The partial inbreeding coefficient is the
probability that an individual is homozygous (identical
by descent) for an allele descended from the specified founder.
The sum, across all founders, of the partial inbreeding
coefficients for a descendant is equal to the inbreeding
coefficient for that individual.

Partial inbreeding coefficients can be determined by using
a modification of the additive matrix method for calculating
inbreeding coefficients. Let Xi designate the inbreeding of
descendant i attributed to founder x, and fij be the
kinship between i and j. The kinship of founder x (for
whose descendants we desire to calculate the partial
inbreeding coefficients) to itself is assigned fxx = 0.5.
The kinships of each other founder (y not equal to x)
to all individuals (i) in the pedigree are assigned
fyi = 0. The kinship of a descendant (i) to each prior
individual (j < i) in the pedigree is given by fij =
0.5(fmj + fpj), in which m and p are the parents of i.
The kinship of a descendant (i) to itself is assigned
fii = 0.5 fmp + fxi. (The term fxi replaces an 0.5
which appears in calculations of full inbreeding
coefficients.) The partial inbreeding coefficient with
respect to founder x of each descendant i (with parents
m and p) is then given by Xi = fmp. A computer program
(PARTINBR, written in C and compiled for computers running
MS-DOS) which calculates inbreeding coefficients and partial
inbreeding coefficients for any arbitrary pedigree is
available on the internet at
http://www.vortex9.org/partinbr.html.