CAPN1 316. Warner Bratzler shear force was measured in l. lumborum samples after a 7-day aging period. A multivariate analysis of variance was performed, including shear force (WBSF), final weight (FW), average daily gain (ADG), backfat thickness (BFT), average monthly fat thickness gain (AMFTG), rib-eye area (REA), and beef rib-eye depth (RED) as dependent variables. The CAPN1 316 genotype was statistically significant. Univariate analyses were done with these variables. The marker genotype was statistically significant (p < 0.05) for WBSF , FW , and ADG  Shear force, final weight and average daily gain were significantly different according to the CAPN1 316 marker genotypes. The marker genotype was statistically significant in the multivariate analysis (p = 0.001). The first characteristic root explained 89% of the differences among genotypes. WBSF, FW and ADG were the most important traits in the first vector, indicating that animals with the marker genotype for lowest WBSF also have the lowest FW and ADG. The objective of this paper was to determine the association of a SNP in the μ-calpain gene at position 316 with growth and quality of meat traits of steers grown on pasture. Fifty-nine Brangus and 20 Angus steers were genotyped for  CAPN1, which encodes the large subunit of μ-calpain, an enzyme involved in the post-mortem tenderization process (CAPN1 316) on meat tenderness, measured after a 7-day aging period.Bovine meat quality is defined by several traits that are difficult to evaluate in the live animal. Recently, significant research efforts have focused on the identification of genes influencing production traits in beef cattle, including meat quality. Because of its relevance, meat tenderness has received special attention. In this context, one of the most studied genes is  process . Page etAccording to The objective of this paper was to determine the association of an SNP in position 316 of the μ-calpain gene with growth and meat quality traits of steers grown on pasture.A study was conducted on 59 Brangus and 20 Angus steers.The Brangus steers were representative of the breeds of three different commercial herds . Each breeder contributed with 20 steers, but one BR3 steer had to be excluded from the analysis because, as its data were out of range (widely exceeding 3σ), it was assumed that an error had occurred in the WBSF measurement. The animals were raised on pastures in their original herds until weaning, which occurred in March, 2004. In April, they were transferred to the Balcarce Experimental Station, National Institute of Agricultural Research (INTA), where they were finished on perennial pastures. Individual sire identifications were not available.The Angus steers were chosen at random from two herds at the Balcarce Experimental Station. One of these herds produced their own replacements (A1). The cows of the other herd had their origin in this same herd, but commercial bulls had been introduced (A2). Ten A1 and ten A2 steers were used in this experiment. In that particular year (2004), the A1 and A2 herds had been sired by four and seven bulls, respectively. Thus, the animals were grouped in five breed-herd-of-origin groups .Fattening started in April, 2004, on perennial, fertilized pastures, when the animals were about 8 to 10 months old, and ended in June, 2005. The steers were weighed monthly, and ultrasound backfat thickness, as well as rib-eye area and depth  were measured. The steers were slaughtered when at least 50% of a breed-herd group reached 6 mm of backfat thickness. Hence, slaughter took place between March and May, 2005, and the slaughter group was deliberately confounded with the breed-herd group.th, 12th and 13th ribs was removed from each left half carcass. The block was deboned and divided into three pieces that were vacuum-packed.The animals were slaughtered at a commercial beef processing facility after 24 h rest in paddocks with available water, following SENASA  rules. Meat tenderness was measured as Warner-Bratzler shear force (kg) at 7 days post-mortem. After slaughter and following a 24 h cooling period at 1 to 5 °C, the block of steaks corresponding to the 11longissimus lumborum muscle. Samples were immersed in plastic bags and boiled in a water bath at 70 °C for 50 min. The cooked steaks were cooled under running tap water for 40 min. The bags were drained and the cuts were gently mopped dry with a paper towel. Five 2.5 cm-diameter cores were removed from each steak, parallel to the muscle fibers. The cores were sheared at their middle point with a 50 kg compression load cell and a Warner-Bratzler V-notch blade mounted on an Instron Testing Machine (model 4442), at a crosshead speed of 50 mm/min. A single peak-shear force measurement was obtained for each core, and these results were averaged to obtain a single WBSF (kg) value for each sample.One of these pieces was randomly assigned to maturation treatment at 1-5 °C. After ageing, the meat samples were frozen and kept at -20 °C until they were thawed for the Warner-Bratzler determination (WBSF), performed at the Meat Laboratory of the School of Agriculture at the University of Buenos Aires. Steaks (2.5 cm thick) were thawed at room temperature for 24 h. External fat, peripheral connective tissue and muscles were removed from each steak, leaving only the DNA was extracted from 500 μL of blood using the phenol/chloroform method and ethanol precipitation, and resuspended in 10 mM Tris HCl buffer.CAPN1 316 is a cytosine/guanine (C/G) polymorphism in exon 9 of the CAPN1 gene on BTA 29 (CAPN1 DNA sequence (GenBank accession AF252504). The primer sequences used for genotyping the 316 marker were:Forward: CCAGGGCCAGATGGTGAA, and reverse: CGTCGGGTGTCAGGTTGC.Btgl enzyme .The annealing temperature was 62.5 °C, and the amplified DNA was digested with the CAPN1 316 genotypes found . Contrast analyses were performed to test for non-additive or dominance effects: CG- (CC+GG) for the statistically significant traits.Monthly weight and backfat measurements were used to calculate individual average daily gain (ADG) and average monthly backfat gain (AMBG) by regression. Univariate analyses of variance were performed for the following dependent variables: WBSF, AMBG, ADG, and final weight (FW), which was the last weight taken before slaughter, and the last ultrasound measurements of backfat thickness (BFT), rib-eye area (REA) and rib-eye depth (RED). Fixed effects were the breed-herd group  and the i.e., breed-herd group and CAPN1 316 genotype.A multivariate analysis of variance was made, including WBSF, AMBG, ADG, FW, BFT, REA and RED. The fixed effects were the same as in the univariate analyses, CAPN1 genotype effect. The alternative was a genotype effect different from zero. For this purpose, we used the Hotelling-Lawley trace test statistics as the multivariate linear hypothesis and Roys greatest characteristic root statistics  means of the two canonical variables for each CAPN1 genotype, obtained by multiplying the vector of the CAPN1 genotypes least squares means of the dependent variables by the characteristic vector. The SAS program  product-moment correlations between the animals' canonical variable and each trait measured in the animal, indicating the importance of the traits in the canonical variable and, consequently, in the differences among  program  was usedIn the univariate analyses, all traits differed (p < 0.05) among breed-herd groups (results not shown), whereas the marker genotype was significant only for WBSF, ADG and FW (p < 0.05). The least squares means for each marker genotype are presented in Multivariate analysis (Hotelling-Lawley Test) indicated differences in genotypes and breed-herd groups. Similarly, the Hotelling-Lawley Trace and Roy's greatest characteristic root tests were statistically significant for genotypes (p = 0.0010 and p < 0.0001 respectively). A difference was also found for breed-herd groups .Characteristic vectors 1 and 2 for genotypes, their characteristic roots and the correlations between canonical variables and the traits are shown in Eighty-nine percent of the differences between genotypes were due mainly to differences in WBSF, FW and ADG. During fattening, steers which were homozygous for allele G at marker position 316 grew faster (higher ADG), were heavier at a similar backfat thickness, and their meat had higher WBSF values than steers with genotypes CG and CC . RED andVector 2, orthogonal to the first one, explained the remaining 11% of the variance. The correlations of RED and REA with the canonical variable were the highest, while the correlations of all the other traits with the canonical variable were low, indicating their small influence on the differences among genotypes explained by this vector.BFT and AMBG were not important for the differentiation of genotypes in any one of the vectors. This result was expected, once all steers were slaughtered at a similar BFT.The canonical variables 1 and 2 for each genotype are shown in According to the results of the multivariate analysis of variance, if animals were selected based on this marker, a genetic improvement regarding WBSF would be expected, as reported by In the present paper, the analysis was based on phenotypic data, but reports from the literature indicate that, along with loci affecting beef tenderness, other loci associated with weaning weight and carcass weight were mapped to the distal region of bovine chromosome 29 BTA29 (Cattle Quantitative Trait Locus data base). On the other hand, it is well known that the genetic and phenotypic correlations among weights at different ages are positive  has an effect on tenderness specifically within this period. No extrapolations can therefore be made to other data