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Comparison of accuracy of genome-wide and BLUP breeding value estimates in sib based aquaculture breeding schemes
Aquaculture 289 (2009) 259–264
Contents lists available at ScienceDirect
Aquaculture j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a q u a - o n l i n e
Comparison of accuracy of genome-wide and BLUP breeding value estimates in sib based aquaculture breeding schemes Hanne M. Nielsen a,⁎, Anna K. Sonesson a, Hossein Yazdi b, Theo H.E. Meuwissen b a b
Nofima Marine, P.O. Box 5010, N-1432 Ås, Norway Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, P.O. Box 5003, N-1432 Ås, Norway
a r t i c l e
i n f o
Article history: Received 12 September 2008 Received in revised form 22 January 2009 Accepted 24 January 2009 Keywords: Sib testing scheme Genomic selection Accuracy of selection Aquaculture
a b s t r a c t This study compared the accuracy for genome-wide breeding values (GWEBV) with traditional BLUP breeding values estimated from phenotypic performance of sibs (BLUPEBV) in a typical sib based aquaculture breeding scheme. The breeding schemes were closed nuclei with 1000 selection candidates from 100 families in each generation G1 to G5. Phenotypes were recorded on sibs of the selection candidates. Both selection candidates and their recorded sibs were genotyped using dense SNP genotyping technology and marker effects estimated from the sibs were used to predict GWEBV of the selection candidates. With 40 sibs, accuracy in G3 was 0.54 for BLUPEBV compared to 0.78 for GWEBV (marker density 0.5Ne / M), i.e. a relative increase of 44%. When the number of sibs for the GWEBV scheme decreased from 40 to 20 sibs, accuracy decreased by 7% in G3. Both for BLUPEBV and GWEBV breeding schemes, the effect of heritability on accuracy was small and accuracy increased around 4% when increasing heritability from 0.2 to 0.4. Contrary to expectations differences in accuracy between BLUPEBV and GWEBV were the same for the low (0.2) and high (0.4) heritability, which may be due to the large number of phenotypic records used. When records were only available in generation G1, accuracy of GWEBV decreased over generations and was 0.66 in G1, 0.57 in G2 and 0.51 in G3 with 40 sibs and marker density 0.5Ne / M. Accuracy increased with increased marker density for GWEBV, but the increase was small when marker density increased from 0.5 to 1.0Ne / M except when the test group size was increased from 20 to 40, indicating that with a higher marker density a higher number of phenotypes is needed. Increasing the size of the genome (1000 cM vs. 2000 cM) decreased the accuracy for the GWEBV breeding values but increased the accuracy for the BLUPEBV breeding values. Overall, accuracy was up to 33% higher for GWEBV than for BLUPEBV for the studied scenarios because both between and within family genetic variances are utilized when estimating genome-wide breeding values. The results indicate that aquaculture breeding companies can increase the accuracy of selection when using genomic selection in a typical sib based aquaculture breeding scheme. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In aquacultural species, traits such as disease resistance and meat quality cannot be measured on live selection candidates. Recording of meat quality traits requires slaughtering of the fish and fish challenge tested for the diseases is not accepted as breeding stock, because of the risks of disease outbreaks in nucleus populations. Therefore, BLUP breeding values (Henderson, 1984) for such traits are usually based on phenotypic records from full and half sibs of the selection candidates. In a traditional sib based breeding scheme, only breeding values of families are obtained, which means that selection can only be performed between families but not within families. Consequently, only half of the total genetic variance is utilized. In addition, when a given trait is only recorded on the sibs or progeny of the selection can-
⁎ Corresponding author. Tel.: +47 93098113; fax: +47 64949502. E-mail address: hanne.nielsen@nofima.no (H.M. Nielsen). 0044-8486/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.aquaculture.2009.01.027
didates, a large full or half sib group is needed in order to achieve a high accuracy of breeding value estimates. This is especially true for lowly heritable traits. Genomic selection is a method that predicts the total genetic value of an individual from phenotypic records using dense SNP marker genotyping and presumes estimates of SNP effects (Meuwissen et al., 2001). Genome-wide breeding values for a given trait are estimated by dividing the genome into segments, which are defined by marker haplotypes or single markers in a dense marker map. For genomic selection, the associations between marker and phenotype are determined in a separate test using a part of the population, e.g. sibs of the selection candidate. Genome-wide breeding values can differentiate between sibs, which may make genomic selection particularly well suited for sib based breeding schemes. Thus, genomic selection also utilizes the within-family component of the genetic variance (Daetwyler et al., 2007). In aquaculture sib breeding schemes, the maximum accuracy for traditional BLUP breeding values without own performance is 0.71
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(Cameron, 1997). Dependent on the method used to estimate breeding values, accuracy of genome-wide breeding values in a parent– offspring design has been estimated to be approximately 0.80 for juvenile animals without phenotypic records (Meuwissen et al., 2001). However, we do not know what level of accuracy of genome-wide breeding values to expect for economically important traits in aquaculture sib breeding schemes. It is expected that over time, accuracy of genome-wide breeding values will be reduced due to recombination between markers and QTL. Thus, accuracy of breeding values depends on the number of generations with phenotypic and genomic records (Habier et al., 2007; Muir, 2007; Solberg et al., 2008b) as well as marker density (Solberg et al., 2008a), and the level of heritability (Kolbehdari et al., 2007) for the considered trait. We hypothesize that the accuracy of estimated genome-wide breeding values in aquaculture sib breeding schemes is higher than for traditional BLUP breeding values (Henderson, 1984), because estimated genome-wide breeding values can utilize within family information. In order to test this, we therefore compared the accuracy of genome-wide and traditional BLUP breeding values. Selection candidates were randomly selected in order to investigate the accuracy of estimated breeding values per se and avoid possible effects of selection on these accuracies. The effects of marker density, number of full sibs per selection candidate, genome size, trait heritability, and whether the sibs in the test group were only full sibs or full and half sibs were studied. Schemes with genotypic and phenotypic records in all generations were compared with schemes with records only in the first generation in order to illustrate the effect of the number of generations included to estimate marker effects. 2. Materials and methods 2.1. Population structure and data We simulated two different breeding schemes; one scheme where breeding values of selection candidates were estimated using BLUP (Henderson, 1984) based on phenotypic performance of their sibs as in traditional breeding value estimation (BLUPEBV) and one scheme with genome-wide breeding values based on genomic information (GWEBV). The estimation of breeding values is explained in detail in Section 2.4. The breeding schemes were closed nuclei with discrete generations modelled by stochastic simulation. A base population with an effective population size of 1000 (500 males and 500 females) was simulated for 4000 generations. Sires and dams were randomly selected and mated within each generation using sampling with replacement as in the Fisher–Wright ideal population model. In generation 4001, hereafter called G1, the size of the population was increased to have next to the selection candidates, a sib test group, which was used as test animals and was performance tested for a single trait recorded on both males and females. In G1 to G5, 100 families were produced by random selection of 100 sires and 100 dams. Each sire was randomly mated to one dam and vice versa, using sampling without replacement. Each family had 10 selection candidates and 20 or 40 sibs in the test group. We also studied a design where 50 sires were mated to 100 dams, i.e. every sire was mated to two dams and a scheme where phenotypic records were only available in generation G1.
