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GEOSTATS: Analysis of spatial point patterns for study of competition between tree species

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  • Martin Béland
    Dear netters, I recently posted some questions to different internet lists about the analysis of spatial point patterns for the study of competition between
    Message 1 of 1 , Mar 27, 2000
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      Dear netters,

      I recently posted some questions to different internet lists about the
      analysis of spatial point patterns for the study of competition between
      jack pine and white birch and between jack pine and trembling aspen in
      the boreal forest of northwestern Quebec, Canada.

      Here is a summary of the questions I posted and responses I have
      received (messages are ordered chronologically):
      ----------------------------------------------------------------------
      To: FOREST@...
      Dear list members,

      I am currently working on a paper on competition between jack pine and
      trembling aspen and jack pine and white birch clay soils of northwestern
      Quebec, Canada. I wish to use tree mapping data to estimate, for each
      tree species in a stand, the intensity of competition coming from each
      species. I want to do this for the whole stand and for a few target
      trees.

      My question is : Do some of you know of a method of analysis of spatial
      pattern and computer program that can account for mixed stands. I am not
      very familiar with this type of analyses. I have found one program on
      the internet, called ADS in ADE4, but couldn’t figure out yet if tree
      species can be differentiated.
      ---------------------------------------------------------------------------
      From: voyteck.zakrzewski@...
      > Suggest two people to contact: Dr. S. Titus or/and Dr. Stan Navratil
      (try
      > at University of Alberta in Edmonton).
      ---------------------------------------------------------------------
      From: "Norm Cimon" <ncimon@...>
      Have you thought of nearest neighbor analysis? One way to examine the
      potential competition would be look at the variations in clustering
      between
      the different species. Nearest neighbor techniques determine whether or
      not a distribution pattern is random, and there are computer programs in
      the
      public domain to perform the computations. For more information,
      contact Andy Younblood (ayounbl/r6pnw_lagrande@...).
      -----------------------------------------------------------------------
      From: Jacques_Begin <jacques.begin@...>
      Salut Martin. Je te suggere de parler a Kim Lowell ou a Geoffrey
      Edwards
      418 656 5491 de la Chaire industrielle en geomatique. Ils ont developpe
      une application pour l'identification individuelle des cimes a partir de
      l'algorithme de Voronoi, si je ne me trompe pas.

      Bonne chance et donne m'en des nouvelles
      -----------------------------------------------------------------------
      From: Phil Carter <PhilC@...>
      A couple of years ago I did some work on inter tree competition. I used
      a
      tree map in a GIS (Arc/Info) to give me information on the spatial
      characteristics of the stand.

      Basically, I used Arc/Info to identify the competitors of each tree,
      then
      applied different definitions of "competitor" to study the different
      competition indices. I used 2 approaches:

      The Arc/info POINTDISTANCE command computes the distance between point
      features in one coverage to all points in a second coverage. If these 2
      coverages are the same, you get all possible combinations in a single
      file,
      and you can select out what you need.

      The BUFFER command identifies a zone of a specified width around a
      specified
      feature. Obviously, if the feature is a point, the buffer is circular.
      Buffer radius was a function of tree diameter at breast height. With the
      Arc/Info version I was using at the time (6 years ago), I could not
      specify
      different buffer sizes on the same cover, so I had to write an Arc macro
      that selected each one of my sample trees in turn, calculate a buffer
      size,
      then clip this buffer out of the stand map. This gave me a sample of
      trees
      inside a known distance from each sample tree.

      Arc/Info will also give you Thiessen polygons.

      My analysis didn't go as far as identifying individual species, but it
      would not be too difficult to identify tree species in you tree map.