sets concerning different meat aging processes.Partial correlation coefficients were obtained among the dependent variables  from theGenetic correlations are the result that dictate the association of breeding values for genes coding for traits of interest. In this paper, only the phenotypic variability of the traits was analyzed. In view of the results, it would be desirable to generate information that allows working with the genetic variability of the traits studied, which might provide a better explanation for our findings. For example, breeding instead of phenotypic values could be used, which were not available for this data set. A larger number of animals would also be desirable, especially because of the low frequency of genotype CC. It is also possible that in this sample there was a particular association of alleles in chromosome 29, which may not necessarily occur in other samples too. The aging of the meat is a very important factor in determining WBSF values. Therefore, experiments with meat maturing periods different from the 7 days considered here will certainly show different results. Considering one gene at a time, their direct and correlated effects are only a small contribution to the phenotypic result. As the number of individual genes studied increases, it will be possible to disentangle the nature of these complex biological processes taking place in particular environments.The method of analysis used in this study is suitable for exploring the association of the molecular markers with several traits.CAPN1 316 marker genotypes in this study. Choosing animals with the favorable CAPN1 316 marker genotype for tenderness resulted in selecting animals with lower average daily gain and final weight. Further experiments with larger samples should be conducted, in order to explore the consequences of selection for the marker on other economically important traits. Since antagonism between selection criteria is not uncommon in animal breeding, a careful analysis of correlated responses is required before establishing long-term selection objectives in beef cattle.In conclusion, along with tenderness of aged meat, other traits such as final weight and average daily gain differentiated the


Genome-wide association studies for complex traits are based on the common disease/common variant (CDCV) and common disease/rare variant (CDRV) assumptions. Under the CDCV hypothesis, classical genome-wide association studies using single-marker tests are powerful in detecting common susceptibility variants, but under the CDRV hypothesis they are not as powerful. Several methods have been recently proposed to detect association with multiple rare variants collectively in a functional unit such as a gene. In this paper, we compare the relative performance of several of these methods on the Genetic Analysis Workshop 17 data. We evaluate these methods using the unrelated individual and family data sets. Association was tested using 200 replicates for the quantitative trait Q1. Although in these data the power to detect association is often low, our results show that collapsing methods are promising tools. However, we faced the challenge of assessing the proper type I error to validate our power comparisons. We observed that the type I error rate was not well controlled; however, we did not find a general trend specific to each method. Each method can be conservative or nonconservative depending on the studied gene. Our results also suggest that collapsing and the single-locus association approaches may not be affected to the same extent by population stratification. This deserves further investigation. Classical genome-wide association studies have successfully detected many common genetic variants that are associated with complex traits. It is likely that low-frequency or rare variants are also contributing to genetic risk . The staSeveral new methods have been recently proposed to tackle the rare variant problem -6. The pIn this paper, we evaluate and compare the power of different collapsing methods for detecting association of multiple rare variants with a quantitative trait. We first focus on the unrelated individuals data and then incorporate some of these approaches within the general framework of the mixed model for association analysis in the family data set of Genetic Analysis Workshop 17 (GAW17). We tried to answer the following questions: Does the use of a subset of rare variants perform better than using all variants? Do the collapsing approaches perform similarly with unrelated individual and family data sets? The analyses were performed using the GAW17 data with knowledge of the answers [We studied the quantitative trait Q1 influenced by 39 variants in nine independent genes.G contains GJ variants denoted jSNP, j = 1, …, GJ, and that jMAF is the minor allele frequency of jSNP. Let Y =  be the observations of the phenotype Q1 in N unrelated individuals, and let iGX be the vector of genotypes of the SNPs in gene G for individual i. The genotypes are coded 0, 1, or 2, depending on the number of minor alleles.We carry out the association test at the gene level. Assume that a gene Tmaf be a selection criterion on minor allele frequency (MAF) values. The association methods we have investigated vary according to a predefined Tmaf value  and on the number of collapsing groups. They are all based on a linear regression modeling the relationship between the trait Y and the SNP data within a gene. We briefly review these methods in this Methods section. More details are given by Dering et al. [Let g et al. .Tmaf, where Tmaf is a predefined selection value.The univariate collapsing approaches use only a subset of variants that satisfy the constraint MAF ≤ iGX(maf) be the vector of genotype scores of the SNPs with MAF <Tmaf, and let GJ(maf) be the length of the vector iGX(maf). The variable C = iGC(maf)  denotes the two collapsing strategies that we used: collapsing absence/presence (CA) and collapsing proportion (CP). For the CA strategy:The first univariate collapsing approach is the collapsing and summation test (CAST). Let and for the CP strategy:G within an individual [Tmaf at which an individual i carries at least one copy of the minor allele [Y = Cβ + ε, where 2 is the residual variance.Equation (1) is based on the presence or absence of the minor allele at any rare variant in gene dividual . Equatior allele . The modβ can be tested with a likelihood ratio test that follows a chi-square distribution with 1 degree of freedom (df).The effect of Tmaf but maximizes the statistic according to Tmaf. All Tmaf values observed in the gene G are considered. For each Tmaf, a regression z-score is computed. Let zmax be the maximum z-score across all Tmaf values. The test of association is based on zmax, and its statistical significance is evaluated empirically by permutation.The second univariate collapsing method is the variable-threshold (VT) approach , which uTmaf = 0.5 . The collapsing variable C for subject i in the WS approach is given by:The last univariate collapsing method is the weighted-sum (WS) approach , which iwhere:G, a genetic score is calculated as:For each gene G is assessed empirically by permutation.The significance of ZTmaf = 1% and includes all k remaining SNPs, jX1,…,k, individually.The combined multivariate and collapsing (CMC) method originally proposed by Li and Leal  uses a mThe multivariate model (denoted here as CMC3) is:j, jβ ≠ 0, j = 0, …, k) is assessed with the likelihood ratio test, which follows a chi-square distribution with (k + 1) df.Evidence of association , the multivariate model also contains the CA collapsing variable of the other SNPs . In contrast, in the second extension (denoted CMC2), the other SNPs are included individually in the multivariate model.The CMC1 model is then written as:and the test of association is a likelihood ratio test with 2 df.k is the number of SNPs and 1% ≤ MAF ≤ 5%. Evidence of association is assessed with the likelihood ratio test with (k + 1) df.The CMC2 model is the same as Eq. (6), where G, association with each SNP was tested using the likelihood ratio test. For each gene G, we obtained GJ likelihood ratio test statistics, each with 1 df. The evidence of association at the gene level was based on the maximum of the GJ likelihood ratio test statistics.For comparison purposes, we also carried out a single-locus association test. For a gene http://genetics.bwh.harvard.edu/vt/dokuwiki/) [Single-marker (SM) tests were conducted with PLINK, version 1.07 . The R.2We used the measured genotype (MG) test , which iwhere:i. The SNP data in relatives were collapsed as described under the CA, CP, and WS collapsing approaches. In these three approaches, the test of association is a likelihood ratio test with 1 df. In addition, we also carried out the bivariate CMC1 approach using the likelihood ratio test with 2 df. We could not evaluate the VT approach because it maximizes Tmaf. We carried out the MG test using the QTDT software (http://www.sph.umich.edu/csg/abecasis/QTDT/).