The simulated genome consisted of 10 or 20 chromosomes each with a length of 100 cM. Mutations were simulated under the infinitesites model (Kimura, 1969), i.e. every mutation occurred at a unique randomly chosen position in the genome which guarantees that every polymorphic position has only 2 alleles. The mutation rate per base pair (assuming 1,000,000 base pairs per cM) per haplotype was 10− 8. Mutations were assumed neutral with respect to the selection of the individuals, i.e. the neutral allele model was assumed. The number of recombinations per chromosome was sampled from the Poisson distribution with an average of 1 per 100 cM. Next, every mutation was randomly distributed on the genome. This mutation process resulted in a large number of SNPs per chromosome where the typical number of SNPs generated was 3000. After 4000 generations, only SNPs with Minor Allele Frequency (MAF) N 2% were considered. Amongst those, 100 SNPs per chromosome were randomly sampled (without replacement) to be quantitative trait loci (QTL). This resulted in a total of 1000 randomly distributed QTL, and, since the number of QTL was large, the genetic model approximately behaved as an infinitesimal model, which is perhaps a worst case scenario for genomic selection, because the effect of very many genes needs to be predicted. The non-QTL SNPs were ranked on their MAF and the highest marker density was achieved by selecting the highest ranking 1000 SNPs per chromosome as genetic markers. Thus there were 10 markers per cM. Lower marker densities (5 and 1 marker per cM) were obtained by taking from these 1000 markers per chromosome every second or every 10th marker to obtain in total 500 and 100 markers per chromosome, respectively. Allelic effects of the QTL alleles were sampled from the gamma distribution with a shape parameter (β) of 0.4 and a scale parameter of 1.66 (Hayes and Goddard, 2001). The simulated cumulative amount of the genetic variance described by the QTL is presented in Fig. 1. Because linkage disequilibrium (LD) depends on both Ne and the distance between loci (d) (LD = 1 / (4 ⁎ Ne ⁎ d + 1)) (Sved, 1971) we expressed marker densities in relation to effective population size (Solberg et al., 2008a). Marker densities were thus 0.1, 0.5, or 1Ne / M with Ne equal to 1000 for the genome with 10 chromosomes. For the genome with 20 chromosomes, the marker density was 0.5Ne / M. For all 3 marker densities 100 QTL were randomly distributed on each chromosome. 2.3. Simulation of phenotypes The true breeding value of an individual was calculated as: 1000
TBVi = ∑j = 1 xij1 gj1 + xij2 gj2
where xijk is the number of copies that individual i has of the k′th QTL allele at the j′th QTL position, and gjk is the true effect of the k′th QTL allele at the j′th position.
2.2. Genomic information In addition to being performance tested for the considered trait, individuals in the test group were in the GWEBV scheme also genotyped in generations G1 to G5 in order to estimate the marker– trait associations of markers. For the scheme with phenotypic records only available in G1, the individuals were only genotyped in G1.
Fig. 1. Cumulative fraction of the genetic variance explained by the QTL.
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allele; 1 / √Hj denotes heterozygous; and 2 / √Hj denotes homozygous for the second allele, where Hj is the marker heterozygosity and thus dividing by 1 / √Hj standardises the variance of the Xij; aj is the random effect of the j′th marker and Var(aj) is assumed Vg / n where n is the number of markers; ei is random residual. The variance ratio for the mixed model equations is here n(1 − h2) / h2. Genome wide breeding values were predicted for selection candidates of the GWEBV scheme by summing the effects of the markers: n
EBVi = ∑j Xij aj : The accuracy of selection (ACC) was calculated as the correlation between true and estimated breeding values for breeding schemes BLUPEBV and GWEBV, respectively and was averaged over 100 replicates within generations G1 to G5. 3. Results 3.1. Effect of marker density and size of test group Fig. 2 presents ACC for breeding schemes BLUPEBV and/or GWEBV with a test group size of either 20 (Fig. 2a) or 40 (Fig. 2b). ACC for both GWEBV and BLUPEBV increased considerably from generations G1 to G2, e.g. from 0.59 to 0.69 with 20 sibs and 0.5Ne / M for GWEBV and from 0.43 to 0.50 for BLUPEBV, as more information became available, and reached a rather constant level at G3. ACC for the GWEBV breeding scheme was higher than ACC for the BLUPEBV scheme for all marker densities. ACC was for example 0.73 in G3 for GWEBV with a Fig. 2. Accuracy of breeding values for breeding schemes with either 20 (a) or 40 (b) sibs of the candidate, 1000 selection candidates, a heritability of 0.4 and phenotypic and genomic records available in all generations. Breeding values based on only phenotypic performance (BLUPEBV) of the sibs (Δ), breeding values based on genomic information (GWEBV) with marker densities of 0.1 (◊), 0.5 (□), or 1 (×) Ne / M.
The phenotypic values (Pi) of the individuals were generated in generations G1 to G5 for both breeding schemes GWEBV and BLUPEBV. These were simulated by adding an error term sampled from a normal distribution to the true breeding value (TBVi): Pi = TBVi + ei where εi is an error term for individual i, which was normally distributed (0, σ e2) and σ e2 was adjusted within each replicate so the heritability, h2, was 0.2 or 0.4. 2.4. Prediction of breeding values and haplotype effects The phenotypic information from the test group was used to calculate the breeding values for the BLUPEBV scheme according to Henderson (1984). The model used to calculate breeding values included the mean as a fixed effect whereas the effects of animal and error were treated as random effects. The variance ratio required in the mixed model equations is (1 − h2) / h2 where the true heritability was used as described above. For the BLUPEBV estimation, it was assumed that pedigree recording started in generation G1, i.e. the parents of generation G1 were assumed unrelated. For the GWEBV scheme, the effects of the markers were predicted using the BLUP of marker effects method described in Meuwissen et al. (2001). The statistical model used to estimate the marker effects was: n
yi = μ + ∑j Xij aj + ei where yi is the record of test individual i; μ is the overall mean; Xij denotes the j′th marker genotype: 0 denotes homozygous for the first
Fig. 3. Accuracy of breeding values for breeding schemes with phenotypic and genomic records only available in generation G1, either 20 (a) or 40 (b) full sibs of the candidate, 1000 selection candidates and a heritability of 0.4. Breeding values based on only phenotypic performance (BLUPEBV) of the sibs (Δ) or breeding values based on genomic information (GWEBV) with 0.1 (◊), 0.5 (□), or 1 (×) Ne / M.