      Hope this helps.
      -----------------------------------------------------------------------
      Martin, vous pouvez contacter François A. Gougeon dans le Pacific Forest
      Centre (http://www.pfc.forestry.ca). Je vous acompagne une page web avec
      laquel vous pouvez decider si ça c'est d'interest pour vous.
      Merci bien
      -----------------------------------------------------------------------
      From: dan.duckert@...
      The only tree mapping program I have used is SVS or SVS2 (Stand
      Visualisation Simulation). It was produced out of University of Oregon
      Corvallis. I haven't used it for a number of years. I am sure they have
      a
      web site and possibly freeware. Good luck.
      -----------------------------------------------------------------------
      From: "West Family" <dwest@...>
      Most GIS systems are capable, with addin software, of doing spatial
      analysis. While GIS is used for mostly large scale mapping applications
      it can be used at smaller scales. We have used our GIS to map and
      analysis individual trees in our seed orchard. You should be able to use
      it to analyses trees in a stand.
      -----------------------------------------------------------------------
      From: Alain Leduc <r13064@...>
      Moeur, M. 1993. Characterizing spatial patterns of trees using
      stem-mapped
      data. Forest Science 39: 756-775.

      Moeur, M. 1995. Ripley's K analysis program. U.S. Dep. of Agriculture,
      Forest Service, Intermountain Research Station, Moscow, Idaho.
      -----------------------------------------------------------------------
      From: guest <alister/ne_fia@...>
      Hi! Saw your note in the FIU. Try the ai-geostats homepage (do a net
      search for ai-geostats). If you get there, go to the soft-faq, where
      there is tons of free software that can be used to analyze spatial point
      patterns. One thing that occurs to me from your description is analyses
      of spatial dependence and joint spatial dependence, via
      variograms/covariograms, etc. The softfaq has a search tool. You
      should also join the ai-geostats discussion list, and ask your question
      to the group.

      Another idea--look at the spatial dependence of similarity (like in
      cluster analysis--Euclidean distance, or something like that---using a
      variogram-like procedure. How does similarity of vegetation quadrats
      change with increasing or decreasing distance apart?

      Good luck.
      -----------------------------------------------------------------------
      From: Pius Hauenstein <Pius.Hauenstein@...>
      I read about your problem of estimating the competition between jack
      pine, trembling aspen and white birch in the FIU of Feb. 14 2000.
      I'm not the "absolute specialist" in tree competition, but I made some
      investigations about forest structure with a spatial approach. While
      searching for good literature I have seen some articels, which have
      competition as main task. During my work (Ph D thesis) I learnd a lot
      about the principle problems of analysing the structure of a forest. So
      I think studies of competition are "only" a special case of structural
      analysis. In the attachment you will find some reflection about this
      theme. This paper is not published, but you can use it. Please make a
      cititaion to the original work (You will find it under my name in the
      the references).
      The second attachment contains a list of titles about your theme, which
      I found after a short search in my personal literature database. Some of
      them are written in german ... . I inserted only the most important.

      I hope my information gives you a little help. Finaly, I'm interested in
      your results, please let me know.

      Best regards
      -----------------------------------------------------------------------
      To: adelist@...-lyon1.fr
      Bonjour,

      J'aimerais savoir si ads peut calculer les fonctions bivariées L(d)
      permettant d'étudier le lien entre deux groupes (exemple: espèce
      d'arbres) de points.

      In English:
      I would like to know if ads can compute Ripley's bivariate functions to
      estimate the dependance between to groups of points (tree species).
      -----------------------------------------------------------------------
      From: Goreaud Francois <francois.goreaud@...>
      To: adelist@...-lyon1.fr,
      Translated in English:
      -> Yes, it is easy to compute intertype functions L1.2(d), which
      characterize the spatial structure of qualitative marks (i.e. species).

      -> The corresponding routines are for the moment available in C upon
      request

      -> They should soon be integrated in a new module in ADS...
      -----------------------------------------------------------------------
      From: Martin Béland <Martin.Beland@...>
      To: ai-geostats@...

      Hi,

      I am looking for a software to compute ripley's K univariate statistics
      for determining if a pattern of point representing the location of trees
      in a forest is random, uniform or aggregated. I also need to compute
      ripley's bivariate statistic to determine if two groups of point (tree
      species) are attracted or repulsed.

      I know that "ads in ade-4" available at
      http://pbil.univ.lyon1.fr/ADE-4/ADE-4.html can compute the univariate
      statistic but the software does not include the bivariate statistic yet.
      The authors told me I could get the C routines upon request. I am not
      familiar with C language and would prefer using a user-friendly
      software.