α = 5%.The empirical distribution of each association approach was evaluated in unrelated individuals and in family data. Type I error and power rates were estimated by testing association of Q1 to each of the seven false causal genes and each of the nine true causal genes, respectively, using the 200 replicates. Type I error and power rates were derived at a nominal level of Tmaf = 1% and 5%, respectively; CP1 and CP5 with Tmaf = 1% and 5%, respectively; and VT, WS, CMC1, CMC2, CMC3, and SM. For the WS and VT tests, we used empirical P-values. For all remaining association tests we used tabulated nominal P-values. In each replicate, we tested for association of Q1 with each of the 16 genes using each of the 10 approaches. For each gene and for each association procedure we computed the proportion of replicates having a P-value ≤ α. For the SM approach, we applied a Bonferroni correction to account for the multiple tests; we computed the proportion of replicates such that the lowest P-value out of the GJ SNPs was less than or equal to α/GJ.In the unrelated individuals data set, we evaluated association with Q1 using 10 approaches: CA1 and CA5 with Tmaf = 1% and 5%, respectively; CP1 and CP5 with Tmaf = 1% and 5%, respectively; and SM. We also evaluated the WS approach but used the tabulated P-value derived from a chi-square distribution with 1 df.In the family data set, we evaluated similarly the following five approaches: CA1 and CA5 with VEGFC, VEGFA) to 11 (FLT1). One causal gene (VEGFC) has one single SNP, and thus only one association approach (SM) can be applied. For the noncausal genes, the number of SNPs per gene ranges from 6 (CTSS) to 83 (LY75), and, as for the causal genes, most (>70%) of the SNPs are uncommon (MAF < 5%).The characteristics of the nine causal and seven noncausal genes are shown in Table MAPT, IFI44). Conversely, for some other genes , the type I error rates of some approaches are inflated, whereas the other approaches tend to be conservative.Table Overall, the SM and CMC3 approaches appear to have inflated type I errors more frequently. Interestingly, these two approaches are the only ones that used the common SNPs individually. Clearly, several SNPs in these sequence data, including those in our noncausal genes, have population-specific allele frequencies. Given that the genotype data were not simulated, we hypothesize that the inflated rates could be explained by the observed differences in the mean of Q1 between the four populations  analysis with Eigenstrat  using thKDR and FLT1 genes. Conversely, all but two methods performed poorly (power < 10%) for two genes: For ELAVL4 the power was greater than 30% using the SM and CMC3 approaches, and for HIF3A the power was greater than 17% for the CMC2 and CMC3 approaches. For the remaining four genes, one of the pooling methods outperformed the SM method after a Bonferroni correction. In these data, the CA and CP approaches had roughly similar power, and so, in what follows, the CP method will serve as a reference.In conclusion, to estimate the power of these approaches in the data sets, we used two strategies Table : Power wTmaf seems to have a large effect on power, and, in general, the power is higher when the criteria are less stringent (Tmaf = 5% vs. 1%). Although this is not surprising for genes with causal SNPs having 1% < MAF < 5% , we made the same observation for genes with all causal SNPs having a MAF < 1%  or multivariate (CMC3) collapsing methods that uses all SNPs showed better power than the CP method. This again may be explained by allele correlation among SNPs. When adjusting for population stratification, again, all approaches had the greatest power for the FLT1 and KDR genes and the lowest power for the ELAVL4 and HIF3A genes. Nonetheless, most power estimates were lower, and the power drop was noticeable, especially for the FLT4 and HIF1A genes. However, it is unclear whether this drop is fully explained by the lower values of the adjusted false-positive rates.The choice of the threshold MAPT gene, for which most type I errors were biased upward. This gene is located in a genomic region with a low recombination rate and a long range of linkage disequilibrium. All association approaches show high and similar power rates for VEGFA. High power (>80%) was observed for FLT1 using the SM and CP approaches and for KDR using the CA(0–5%), CP(0–5%), VT, and CMC1 approaches. In general, as observed in the unrelated individuals data set, the CA and CP approaches showed greater power under the less stringent Tmaf criterion of 5% versus when Tmaf = 1%.Table FLT1, KDR) were consistently detected with good power (>80%) in the unrelated individual and family data sets, irrespective of the association approach. One gene (VEGFA) was detected in the family sample but not in the unrelated individuals data set . Conversely, ARNT was detected in the unrelated individuals data set  but not in the family data (power = 12%).Two causal genes . In the same vein, including all SNPs, whether by means of a univariate or a multivariate collapsing approach, can improve the power. In addition, a few of the causal genes were detected in both the related and the unrelated individuals data, whereas other causal genes were detected only in either the unrelated individuals or the family data. However, in these data the power of association was often limited. More important, we found that type I error rates may be highly variable between genes and between approaches.We found that for some genes collapsing approaches may be powerful tools to detect multiple rare variants for complex traits. In particular, the choice of the threshold We faced the challenge of assessing the proper type I error to validate our power comparisons. We acknowledge that our type I and type II error rates may not be generalized because of the way the GAW17 data were simulated: Phenotype but not genotype data were generated. Further, because the genotypes of founders did not vary between replicates, each family was either always informative  or never informative  for testing association to a given causal variant.Finally, our results also raise an interesting point that might deserve future investigation, namely, that the collapsing and the single-locus association approaches may not be affected to the same extent by population stratification. Our results suggest that collapsing approaches may be more robust, especially in the presence of multiple variants.The authors declare that there are no competing interests.MS, ASP and MMacé performed the statistical analyses. MS, NB, and MMartinez drafted the manuscript. MMartinez conceived the study design and coordinated the study. All authors read and approved the final manuscript.


Genomic evaluations in Holstein dairy cattle have quickly become more reliable over the last two years in many countries as more animals have been genotyped for 50,000 markers. Evaluations can also include animals genotyped with more or fewer markers using new tools such as the 777,000 or 2,900 marker chips recently introduced for cattle. Gains from more markers can be predicted using simulation, whereas strategies to use fewer markers have been compared using subsets of actual genotypes. The overall cost of selection is reduced by genotyping most animals at less than the highest density and imputing their missing genotypes using haplotypes. Algorithms to combine different densities need to be efficient because numbers of genotyped animals and markers may continue to grow quickly.Genotypes for 500,000 markers were simulated for the 33,414 Holsteins that had 50,000 marker genotypes in the North American database. Another 86,465 non-genotyped ancestors were included in the pedigree file, and linkage disequilibrium was generated directly in the base population. Mixed density datasets were created by keeping 50,000 (every tenth) of the markers for most animals. Missing genotypes were imputed using a combination of population haplotyping and pedigree haplotyping. Reliabilities of genomic evaluations using linear and nonlinear methods were compared.Differing marker sets for a large population were combined with just a few hours of computation. About 95% of paternal alleles were determined correctly, and > 95% of missing genotypes were called correctly. Reliability of breeding values was already high (84.4%) with 50,000 simulated markers. The gain in reliability from increasing the number of markers to 500,000 was only 1.6%, but more than half of that gain resulted from genotyping just 1,406 young bulls at higher density. Linear genomic evaluations had reliabilities 1.5% lower than the nonlinear evaluations with 50,000 markers and 1.6% lower with 500,000 markers.Methods to impute genotypes and compute genomic evaluations were affordable with many more markers. Reliabilities for individual animals can be modified to reflect success of imputation. Breeders can improve reliability at lower cost by combining marker densities to increase both the numbers of markers and animals included in genomic evaluation. Larger gains are expected from increasing the number of animals than the number of markers. Breeders now use thousands of genetic markers to select and improve animals. Previously only phenotypes and pedigrees were used in selection, but performance and parentage information was collected, stored, and evaluated affordably and routinely for many traits and many millions of animals. Genetic markers had limited use during the century after Mendel's principles of genetic inheritance were rediscovered because few major QTL were identified and because marker genotypes were expensive to obtain before 2008. Genomic evaluations implemented in the last two years for dairy cattle have greatly improved reliability of selection, especially for younger animals, by using many markers to trace the inheritance of many QTL with small effects.More genetic markers can increase both reliability and cost of genomic selection. Genotypes for 50,000 markers now cost <US$200 per animal for cattle, pigs, chickens, and sheep. Lower cost chips containing fewer  markers and higher cost chips with more  markers are already available for cattle, and additional genotyping tools will become available for cattle and other species in the near future. All three billion DNA base pairs of several Holstein bulls have been fully sequenced and costs of sequence data are rapidly