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Fig. 4. Accuracy of breeding values based on only phenotypic performance (BLUPEBV) of 80 half and full sibs (◊) or 40 full sibs (Δ) or breeding values with genomic information (GWEBV) from 80 half and full sibs (□) or 40 full sibs (×) and a marker density of 0.5Ne / M. The number of selection candidates was 1000 and the heritability was 0.4.
Fig. 6. Accuracy of breeding values based on only phenotypic performance of the sibs (BLUPEBV) with heritability of the trait of 0.2 (×) or 0.4 (□), or breeding values based on genomic information (GWEBV) with 0.5Ne / M and heritability of 0.2 (Δ) or 0.4 (◊). The number of selection candidates is 1000 and there were 40 sibs per selection candidate.
marker density of 0.5Ne / M, while ACC for BLUPEBV was 0.50 (Fig. 2a). ACC increased with increased marker density and was for example 0.60, 0.73, and 0.75 in generation G3 with marker densities 0.1, 0.5, and 1Ne / M for the scheme with 20 sibs. When the number of sibs of the candidates was increased from 20 (Fig. 2a) to 40 (Fig. 2b), ACC in generation G3 increased from 0.73 to 0.78 for the GWEBV breeding values with marker density 0.5Ne / M and from 0.50 to 0.54 for BLUPEBV. Highest ACC of 0.83 was as expected observed in generation G5 with the highest number of sibs of 40 and the highest marker density of 1Ne / M.
3.3. Effect of family structure ACC for both the GWEBV and the BLUPEBV schemes was only slightly higher when selection candidates were evaluated based on both a half sib and a full sib group compared to when they were evaluated based on 40 full sibs only (Fig. 4). ACC in generation G2 for the GWEBV scheme was for example 0.75 for the full sib design and 0.79 for the half sib design. The reason for the slightly higher ACC for the half sib design is that the total family size is doubled because each of the 50 sires has two groups of full sibs. However, the difference in ACC between the two sib designs was small due to the large family sizes used.
3.2. Effect of number of generations with records 3.4. Effect of genome size Fig. 3 presents ACC when phenotypic and genomic information from fish in the test group was only available in generation G1. For GWEBV, marker densities of 0.1, 0.5, and 1Ne / M are presented. With 20 sibs and a marker density of 0.5Ne / M, ACC for GWEBV decreased from 0.59 in G1 to 0.49 in G2 and 0.32 in G5. The reason for the decrease in ACC is because the LD changes over generations due to recombination and thus LD estimated in generation G1 does not hold several generations later. The decrease in ACC from G1 to G2 was 23.5, 16.9, and 16.7% for marker densities 0.1Ne / M, 0.5Ne / M, and 1Ne / M and 20 sibs and was thus largest for the lowest marker density (0.1Ne / M). The latter is because there is a higher probability of recombination between markers and QTL when marker density is low.
ACC for schemes with 10 or 20 chromosomes is presented in Fig. 5. For the GWEBV scheme, ACC was lower with 20 chromosomes compared to 10 chromosomes (0.71 vs. 0.75 in G2). On the contrary, ACC for the BLUPEBV scheme, was slightly higher with 20 (0.56) chromosomes than with 10 chromosomes (0.53 in G2). 3.5. Effect of heritability ACC for both the GWEBV and BLUPEBV schemes increased as expected when the heritability of the trait was 0.4 compared to 0.2 (Fig. 6). The level of ACC for the BLUPEBV scheme in generation G2 was 0.50 with a heritability of 0.2 and 0.53 with a heritability of 0.4. For the GWEBV scheme (marker density = 0.5Ne / M), ACC was 0.72 and 0.75 in generation G2 with a heritability of 0.2 and 0.4, respectively. Hence, both for BLUPEBV and GWEBV breeding schemes the effect of heritability on ACC was small but significant (P ≤ 0.05) with the large family sizes used here. 4. Discussion
Fig. 5. Accuracy of breeding values based on only phenotypic performance (BLUPEBV) of the full sibs with 10 (□) or 20 (Δ) chromosomes or breeding values with genomic information (GWEBV) with 0.5Ne / M. and with 10 (×) or 20 (◊) chromosomes. The heritability is 0.4 and the number of sibs per candidate is 40.
