[R] Distance between sets of points in transformed environmental space

[Corrado]

Dear friends,

I have several sets of points in a transformed environmental space. Each set 
of points can be represented as a cloud in the environmental space.

This space is spanned by n coordinates, corresponding to the first n PCs of 36 
PCs of some environmental variables (12 monthly minimum temperatures, 12 
monthly maximum temperature, 12 monthly precipitations).

I would like to calculate a "distance" or dissimilarity between each pair of 
sets of points.

Let's label two of those sets as X,Y, where x is in X and y is in Y. We are 
interested in defining a distance between X and Y. I have thought of using the 
following:

1) The Euclidean distance between the centroids of X and Y. Simple and 
effective but does not give much real information on the actual degree of 
overlapping.
2) The median of the all the distances between all pairs of points (x,y). Same 
problem as (1), partially resolved.
3) The proportion of points of X U Y which fall outside the intersection of 
the convex or concave hulls (defined with a smoothing parameter) of X and Y, 
i.e. C(X) intersect C(Y). Very complicated, and does not necessarily lead to

What do you think? Are there any other approaches worth considering?  

Kind Regards
-- 
Corrado Topi

Global Climate Change & Biodiversity Indicators
Area 18,Department of Biology
University of York, York, YO10 5YW, UK
Phone: + 44 (0) 1904 328645, E-mail: ct529 at york.ac.uk