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

From: Martin Béland (
Date: Mon Mar 27 2000 - 22:45:05 MET DST

<x-charset iso-8859-1>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):
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

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.
> Suggest two people to contact: Dr. S. Titus or/and Dr. Stan Navratil
> at University of Alberta in Edmonton).
From: "Norm Cimon" <>
Have you thought of nearest neighbor analysis? One way to examine the
potential competition would be look at the variations in clustering
the different species. Nearest neighbor techniques determine whether or
not a distribution pattern is random, and there are computer programs in
public domain to perform the computations. For more information,
contact Andy Younblood (ayounbl/
From: Jacques_Begin <>
Salut Martin. Je te suggere de parler a Kim Lowell ou a Geoffrey
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 <>
A couple of years ago I did some work on inter tree competition. I used
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,
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
and you can select out what you need.

The BUFFER command identifies a zone of a specified width around a
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
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
then clip this buffer out of the stand map. This gave me a sample of
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 ( Je vous acompagne une page web avec
laquel vous pouvez decider si ça c'est d'interest pour vous.
Merci bien
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
web site and possibly freeware. Good luck.
From: "West Family" <>
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 <>
Moeur, M. 1993. Characterizing spatial patterns of trees using
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/>
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 <>
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

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 <>
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

-> They should soon be integrated in a new module in ADS...
From: Martin Béland <>


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 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

Any help would be appreciated.
From: Baz <>
 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
yourself. Its in fortran.

 Download the unix source code release from:
From: Roger Bivand <>

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

This is a library of functions for S-Plus, including both the ones you
need. I have made a port for R (see for

The "spatial" library by Venables and Ripley (the same Ripley),
the single pattern K measure, is part of the VR bundle for both S-Plus
From: "Russell 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

Have you considered the CrimeStat application available @

Hope this helps,
From: Norm Finkelstein <finkelst@columbus.geography.McMaster.CA>

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

Two more points:

1) if you just might have to work with non-rectangular bounding
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
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 <>

John Brzustowski at the University of Alberta (Edmonton, Canada) has
written a program called Potemkin that has Ripley's K (univariate and
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
Programs you should find the page. I copied some of the potemkin page
below). I hope this helps.

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

It currently has a simple table-editor that reads and writes
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
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

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

Source code (for Borland C++ Builder) is available in

Please send any feedback to John Brzustowski at There are more free programs at

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@BOT.KU.DK>

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
know if you find any useable solution. I will of course tell you if I

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

If yes - then have a look at:

Here is some of it:

"Silva Fennica abstract

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

     The horizontal and vertical stand structure of living trees was
examined in a managed and in a primeval spruce-dominated forest in
Finland. Tree size distributions (DBHs, tree heights) were compared
frequency histograms. The vertical distribution of tree heights was
illustrated as tree height plots and quantified as the tree height
(THD) using the Shannon-Weaver formula. The horizontal spatial pattern
trees was described with stem maps and quantified with Ripley's
The spatial autocorrelation of tree sizes was examined with
analysis. In the managed forest the DBH and height distributions of
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" <>

I would suggest you try to use the CrimeStat Software available at:
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 <>

Dear Mr Brzustowski,

I have downloaded your software called Potemkin from 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

> 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
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 <>
Hello, Martin

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

   u = distance between points i and j

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

   point i that lies within the sampled region

   see: Andersen, M. (1992) Spatial analysis of two-species
   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
> 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
Ripley, parmi d'autres.

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

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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