statistics for recombinant inbred strains

Ken Manly cammanly at
Thu Dec 24 09:42:00 EST 1992

Recombinant inbred (RI) strains are sets of organisms which have been
derived by inbreeding F2 progeny from a cross of two inbred strains.  For
RI strains of mice, which are created by sib-mating, Haldane and Waddington
showed that

r = R/(4-6R)

where r is the estimated probability of recombination between two Mendelian
loci and R is the proportion of RI strains which are recombinant for those
loci.  For RI strains of plants, which are created by self-pollination,
Haldane and Waddington showed that

r = R/(2-2R)

Green showed that, for RI strains of mice, the variance of r is given by

v = r(1+2r)(1+6r)^2/4N

where v is the estimated variance, N is the number of strains in the set,
and ^ indicates exponentiation.

By analogy with Green's derivation, I find that the variance of r for selfed
RI strains is given by

v = r(1+2r)^2/2N

I'm sure I am not the first to derive this formula.  However, not being a
plant geneticist and not having easy access to most of the plant genetics
literature, I don't know how to find who did derive it.  Can anyone help
me with a reference?

Ken Manly
cammanly at
kmanly at

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