In this study, we tested the hypothesis that ACC for genome-wide breeding values in aquaculture sib breeding schemes (GWEBV) is higher than ACC for traditional BLUP breeding values (BLUPEBV). The ACC was up to 33% higher for GWEBV than for BLUPEBV for all studied scenarios (marker densities, heritability values, number of sibs) because both between and within family genetic variances are utilized when estimating genome-wide breeding values compared to traditional BLUP breeding values. These results indicate that selection response in aquaculture sib breeding schemes will increase with genomic selection. Consequently, depending on the cost of genotyping, aquaculture breeding companies may benefit from including
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genomic information into their breeding scheme for traits which cannot be measured on selection candidates. 4.1. Effect of marker density, heritability, and genome size Increased marker density was expected to increase ACC (e.g. Solberg et al., 2008a) and was observed when marker density was increased from 0.1 to 0.5 and from 0.5 to 1Ne / M (e.g. from 0.62 to 0.75 and 0.77 in generation G2 and 40 full sibs). We also found a slightly higher effect on ACC of increasing marker density for a test group of size 40 than 20, indicating that with a higher marker density a higher number of phenotypes is needed. The fact that more phenotypic records are needed to increase ACC with higher marker density is also supported by the little increase in ACC that was found when increasing marker density from 0.5 to 1Ne / M. This indicates that there is an upper limit to the increase in ACC with increasing marker density if the number of phenotypic records is not increased. Figs. 2, 4 and 5 show generally an increase in accuracy with generation number with a plateau after 4 generations. The increase in accuracy may be explained by the increased number of records used to estimate marker effects, as generation number increases. However, after about four generations a balance is reached between the new information entering every generation and the decay of the value of the old records due to changes of the LD between the markers and the QTL over generations. In our study, increasing the size of the genome decreased ACC for the GWEBV breeding values but increased ACC for the BLUPEBV breeding values. An explanation for these results is that with 20 chromosomes, and twice as many QTL, the variation from the expected correlation of 0.5 between sibs is smaller than for 10 chromosomes, because with increased sample size (number of chromosomes) the coefficient of variation of the fraction of genes that the sibs have in common is reduced. Therefore, for BLUPEBV the assumed correlation of 0.5 between sibs is closer to the actual correlation between sibs with 20 chromosomes than with 10 chromosomes. However, for GWEBV, the small deviation from the expected correlation between sibs with 20 chromosomes is more difficult to predict than the larger deviation with 10 chromosomes. Thus, it is expected that, as the number of chromosomes increases the difference between BLUPEBV and GWEBV becomes smaller. In this study, ACC increased when heritability of the trait was increased from 0.2 to 0.4, which corresponds to results by Kolbehdari et al. (2007). However, contrary to expectations (Meuwissen et al., 2001), differences in ACC between BLUPEBV and GWEBV were the same for the low (0.2) and high (0.4) heritabilities. With a low heritability, sampling errors on the estimates of the haplotype effects will in general increase with increased environmental variance (Meuwissen et al., 2001). However, in this study we used a relatively high number of phenotypic records, which may explain the lack of difference in ACC between BLUPEBV and GWEBV for the two different levels of heritability. Often disease traits are recorded as all-or-none-traits, instead of as a continuous trait as was used in our simulations. The effect of this is that the information content of the records is reduced and thus that every record has less predictive value for the genetics of the individual. This effect is very similar to that of a reduced heritability, as was investigated in Fig. 6, where also the predictive value is reduced. 4.2. Assumptions and simulation design In this study, random selection was applied in order to investigate the effects of the studied design factors on ACC per se. With selection there will be a confounding between the individuals selected and the factors investigated which will depend on the design of the data and differ for different selection methods. Furthermore, ACC will be reduced due to selection to an extent that depends on the ACC itself
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and the intensity of selection. There are indications that the effect of selection on genetic variances and ACC, i.e. the Bulmer effect (Muir, 2007), can be large in GS schemes because selection changes allele frequencies and creates unfavourable linkage disequilibrium. In our study, ACC for GWEBV was higher than for BLUPEBV in all generations. Results of Muir (2007) suggest that more than 1 generation with records are needed in order to get higher ACC for GWEBV compared to BLUPEBV. However, in the present study selection candidates had no own performance for the trait, instead their breeding values were based on records from their sibs. When selection candidates have own performance for the trait, like in Muir's study ACC for BLUP breeding values is already quite high, which may explain the lower advantage of applying genomic selection in Muir's study compared to this study. Recombination between markers and QTL will over time reduce the ACC of the genome-wide breeding values using marker effects predicted from the population in the first generations. In the present study, ACC decreased with 14.7% from generations G1 to G2 and with 10.5% from G2 to G3 for the situation with 40 sibs and 0.5Ne / M. The decline in ACC was even higher for the low level of marker density (23.5% from G1 to G2 and 18% from G2 to G3), which agrees with the results of Solberg et al. (2008b). The decline in ACC was higher than estimated by Meuwissen et al. (2001) who found a decline in ACC of about 5% with an increasing number of generations between the test population and the population for which genomic breeding values were estimated. In our study, we used one generation of records while Meuwissen used two generations of records, which may explain the more rapid decline in ACC found in our study. In addition, we used a (full) sib design whereas Meuwissen et al. (2001) used a parent– offspring design for estimation of marker effects. We used the best-linear unbiased prediction (BLUP) method of marker effects by Meuwissen et al. (2001) to estimate breeding values in the current study. Bayesian methods have been found to yield higher ACC than BLUP (Habier et al., 2007; Meuwissen et al., 2001; Solberg et al., 2008a). In practice, if reliable prior distributions of variances of marker effects are available, Bayesian methods could be applied to estimate breeding values which may yield higher ACC than estimated in the current study. However, even when the BLUP method was used to estimate GWEBV, ACC was still considerably higher than that of the BLUPEBV scheme. Also in the present study, the number of QTL was rather large (1000), which implies that the genetic model was approximately polygenic (many relatively small QTL). The BLUP of marker effects model assumes exactly such a model i.e. every marker has a small effect and none have very large effects. The higher ACC for GWEBV obtained in this study compared to BLUPEBV may in particular be an advantage for traits such as disease resistance, where a large number of sibs of the selection candidates are challenge tested for the disease. Challenge testing is rather expensive and the results from this study suggest that with phenotypic records in G1 only, ACC for GWEBV in G2 (0.57 with 40 sibs and 0.5Ne / M) is much lower compared to ACC for GWEBV (0.75) with phenotypic records in all generations. This indicates that more than one generation of phenotypic records is needed to obtain a high ACC with the number of tested sibs and marker densities used in the current study. References Cameron, N.D., 1997. Selection Indices and Prediction of Genetic Merit in Animal Breeding. CAB International, Wallingford. Daetwyler, H.D., Villanueva, B., Bijma, P., Woolliams, J.A., 2007. Inbreeding in genomewide selection. J. Anim. Breed. Genet. 124, 369–376. Habier, D., Fernando, R.L., Dekkers, J.C.M., 2007. The impact of genetic relationship information on genome-assisted breeding values. Genetics 177, 2389–2397. Hayes, B., Goddard, M.E., 2001. The distribution of the effects of genes affecting quantitative traits in livestock. Genet. Sel. Evol. 33, 209–229. Henderson, C.R., 1984. Applications of Linear Models in Animal Breeding. Guelph Univ. Press, Guelph, Canada. Kimura, M., 1969. The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. Genetics 61, 893–903.
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Kolbehdari, D., Schaeffer, L.R., Robinson, J.A.B., 2007. Estimation of genome-wide haplotype effects in half-sibs designs. J. Anim. Breed. Genet. 124, 356–361. Meuwissen, T.H.E., Hayes, B.J., Goddard, M.E., 2001. Prediction of total genetic value using genome-wide dense marker maps. Genetics 157, 1819–1829. Muir, W.M., 2007. Comparison of genomic and traditional BLUP-estimated breeding value accuracy and selection response under alternative trait and genomic parameters. J. Anim. Breed. Genet. 124, 342–355. Solberg, T.R., Sonesson, A.K., Woolliams, J.A., Meuwissen, T.H.E., 2008a. Genomic selection using different marker types and density. J. Anim. Sci. 86, 2447–2454.
