Free Access
Genet. Sel. Evol.
Volume 34, Number 4, July-August 2002
Page(s) 409 - 421

Genet. Sel. Evol. 34 (2002) 409-421
DOI: 10.1051/gse:2002015

An indirect approach to the extensive calculation of relationship coefficients

Jean-Jacques Colleau

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

(Received 12 July 2001; accepted 25 January 2002)

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.

Key words: relationship coefficient / inbreeding coefficient / pedigree

Correspondence and reprints: Jean-Jacques Colleau

© INRA, EDP Sciences 2002