declining.Reliabilities of genomic predictions were compared in previous studies for up to 50,000 actual or 1 million simulated markers. Reliabilities for young animals increased gradually as marker numbers increased from a few hundred up to 50,000 , and incIncreasing marker numbers above 20,000 up to 1 million linked markers resulted in almost no gains in reliability in a simulation of 10 chromosomes and 1,500 QTL . Larger Many genotypes will be missing in the future when data from denser or less dense chips are merged with current genotypes from 50,000-marker chips or when two different 50,000-marker sets are merged, as is being done in the EuroGenomics project ,12. MissFewer markers can be used to trace chromosome segments within a population once identified by high-density haplotyping. Without haplotyping, regressions could simply be computed for available SNP and the rest disregarded. With haplotyping, effects of both observed and unobserved SNP can be included. Transition to higher density chips will require including multiple marker sets in one analysis because breeders will not re-genotype most animals.Simulated genotypes and haplotypes can be more useful than real data to test programs and hypotheses. Examples are analyses of larger data sets than are currently available or comparison of estimated haplotypes with true haplotypes, which are not observable in real data. Most simulations begin with all alleles in the founding generation in Hardy-Weinberg equilibrium and then introduce linkage disequilibrium (LD) using many non-overlapping generations of hypothetical pedigrees  or fewerGoals of this study are to 1) impute genotypes using a combination of population and pedigree haplotyping, 2) compute genomic evaluations with up to 500,000 simulated markers, and 3) evaluate potential gains in reliability from increasing numbers of markers.Unknown genotypes can be made known (imputed) from observed genotypes at the same or nearby loci of relatives using pedigree haplotyping or from matching allele patterns (regardless of pedigree) using population haplotyping. Haplotypes indicate which alleles are on each chromosome and can distinguish the maternal chromosome provided by the ovum from the paternal chromosome provided by the sperm. Genotypes indicate only how many copies of each allele an individual inherited from its two parents.Fortran program findhap.f90 was designed to combine population and pedigree haplotyping. Genotypes were coded numerically as 0 if homozygous for the first allele, 2 if homozygous for the second allele, and 1 if heterozygous or not known; haplotypes were coded as 0 for the first allele, 2 for the second allele, and 1 for unknown to simplify matching. The algorithm began by creating a list of haplotypes from the genotypes in the first pass, and the process was iterated so genotypes earlier in the file could be matched again using haplotype refinements that occurred later.Steps used in the population haplotyping algorithm were: 1) each chromosome was divided into segments of about 500 markers each when analyzing the 500,000 marker or mixed datasets and 100 markers each for 50,000 marker data; 2) the first genotype was entered into the haplotype list as if it was a haplotype; 3) any subsequent genotypes that shared a haplotype were then used to split the previous genotypes into haplotypes; 4) as each genotype was compared to the list, a match was declared if no homozygous loci conflicted with the stored haplotype; 5) any remaining unknown alleles in that haplotype were imputed from homozygous alleles in the genotype; 6) the individual's second haplotype was obtained by subtracting its first haplotype from its genotype, and the second haplotype was checked against remaining haplotypes in the list; 7) if no match was found, the new genotype (or haplotype) was added to the end of the list. Unknown alleles in the genotype were stored as unknown alleles in the haplotype; 8) the list of currently known haplotypes was sorted from most to least frequent as haplotypes were found for efficiency and so that more probable haplotypes were preferred.Steps 4) and 6) of the algorithm for population haplotyping are demonstrated in Figure Iteration proceeded as follows. The first two iterations used only population haplotyping and not the pedigree. The first used only the highest density genotypes, and later iterations used all genotypes. The third and fourth iterations used both pedigree and population methods to locate matching haplotypes. Known haplotypes of genotyped parents (or grandparents if parents were not genotyped) were checked first, and if either of the individual's haplotypes were not found with this quick check then checking restarted from the top of the sorted list. For example, the algorithm in Figure Imputation success was measured in several ways. Percentages of alleles missing before and after imputation indicated the amount of fill needed and remaining. Percentages of incorrect genotypes were calculated across all loci including the genotypes observed, the haplotypes imputed, and the remaining haplotypes not imputed but simply assigned alleles using allele frequency. An alternative error rate counted differences between heterozygous and homozygous genotypes as only half errors and differences between opposite homozygotes as full errors across the imputed and assigned loci but not including the observed loci . The perMethods to simulate LD were derived and the simulation program of  was modiInitial LD was generated by establishing marker properties for the population, simulating underlying, unobservable, linked bi-allelic markers that each have an allele frequency of 0.5, and setting minor allele frequencies for observed markers to <0.5 by randomly replacing a corresponding fraction of the underlying alleles by the major allele.Direction of linkage phase for each marker with the previous marker was set to positive (coupling) or negative (repulsion) with 0.5 probability, and this process was repeated across each chromosome. Marker alleles were coded as 1 or 2 and their frequencies were distributed uniformly between 0 and 1. After establishing these initial marker properties, each founding haplotype from an unknown founder parent was generated as follows: 1) for the first locus on each chromosome, an underlying allele was chosen randomly with 0.5 frequency; 2) subsequent loci on the same chromosome were set to the same allele or opposite allele based on direction of initial linkage phase until a break point occurred; 3) if a uniform variate exceeded the LD decay parameter defined as 1 - the fraction of recombinations that had occurred between adjacent loci, then that haplotype block ended and the next allele was chosen randomly with 0.5 frequency; and 4) observed alleles were obtained from the underlying alleles using the allele frequencies. A uniform number was generated at the beginning of each block, and underlying alleles within the block were replaced by the major allele if the minor allele frequency was greater than twice the minor allele frequency at that locus.The benefit of the underlying markers is that a single parameter can model the gradual decay of linkage disequilibrium as marker distances increase, similar to an autoregressive correlation structure. The idea is similar to using underlying normal variables for categorical traits because the math is simpler on the underlying scale. Each allele in the founding haplotypes required generating only two uniform random numbers: one to determine underlying LD blocks and a second to increase frequency of the major allele. The LD blocks mimic segments preserved from unknown generations prior to the pedigree. The simulation process resulted in different lengths, locations of breakpoints, and patterns of rare alleles for each founding haplotype segment.The population simulated included 8,974 progeny-tested bulls, 14,061 young bulls, 4,348 cows with records and 6,031 heifers, as well as 86,465 non-genotyped ancestors in the pedigrees. The founding animals were mostly born before 1960, about 10 generations ancestral to the current population. This population structure was identical to the 33,414 Holstein animals with BovineSNP50 genotypes in the North American database as of January 2010. Many of these animals share long haplotypes because, for example, three bulls each had >1,000 genotyped progeny in the dataset.Genotypes for 500,000 markers were simulated, and the 50,000 marker subset was constructed using every 10th marker. The simulated percentages of missing genotypes and incorrect reads were 1.00 and 0.02%, respectively, based on rates observed for the BovineSNP50 chip. The LD decay parameter for adjacent underlying alleles was set to 0.998, with an average of 16,667 markers per chromosome, spaced randomly. Linkage disequilibria derived from the simulated and from real genotypes were compared by squared correlations of marker genotypes plotted against physical distance between markers. The haplotyping algorithm was tested using a single simulated chromosome with a length of 1 Morgan, which is the average length for cattle chromosomes. Gains in reliability from genomic evaluation were tested using sums of estimated allele effects across all 30 simulated chromosomes.True haplotypes from the simulation allow proportions of correctly called linkage phases and paternal allele origins to be checked. Correct calls were summarized for each animal to determine how successful the algorithm was for different members of the pedigree. These estimates of genotype or haplotype accuracy from simulation are needed because true values are not available for comparison with real data. Genotypes, linkage phases and haplotypes were estimated for all animals