[R-sig-Geo] Fwd: Conceptual Question about using bivariate second order function

[Rolf Turner]

On 15/03/14 01:45, Felipe Sodre Barros wrote:

> I have some questions that are more conceptual of the use of k-function,
> than a doubt of how to use it. So, I would like to know if any of you could
> help:
> I want to assess if the fires (mapped as a point) registered during the
> year of 2013 had the tendency of occur next to the occurences of a certain
> species (mapped as a point, too), and so  infer whether the fire is a
> threat or not.
> I've been studying the analysis of point processes and thought that I could
> use the bivarite K-function, but never saw any use of the bivariate
> K-function (or any other second order function) for analysis like this.
>
> So I would like to know if you know any research that already have used a
> second order function for  similar cases? Do you think this use of the
> bivariate second order function for this propose is conceptually
> consistently?
>
> Thanks in advance, and sorry for any english mistakes.

The multitype K function (e.g Kcross() in the spatstat package) will 
provided information about the expected number of points of one type 
within radius "r" of an arbitrary point of another type, for a range of 
values of "r".  This will give some insight as to whether points of type 
"fire" are "attracted to" points of type "species X".

This is probably not a good way of going at the problem however since 
fires and species locations are conceptually very different sorts of 
entity and considering them both to be points of a single pattern, 
distinguished by marks, seems to me to be highly inappropriate.

The way that I would approach the problem is to take the points at which 
the species of interest occur as a "given" and to *MODEL* the intensity 
of the fire pattern using the "species pattern" as a predictor. You 
could form the distance map of the species pattern and use the resulting 
image as a covariate from which to predict the intensity of the fires. 
A first order log-linear model for the intensity could easily be fitted 
using ppm().  There are various ways that non-parametric models could be 
fitted, e.g. using rhohat() or using quadrat counts where the "quadrats" 
are tiles of a tessellation formed in terms of level sets of the 
distance map.

To answer your question about whether any other researchers have used 
the multitype K function to analyse the relationship between points of 
different types:  Yes, I am sure that they have.  That is what the 
multitype K function is for.  See the references given in the help for 
the Kcross() function in spatstat.  Another piece of published research 
that I know of is "Spatial patterns in species-rich sclerophyll 
shrublands of southwestern Australia" by G.L.W. Perry, N.J. Enright, 
B.P. Miller, and B.B. Lamont, Journal of Vegetation Science, Volume 19, 
Issue 5, pages 705–716, October 2008.

However Perry et al. were looking at a pattern consisting of the 
locations of plants of different species, so the points of the marked 
pattern were all of a comparable nature, unlike your situation.

HTH

cheers,

Rolf Turner