to check if a group of values is randomly distributed

elaine kuo <elaine.kuo.tw <at> gmail.com> writes:

Dear list,

I have 603 numbers depicting range sizes of birds in Japan.
I would like to learn if the 603 range sizes are randomly distributed or
not, in order to check if they meet mid-domain effects.

Please kindly advise if any R package or function can check the fit.
Also, any more references are highly appreciated.
Thank you

If you are really interested in mid-domain effects in ecology,
there is a whole literature on the proper way to do randomization
tests -- generally different variants of placing the observed ranges
randomly within a specified domain with the constraint that the
entire range must fall within the domain, then computing something
about the spatial distribution of range densities (i.e. number of
coincident ranges at a particular point, or local diversity).
I wrote stuff like this for a special case (turtle nesting ranges)
a long time ago, but the code is probably several computer systems
ago and unretrievable.  You might try a query on the r-sig-ecology
list.  For references, just try searching "mid-domain effect"
or "mid-domain hypothesis" -- Colwell and Gotelli have done a lot
in this area.
  Not in R, but googling finds this:
<http://viceroy.eeb.uconn.edu/RangeModelPages/MDEReferences.htm>
   Other than that, "are the range sizes randomly distributed"
is a fairly poorly posed question -- they fit *some* distribution.
Your question above is different from the typical mid-domain hypothesis
question, which is about the arrangement of ranges rather than
their distribution of sizes.

  Ben Bolker