Fernandez, Jesus

Gómez-Romano, Fernando

Pong-Wong, Ricardo

Villanueva, Beatriz

Woolliams, John

English

Optimal contribution methods have proved tobe very efficient for controlling the rate at which coancestryand inbreeding increase and therefore for maintaining geneticdiversity. These methods have usually used pedigreeinformation for estimating expected genetic relationshipsbetween animals. However, the large amount of genomicinformation now available (dense chips containing thousandof SNP markers), provides us with a good opportunity ofobtaining more accurate estimates of relationships. Genomicinformation also permits us now to target specific regions inthe genome where there is an interest in maximising diversity.Using a semidefinite programming optimisation approach,we have investigated the effectiveness of usinggenomic coancestry matrices for controlling the loss ofgenetic variability in specific genomic regions while restrictingthe overall loss in the rest of the genome. The resultsshow that genomic management was very successfulfor avoiding loss of diversity at specific genomic regions(even increased diversity). This management was also successfulin restricting the loss of diversity in the remaininggenome although the realised rate of coancestry resultedhigher than the restriction imposed. There is thus a need ofrefining the theory of genetic contributions when realisedgenomic matrices are used

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     Edinburgh Research Explorer                                      The use of genomic coancestry matrices in the optimization ofcontributions for maintaining diversity at specific regions of thegenomeCitation for published version:Gómez-Romano, F, Villanueva, B, Fernandez, J, Woolliams, J & Pong-Wong, R 2014, 'The use of genomiccoancestry matrices in the optimization of contributions for maintaining diversity at specific regions of thegenome'. in Proceedings, 10th World Congress of Genetics Applied to Livestock Production . 10th WorldCongress on Genetics Applied to Livestock production (WCGALP), Vancouver, Canada, 17-22 August.Link:Link to publication record in Edinburgh Research ExplorerDocument Version:Publisher final version (usually the publisher pdf)Published In:Proceedings, 10th World Congress of Genetics Applied to Livestock ProductionGeneral rightsCopyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s)and / or other copyright owners and it is a condition of accessing these publications that users recognise andabide by the legal requirements associated with these rights.Take down policyThe University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorercontent complies with UK legislation. If you believe that the public display of this file breaches copyright pleasecontact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately andinvestigate your claim.Download date: 20. Feb. 2015Proceedings, 10th World Congress of Genetics Applied to Livestock Production  The use of genomic coancestry matrices in the optimization of contributions  for maintaining diversity at specific regions of the genome  F. Gómez-Romano1, B. Villanueva1, J. Fernández1, J. A. Woolliams2 and R. Pong-Wong2 1Departamento de Mejora Genética Animal, INIA, Madrid, Spain,  2The Roslin Institute and the R(D)SVS, University of Edinburgh, UK   ABSTRACT: Optimal contribution methods have proved to be very efficient for controlling the rate at which coancestry and inbreeding increase and therefore for maintaining genet-ic diversity. These methods have usually used pedigree information for estimating expected genetic relationships between animals. However, the large amount of genomic information now available (dense chips containing thousand of SNP markers), provides us with a good opportunity of obtaining more accurate estimates of relationships. Genomic information also permits us now to target specific regions in the genome where there is an interest in maximising diversi-ty. Using a semidefinite programming optimisation ap-proach, we have investigated the effectiveness of using genomic coancestry matrices for controlling the loss of genetic variability in specific genomic regions while re-stricting the overall loss in the rest of the genome. The re-sults show that genomic management was very successful for avoiding loss of diversity at specific genomic regions (even increased diversity). This management was also suc-cessful in restricting the loss of diversity in the remaining genome although the realised rate of coancestry resulted higher than the restriction imposed. There is thus a need of refining the theory of genetic contributions when realised genomic matrices are used. Keywords: Genetic diversity; Inbreeding; Coancestry; Optimal