Free Access
Genet. Sel. Evol.
Volume 38, Number 2, March-April 2006
Page(s) 127 - 146
Published online 24 February 2006
Genet. Sel. Evol. 38 (2006) 127-146
DOI: 10.1051/gse:2005032

Prediction of genetic gain from quadratic optimisation with constrained rates of inbreeding

Beatriz Villanuevaa, Santiago Avendañoa and John A. Woolliamsb

a  Scottish Agricultural College, West Mains Road, Edinburgh, EH9 3JG, Scotland, UK
b  Roslin Institute (Edinburgh), Roslin, Midlothian, EH25 9PS, UK

(Received 11 April 2005; accepted 7 October 2005 ; published online 24 February 2006)

Abstract - There are selection methods available that allow the optimisation of genetic contributions of selection candidates for maximising the rate of genetic gain while restricting the rate of inbreeding. These methods imply selection on quadratic indices as the selection merit of a particular individual is a quadratic function of its estimated breeding value. This study provides deterministic predictions of genetic gain from selection on quadratic indices for a given set of resources (the number of candidates), heritability, and target rate of inbreeding. The rate of gain was obtained as a function of the accuracy of the Mendelian sampling term at the time of convergence of long-term contributions of selected candidates and the theoretical ideal rate of gain for a given rate of inbreeding after an exact allocation of long-term contributions to Mendelian sampling terms. The expected benefits from quadratic indices over traditional linear indices (i.e. truncation selection), both using BLUP breeding values, were quantified. The results clearly indicate higher gains from quadratic optimisation than from truncation selection. With constant rate of inbreeding and number of candidates, the benefits were generally largest for intermediate heritabilities but evident over the entire range. The advantage of quadratic indices was not highly sensitive to the rate of inbreeding for the constraints considered.

Key words: prediction of genetic gain / quadratic indices / control of inbreeding / genetic contributions

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© INRA, EDP Sciences 2006