This question is only slightly related to bio-software but...
In 1984, G. Wagner published a paper on the eigenvalue distribution of genetic
covariance matrices in order to compare random matrices with observed matrices
(to quantify morphological integration). Random covariance matrics were
calculated from a matrix of developmental parameters describing the effects of
m loci on p characters. Wagner gave the expected values of Cheverud et al.
(1983) Index of morphological integration, I, with m = p and m = 2*p. The
expected value of I with m=p was quite high and Wagner concluded that
integration in mammals (as calculated by the index) was not significantly
different from random and that integration in insects was LESS than randomly
integrated (I have not been able to repeat this, however). Of course if m>>p
then integration in both mammals and insects would probably be significant.
It seems that p characters would have >>p loci that contribute variance to the
characters (i.e. m>>p), although this would certainly depend on the characters
chosen. I know there is literature on the number of loci that contribute
variance to a single character but what about literature on the number of loci
that contribute to p characters? Is there any evidence that m>>p? would m/p
decrease with increasing p?
Jeff Walker
SUNY at Stony Brook