and compared with their true genotypes and haplotypes from simulation. For each heterozygous marker, paternity was considered to be correctly called if the allele presumed to be from the sire was actually from the sire. Linkage phase was considered to be correctly called if estimated phase matched true phase for each adjacent pair of heterozygous markers.s) were converted to have heavy tails using the function 2abs(s - 2). The locus with the largest effect contributed 2 to 4% of the additive genetic variance across five replicates, and the number of QTL was 10,000, which is greater than the 100 QTL used previously [Effects of quantitative trait loci (QTL) were simulated with a heavy-tailed distribution. Standard, normal effects , and error variance for each animal equalled additive genetic variance times the reciprocal of reliability minus one, i.e. σa2 (1/RELprog -1).Five replicates of the simulated data were analyzed as five traits, and QTL effects for each trait were independent. Just one set of genotypes contained the five QTL replicates for efficiency as in . All QTLTwo mixed density data sets were simulated, which included genotypes from both 500,000- and 50,000- marker chips, to determine if a few thousand higher density genotypes would be sufficient to impute, using program findhap.f90, the missing genotypes for the other animals genotyped with 50,000 markers. The first analysis included 1,406 randomly chosen young bulls with 500,000 markers and the other 32,008 animals with 50,000 markers. The second analysis had 3,726 bulls with 500,000 markers, including 2,140 older bulls that had 99% reliability plus the same 1,406 young bulls, and the other 29,788 animals had 50,000 markers.y) was modelled with an overall mean (Xb), genotypes minus twice the base allele frequency (Z) multiplied by allele effects (u), a vector of polygenic effects for genotyped animals (p), and a vector of errors (e) with differing variance depending on RELprog:The vector of observed, deregressed observations  assumed to be 10 and 0% of genetic variance with 50,000 and 500,000 markers, respectively. Values of poly have been assumed to equal from 0 to 20% of additive genetic variance in most national evaluations of actual 50,000-marker data; poly should increase with fewer or decrease with more available markers. An initial test with 500,000 markers indicated a 0.1% decrease in reliability and slower convergence with 5% poly as compared to 0% poly in the model.Dense markers account for most but not all of the additive genetic variation, and the remaining fraction of variance is the polygenic contribution (Linear and nonlinear models were both applied to the simulated data using the same methods as . The nonmax) is limited by the maximum marker density and by the size of the reference population. As the reference population becomes infinitely large, reliability should approach 1 minus poly because poly is the residual QTL variance not traceable by the markers on the chip.Approximate reliability formulas are needed because correlations of true breeding value (BV) with genomic estimated breeding value (GEBV) are not available in actual data. The maximum genomic reliability that can be obtained in practice (RELmax) from the reference population can be obtained by summing traditional reliabilities (RELtrad) minus the reliabilities of parent average (RELpa), multiplying by the ratio of error to sire variance (k), and dividing by the equivalent reference size (n) needed to achieve 50% genomic REL [Total daughter equivalents , and these are added to DEmax adjusted for any additional error introduced by genotyping at lower SNP density. The reduced daughter equivalents from genomics (DEgen) can be calculated from the squared correlation between estimated and true genotypes averaged across loci (RELsnp) for each animal as:Each animal's traditional REL is converted to daughter equivalents  = 6927, and the variance ratio assumed was 15. For the GEBV of young animals, the observed RELtot was 84.0% with 500,000 markers. Removal of the contribution from PA reduced this slightly to 82.5%. The remaining polygenic variation not captured by the 500,000 markers was not estimated but assumed to be only 1%. Thus, DEmax equalled 15(.825/.99)/(1 - .825/.99) = 74.8 and from this the value of n was 1389.Calculations to obtain the REL in Figure tot expected from different reference populations and marker numbers were calculated as follows. With 50,000 instead of 500,000 markers, DEmax is the same but RELmax from the observed reference population after removing the contribution from RELpa was 80.5% instead of 82.5%. This difference in RELmax gave a solution for poly of 1 - .99(.805/.825) = 3.4% with 50,000 markers instead of 1% assumed with 500,000 markers. Similar math applied to RELmax from 3,000 vs. 43,000 markers with real data in another study [poly of 30%. Those values of poly produced the differing RELtot expected with 3,000, 50,000, or 500,000 markers, for example 72.8%, 94.3%, 96.5%, respectively, with 100,000 animals in the reference population. Methods to estimate proportions of correctly called genotypes or squared correlations of estimated and true genotypes are needed for individual animals so that RELsnp can be included in the published REL.The RELer study  gave a sObserved reliabilities from actual genotypes may be lower than those from simulation  and are http://aipl.arsusda.gov/software/index.cfm for download. Official genomic evaluations of USDA have used findhap.f90 to impute and include genotypes of dams since April 2010 and 3,000-marker genotypes since December 2010.Algorithms for imputation are rapidly evolving to meet the demands of growing genomic datasets. Several programs such as those tested by Weigel et al.  are avaiFurther improvements to imputation algorithms will increase accuracy and allow smaller fractions of animals to be genotyped at highest density. New methods are needed for combining multiple densities, for example 3,000, 50,000, and 500,000 markers, in the same dataset. During the 5 months of review for this manuscript, version 2 of findhap.f90 was released with better properties than those documented here for version 1. Use of pedigree haplotyping followed by population haplotyping can further improve call rates and reduce error rates with similar computation required .The expense of genotyping 1,000-2,000 animals at higher density can be justified for a large population such as Holstein, but larger benefits may be needed if similar numbers are required within each breed. Experimental design is becoming a more important part of animal breeding to balance the speed, reliability and cost of selection. With many new technologies and options available, breeders and breeding companies need accurate advice on the potential of each investment to yield returns. Costs of genotyping are decreasing rapidly, and imputation using less dense marker sets allows the missing genotypes to be obtained almost for free.Genotypes and genomic computations are rapidly expanding the data and tools available to breeders. Very high marker density increases reliability of within-breed selection slightly (1.6%) in simulation, whereas lower densities allow breeders to apply cost-effective genomic selection to many more animals. Numbers of reference animals affect reliability more than number of markers, and animals with imputed genotypes contribute to the reference population. New methods for combining information from multiple data sets can improve gains with less cost. Individual reliabilities can be adjusted to account for the number of markers and the accuracy of imputation. More precise estimates of reliability allow breeders to properly balance benefits vs. costs of using different marker sets.Computer programs that combined population haplotyping with pedigree haplotyping performed well with mixtures of 500,000 and 50,000 marker genotypes simulated for subsets of 33,414 animals. Population haplotyping methods rapidly matched DNA segments for individuals with or without genotyped ancestors, and pedigree haplotyping efficiently imputed genotypes of the non-genotyped parents and correctly filled most missing alleles for progeny genotyped with lower marker density. Accurate imputation can give breeders more reliable genomic evaluations on more animals without genotyping each for all markers.max: genomic daughter equivalents with all markers observed; DEtrad: traditional daughter equivalents; DEgen: reduced daughter equivalents from genomics; e: vector of errors; GEBV: genomic estimated breeding value; k: ratio of error to sire variance; n: equivalent reference size needed to achieve 50% genomic reliability; p: vector of polygenic effects for each genotyped animal; poly: ratio of polygenic variance to additive genetic variance; RELmax: maximum genomic reliability for an animal with all markers observed; RELpa: reliability of parent average; RELprog: reliability from own records and progeny; RELsnp: squared correlation between estimated and true genotypes averaged across loci for each animal; RELtot: animal's total reliability from all sources; RELtrad: reliability of traditional evaluation; u: vector of allele effects; X: incidence matrix (= 1) for intercept; y: vector of observations; Z: matrix of genotypes minus twice the base allele frequency; σa2: additive genetic variance.b: intercept (genetic base); BV: true breeding value; DEThe authors declare that they have no competing interests.PV derived and programmed the algorithms and drafted the paper. JO and GW suggested several improvements to the imputation methods. KW reviewed available imputation algorithms and suggested experimental designs. All authors read and approved the final manuscript.