Solberg, T.R., Sonesson, A.K., Woolliams, J.A., Ødegård, J., Meuwissen, T.H.E., 2008b. Persistence of estimates of effects of genome-wide markers over generations when including a polygenic effects. In: Methods for Prediction of Genome-wide Breeding Values using Dense Marker Genotyping, PhD thesis, Norwegian University of Life Sciences. Sved, J.A., 1971. Linkage disequilibrium and homozygosity of chromosome segments in finite populations. Theor. Popul. Biol. 2, 125–141.
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Aquaculture j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a q u a - o n l i n e
Comparison of accuracy of genome-wide and BLUP breeding value estimates in sib based aquaculture breeding schemes Hanne M. Nielsen a,⁎, Anna K. Sonesson a, Hossein Yazdi b, Theo H.E. Meuwissen b a b
Nofima Marine, P.O. Box 5010, N-1432 Ås, Norway Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, P.O. Box 5003, N-1432 Ås, Norway
a r t i c l e
i n f o
Article history: Received 12 September 2008 Received in revised form 22 January 2009 Accepted 24 January 2009 Keywords: Sib testing scheme Genomic selection Accuracy of selection Aquaculture
a b s t r a c t This study compared the accuracy for genome-wide breeding values (GWEBV) with traditional BLUP breeding values estimated from phenotypic performance of sibs (BLUPEBV) in a typical sib based aquaculture breeding scheme. The breeding schemes were closed nuclei with 1000 selection candidates from 100 families in each generation G1 to G5. Phenotypes were recorded on sibs of the selection candidates. Both selection candidates and their recorded sibs were genotyped using dense SNP genotyping technology and marker effects estimated from the sibs were used to predict GWEBV of the selection candidates. With 40 sibs, accuracy in G3 was 0.54 for BLUPEBV compared to 0.78 for GWEBV (marker density 0.5Ne / M), i.e. a relative increase of 44%. When the number of sibs for the GWEBV scheme decreased from 40 to 20 sibs, accuracy decreased by 7% in G3. Both for BLUPEBV and GWEBV breeding schemes, the effect of heritability on accuracy was small and accuracy increased around 4% when increasing heritability from 0.2 to 0.4. Contrary to expectations differences in accuracy between BLUPEBV and GWEBV were the same for the low (0.2) and high (0.4) heritability, which may be due to the large number of phenotypic records used. When records were only available in generation G1, accuracy of GWEBV decreased over generations and was 0.66 in G1, 0.57 in G2 and 0.51 in G3 with 40 sibs and marker density 0.5Ne / M. Accuracy increased with increased marker density for GWEBV, but the increase was small when marker density increased from 0.5 to 1.0Ne / M except when the test group size was increased from 20 to 40, indicating that with a higher marker density a higher number of phenotypes is needed. Increasing the size of the genome (1000 cM vs. 2000 cM) decreased the accuracy for the GWEBV breeding values but increased the accuracy for the BLUPEBV breeding values. Overall, accuracy was up to 33% higher for GWEBV than for BLUPEBV for the studied scenarios because both between and within family genetic variances are utilized when estimating genome-wide breeding values. The results indicate that aquaculture breeding companies can increase the accuracy of selection when using genomic selection in a typical sib based aquaculture breeding scheme. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In aquacultural species, traits such as disease resistance and meat quality cannot be measured on live selection candidates. Recording of meat quality traits requires slaughtering of the fish and fish challenge tested for the diseases is not accepted as breeding stock, because of the risks of disease outbreaks in nucleus populations. Therefore, BLUP breeding values (Henderson, 1984) for such traits are usually based on phenotypic records from full and half sibs of the selection candidates. In a traditional sib based breeding scheme, only breeding values of families are obtained, which means that selection can only be performed between families but not within families. Consequently, only half of the total genetic variance is utilized. In addition, when a given trait is only recorded on the sibs or progeny of the selection can-
⁎ Corresponding author. Tel.: +47 93098113; fax: +47 64949502. E-mail address: hanne.nielsen@nofima.no (H.M. Nielsen). 0044-8486/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.aquaculture.2009.01.027
didates, a large full or half sib group is needed in order to achieve a high accuracy of breeding value estimates. This is especially true for lowly heritable traits. Genomic selection is a method that predicts the total genetic value of an individual from phenotypic records using dense SNP marker genotyping and presumes estimates of SNP effects (Meuwissen et al., 2001). Genome-wide breeding values for a given trait are estimated by dividing the genome into segments, which are defined by marker haplotypes or single markers in a dense marker map. For genomic selection, the associations between marker and phenotype are determined in a separate test using a part of the population, e.g. sibs of the selection candidate. Genome-wide breeding values can differentiate between sibs, which may make genomic selection particularly well suited for sib based breeding schemes. Thus, genomic selection also utilizes the within-family component of the genetic variance (Daetwyler et al., 2007). In aquaculture sib breeding schemes, the maximum accuracy for traditional BLUP breeding values without own performance is 0.71
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(Cameron, 1997). Dependent on the method used to estimate breeding values, accuracy of genome-wide breeding values in a parent– offspring design has been estimated to be approximately 0.80 for juvenile animals without phenotypic records (Meuwissen et al., 2001). However, we do not know what level of accuracy of genome-wide breeding values to expect for economically important traits in aquaculture sib breeding schemes. It is expected that over time, accuracy of genome-wide breeding values will be reduced due to recombination between markers and QTL. Thus, accuracy of breeding values depends on the number of generations with phenotypic and genomic records (Habier et al., 2007; Muir, 2007; Solberg et al., 2008b) as well as marker density (Solberg et al., 2008a), and the level of heritability (Kolbehdari et al., 2007) for the considered trait. We hypothesize that the accuracy of estimated genome-wide breeding values in aquaculture sib breeding schemes is higher than for traditional BLUP breeding values (Henderson, 1984), because estimated genome-wide breeding values can utilize within family information. In order to test this, we therefore compared the accuracy of genome-wide and traditional BLUP breeding values. Selection candidates were randomly selected in order to investigate the accuracy of estimated breeding values per se and avoid possible effects of selection on these accuracies. The effects of marker density, number of full sibs per selection candidate, genome size, trait heritability, and whether the sibs in the test group were only full sibs or full and half sibs were studied. Schemes with genotypic and phenotypic records in all generations were compared with schemes with records only in the first generation in order to illustrate the effect of the number of generations included to estimate marker effects. 2. Materials and methods 2.1. Population structure and data We simulated two different breeding schemes; one scheme where breeding values of selection candidates were estimated using BLUP (Henderson, 1984) based on phenotypic performance of their sibs as in traditional breeding value estimation (BLUPEBV) and one scheme with genome-wide breeding values based on genomic information (GWEBV). The estimation of breeding values is explained in detail in Section 2.4. The breeding schemes were closed nuclei with discrete generations modelled by stochastic simulation. A base population with an effective population size of 1000 (500 males and 500 females) was simulated for 4000 generations. Sires and dams were randomly selected and mated within each generation using sampling with replacement as in the Fisher–Wright ideal population model. In generation 4001, hereafter called G1, the size of the population was increased to have next to the selection candidates, a sib test group, which was used as test animals and was performance tested for a single trait recorded on both males and females. In G1 to G5, 100 families were produced by random selection of 100 sires and 100 dams. Each sire was randomly mated to one dam and vice versa, using sampling without replacement. Each family had 10 selection candidates and 20 or 40 sibs in the test group. We also studied a design where 50 sires were mated to 100 dams, i.e. every sire was mated to two dams and a scheme where phenotypic records were only available in generation G1.
