[R-sig-Geo] Characterizing the position (central vs peripheral) of a point in a point pattern

[Adrian.Baddeley at csiro.au]

Alexandre VILLERS alexandre.villers at cebc.cnrs.fr<mailto:alexandre.villers at cebc.cnrs.fr> wrote:
> I would like to characterize the position of  a given nest in a
> population of breeding birds. Does anyone know a statisitics (and
> associated R package) that could objectively tell whether a nest has a
> central or peripheral location ? It also needs to be density independent
> (not affected by sample size)

There are many ways of doing this. A pivotal question is: what do you want to happen
in the situation where the majority of birds cluster around the edge of the spatial domain,
or where the majority of bords cluster in the middle of the domain.
For example, suppose most birds prefer to nest close to the edge of a rocky island. Where should we draw the 50/50 line (i.e. where nests are neither central nor peripheral)? Is it (a)  through the middle of the island, halfway between the centre and the periphery of the rookery? or (b) through the middle of the population, with 50% of the nests on one side and 50% on the other side?

If the answer is (a) then you could simply measure distances. In the 'spatstat' package for example, if X is a point pattern of birds' nests,
               B <- ripras(X)
               C <- centroid.owin(B)
               DB <- distmap(as.psp(B))
               DC <- distmap(as.ppp(C, B))
               value <- DC[X]/(DC[X] + DB[X])
Then 'value' is a fraction that equals 0 at the centroid, 1 at the boundary, and 0.5 halfway between.

If the answer is (b) then you probably need to use quantiles of the distances.

               B <- ripras(X)
               DB <- distmap(as.psp(B))
               value <- rank(DB[X])/X$n

then 'value' is a fraction that approaches 1 for nests close to the boundary, approaches 0 for nests furthest from the boundary, and 0.5 for a nest which is closer to the boundary than 50% of the other nests, and further from the boundary than 50% of other nests.

Adrian Baddeley