      Any help would be appreciated.
      -----------------------------------------------------------------------
      From: Baz <B.Rowlingson@...>
      I have code to do this with edge corrections on a polygon. Its part of
      my 'splancs' library for S-plus, so you'll have to unwrap the relevant
      code
      yourself. Its in fortran.

      Download the unix source code release from:

      http://www.maths.lancs.ac.uk/~rowlings/Splancs
      -----------------------------------------------------------------------
      From: Roger Bivand <rsb@...>
      Reply-To: Roger.Bivand@...

      One possibility is Splancs (Rowlingson, B. and Diggle, P. 1993 Splancs:
      spatial point pattern analysis code in S-Plus. Computers and
      Geosciences,
      19, 627-655.) at:

      http://www.maths.lancs.ac.uk/~rowlings/Splancs/

      This is a library of functions for S-Plus, including both the ones you
      need. I have made a port for R (see http://cran.r-project.org) for
      Splancs:

      ftp://reclus.nhh.no/pub/R/splancs-2.01-1.tar.gz

      The "spatial" library by Venables and Ripley (the same Ripley),
      including
      the single pattern K measure, is part of the VR bundle for both S-Plus
      and
      R.
      -----------------------------------------------------------------------
      From: "Russell Cole" <r.cole@...>
      I've got, but haven't tried, a prog by DongMei Chen & Art Getis
      called PPA. Prof. Getis sold me a copy for US$15. It's written &
      compiled in C.
      It does: nearest neighbour, refined nearest neighbour, K-function,
      weighted K-function, space-time Knox (no idea), Join-Count
      statistics, Global Moran's I & Geary's C, general Getis-Ord's G,
      local moran's I(d), local G(d) & G(d)*, and local K-function. It looks
      pretty simple.

      Try him at: Dept of Geography, San Diego State Uni, San Diego,
      CA92118-4493, USA. email arthur.getis@....
      -----------------------------------------------------------------------
      From: Justin_Quirouette@...

      Have you considered the CrimeStat application available @
      http://www.icpsr.umich.edu/NACJD/crimestat.html

      Hope this helps,
      Justin
      -----------------------------------------------------------------------
      From: Norm Finkelstein <finkelst@...>

      The short answer is S-PLUS software with its S-Plus Spatial Stats
      module.

      Two more points:

      1) if you just might have to work with non-rectangular bounding
      region(s);
      2) if you want to analyse the processes both in time and space,

      it would be a good idea to obtain an S-PLUS' library of functions called
      SPLANCS from Lancaster U. in the UK.

      I have referred a couple of researchers to that URL in the last couple
      of
      years and they seemed to be pleased with SPLANCS' capabilities, as am I.
      I am including below their summaries to the list on the subject (they
      contain the URL) in lieu my directions and descriptions anew.

      Best of luck,
      -----------------------------------------------------------------------
      From: Lisa Cuthbertson <lcuthber@...>

      John Brzustowski at the University of Alberta (Edmonton, Canada) has
      written a program called Potemkin that has Ripley's K (univariate and
      bivariate
      point patterns) within it. He uses Haase's edge correction (1995) and
      I think you
      can choose the wrap around edge correction as well. John has many other
      programs that may be useful and if you do a search for John
      Brzustowski's
      Programs you should find the page. I copied some of the potemkin page
      (see
      below). I hope this helps.

      Potemkin, very preliminary, is a front end for making command line
      programs
      look prettier to the user under Win95.

      It currently has a simple table-editor that reads and writes
      TAB-delimited
      text, and allows you to glue several files together, as well as to
      selectively hide rows and/or columns. The data visible in the table can
      be
      saved, or sent to other programs, whose output appears in a window.