The simulated genome consisted of 10 or 20 chromosomes each with a length of 100 cM. Mutations were simulated under the infinitesites model (Kimura, 1969), i.e. every mutation occurred at a unique randomly chosen position in the genome which guarantees that every polymorphic position has only 2 alleles. The mutation rate per base pair (assuming 1,000,000 base pairs per cM) per haplotype was 10− 8. Mutations were assumed neutral with respect to the selection of the individuals, i.e. the neutral allele model was assumed. The number of recombinations per chromosome was sampled from the Poisson distribution with an average of 1 per 100 cM. Next, every mutation was randomly distributed on the genome. This mutation process resulted in a large number of SNPs per chromosome where the typical number of SNPs generated was 3000. After 4000 generations, only SNPs with Minor Allele Frequency (MAF) N 2% were considered. Amongst those, 100 SNPs per chromosome were randomly sampled (without replacement) to be quantitative trait loci (QTL). This resulted in a total of 1000 randomly distributed QTL, and, since the number of QTL was large, the genetic model approximately behaved as an infinitesimal model, which is perhaps a worst case scenario for genomic selection, because the effect of very many genes needs to be predicted. The non-QTL SNPs were ranked on their MAF and the highest marker density was achieved by selecting the highest ranking 1000 SNPs per chromosome as genetic markers. Thus there were 10 markers per cM. Lower marker densities (5 and 1 marker per cM) were obtained by taking from these 1000 markers per chromosome every second or every 10th marker to obtain in total 500 and 100 markers per chromosome, respectively. Allelic effects of the QTL alleles were sampled from the gamma distribution with a shape parameter (β) of 0.4 and a scale parameter of 1.66 (Hayes and Goddard, 2001). The simulated cumulative amount of the genetic variance described by the QTL is presented in Fig. 1. Because linkage disequilibrium (LD) depends on both Ne and the distance between loci (d) (LD = 1 / (4 ⁎ Ne ⁎ d + 1)) (Sved, 1971) we expressed marker densities in relation to effective population size (Solberg et al., 2008a). Marker densities were thus 0.1, 0.5, or 1Ne / M with Ne equal to 1000 for the genome with 10 chromosomes. For the genome with 20 chromosomes, the marker density was 0.5Ne / M. For all 3 marker densities 100 QTL were randomly distributed on each chromosome. 2.3. Simulation of phenotypes The true breeding value of an individual was calculated as: 1000
TBVi = ∑j = 1 xij1 gj1 + xij2 gj2
where xijk is the number of copies that individual i has of the k′th QTL allele at the j′th QTL position, and gjk is the true effect of the k′th QTL allele at the j′th position.
2.2. Genomic information In addition to being performance tested for the considered trait, individuals in the test group were in the GWEBV scheme also genotyped in generations G1 to G5 in order to estimate the marker– trait associations of markers. For the scheme with phenotypic records only available in G1, the individuals were only genotyped in G1.
Fig. 1. Cumulative fraction of the genetic variance explained by the QTL.
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allele; 1 / √Hj denotes heterozygous; and 2 / √Hj denotes homozygous for the second allele, where Hj is the marker heterozygosity and thus dividing by 1 / √Hj standardises the variance of the Xij; aj is the random effect of the j′th marker and Var(aj) is assumed Vg / n where n is the number of markers; ei is random residual. The variance ratio for the mixed model equations is here n(1 − h2) / h2. Genome wide breeding values were predicted for selection candidates of the GWEBV scheme by summing the effects of the markers: n
EBVi = ∑j Xij aj : The accuracy of selection (ACC) was calculated as the correlation between true and estimated breeding values for breeding schemes BLUPEBV and GWEBV, respectively and was averaged over 100 replicates within generations G1 to G5. 3. Results 3.1. Effect of marker density and size of test group Fig. 2 presents ACC for breeding schemes BLUPEBV and/or GWEBV with a test group size of either 20 (Fig. 2a) or 40 (Fig. 2b). ACC for both GWEBV and BLUPEBV increased considerably from generations G1 to G2, e.g. from 0.59 to 0.69 with 20 sibs and 0.5Ne / M for GWEBV and from 0.43 to 0.50 for BLUPEBV, as more information became available, and reached a rather constant level at G3. ACC for the GWEBV breeding scheme was higher than ACC for the BLUPEBV scheme for all marker densities. ACC was for example 0.73 in G3 for GWEBV with a Fig. 2. Accuracy of breeding values for breeding schemes with either 20 (a) or 40 (b) sibs of the candidate, 1000 selection candidates, a heritability of 0.4 and phenotypic and genomic records available in all generations. Breeding values based on only phenotypic performance (BLUPEBV) of the sibs (Δ), breeding values based on genomic information (GWEBV) with marker densities of 0.1 (◊), 0.5 (□), or 1 (×) Ne / M.
