[R-sig-Geo] help with multivariate pt pattern analysis

[Robin W Hunnewell]

Dear list,

Is there a way to perform kernel density estimation on a density surface of spatial polygon objects, obtaining an estimate of the # of polygons contributing to the intensity of a spatial process? The polygons would be narrow zig-zag strips that -- taken together -- overlap within and constitute a composite search region; each one the realization of an aerial line transect survey that followed an idealized zig-zag transect layout.

Further to this query, I've hit a wall with thinking about how to handle some potentially unusual pt pattern data; hope it's okay to post a spatial stats methodology question here as well -- need help! 

I have multivariate pt pattern data consisting of seabird flock locations observed during repeat aerial surveys. The data consist of flock locations (w/ marks) from ~30 line transect flights that used the same zig-zag transect layout. The flights followed the layout each time, but mapped together they do vary spatially about the idealized path -- so I have a set of polylines from which I created spatial polygon objects that correspond to the region of sea overflown on each flight. The flightpaths therefore are interwoven and occur (with varying intensity) in a composite search window, which is zig-zag shaped and constitutes a sizable buffer to the idealized transect layout. Hope this is clear.

I'm interested to investigate flock pt pattern data with the type of 'further methods for point patterns' outlined in Bailey & Gatrell (1995), i.e., analysis of multiple types of events and correcting for spatial variation in distribution of a 'background population.'

I'd like to examine flock pt patterns taken together, through time, and explore potential interactions/relationships between different types of flock events in the overall pattern. I'm interested to see if flock patterns from one survey to next exhibit independence: I'm reasonably confident they do, but want to test for this  -- following methods outlined in Bailey&Gatrell.
I have a few hypotheses of clustering that are of interest, but comparison with CSR is not meaningful as the intensity of flocks is expected to vary with a 'background population' -- varying density surface of aerial coverage itself; the flightpaths from which my flock sightings can be said to 'arise' on any given survey occasion. I think I need is to adjust for this heterogeneity in order to detect any additional spatial structure that flock events might display over and above non-homogeneous distribution of aerial coverage itself.

Bailey& Gatrell discuss ways to adjust for an obvious covariate which is known to affect the rate at which events of interest occur, since otherwise - any patterns in event distribution may be obscured/eclipsed by spatial variation in the underlying covariate itself. One method they suggest is taking a ratio of kernel estimates for the intensity of events and population density respectively, thus obtaining an adjusted estimate of the intensity of events on that basis. Hence my kernel estimation question above relating to polygon objects.
This way of correcting for a 'population at risk' applies in epidemiology, but Please can anyone comment as to the validity of using this approach in a flock event/flightpaths setting? 

Thanks very much in advance,
Robin

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Robin Hunnewell
University of New Brunswick
Fredericton, NB  
Canada 

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