🚀 go-pugleaf

Hi everybody,

 I'm writing up a "D.Phil." in Zoology here at Oxford and I'm stuck with the
following stat problem about chromosomes that join together. 

The background:
1) mice have usually 2n=40 (which means 20 pairs of chromosomes)
   -> these chromosomes look [schematically] like this:

          *
      a  / \

2) some populations 'fuse' the chromosomes of two pairs 
   -> looks like this and is written as Rb(a.b) 

     a   \ /          Rb = Robertsonian fusion or centric translocation
          %           % = **, but now they segregate as one chromosome
     b   / \

3) a maximum of 9 fusions (2n=22) is known from some populations
  (leaving one pair and the sex chromosomes unfused)
  
    ex: Rb(a.b), (c.d), (e.f), (g.h), (i.j), (k.l), (m.n), (o.p), (q.r)
        with s,t, X,Y unfused

4) the same chromosome combination can be found in mice with 1 fusion (2n=38)
   or mice with more fusions (2n=36-22)
 
     ex: 2n=34; Rb(a.b), (c.d), (e.f) 
         2n=26; Rb(a.s), (c.t), (e.f), (g.h), (i.j), (k.l), (m.n)
                                ^^^^^
5) fusions are not independent, because they are sampled without replacement 
   from the initial pool (N) of 20 different chromosomes; this reduces the 
   number of free partners after each subsequent fusion
    -> the number of different combinations [written C(N,k)] for a chromosome 
       set with a given number of fusions (k) is thus

                          N!
         C(N,k) =  ------------------          k=1,2,...9
                   2^k * k! * (N-2k)!

The question: How to test for random association given that the probability of
a fusion in a certain context should be quite different? (Some people think
that I should just take  1/C(N,2) as the expected value, but I believe they are
wrong). Furthermore, because I may not be absolutely sure about the sequence of
fusions in a particular population, is there any other way to test for random
association here? Does somebody know about analogue systems (lottery?) and
point out where the solution may have been published? Or is this a totally 
uncommon and 'desperate' situation?

Thanks for any hint!
     Roland                                             [rhubner@ox.path.ac.uk]


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            * Roland Huebner, Dept. Zoology, Univ. Oxford *
            * South Parks Road, OX1 3PS, Oxford, England  *
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