysis). Duncan, R. P. and G. H. Stewart. 1991. The temporal and spatial analysis of tree age distributions. Can. J. For. Res., 21: 1703-1710. Duncan, R. P. 1991. Competition and the coexistence of species in a mixed podocarp stand. J. Ecol., 79: 1073-1084. Fisher, M. 1990. Algorithms for the computation of spatial statistics. Comput. Biol. Med. 20: 311-317. Hatton, T. J. 1989. Spatial analysis of a subalpine heath woodland. Austr. J. Ecol., 14: 65-75. Hatton, T. J. 1989. Spatial patterning of sweet briar (Rosa rubiginosa) by two vertebrate species. Austr. J. Ecol., 14: 199-205. Kenkel, N.C. 1988. Pattern of self-thinning in jack pine: testing the random mortality hypothesis. Ecology 69:1017-1024. Kenkel, N.C. 1993. Ecology 74:1700-1706. Lotwick, H. W. and B. W. Silverman. 1983. Methods for analysing spatial processes of several types of points. J. Royal Stat. Soc., Series B, 39: 172-212. Lusk, C. and J. Ogden. 1992. Age structure and dynamics of a podocarp - broadleaf forest in Tongariro National Park, New Zealand. J. Ecol., 80: 379-393. Moeur, M. 1993. Characterizing spatial patterns of trees using stem-mapped data. For. Sci., 39(4): 756-775. Ripley, B.D. 1977. Modelling spatial patterns. J. Royal Statistical Soc. Ser. B 39: 172-212. Sterner, R. W., C. A. Ribic and G. E. Schatz. 1986. Testing for life historical changes in spatial patterns of four tropical tree species. J. Ecol., 74: 621-633. Stewart, G. H. and A. B. Rose. 1990. The significance of life history strategies in the developmental history of mixed beech (Nothofagus) forests, New Zealand. Vegetatio, 87: 101-114. Upton, G.J.G., Fingleton, B. 1985. Spatial data analysis by example. Volume 1: point pattern and quantitative data. Wiley, London. 410 p. (see pp. 87-88 for univariate K(t) analysis, pp. 255-256 for bivariate K(t) analysis). Tomppo, E. 1986. Models and methods for analysing spatial patterns of trees. Comm. Inst. For. Fenniae, 138: 65 pp. West, P. W. 1984. Inter-tree competition and small-scale pattern in monoculture of Eucalyptus obliqua L'Herit. Austr. J. Ecol., 9: 405-411.
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