Free Access
Genet. Sel. Evol.
Volume 37, Number 1, January-February 2005
Page(s) 57 - 81
Genet. Sel. Evol. 37 (2005) 57-81
DOI: 10.1051/gse:2004036

The advantage of factorial mating under selection is uncovered by deterministically predicted rates of inbreeding

Anders Christian Sørensena, b, c, Peer Bergb and John A. Woolliamsa

a  Roslin Institute (Edinburgh), Roslin, Midlothian, EH25 9PS, UK
b  Department of Animal Breeding and Genetics, Danish Institute of Agricultural Science, PO Box 50, 8830 Tjele, Denmark
c  Department of Large Animal Sciences, Royal Veterinary and Agricultural University, Ridebanevej 12, 1870 Frederiksberg C, Denmark

(Received 14 October 2003; accepted 18 August 2004)

Abstract - Rates of inbreeding ( $\Delta F$) in selected populations were predicted using the framework of long-term genetic contributions and validated against stochastic simulations. Deterministic predictions decomposed $\Delta F$ into four components due to: finite population size, directional selection, covariance of genetic contribution of mates, and deviation of variance of family size from that expected from a Poisson distribution. Factorial (FM) and hierarchical (HM) mating systems were compared under mass and sib-index selection. Prediction errors were in most cases for $\Delta F$ less than 10% and for rate of gain less than 5%. $\Delta F$ was higher with index than mass selection. $\Delta F$ was lower with FM than HM in all cases except random selection. FM reduced the variance of the average breeding value of the mates of an individual. This reduced the impact of the covariance of contributions of mates on $\Delta F$. Thus, contributions of mates were less correlated with FM than HM, causing smaller deviations of converged contributions from the optimum contributions. With index selection, FM also caused a smaller variance of number of offspring selected from each parent. This reduced variance of family size reduced $\Delta F$ further. FM increases the flexibility in breeding schemes for achieving the optimum genetic contributions.

Key words: mating system / inbreeding / selection / prediction / genetic contribution

Correspondence and reprints:

© INRA, EDP Sciences 2004