Mathematical ecologists have tools for testing if individuals in a
population is dispersed without regard to their neighbors ('randomly') or
according to some other law.  A useful source is

Pielou, E.C. (1977) Mathematical ecology (Wiley and Sons, New York).

Most of it addresses 2-D distributions, but one test for randomness
ought to apply: if you count the number of neighbors within a fixed radius
of  individuals, that number should be Poisson-distributed.  I don't have the
original e-mail query but I the polynomial in question might be an
approximation for the Poisson distribution.

        Another convenient measure is the incidence of no neighbors in this
radius.  In an act of shameless self-promotion, I feel compelled to
cite one particularly insightful paper:

Wang, S.S.-H. and S.H. Thompson (1992) A-type potassium channel
clusters revealed using a new statistical analysis of loose patch data.
Biophys. J. 63:1018-1025.

This paper covers the cases of evaluating data with varying sample area and
clustered distributions.

Sam Wang

At 09:09 AM 2/19/97, you wrote:
>> In an aricle entitled: Cell cycle-dependent distribution of telemeres,
>> centromeres, and chromosome-specific subsatelitte domains in the
>> interphase nucleus of mouse lymphocytes (Exp.Cell Res. 205p142-151,1993)
>> Claire Vourc'h, Domenica Taruscio, Ann Boyle and David Ward quoted a
>> formule for the calculation of the distribution of two random signals in a
>> sphere with diameter 1.
>> ....
>> I suppose the r2 etc. are exponents, but is there anybody here who can
>> explain the basics of the formule or where we can find more about it.
>
>Recently, I started a short study on the theory of nearest neighbours
>(of differtent colours). Distances between nearest neighbours are
>measured to test if a single population is distributed randomly (e.g.
>trees in a forrest). I have found something in these books:
>
>*Quantitative Stereology, Ervin E. Underwood, 1970, Addison Wesley
>  Publishing Company.
>*Stochastic Geometry and its applications, D. Stoyan, Kendall and Mecke,
>  1987, John Wiley and Sons. (not a very clear story; distance
>  measurement as a stochastic test).
>
>Erik Manders
>CRC Nuclear Structure and Function Group
>Sir William Dunn School of Pathology
>Oxford University
>South Parks Road, Oxford OX1 3RE, UK
>Tel: (+44/0) 1865 275529 (/275500)
>Fax: (+44/0) 1865 275501
>E-Mail: [log in to unmask]