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<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
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*> K here, but what I think is happening is this:
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*> The obvious definition for bivariate K(t) would be the proportion of
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*> pairs of individuals, the first of species 1, the second of species 2,
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*> that lie within a distance t or less of each other. That would give a
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*> symmetric definition. But I think Ripley does this a bit differently:
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*> K1,2 (t) is the average, over all individuals in species 1, of the
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*> proportion of species 2 neighbours that are within distance t of the
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*> individual in species 1. This is a bit tricky, but it just amounts to
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*> weighting the pairs differently in each case. I suppose an advantage
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*> of this approach is it should allow one to detect attraction of
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*> species 1 by species 2, as opposed to the other way around. Maybe.
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*>
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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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