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GEOSTATS: Bivariate Ripley's K

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  • Martin Béland
    Dear all, 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
    Message 1 of 1 , Apr 5, 2000
      Dear all,

      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:
      > 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
      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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