DOI: 10.5061/dryad.0rxwdbs1k
title: How to achieve a higher selection plateau in forest tree breeding? Fostering heterozygote x homozygote relationships in optimal contribution selection in the case study of Populus nigra

description: 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.
description: The entire dataset was simulated with the R script freely
 available at: https://github.com/mtiret/ocs.git.
description: Each line corresponds to one generation of a simulation, and
 successive lines with the same simulation inputs corresponds to one
 simulation. Metadata: -
 <em>alpha</em> (simulation input): value of the parameter
 alpha, representing the weight of coancestry compared to that of genetic
 gain in the OCS equation. - <em>beta</em>
 (simulation input): value of the parameter beta, representing the score in
 the genomic relationship matrix of the relationship Heterozygote x
 Homozygote. - <em>gamma </em>(simulation
 input): unused parameter. <em>- mate
 </em>(simulation input): boolean indicating whether the simulation
 performed mate allocation. <em>- shuffle
 </em>(simulation input): boolean indicating whether the dataset was
 shuffled in order to remove LD. <em>-
 gen</em>: the number of generation. <em>-
 cgc.p</em>: predicted coancestry with the OCS equation. Generation 0
 is filled NA<em>.</em> <em>-
 cy.p</em>: predicted genetic gain with the OCS equation. Generation
 0 is filled NA<em>.</em> <em>-
 cgc.r</em>: realized coancestry. <em>-
 cy.r</em>: realized genetic gain. -
 <em>mate.gain</em>: gain in terms of coancestry of mate
 allocation. <em>- mate.gain.t</em>: gain in
 terms of true coancestry of mate allocation.
 <em>- cgc.t</em>: true coancestry (without
 considering beta). <em>- nparent</em>:
 number of parents selected in the OCS process.
 <em>- he</em>: theoretical heterozygosity
 (2pq). <em>- ho</em>: theoretical
 homozygosity (1-2pq). <em>- vtot</em>:
 genetic variance. <em>- vgen</em>: genic
 variance. <em>- lal.b</em>: number of
 benefical allele lost. <em>-
 lal.b.effect</em>: total effect of lost benefical alleles.
 <em>- lal.d</em>: number of deleterious allele
 lost. <em>- lal.d.effect</em>: total effect
 of lost deleterious alleles. <em>-
 gal.b</em>: number of beneficial allele fixed.
 <em>- gal.b.effect</em>: total effect of fixed
 benefical alleles. <em>- gal.d</em>: number
 of deleterious allele fixed. <em>-
 gal.d.effect</em>: total effect of fixed deleterious
 alleles. <em>- ir</em>: 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.