      Current features:

      calculate distances and perform clustering between rows or columns of a
      table merge rows or columns that have the same values in certain cells
      e.g. merge
      all rows having the same values in columns 1 and 2. Merged values can be
      the sum, mean, min, or max of the values in the merged columns or rows.
      export data in Cornell condensed format, suitable for either Canoco or
      Twinspan. compute Ripley's K(t) index of spatial point pattern variance

      More to come...
      Potemkin is free software. You can download the self-extracting
      executable
      from: ftp://www.biology.ualberta.ca/pub/jbrzusto/potemkin/potzip.exe

      To install it, create a new directory where you want to store the
      program,
      put potzip.exe in it, and run it there. Once it has extracted itself,
      you
      can delete potzip.exe To run the program, execute potemkin.exe

      Source code (for Borland C++ Builder) is available in
      ftp://www.biology.ualberta.ca/pub/jbrzusto/potemkin/potsrc.zip

      Please send any feedback to John Brzustowski at
      jbrzusto@.... There are more free programs at
      http://www.biology.ualberta.ca/jbrzusto

      This http link doesn't work so you'll have to do a search for John B
      like I
      said above!

      Hope this helps!
      -----------------------------------------------------------------------
      From: Søren Ring Ibsen <SOERENRI@...>

      Hello Martin Biland

      What a coincidense - I'm looking for the same thing, that is a user
      friendly free Software for calculating Ripsleys K-function. Please let
      me
      know if you find any useable solution. I will of course tell you if I
      find
      some.

      Are you doing semivariance analysis on your tree-coordinate data as
      well?

      If yes - then have a look at:
      http://www.metla.fi/silvafennica/SF-Abstracts/sa302315.htm
      <http://www.metla.fi/silvafennica/SF-Abstracts/sa302315.htm>

      Here is some of it:

      "Silva Fennica abstract

      Kuuluvainen, T., Penttinen, A., Leinonen, K. & Nygren, M. 1996.
      Statistical
      opportunities for
      comparing stand structural heterogeneity in managed and primeval
      forests:
      An
      example from
      boreal spruce forest in southern Finland. Silva Fennica 30(2-3):
      315-328.

      The horizontal and vertical stand structure of living trees was
      examined in a managed and in a primeval spruce-dominated forest in
      southern
      Finland. Tree size distributions (DBHs, tree heights) were compared
      using
      frequency histograms. The vertical distribution of tree heights was
      illustrated as tree height plots and quantified as the tree height
      diversity
      (THD) using the Shannon-Weaver formula. The horizontal spatial pattern
      of
      trees was described with stem maps and quantified with Ripley's
      K-function.
      The spatial autocorrelation of tree sizes was examined with
      semivariogram
      analysis. In the managed forest the DBH and height distributions of
      trees
      were bimodal, indicating a two-layered vertical structure with a single
      dominant tree layer and abundant regeneration in the understory......."


      Best regards
      -----------------------------------------------------------------------
      From: "Gaston Pezzuchi" <gpezzuchi@...>

      I would suggest you try to use the CrimeStat Software available at:
      www.icpsr.umich.edu/NACJD/Crimestat.html

      It is a really great program if you wish to perform spatial statistical
      analysis of point incidents...

      The Ripley's K function can be easily calculated and it works great with
      most of GIS packages....

      On the Other hand its manual is really impressive and self explanatory

      hope it helps
      -----------------------------------------------------------------------
      From: Martin Béland <Martin.Beland@...>
      To: jbrzusto@..., jbrzusto@...

      Dear Mr Brzustowski,

      I have downloaded your software called Potemkin from
      ftp://www.biology.ualberta.ca/pub/jbrzusto/potemkin/potzip.exe. I have
      succeeded in importing my data files in the data sheet and tried to
      perform Ripley's K function on xy coordinates. I want to use these
      statistics to study competition in forests stands composed of mixtures
      of jack pine
      and trembling aspen or white birch. The data I have come from square 20
      m by 20 m plots.

      It doesn't seem to work. The message I get in the output window is the
      following:

      > kindex TMP1.$$$ -rb square 20 20 100 0.05
      *** Error:

      I wonder:

      Is the program still under development or is it supposed to be working
      properly?
      Do you have a help file or instructions for use of this software?
      Do you have a description of the edge effect correction used?
      Does the program need decimals to be , or . ?
      How do the species data need to be entered: characters or numerals?
      I guess the units of measurement for xy coordinates and study area size
      don't matter if they are the same?