contributions   Introduction  It is generally accepted that controlling the rate of coancestry provides a general framework for managing genetic variability. Optimal Contribution (OC) methods (Meuwissen (1997); Grundy et al. (1998)) permit to deter-mine the optimal number of offspring that each breeding candidate should have to minimise coancestry. These meth-ods were initially developed assuming the pedigree-based relationship matrix (A) which does not take into account variation due to Mendelian sampling. Thus, A represents expected relationships assuming neutrality. Although its use has proved to be efficient to manage diversity it has some limitations. For instance, individuals from the same (full-sib) families would inherit different set of alleles but they are assumed to be equally related. Additionally, since A does not consider variation between genomic regions, the optimisation of contributions would, in average, control the rate of coancestry to the chosen value, but some genomic regions may have substantially higher rates than those de-sired by the breeder. For example, regions harbouring QTL affecting a trait under selection will have higher rates of inbreeding than those expected from neutral regions (Roughsedge et al. (2008)). Thus, controlling loss of genetic diversity using pedigree information in a population under selection will, undoubtable, result in much higher loss of variation in regions under selection than the rest of genome. Relationship matrices calculated from markers at particular genomic regions can be used to set specific constraints for variability loss. In this way, diversity could be managed independently providing losses in diversity are not higher than a given predetermined rate for each genomic region.  The objective of this study was to assess the effec-tiveness of using dense SNP panels in controlling the loss of genetic variability in specific genomic regions while re-stricting the overall loss in the rest of the genome.  Materials and Methods  Optimisation of contributions. Let assume a set of N breeding candidates at a given time t. The pedigree-based genetic relationships between candidates are given in matrix A. Now, let c be the vector of genetic contributions of the candidates to the next (offspring) generation. When the main objective is to minimize the loss of genetic diversi-ty, the OC problem can be formulated as to optimise c for minimising c’Ac/2. In order to keep the solution for c within the valid range, the optimisation problem should also in-clude the constraints that the sum of contributions of males and the sum of contributions of females are 0.5 each and that individual contributions are in the range [0,0.5]. The incorporation of realised genomic matrices (denoted here as G) calculated using SNP genotypes can be done with differ-ent levels of complexity. The simplest implementation is to calculate the average G matrix across the whole genome and use it to replace A in the optimisation problem described above. A more refined extension of the optimisation is the use of the relationship matrices specific for (some) genomic regions so their diversity can be managed independently. When minimising the loss of diversity at specific genomic regions, the OC problem can be formulated as to optimise c for minimising c’Gxc/2 subject to the restriction c’Gic/2 ≤ fi*, i = 1, …, k, where x identifies a particular region in the genome, Gx represents the molecular relationship matrix calculated using only the markers from the target region where the loss of coancestry is to be minimised and Gi is the relationship matrix calculated with all the markers not locat-ed in that region. The optimisation method followed the semidefinite programming approach as described by Pong-Wong and Woolliams (2007) due to its flexibility for adding extra constraints.  Simulations and genetic model. The study con-sidered a population of N animals (20 or 100) per genera-tion. The sex of the individuals was randomly assigned at each generation but ensuring that half were males and half were females. The population was managed for 10 genera-tions. The number of individuals per generation was kept constant. The genetic model assumed the genome divided into 20 chromosomes of one Morgan each. Each chromo-some had 2,000 biallelic loci equally spaced. The genotypes of 1,000 of them (at alternate positions) were assumed to be known and used to calculate the genomic matrices, simulat-ing SNP markers. The remaining 1,000 loci were used to assess the performance of the different managing strategies. The simulation of the base population was described in detail in Gomez-Romano et al. (2013). In brief, a historical population of size N is allowed to reproduce for 5,000 gen-erations with random mating. The last generation of this process was considered to be the base population of this study. The historical population was initialised assuming that the 40,000 loci were fixed. Mutations were allowed and being retained or lost due to genetic drift creating a distinc-tive linkage disequilibrium and gene frequency pattern. It should be noted that there were no mutations when creating the generations where management took place (i.e., after creating the base population).  