A fast Newton-Raphson based iterative algorithm for large scale optimal contribution selection

Abstract

Background: The management of genetic variation in a breeding scheme relies very much on the control of the average relationship between selected parents. Optimum contribution selection is a method that seeks the optimum way to select for genetic improvement while controlling the rate of inbreeding.

Methods: A novel iterative algorithm, Gencont2, for calculating optimum genetic contributions was developed. It was validated by comparing it with a previous program, Gencont, on three datasets that were obtained from practical breeding programs in three species (cattle, pig and sheep). The number of selection candidates was 2929, 3907 and 6875 for the pig, cattle and sheep datasets, respectively.

Results: In most cases, both algorithms selected the same candidates and led to very similar results with respect to genetic gain for the cattle and pig datasets. In cases, where the number of animals to select varied, the contributions of the additional selected candidates ranged from 0.006 to 0.08 %. The correlations between assigned contributions were very close to 1 in all cases; however, the iterative algorithm decreased the computation time considerably by 90 to 93 % (13 to 22 times faster) compared to Gencont. For the sheep dataset, only results from the iterative algorithm are reported because Gencont could not handle a large number of selection candidates.

Conclusions: Thus, the new iterative algorithm provides an interesting alternative for the practical implementation of optimal contribution selection on a large scale in order to manage inbreeding and increase the sustainability of animal breeding programs.

Fig. 1

Association between EBV and optimized genetic contribution for the selected candidates in the cattle dataset by applying two levels of constraints on rate of inbreeding $(\mathrm{\Delta }F)$). $\mathrm{\Delta }G$ = genetic gain

Fig. 2

Pedigree structure for the example data. The values in brackets are estimated breeding values and the relationships were calculated based on the pedigree (from Pong-Wong and Woolliams [7])