In this study, a single-trait genomic model (STGM) is compared with a multiple-trait genomic model (MTGM) for genomic prediction using conventional estimated breeding values (EBVs) calculated using a conventional single-trait and multiple-trait linear mixed models as the response variables. Three scenarios with and without missing data were simulated; no missing data, 90% missing data in a trait with high heritability, and 90% missing data in a trait with low heritability. The simulated genome had a length of 500 cM with 5000 equally spaced single nucleotide polymorphism markers and 300 randomly distributed quantitative trait loci (QTL). The true breeding values of each trait were determined using 200 of the QTLs, and the remaining 100 QTLs were assumed to affect both the high (trait I with heritability of 0.3) and the low (trait II with heritability of 0.05) heritability traits. The genetic correlation between traits I and II was 0.5, and the residual correlation was zero.The results showed that when there were no missing records, MTGM and STGM gave the same reliability for the genomic predictions for trait I while, for trait II, MTGM performed better that STGM. When there were missing records for one of the two traits, MTGM performed much better than STGM. In general, the difference in reliability of genomic EBVs predicted using the EBV response variables estimated from either the multiple-trait or single-trait models was relatively small for the trait without missing data. However, for the trait with missing data, the EBV response variable obtained from the multiple-trait model gave a more reliable genomic prediction than the EBV response variable from the single-trait model.These results indicate that MTGM performed better than STGM for the trait with low heritability and for the trait with a limited number of records. Even when the EBV response variable was obtained using the multiple-trait model, the genomic prediction using MTGM was more reliable than the prediction using the STGM. The genomic prediction principle was first proposed by Meuwissen et al.. A typicet al.,2. Genomet al.-5. Recenet al.-9.Numerous genomic selection studies have focused on single-trait analyses. However, many traits are genetically correlated, such as the reproductive and milk yield traits in dairy cattle and these traits may have different heritabilities. Some traits, such as feed efficiency, may be recorded only in a small number of animals because of the difficulty of measuring them. Like traditional genetic evaluation, a multiple-trait model is expected to increase the accuracy of the GEBV by making use of information from genetically correlated traits. The benefit of using a multiple-trait model will be more profound for traits with low heritability and a small number of phenotypic records. Multiple-trait models for genomic prediction have been reported recently -14. It het al.[et al.[et al.[et al.[Drosophila melanogaster. The main advantages of GBLUP over Bayesian methods are, its implementation is straightforward using existing residual maximum likelihood (REML) and BLUP programs, and it requires less computation time, which can be an important factor in the practical application of a genomic prediction method. Although some studies have shown that computing time for Bayesian models can be reduced greatly using the expectation–maximization (EM) and variational Bayes algorithms [Bayesian variable selection methods generally outperform linear mixed models; often called the genomic best linear unbiased prediction (GBLUP) method ,15. Howeet al. found thl.[et al. and Li el.[et al.. Many stl.[et al.-22. Oberl.[et al. showed tgorithms ,24, GBLUgorithms ,7,25.Three types of response variables that have been used widely to predict the GEBV are EBV, daughter yield deviation (DYD), and deregressed proof (DRP) ,13,14,26The objective of this study was to compare a STGM and a MTGM for genomic prediction using conventional EBVs estimated with a conventional single-trait linear mixed model and a conventional multiple-trait linear mixed model as response variables. The comparison was carried out using data from various simulation scenarios considering heritability of two genetically correlated traits and the proportion of missing records in the data for the two traits.2 = 0.3) and trait II was assumed to have low heritability (h2 = 0.05). The genetic correlation was set as 0.5 and the residual error correlation was 0.Genomic predictions were obtained using both a STGM and MTGM with simulated data for two genetically correlated traits. Trait I was assumed to have high heritability  were generated to obtain the data used for the analysis. The population was assumed to be under random mating conditions with no overlapping generations. In G1–G4, all the bulls were genotyped and all the cows had a phenotypic record. The G1–G3 bulls were used as “reference animals” and their EBVs were used as the response variables for the genomic predictions; the G4 bulls were used as “validation animals”.i.e. the EBVs of only 300 of the 3000 bulls in the reference population were used for genomic prediction); and (3) no missing EBVs of trait I, but 90% of the EBVs for trait II were missed at random.The simulations also generated reference populations with a small amount of data for one of the two traits. To simplify the simulation and analysis without losing the generality of the data, traits with a small number of records were handled by masking the EBVs of some individuals in the reference population, instead of by generating incomplete phenotype data. In this way, three response variable datasets were generated: (1) no missing EBVs for either of the traits; (2) no missing EBVs for trait II, but 90% of the EBVs for trait I were missed at random /h2).The simulated genome consisted of five chromosomes (100 cM each). A total of 5000 biallelic SNP markers were spaced equally across the whole genome at distances of 0.1 cM. Three hundred biallelic QTLs were generated and divided randomly into three groups (100 each). One hundred of the QTLs affected only trait I, 100 affected only trait II, and 100 affected traits I and II. The QTL positions were located randomly according to the gene distribution in the first 500 cM of the standard mouse genome (NCBI 2005). The QTL effects were drawn from a gamma distribution with a shape parameter of 0.84 and scale parameter of 5.4, and assigned positive or negative by equal chance. Hayes and Goddard  noted thThe GEBVs were predicted using the performance and genotype information of the bulls in the reference population. The genomic prediction model used in this study was GBLUP, which is a linear mixed model with a genomic relationship matrix.The STGM is defined as:y is the vector of response variables , 1 is the vector with elements of 1, μ is the intercept, g is the vector of genomic breeding values, Z is the design matrix that associates genomic breeding values with response variables, and e is the vector of random residuals. It is assumed that G is the realized relationship matrix calculated from the SNP marker information, and I is the n × n identity matrix. A detailed description of how G is computed can be found in VanRaden [et al.[where VanRaden  and Hayen [et al..The MTGM is defined as:I1 and I2 are the identity matrices, Z1 and Z2 are the design matrix that associate genomic breeding values with response variables, and where Although DRP is usually used as the response variable for genomic predictions, in this study, conventional EBVs were used to omit the extra calculation of DRP but without losing the generality of the comparisons between the different scenarios. The EBVs of the animals were estimated from phenotypic data of all the dams in G1–G4 using both a single-trait and a multiple-trait animal model. The models for estimating EBVs were consistent with the genomic prediction models described above, but incorporating a pedigree-based genetic relationship matrix, instead of a genomic relationship matrix. The variance components were estimated from the data and used to calculate the EBVs and GEBVs using the average information REML algorithm (AI-REML). The analysis was executed using the DMU package .t test [The evaluation was based on 10 replicates for each scenario and the average of the results was reported. The positions and effects of the QTLs were randomized, and the initial population was generated separately for each replicate. For each scenario, the reliability of the genomic predictions was measured as the squared correlation between the GEBVs and the TBVs  had much higher reliability than the EBV for trait II (h2 = 0.05), as shown in Table For the animals with no records, the EBVs were predicted from the information of their relatives. For the validation animals, the EBV for trait I  were greater than 1 for all scenarios, and this was more serious for trait II (low heritability) than for trait I (high heritability). After rescaling the GEBVs (by dividing the GEBVs by the average reliability of the EBVs), the newly calculated regression coefficients (bGEBV_mc and bGEBV_sc) ranged from 0.832 to 1.002 (with an average of 0.907) using EBV_m, and from 0.964 to 1.069 (with an average of 1.021) using EBV_s. In general, the differences between the regression coefficients for STGM and MTGM using the same response variables were small.Table 2 = 0.1) that had a high genetic correlation (0.7) with a high heritability trait (h2 = 0.8), using Bayesian variable selection models. In the present study, MTGM was favorable for the trait with a small number of records, which is very important in practical breeding programs because phenotype information for all traits of interest is often not available for all the animals in a reference population. For example, there is usually a limited amount of data for traits that are difficult or expensive to measure, such as carcass, feed efficiency, and disease traits. The accuracies of GEBVs obtained using a STGM will be low for traits with limited phenotypic data. By using information from the correlated and more easily measured traits, a MTGM will improve the accuracies of the GEBVs that are obtained. However, a MTGM will not be distinctly better than a STGM for traits with high heritability and for traits whose complete phenotypic data are available. This result was congruent with the findings of Hayashi and Iwata [2 = 0.8).The main advantage of MTGM over STGM is that MTGM uses information from genetically correlated traits ,11. The nd Iwata  who repo2 = 0.3) ranged from 0.873 to 0.874, and for low heritability trait (0.05) the reliability of GEBVs ranged from 0.718 to 0.756. However, the reliability of EBVs for the same animals ranged from 0.348 to 0.350 for the high heritability trait and from 0.182 to 0.229 for low heritability trait. These results showed that the reliability of GEBV was much higher than the reliability of EBV, and there were smaller differences in the reliability of GEBV between the low heritability and high heritability traits compared with the differences in the reliability of EBV. Su et al.[In this study, for the validation animals with no missing data, the reliability of GEBVs for the high heritability trait  were used as response variables for genomic prediction. The results indicated that the reliability of GEBVs using EBV_m as the response variable were slightly higher than their reliability using EBV_s, except for trait II with no missing data. The reliability of GEBVs using EBV_m improved by 0.1% to 3.5% points compared with their reliability using EBV_s, because, in the multi-trait model, information about the correlated trait was used. Because the correlated trait data were used to estimate EBV_m, it can be argued that a multiple-trait model will be better than a single-trait model for genomic prediction when EBV_m is used as the response variable. The results from this study showed that even when the response variable was obtained from the multiple-trait model, the reliability of genomic prediction using MTGM was further improved over the reliability of STGM. A possible reason could be that the use of information from the correlated trait may not be exactly the same in the conventional BLUP and GBLUP methods. Thus, additional information from the correlated trait may be available for genomic prediction of the target trait, even though the response variable was obtained using the information of the correlated trait. A more important reason is that the prediction of GEBVs for the validation animals can use the information of the correlated trait directly through the covariance structure among the traits.In the simulations, all the phenotypic records were available for the estimation of EBVs. The data with missing records for genomic prediction were generated by masking some of the EBVs. In a real world application however, missing phenotypes cannot be used to estimate EBVs. Therefore, in the scenarios with missing records, the prediction accuracy that was obtained in this study could be higher than the accuracy expected in the real world. On the other hand, the gain from using a multi-trait model in a real scenario with missing records might be larger than the gain from the simulated scenario, because the amount of information of the related trait in relation to the trait of interest would be relatively larger.In this study, a GBLUP model was used for multiple-trait genomic prediction. Compared with the Bayesian variable selection models, the advantages of the multiple-trait GBLUP model are its low computational demand and its straightforward implementation using existing methodologies and standard linear mixed model software. However, the GBLUP model assumes that the effects of all the SNPs have the same normal distribution for a trait, and that the covariance between traits is the same for all SNP effects. This assumption may be not very appropriate and could limit the advantage of the GBLUP multiple-trait genomic prediction method. Hayashi and Iwata  used BayThe results reported here suggest that a MTGM can improve the accuracy of genomic predictions, especially for low heritability traits and for traits with only a small amount of phenotype data. The EBV response variables derived from the multiple-trait and single-trait models had a relatively small influence on the reliability of GEBVs for the trait without missing data. However, for the trait with missing data, the response variable obtained from the multiple-trait model gave better genomic predictions than the response variable obtained from the single-trait model. Even when response variables derived from the multiple-trait model were used, the genomic prediction using MTGM still generated GEBVs with higher reliability than the GEBVs generated using STGM.The authors declare that they have no competing interests.GG and FZ performed the data analyses and drafted the manuscript. YW assisted in the study design. GS and YZ reviewed the manuscript. LD and GS conceived and designed the study as well as co-supervised the work. All authors read and approved the final manuscript.


