My objective is to be able to rapidly compute the condensed identity coefficients for many pairs of individuals within a very large, complex pedigree. In fact, computation of the identity coefficients is not done directly, but rather as the final step after computing a set of generalized kinship coefficients. Recursive algorithms for doing this have been known for some time (e.g. Karigl 1981, also take a look at Ken Lange’s (2002) book for other references and a good description of generalized kinship coefficients and identity coefficients), but they can take impractical amounts of time when applied to very large pedigrees, particularly when coefficients are desired for many pairs of individuals.

I have previously (Abney et al. 2000) implemented Karigl’s algorithms with a hashing scheme to allow fast recall of previously computed values. This can still take a long time and, in at least some circumstances, is not practical. The basic problem is that each generalized kinship coefficient requires a separate recursion through the pedigree, which can be very time consuming if the pedigree is very deep. Now, what I have done is to devise a novel algorithm that requires only a single recursion through the pedigree. I have also completely re-implemented the hashing algorithm to be significantly more efficient. These improvements greatly enhance the speed of computing the coefficients. The paper describing the new algorithms are not yet published, but in the mean time feel free to download the software. Citation information for the new method will appear here when it is available.


Abney M, McPeek MS, Ober C (2000) Estimation of variance components of quantitative traits in inbred populations. Am J Hum Genet 66:629–650

Lange K (2002) Mathematical and Statistical Methods for Genetic Analysis. Springer-Verlag, NY.

Karigl G (1981) A recursive algorithm for the calculation of identity coefficients. Ann Hum Genet 45:299–305

Updated: July 3, 2007