In breeding, Optimal Contribution Selection (OCS) is one of the most effective strategies to balance short- and long-term genetic responses, by maximizing genetic gain and minimizing global coancestry. Considering genetic diversity in the selection dynamic – through coancestry – is undoubtedly the reason for the success of OCS, as it avoids intial loss of favorable alleles. Originally formulated with the pedigree relationship matrix, global coancestry can nowadays be assessed with one of the possible formulations of the realized genomic relationship matrix. Most formulations were optimized for genomic evaluation, but few for the management of coancestry. We introduce here an alternative formulation specifically developed for Genomic OCS (GOCS), intended to better control heterozygous loci, and thus better account for Mendelian sampling. We simulated a multi-generation breeding program with mate allocation and under GOCS for twenty generations, solved with quadratic programming. With the case study of Populus nigra, we have shown that, although the dynamic was mainly determined by the trade-off between genetic gain and genetic diversity, better formulations of the genomic relationship matrix, especially those fostering individuals carrying multiple heterozygous loci, can lead to better short-term genetic gain and a higher selection plateau.

The entire dataset was simulated with the R script freely available at: https://github.com/mtiret/ocs.git.

Each line corresponds to one generation of a simulation, and successive lines with the same simulation inputs corresponds to one simulation.

Metadata:

- alpha (simulation input): value of the parameter alpha, representing the weight of coancestry compared to that of genetic gain in the OCS equation.

- beta (simulation input): value of the parameter beta, representing the score in the genomic relationship matrix of the relationship Heterozygote x Homozygote.

- gamma (simulation input): unused parameter.

- mate (simulation input): boolean indicating whether the simulation performed mate allocation.

- shuffle (simulation input): boolean indicating whether the dataset was shuffled in order to remove LD.

- gen: the number of generation.

- cgc.p: predicted coancestry with the OCS equation. Generation 0 is filled NA.

- cy.p: predicted genetic gain with the OCS equation. Generation 0 is filled NA.

- cgc.r: realized coancestry.

- cy.r: realized genetic gain.

- mate.gain: gain in terms of coancestry of mate allocation.

- mate.gain.t: gain in terms of true coancestry of mate allocation.

- cgc.t: true coancestry (without considering beta).

- nparent: number of parents selected in the OCS process.

- he: theoretical heterozygosity (2pq).

- ho: theoretical homozygosity (1-2pq).

- vtot: genetic variance.

- vgen: genic variance.

- lal.b: number of benefical allele lost.

- lal.b.effect: total effect of lost benefical alleles.

- lal.d: number of deleterious allele lost.

- lal.d.effect: total effect of lost deleterious alleles.

- gal.b: number of beneficial allele fixed.

- gal.b.effect: total effect of fixed benefical alleles.

- gal.d: number of deleterious allele fixed.

- gal.d.effect: total effect of fixed deleterious alleles.

- ir: inbreeding rate (Falconer, 1996): [ Ho(t+1) - Ho(t) ] / [ 1 - Ho(t) ]

For any additional information, please contact mathieu.tiret@ebc.uu.se or mathieu.y.tiret@gmail.com.