In the paper entitled "Hierarchical analysis of inbreeding

depression in Peromyscus polionotus" (R. C. Lacy, G. Alaks,

and A. Walsh. 1996. Evolution 50:2187-2200), the method

for calculating partial inbreeding coefficients was

incompletely described. The calculations performed for the

analyses presented in the paper were done correctly,

however. 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, and this is the step that was omitted

in the paper.) 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.vortex10.org/PMx.html.

I am grateful to Miguel Angel Toro Ibanez for notifying

me that the method given in the paper was not correct.

I regret any inconvenience this may have caused to those

using this approach.

Sincerely,

Robert C. Lacy

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