Summary: TrioVis is a visual analytics tool developed for filtering on coverage and variant frequency for genomic variants from exome sequencing of parent–child trios. In TrioVis, the variant data are organized by grouping each variant based on the laws of Mendelian inheritance. Taking three Variant Call Format files as input, TrioVis allows the user to test different coverage thresholds (i.e. different levels of stringency), to find the optimal threshold values tailored to their hypotheses and to gain insights into the global effects of filtering through interaction.Availability: Executables, source code and sample data are available at https://bitbucket.org/biovizleuven/triovis. Screencast is available at http://vimeo.com/user6757771/triovis.Contact:ryo.sakai@esat.kuleuven.be Recent advances in massively parallel sequencing technologies, especially sequencing of the entire protein-coding portion of the genome (exome), have introduced new strategies for identifying Mendelian disease genes  of variants were consistent with the Mendelian laws when we analysed those variants that are in common between the exome sequencing and an SNP genotyping array for a trio-case (data not shown). One of the metrics commonly used to filter variants is the depth of coverage. Researchers we interviewed adjust the coverage threshold based on the overall coverage and their intuition without any visual aids. The optimal coverage thresholds also depend on other factors, such as the suspected type of mutation, whether somatic or inherited, and the stringency of analysis. Although finding the optimal coverage threshold can be automated to some extent, it still requires fine adjustments of the filtering setting for variant discovery.Although filtering based on inheritance pattern seems to be straight-forward, distinguishing true variation from artefacts and false negatives while retaining sensitivity is a challenging task because of the sequencing error rate and the interdependency of sequencing quality for multiple samples. A previous study  for further analysis. The ‘optimize’ function finds the best-weighted average of the precision and recall (f-score) based on the number of filtered consistent and inconsistent variants, providing the user a good initial setting for further investigation and adjustment.The variant data can be investigated under two assumptions: with the ‘migration’ assumption, any variant below the coverage threshold is considered homozygous reference; when this assumption is inactive, variants below the coverage threshold are considered invalid and discarded from the combined set of variants. Filtered results can be exported using the ‘export VCF’ button and saved as VCF files. The researcher can also select specific blocks to export variants of a specific inheritance pattern (i.e. TrioVis provides an interactive interface and optimization function to calibrate coverage thresholds based on Mendelian inheritance laws for parent–child trio cases. By visualizing variants in a novel table layout based on the inheritance laws, it allows the researcher to gain insights into the global effect of filtering in the context of trio analysis. The researcher can export the filtered result as VCF files for subsequent analysis to annotate variants to genes, using annotation tools, such as Annotate-It (


There was, however, a high degree of heterogeneity among populations: whereas the direction of the effect was consistent across most population samples, the effect size differed significantly among populations. It is likely that this reflects true biological heterogeneity: whether or not an effect can be observed will depend on both the variance in homozygosity in the population and the chance inheritance of individual recessive genotypes. These results predict that multiple, rare, recessive variants influence human height. Although this exploratory work focuses on height alone, the methodology developed is generally applicable to heritable quantitative traits (QT), paving the way for an investigation into inbreeding effects, and therefore genetic architecture, on a range of QT of biomedical importance.Stature is a classical and highly heritable complex trait, with 80%–90% of variation explained by genetic factors. In recent years, genome-wide association studies (GWAS) have successfully identified many common additive variants influencing human height; however, little attention has been given to the potential role of recessive genetic effects. Here, we investigated genome-wide recessive effects by an analysis of inbreeding depression on adult height in over 35,000 people from 21 different population samples. We found a highly significant inverse association between height and genome-wide homozygosity, equivalent to a height reduction of up to 3 cm in the offspring of first cousins compared with the offspring of unrelated individuals, an effect which remained after controlling for the effects of socio-economic status, an important confounder  were predicted to be up to 3 cm shorter on average than the offspring of unrelated parents. Height is influenced by the combined effect of many recessive variants dispersed across the genome. This may also be true for other human characteristics and diseases, opening up a new way to understand how genetic variation influences our health. Height is a classic complex trait, which is influenced by both genetic and non-genetic factors. Observed increases in height in developed countries over the last few generations suggest that environmental factors such as nutrition and childhood healthcare play an important role in determining adult height In a seminal work published almost a century ago, Fisher first proposed that the heritability of height results from the combined effects of many genetic variants of individually small effect size This study explores whether there is evidence for genome-wide recessive genetic effects, or inbreeding depression, on height. Inbreeding depression implies directional dominance: i.e. that dominance is on average in the same direction across loci. An association between height and genome-wide homozygosity would imply that height was influenced by the combined effects of many recessive variants of individually small effect size, scattered across the genome. On the face of it, this endeavour looks unpromising. Most pedigree and GWAS studies investigating the genetic architecture of height to date have found no strong evidence of deviation from an additive genetic model The aim of this study was to explore the association between genome-wide homozygosity and adult height, controlling for the effects of potential confounding factors. The study involved over 35,000 subjects, drawn from 21 population samples. We invited studies to participate in the consortium which we knew were conducted in isolated populations, where both the mean and variance in genome-wide homozygosity are higher. In this way, we optimised our chances of being able to detect an effect, should one exist. We found highly significant evidence of an inverse association between genome-wide homozygosity and height, with significant heterogeneity among sample sets.We explored the association between genome-wide homozygosity and height in 21 European or European-heritage populations . All samROH is defined as the percentage of the typed autosomal genome in runs of homozygosity (ROH) greater than or equal to 1.5 Mb in length. FROH is strongly correlated with the degree of relatedness between an individual's parents ROHLD is a modification of FROH, derived using a panel of independent SNPs, where all SNPs in strong linkage disequilibrium (LD) have been removed. This is a more stringent estimate of parental relatedness: removing SNPs that are in strong LD with other SNPs means that all ROH detected are likely to be the result of recent parental relatedness and not ancient patterns of shared ancestry. The third measure we used was observed homozygosity (Fhom). This is defined as the number of observed homozygous genotypes per individual, expressed as a percentage of the number of non-missing genotypes for that individual. This is a much less precise estimate of parental relatedness, as Fhom is a single-point measure which captures all genotyped homozygous loci, not just those located in long ROH. Thus it reflects not only recent parental relatedness but also more ancient aspects of population history, such as population isolation and bottlenecks.We used three different measures of genome-wide homozygosity. FROHLD and Fhom. For example, the Estonian sample (Estonian Genome Centre of University of Tartu [EGCUT]) had the second highest mean value for Fhom, but it had one of the lowest mean values for FROHLD. For all three measures of genome-wide homozygosity there is a continuum of values. The isolate populations are generally located at the more homozygous end of the spectrum, but with considerable variation amongst the different sample sets. For example, there is almost a three-fold difference in mean FROHLD between the Northern Sweden Population Health Study (NSPHS) and ORCADES. The Finnish sample sets and some others  have intermediate levels of homozygosity, whilst the urban and national collections from Scotland, the Netherlands and Australia are the least homozygous. There was more than an order of magnitude difference in mean FROHLD between the most and the least homozygous population samples.ROH, adjusting for age, sex and  genomic kinship (p = 1.23×10−11) inverse association