      Thank you very much in advance for your help.
      -----------------------------------------------------------------------
      From: John Brzustowski <jbrzusto@...>
      Hello, Martin

      > It doesn't seem to work. The message I get in the output window is
      the
      > following:
      >
      > > kindex TMP1.$$$ -rb square 20 20 100 0.05
      > *** Error:

      There may be a problem with the setup. Is potemkin installed in a
      directory called "c:\Potemkin"? Potemkin is not very smart,
      especially about that kind of thing.

      > Is the program still under development or is it supposed to be
      working
      > properly?

      What's there is supposed to work, but I'm not actively developing it -
      I don't use Windows any more. I will try to fix bugs, though.

      > Do you have a help file or instructions for use of this software?

      Unfortunately not - it was supposed to be fairly straightforward to use,
      but
      that doesn't seem to be the case. There aren't any hidden features or
      options that would affect what you're trying to do.

      > Do you have a description of the edge effect correction used?

      For points too close to the edge for their circular neighbourhood to
      lie entirely within the sampling region, the count of points within
      that neighbourhood is scaled, although in a slightly funny way, by
      circumference rather than area. (e.g. if only half the neighbourhood
      is within the sampling region, the count there gets doubled)
      Here's the math, from the source code (kindex.c):

      The index K(t) is given by:

      A / n * sum (I (u ) / w )
      i,j t ij ij


      where I (x) = 0 if x > t, else 1
      t

      u = distance between points i and j
      ij


      w = fraction of circumference of circle of radius u centred at
      sample
      ij ij

      point i that lies within the sampled region

      see: Andersen, M. (1992) Spatial analysis of two-species
      interactions.
      Oecologia 91:134-140.

      > Does the program need decimals to be , or . ?

      Decimals as '.' e.g. 2.123 2.3451

      > How do the species data need to be entered: characters or numerals?

      Species should be coded as '1' or '2' for the bivariate K function.

      > I guess the units of measurement for xy coordinates and study area
      size
      > don't matter if they are the same?

      The calculations implicitly assume all
      measurements are in comparable units, but it doesn't matter what they
      are. So the unit of area should be the square of the unit of length.
      (e.g. m^2 and m)

      >
      > Thank you very much in advance for your help.
      >

      Il n'y pas de quoi. Tant que j'espère que ce logiciel vous soit util,
      je suis de l'avis que vous auriez plus de succès en utilisant le
      language "R", un logiciel libre/gratuit qui remplace "S+". Il y a
      dedans un ensemble de statistiques spatiales, où se trouve la fonction
      "K"
      de
      Ripley, parmi d'autres.

      Si ça vous intéresse, "R" se trouve ici:

      ftp://sunsite.ualberta.ca/pub/Mirror/CRAN/bin/windows

      Bien sûr, ça n'a pas l'aire aussi amicable que Potemkin, mais c'est un
      vrai ensemble de logiciels pour statistiques, utilisé partout, et vaut
      bien la peine d'apprendre (je m'excuse si je vous raconte des choses
      bien connues!)

      Bonne chance!
      -----------------------------------------------------------------------
      Hello John,

      Thanks for your prompt answer!! Don't worry, you are telling me nothing
      I already knew!

      After moving the program to the root of C:, it seems to work! However I
      still have two questions for you:

      First, after running the program with some of my data, I am surprised to
      see values of K(t) that are very high. From the readings I have done in
      the literature, I thought that K(t) should have a max value of 1?

      Secondly, I thought that bivariate analysis of interaction between
      species 1 and 2 should be the same as that of interaction between
      species 2 and 1. The output given by potemkin for the bivariate analysis
      includes K1,1 K1,2 K2,1 and K2,2. The values for K1,2 and K2,1 for short
      values of t are the same but as t increases, K2,1 becomes larger that
      K1,2. The confidance intervals are different from the beginning.

      I would greatly appreciate your help on these two questions.

      -----------------------------------------------------------------------
      Martin Béland
      Université du Québec en Abitibi-Témiscamingue
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