Estimation of genomic matrices. The calculation of the genomic relationship was based on the allelic rela-tionship method proposed by Nejati-Javaremi et al. (1997). At a given SNP the allelic relationship between two indi-viduals is 0.5 𝛿!"!!!!!!!! , where  𝛿!" is the allele sharing status being equal to 1 if allele i from the first individual is the same to allele j from the second individual and 0 other-wise. The estimated genomic relationship between two individuals is the average value across all SNP in the ge-nome (for the whole genome matrix) or in the region of interest (for a regional genomic matrix).  Scenarios compared. Four different management scenarios were considered: i) minimising pedigree coances-try (fp); ii) minimising overall molecular coancestry (fm_ov); iii) minimising coancestry in chromosome 1 (fm_c1); and iv) minimising coancestry in chromosome 1 but restricting the coancestry rate in the rest of the genome (Δfm_ov-c1) to be ≤ 1%. An extra scenario where contributions were randomly assigned was also considered. The restriction for scenario iv) was calculated as 𝑓!!!∗  = 1 − (1 – Δf)(1 − ft), where ft is the average coancestry in the candidates’ population using all the markers except those in the chromosome 1 and Δf is the preselected target rate of inbreeding (1%).  Criteria of comparison. The main criteria of comparison were the average coancestry (f) and its rate (Δf) which represents the amount of genetic diversity that has been lost at a given time. Three estimates of coancestry were calculated at each generation: (i) the pedigree-based coancestry calculated using A; (ii) the overall realised mo-lecular coancestry calculated with the overall G matrix; and (iii) the molecular coancestry at chromosome 1 representing the diversity remaining in such chromosome. The average coancestry at a given generation is half therelationship ma-trix of all individuals from that generation.  In order to make the results comparable, the aver-age molecular coancestry was adjusted so the value in the base population was the same as the value calculated using A. Since animals in the base population are assumed to be (pedigree) unrelated, their A is the identity matrix so their average coancestry is 1/2N. Hence, the adjusted average coancestry for generation t was equal to (ft − f0)/(1 − f0) + 1/2N, where ft is the unadjusted average coancestry at gen-eration t.  Results and Discussion  Table 1 shows the average rates of pedigree and molecular coancestries for the four scenarios simulated in populations with N = 20 and 100. The scheme minimising the rate of molecular coancestry (Min Δfm_ov) was clearly more efficient in maintaining diversity (i.e., it gave substan-tially lower Δfm_ov) than that minimising the rate of pedigree coancestry (Min Δfp). For instance, with N = 100, Δfm_ov ranged from 0.24 to 0.30% when minimising Δfp and from −0.33% to 0.06% when minimising Δfm_ov. Hence, substan-tial improvements in retaining true realised genetic diversity can be achieved by using the genomic matrix rather than the pedigree-based A. The estimated Δfp was very similar to Δfm_ov when the contributions were assigned wat random or when they were optimised using pedigree information, sug-gesting that the use of pedigree coancestry as an indicator of the true realised molecular coancestry is only justified under this condition. The other schemes resulted in the pedigree coancestry not being a reliable estimator of the true molecu-lar coancestry.  The optimisation method was very successful in reducing the rate of increase of their target coancestries (see also fm_c1 in Table 2) but they were less efficient in reducing other coancestries. The relatively high Δfm_ov-c1 obtained under scenario iii) highlight the need of making the optimi-sation more complex by including a restriction on the rate of coancestry in the rest of the genome. Table 2 compares results of scenarios where coancestry was minimised in chromosome 1 with and without a restriction on Δfm_ov-c1 (Δfm_ov-c1 ≤ 1%). The scheme aiming to avoid loss of diversi-ty at chromosome 1 was very successful in that it even in-creased genetic diversity in this chromosome (i.e. negative Δfm_c1). After 