I found an answer to my question (pasted below). Andersen(1992) uses an

estimator of K1,2(d) that combines the estimators K1,2 and K2,1 into a

single estimator. This estimator, mentionaed by Lotwick and Silverman

(1983), is the linear combination:

(n2K12(d) + n1K21(d))/(n1 + n2)

where n1 and n2 are the number of type 1 and type 2 events.

I hope this can help others with the same problem.

Martin Béland wrote:>

Martin Béland, biologiste, Ph.D. Env.

> 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,

>

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@...

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