Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học thế giới đề tài: An indirect approach to the extensive calculation of relationship coefficients | 409 Genet Sei. Evol. 34 2002 409-421 INRA EDP Sciences 2002 DOI gse 2002015 Original article 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 Abstract - 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 1. introduction Selection has been very well known to increase inbreeding and relationship coefficients which in turn contribute to the decrease in the ultimate rates of genetic gain after many generations. Consequently many research works have been devoted to dehning selection methods efficient for the long term. For instance procedures have been proposed for maximizing genetic gains with inbreeding rates constrained at desired values 4 8 or alternatively minimizing inbreeding rates with constrained selection differentials 10 . These methods are either analytical . constraint handling through Lagrange multipliers or linear programming 4 11 13 or .
