# Re: Potemkin

From: Martin Béland (Martin.Beland@uqat.uquebec.ca)
Date: Wed Mar 29 2000 - 21:48:14 MET DST

<x-charset iso-8859-1>Dear netters,

I recently posted a summary of questions and responses about analyses of
point patterns to study competition in mixed jack pine stands. Here is
one more question that arose from running the software called
"Potempkin" to compute intertype Ripley's K(d) analysis :

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 d are
the same but as d increases, K2,1 becomes larger that K1,2. The
confidance intervals are different from the beginning. How do you
explain this?

To this, John Brzustowski, the author of the programm replied to me

> Good question. I don't seem to have a paper describing the bivariate
> K here, but what I think is happening is this:
> The obvious definition for bivariate K(t) would be the proportion of
> pairs of individuals, the first of species 1, the second of species 2,
> that lie within a distance t or less of each other. That would give a
> symmetric definition. But I think Ripley does this a bit differently:
> K1,2 (t) is the average, over all individuals in species 1, of the
> proportion of species 2 neighbours that are within distance t of the
> individual in species 1. This is a bit tricky, but it just amounts to
> weighting the pairs differently in each case. I suppose an advantage
> of this approach is it should allow one to detect attraction of
> species 1 by species 2, as opposed to the other way around. Maybe.
>

Does any of you know:
1- if other software compute the bivariate K(t) in a different way that
use a symmetric definition of the interaction? and
2- if there is no other way to compute the bivariate K(t), how do you
suggest the result must be interpreted, that is, which of K1,2 or K2,1
must be used in which situation?

Any help would be appreciated,

Martin Béland, biologiste, Ph.D. Env.
Unité de recherche et de développement forestiers de
l'Abitibi-Témiscamingue
Université du Québec en Abitibi-Témiscamingue
445, boulevard Université
Rouyn-Noranda (Québec) J9X 5E4
Téléphone : (819) 762-0971 #2458
Fax : (819) 797-4727
Courriel : martin.beland@uqat.uquebec.ca

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