Email updates

Keep up to date with the latest news and content from Genetics Selection Evolution and BioMed Central.

Open Access Open Badges Research

An indirect approach to the extensive calculation of relationship coefficients

Jean-Jacques Colleau

Author Affiliations

Station de génétique quantitative et appliquée, Institut national de la recherche agronomique, 78352 Jouy-en-Josas Cedex, France

Genetics Selection Evolution 2002, 34:409-421  doi:10.1186/1297-9686-34-4-409

The electronic version of this article is the complete one and can be found online at:

Received:12 July 2001
Accepted:25 January 2002
Published:15 July 2002

© 2002 INRA, EDP Sciences


A method was described for calculating population statistics on relationship coefficients without using corresponding individual data. It relied on the structure of the inverse of the numerator relationship matrix between individuals under investigation and ancestors. Computation times were observed on simulated populations and were compared to those incurred with a conventional direct approach. The indirect approach turned out to be very efficient for multiplying the relationship matrix corresponding to planned matings (full design) by any vector. Efficiency was generally still good or very good for calculating statistics on these simulated populations. An extreme implementation of the method is the calculation of inbreeding coefficients themselves. Relative performances of the indirect method were good except when many full-sibs during many generations existed in the population.

relationship coefficient; inbreeding coefficient; pedigree


(To access the full article, please see PDF)