10 generations, the diversity in chromosome 1 increased by 3% with N = 20 and about 8% with N = 100. However, the success in retaining diversity in this chromo-some comes at a price in the remaining genome, where the rate of increase in coancestry was substantially larger than the other scenarios (even larger than the scenario of random selection). These results clearly suggest that when the main objective is to retain diversity at a specific region of the genome, a restriction should also be added to avoid exces-sive loss of diversity of other areas of the genome. The optimisation performed imposing such restriction (i.e., sce-nario iv) has some success in reducing the loss of diversity in these other areas of the genome. Note that Δfm_ov-c1 was lower with than without the restriction. However, the real-ised Δf was higher than 1% (across the 10 generations it averaged 2.43% and 1.12% for N = 20 and N = 100, respec-tively).  Table 1. Rates of pedigree (Δfp) and overall molecular (Δfm_ov) coancestry across generations (t) when contribu-tions are selected at random (Rand) or optimized for minimising fp (Min Δfp), fm_ov (Min Δfm_ov) or fm_c1 (Min Δfm_c1).   Table 2. Rate of coancestry at chromosome 1 (Δfm_c1) and at the whole genome except chromosome 1 (Δfm_ov-c1) across generations (t) when contributions are optimized for minimising coancestry at chromosome 1 restricting or not Δfm_ov-c1 with N = 20.  No restriction  With restriction t Δfm_c1 Δfm_ov-c1  Δfm_c1 Δfm_ov-c1 1 −3.83 3.98  −3.14 2.54 2 −0.70 2.95  −1.18 2.53 3 −1.00 3.46  −0.50 2.41 4 0.07 2.67  −0.17 1.86 5 −0.69 3.11  −0.56 2.55 10 0.10 3.98  −0.20 2.38   Surprisingly, the solutions from the optimisation were valid in the sense that those found as optimum did, indeed, fulfil the restriction that the expected Δfm_ov-c1 should not be greater than 1%. Figure 1 shows the expected Δfm_ov-c1 given the assigned contributions to candidates and the realised value observed in the offspring generation. Across the 10 generations of management, the optimisation proce-dure yielded solutions with expected Δfm_ov-c1 lower than the imposed 1% restriction. However, the realised Δfm_ov-c1 observed in the offspring was consistently higher than the value aimed during the optimisation.    Figure 1: Expected and observed Δfm_ov-c1 when the op-timisation was performed for minimising coancestry in chromosome 1 while restricting the rate of coancestry at the rest of the genome to 1%.  Conclusion  This study shows that the use of molecular coancestry in the optimisation is substantially more efficient in retaining genetic diversity than the use of pedigree coancestry. Moreover, the use of molecular coancestry per-mits us to target specific genomic regions for minimising the loss of diversity and extend the optimisation procedure to include restrictions in regions different to those where the loss of diversity is minimized. Under this scenario, howev-er, the realised	  Δf	  did not fullfil the restriction that was im-posed. This clearly highlight the need of refining the theory of genetic contributions using realised genomic matrices in order to assure that  constraints on Δf are properly included in the model.    Acknowledgements  This work was funded by the MINECO and INIA, Spain (CGL2012-39861-C02-02). The Roslin Institute re-ceives financial support from the BBSRC. We also thank funding from the QUANTOMICS EU Project (222664-2).  Literature Cited  Gómez-Romano, F., Villanueva, B., de Cara, M. A. R. et al. (2013). Genet. Sel. Evol. 45:38-45. Grundy, B., Villanueva, B., and Woolliams, J. A. (1998). Genet. Res. 72: 159-168. Meuwissen, T. H. E. (1997). J. Anim. Sci. 75: 934-940. Nejati-Javaremi, A., Smith, C. and Gibson, J. P. (1997). J. Anim. Sci. 75: 1738-1745. Pong-Wong, R. and Woolliams, J. A. (2007). Genet. Sel. Evol. 39: 3-25. Roughsedge, T., Pong-Wong, R., Woolliams, J. A. et al. (2008). Genet. Res. 90: 199-208. 	   Δfp (%)  Δfm_ov (%) t Rand Min Δfp Min Δfm_ov Min Δfm_c1  Rand Min Δfp Min Δfm_ov Min Δfm_c1 N = 20 1 2.44 1.28 2.52 5.10  2.69 1.33 0.25 3.98 2 2.64 1.30 1.77 3.66  2.99 1.34 0.93 2.95 3 2.17 1.31 1.76 3.23  2.28 1.18 0.94 3.46 4 2.81 1.30 1.73 3.03  2.95 1.30 1.14 2.67 5 2.76 1.30 1.78 3.40  3.40 1.25 0.85 3.11 10 2.26 1.30 1.78 3.14  2.21 1.42 0.97 2.59 N = 100 1 0.50 0.30 0.70 2.21  0.51 0.24 -0.33 1.86 2 0.48 0.20 0.52 1.36  0.51 0.30 -0.06 1.07 3 0.47 0.25 0.47 1.22  0.45 0.27 -0.03 1.05 4 0.50 0.25 0.47 1.44  0.52 0.24 0.00 1.40 5 0.53 0.25 0.48 1.35  0.52 0.27 0.03 1.17 10 0.50 0.26 0.45 0.97  0.53 0.25 0.06 0.87 

The use of genomic coancestry matrices in the optimization of contributions for maintaining diversity at specific regions of the genome

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