The phenotypic values (Pi) of the individuals were generated in generations G1 to G5 for both breeding schemes GWEBV and BLUPEBV. These were simulated by adding an error term sampled from a normal distribution to the true breeding value (TBVi): Pi = TBVi + ei where εi is an error term for individual i, which was normally distributed (0, σ e2) and σ e2 was adjusted within each replicate so the heritability, h2, was 0.2 or 0.4. 2.4. Prediction of breeding values and haplotype effects The phenotypic information from the test group was used to calculate the breeding values for the BLUPEBV scheme according to Henderson (1984). The model used to calculate breeding values included the mean as a fixed effect whereas the effects of animal and error were treated as random effects. The variance ratio required in the mixed model equations is (1 − h2) / h2 where the true heritability was used as described above. For the BLUPEBV estimation, it was assumed that pedigree recording started in generation G1, i.e. the parents of generation G1 were assumed unrelated. For the GWEBV scheme, the effects of the markers were predicted using the BLUP of marker effects method described in Meuwissen et al. (2001). The statistical model used to estimate the marker effects was: n
yi = μ + ∑j Xij aj + ei where yi is the record of test individual i; μ is the overall mean; Xij denotes the j′th marker genotype: 0 denotes homozygous for the first
Fig. 3. Accuracy of breeding values for breeding schemes with phenotypic and genomic records only available in generation G1, either 20 (a) or 40 (b) full sibs of the candidate, 1000 selection candidates and a heritability of 0.4. Breeding values based on only phenotypic performance (BLUPEBV) of the sibs (Δ) or breeding values based on genomic information (GWEBV) with 0.1 (◊), 0.5 (□), or 1 (×) Ne / M.
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Fig. 4. Accuracy of breeding values based on only phenotypic performance (BLUPEBV) of 80 half and full sibs (◊) or 40 full sibs (Δ) or breeding values with genomic information (GWEBV) from 80 half and full sibs (□) or 40 full sibs (×) and a marker density of 0.5Ne / M. The number of selection candidates was 1000 and the heritability was 0.4.
Fig. 6. Accuracy of breeding values based on only phenotypic performance of the sibs (BLUPEBV) with heritability of the trait of 0.2 (×) or 0.4 (□), or breeding values based on genomic information (GWEBV) with 0.5Ne / M and heritability of 0.2 (Δ) or 0.4 (◊). The number of selection candidates is 1000 and there were 40 sibs per selection candidate.
marker density of 0.5Ne / M, while ACC for BLUPEBV was 0.50 (Fig. 2a). ACC increased with increased marker density and was for example 0.60, 0.73, and 0.75 in generation G3 with marker densities 0.1, 0.5, and 1Ne / M for the scheme with 20 sibs. When the number of sibs of the candidates was increased from 20 (Fig. 2a) to 40 (Fig. 2b), ACC in generation G3 increased from 0.73 to 0.78 for the GWEBV breeding values with marker density 0.5Ne / M and from 0.50 to 0.54 for BLUPEBV. Highest ACC of 0.83 was as expected observed in generation G5 with the highest number of sibs of 40 and the highest marker density of 1Ne / M.
3.3. Effect of family structure ACC for both the GWEBV and the BLUPEBV schemes was only slightly higher when selection candidates were evaluated based on both a half sib and a full sib group compared to when they were evaluated based on 40 full sibs only (Fig. 4). ACC in generation G2 for the GWEBV scheme was for example 0.75 for the full sib design and 0.79 for the half sib design. The reason for the slightly higher ACC for the half sib design is that the total family size is doubled because each of the 50 sires has two groups of full sibs. However, the difference in ACC between the two sib designs was small due to the large family sizes used.
3.2. Effect of number of generations with records 3.4. Effect of genome size Fig. 3 presents ACC when phenotypic and genomic information from fish in the test group was only available in generation G1. For GWEBV, marker densities of 0.1, 0.5, and 1Ne / M are presented. With 20 sibs and a marker density of 0.5Ne / M, ACC for GWEBV decreased from 0.59 in G1 to 0.49 in G2 and 0.32 in G5. The reason for the decrease in ACC is because the LD changes over generations due to recombination and thus LD estimated in generation G1 does not hold several generations later. The decrease in ACC from G1 to G2 was 23.5, 16.9, and 16.7% for marker densities 0.1Ne / M, 0.5Ne / M, and 1Ne / M and 20 sibs and was thus largest for the lowest marker density (0.1Ne / M). The latter is because there is a higher probability of recombination between markers and QTL when marker density is low.
ACC for schemes with 10 or 20 chromosomes is presented in Fig. 5. For the GWEBV scheme, ACC was lower with 20 chromosomes compared to 10 chromosomes (0.71 vs. 0.75 in G2). On the contrary, ACC for the BLUPEBV scheme, was slightly higher with 20 (0.56) chromosomes than with 10 chromosomes (0.53 in G2). 3.5. Effect of heritability ACC for both the GWEBV and BLUPEBV schemes increased as expected when the heritability of the trait was 0.4 compared to 0.2 (Fig. 6). The level of ACC for the BLUPEBV scheme in generation G2 was 0.50 with a heritability of 0.2 and 0.53 with a heritability of 0.4. For the GWEBV scheme (marker density = 0.5Ne / M), ACC was 0.72 and 0.75 in generation G2 with a heritability of 0.2 and 0.4, respectively. Hence, both for BLUPEBV and GWEBV breeding schemes the effect of heritability on ACC was small but significant (P ≤ 0.05) with the large family sizes used here. 4. Discussion
Fig. 5. Accuracy of breeding values based on only phenotypic performance (BLUPEBV) of the full sibs with 10 (□) or 20 (Δ) chromosomes or breeding values with genomic information (GWEBV) with 0.5Ne / M. and with 10 (×) or 20 (◊) chromosomes. The heritability is 0.4 and the number of sibs per candidate is 40.
In this study, we tested the hypothesis that ACC for genome-wide breeding values in aquaculture sib breeding schemes (GWEBV) is higher than ACC for traditional BLUP breeding values (BLUPEBV). The ACC was up to 33% higher for GWEBV than for BLUPEBV for all studied scenarios (marker densities, heritability values, number of sibs) because both between and within family genetic variances are utilized when estimating genome-wide breeding values compared to traditional BLUP breeding values. These results indicate that selection response in aquaculture sib breeding schemes will increase with genomic selection. Consequently, depending on the cost of genotyping, aquaculture breeding companies may benefit from including
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genomic information into their breeding scheme for traits which cannot be measured on selection candidates. 4.1. Effect of marker density, heritability, and genome size Increased marker density was expected to increase ACC (e.g. Solberg et al., 2008a) and was observed when marker density was increased from 0.1 to 0.5 and from 0.5 to 1Ne / M (e.g. from 0.62 to 0.75 and 0.77 in generation G2 and 40 full sibs). We also found a slightly higher effect on ACC of increasing marker density for a test group of size 40 than 20, indicating that with a higher marker density a higher number of phenotypes is needed. The fact that more phenotypic records are needed to increase ACC with higher marker density is also supported by the little increase in ACC that was found when increasing marker density from 0.5 to 1Ne / M. This indicates that there is an upper limit to the increase in ACC with increasing marker density if the number of phenotypic records is not increased. Figs. 2, 4 and 5 show generally an increase in accuracy with generation number with a plateau after 4 generations. The increase in accuracy may be explained by the increased number of records used to estimate marker effects, as generation number increases. However, after about four generations a balance is reached between the new information entering every generation and the decay of the value of the old records due to changes of the LD between the markers and the QTL over generations. In our study, increasing the size of the genome decreased ACC for the GWEBV breeding values but increased ACC for the BLUPEBV breeding values. An explanation for these results is that with 20 chromosomes, and twice as many QTL, the variation from the expected correlation of 0.5 between sibs is smaller than for 10 chromosomes, because with increased sample size (number of chromosomes) the coefficient of variation of the fraction of genes that the sibs have in common is reduced. Therefore, for BLUPEBV the assumed correlation of 0.5 between sibs is closer to the actual correlation between sibs with 20 chromosomes than with 10 chromosomes. However, for GWEBV, the small deviation from the expected correlation between sibs with 20 chromosomes is more difficult to predict than the larger deviation with 10 chromosomes. Thus, it is expected that, as the number of chromosomes increases the difference between BLUPEBV and GWEBV becomes smaller. In this study, ACC increased when heritability of the trait was increased from 0.2 to 0.4, which corresponds to results by Kolbehdari et al. (2007). However, contrary to expectations (Meuwissen et al., 2001), differences in ACC between BLUPEBV and GWEBV were the same for the low (0.2) and high (0.4) heritabilities. With a low heritability, sampling errors on the estimates of the haplotype effects will in general increase with increased environmental variance (Meuwissen et al., 2001). However, in this study we used a relatively high number of phenotypic records, which may explain the lack of difference in ACC between BLUPEBV and GWEBV for the two different levels of heritability. Often disease traits are recorded as all-or-none-traits, instead of as a continuous trait as was used in our simulations. The effect of this is that the information content of the records is reduced and thus that every record has less predictive value for the genetics of the individual. This effect is very similar to that of a reduced heritability, as was investigated in Fig. 6, where also the predictive value is reduced. 4.2. Assumptions and simulation design In this study, random selection was applied in order to investigate the effects of the studied design factors on ACC per se. With selection there will be a confounding between the individuals selected and the factors investigated which will depend on the design of the data and differ for different selection methods. Furthermore, ACC will be reduced due to selection to an extent that depends on the ACC itself
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and the intensity of selection. There are indications that the effect of selection on genetic variances and ACC, i.e. the Bulmer effect (Muir, 2007), can be large in GS schemes because selection changes allele frequencies and creates unfavourable linkage disequilibrium. In our study, ACC for GWEBV was higher than for BLUPEBV in all generations. Results of Muir (2007) suggest that more than 1 generation with records are needed in order to get higher ACC for GWEBV compared to BLUPEBV. However, in the present study selection candidates had no own performance for the trait, instead their breeding values were based on records from their sibs. When selection candidates have own performance for the trait, like in Muir's study ACC for BLUP breeding values is already quite high, which may explain the lower advantage of applying genomic selection in Muir's study compared to this study. Recombination between markers and QTL will over time reduce the ACC of the genome-wide breeding values using marker effects predicted from the population in the first generations. In the present study, ACC decreased with 14.7% from generations G1 to G2 and with 10.5% from G2 to G3 for the situation with 40 sibs and 0.5Ne / M. The decline in ACC was even higher for the low level of marker density (23.5% from G1 to G2 and 18% from G2 to G3), which agrees with the results of Solberg et al. (2008b). The decline in ACC was higher than estimated by Meuwissen et al. (2001) who found a decline in ACC of about 5% with an increasing number of generations between the test population and the population for which genomic breeding values were estimated. In our study, we used one generation of records while Meuwissen used two generations of records, which may explain the more rapid decline in ACC found in our study. In addition, we used a (full) sib design whereas Meuwissen et al. (2001) used a parent– offspring design for estimation of marker effects. We used the best-linear unbiased prediction (BLUP) method of marker effects by Meuwissen et al. (2001) to estimate breeding values in the current study. Bayesian methods have been found to yield higher ACC than BLUP (Habier et al., 2007; Meuwissen et al., 2001; Solberg et al., 2008a). In practice, if reliable prior distributions of variances of marker effects are available, Bayesian methods could be applied to estimate breeding values which may yield higher ACC than estimated in the current study. However, even when the BLUP method was used to estimate GWEBV, ACC was still considerably higher than that of the BLUPEBV scheme. Also in the present study, the number of QTL was rather large (1000), which implies that the genetic model was approximately polygenic (many relatively small QTL). The BLUP of marker effects model assumes exactly such a model i.e. every marker has a small effect and none have very large effects. The higher ACC for GWEBV obtained in this study compared to BLUPEBV may in particular be an advantage for traits such as disease resistance, where a large number of sibs of the selection candidates are challenge tested for the disease. Challenge testing is rather expensive and the results from this study suggest that with phenotypic records in G1 only, ACC for GWEBV in G2 (0.57 with 40 sibs and 0.5Ne / M) is much lower compared to ACC for GWEBV (0.75) with phenotypic records in all generations. This indicates that more than one generation of phenotypic records is needed to obtain a high ACC with the number of tested sibs and marker densities used in the current study. References Cameron, N.D., 1997. Selection Indices and Prediction of Genetic Merit in Animal Breeding. CAB International, Wallingford. Daetwyler, H.D., Villanueva, B., Bijma, P., Woolliams, J.A., 2007. Inbreeding in genomewide selection. J. Anim. Breed. Genet. 124, 369–376. Habier, D., Fernando, R.L., Dekkers, J.C.M., 2007. The impact of genetic relationship information on genome-assisted breeding values. Genetics 177, 2389–2397. Hayes, B., Goddard, M.E., 2001. The distribution of the effects of genes affecting quantitative traits in livestock. Genet. Sel. Evol. 33, 209–229. Henderson, C.R., 1984. Applications of Linear Models in Animal Breeding. Guelph Univ. Press, Guelph, Canada. Kimura, M., 1969. The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. Genetics 61, 893–903.
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