between FROH and height. This association was significant in nine of the twenty-one sample sets in the study. In nine further sample sets, confidence intervals overlapped with zero but the direction of the effect was consistent with an inverse association between FROH and height. In none of the sample sets was there a significant positive association between FROH and height. An increase of 1% in FROH was associated with a decrease of 0.012 (SE = 0.0018) in the z-score for height (approximately 0.09 cm). Using pedigree and FROH data from three separate population samples, we estimated that this is equivalent to a reduction in height of 0.7 cm in the offspring of first cousins, compared with the offspring of unrelated individuals , ORCADES and Irish data sets respectively – see The purpose of the first part of the analysis was to explore the association between height and homozygosity, as measured in different ways. First, we estimated the association between height and F kinship . We founROHLD, adjusted for age, sex and genomic kinship. Again, there was evidence of a very strongly significant inverse association (p = 1.40×10−88) between FROHLD and height (ROHLD and height. In none of the sample sets was there a significant effect in the other direction. A 1% increase in FROHLD was associated with a decrease of 0.065 (SE = 0.0032) in the z-score for height (approximately 0.6 cm). Again using pedigree and FROHLD data from three separate population samples, this gave a much higher estimate of a reduction in height of between 2.8 and 3.3 cm in the offspring of first cousins compared with the offspring of unrelated parents .The second analysis estimated the association between height and Fd height . This ashom, adjusting for age and sex (hom and height (p = 1.10×10−83). The direction of effect was consistent for fourteen sample sets, significantly so for seven of these, and not significantly different from zero but of opposite sign in the final seven studies. A 1% increase in Fhom was associated with a decrease of 0.11 (SE = 0.0057) in the z-score for height (approximately 1 cm). Again using pedigree and Fhom data from three separate population samples, this gave an estimate of a reduction in height of between 2.7 and 3.3 cm in the offspring of first cousins compared with the offspring of unrelated people, identical to the estimate obtained using FROHLD .The third analysis estimated the association between height and F and sex . Again, hom analysis was driven by homozygous genotypes located in long ROH, or from the more common, homozygous genotypes resulting from the chance inheritance of identical shorter haplotypes from both parents. This analysis estimated the association between height and Fhom, adjusted for age, sex and FROH. Again, a significant association was observed, but both the magnitude and the significance of the effect were reduced compared to the previous analysis .Although these results were highly significant, there was also a high degree of heterogeneity across population samples. Some further analyses were performed to explore the source of this heterogeneity. Three of the twenty-one study samples  consistently showed a (non-significant) positive association between genome-wide homozygosity and height. In the LBC1936 and INGI-VB cohorts, the parameter estimate was positive for all three measures. In INGI-CARL, the parameter estimate was positive for Fhom  and FROH meta-analyses . For both these measures, other outliers also contributed to the heterogeneity. In the case of FROH the Rotterdam Study (RS) showed a non-significant positive association with height. Four additional cohorts showed a non-significant positive association between Fhom and height .Removing these cohorts only slightly reduced heterogeneity in the FROH. The effect estimate for this analysis was lower than those for the other 2 homozygosity measures. The most heterogeneous result was for Fhom. The Fhom analysis was similar to FROHLD in terms of effect size and significance; however, when FROH was included in the Fhom model, although the association remained significant, the effect size fell, the p-value increased and heterogeneity increased. This suggests that the effect was being driven mainly by longer ROH which are more effectively captured by FROHLD. It is important not to overstate this, however: even after controlling for FROH, there is a significant, although highly heterogeneous inverse association between Fhom and height, which suggests that a signal is also coming from homozygous genotypes that are not found in the long ROH characteristic of parental relatedness (ROHLD and effect size (r = 0.03). Correlation between these two measures would be expected if the observed effect was entirely attributable to parental relatedness of recent origin. Nevertheless, the most significant and least heterogeneous result was seen with FROHLD. Furthermore, a moderate negative correlation was observed between average FROHLD and the standard error of the effect estimate (r = −0.4), suggesting that the higher the level of parental relatedness present in the sample, the greater the precision of the effect estimate. This is because mean FROHLD is related to its standard deviation  and it is the variance in FROHLD that determines the standard error of the estimate of the regression coefficient . For these reasons, it was decided to use FROHLD in further analyses to explore possible confounding factors.To summarise, these results provide evidence of a highly significant inverse association between genome-wide homozygosity and height, regardless of which homozygosity estimate was used. The weakest result was for Fatedness . Furtherp = 0.002) between FROHLD and height, with a 1% increase in FROHLD associated with a decrease of 0.13 in the z-score for height . This is equivalent to a reduction in height of 5.3 cm  in the offspring of first cousins compared with the offspring of unrelated parents, a stronger effect than observed in the meta-analysis of the full sample. We also repeated the FROHLD analysis for a subset of individuals aged under 40 years of age  and the relationship remained significant, although the effect size was much smaller . This is equivalent to a reduction in height of 0.4 cm  in the offspring of first cousins compared with the offspring of unrelated parents.All analyses were adjusted for age but, because the mean age of most of the population samples in this study was over 50 years at the time of genotyping, it was important to undertake additional checks to ensure that the observed effect was not confounded by the effects of osteoporotic, age-related shrinking. We used the Northern Finland Birth Cohort 1966 (NFBC1966), where all subjects were under 40 at the time of measurement. In this cohort, there was a significant inverse association (ROHLD) and height. First, we analysed the eleven cohorts with educational attainment data available. Two meta-analyses were performed, one adjusting for age, sex, genomic kinship and FROHLD only and one adjusting for age, sex, genomic kinship, FROHLD and educational attainment. Results were then compared to assess possible confounding by educational attainment. This process was then repeated for the seven cohorts with data available on occupational status. Results are summarised in The final stage in this analysis was to investigate possible confounding by socio-economic status (SES) of the observed association between genome-wide homozygosity and reduced height. Four of the 21 cohorts  did not collect data on SES and so were excluded from further analyses. SOCCS estimated SES using a composite measure of deprivation based on residential address; however, because this was an area- rather than an individual-level estimate and because only one other cohort (ORCADES) used this measure, SOCCS was also excluded from analyses of SES. Eleven cohorts recorded an ordinal measure of educational attainment . Seven cohorts provided an ordinal measure of occupational status ; however, the maximum likelihood method used to find the parameter estimate failed to converge for INGI-FVG so this cohort was excluded from the occupational status analysis. We conducted four meta-analyses to investigate whether educational attainment or occupational status confounded the association between genome-wide homozygosity  had the second highest mean value for Fhom, it had one of the lowest mean values for FROHLD. There are several possible explanations for this. Firstly, it may be suggestive of a small, isolated population deep in the past but with a larger population size and low levels of parental relatedness in recent generations. Secondly, ascertainment bias in the selection of SNPs may also influence these patterns, as markers present in the HumanHap300 panel are more likely to be heterozygous in NW Europeans This study found evidence for a strongly significant inverse association between genome-wide homozygosity and height (i.e. inbreeding depression) using three alternative estimates of genomic homozygosity, with each method capturing a somewhat different aspect of this phenomenon. Whereas all three measures are strongly correlated, there are also important differences, particularly between FROHLD, a measure which estimates homozygosity attributable to recent parental relatedness. There is, however, an important caveat: a significant association was also observed between reduced height and Fhom, controlled for FROHLD, suggesting that homozygous genotypes not located in the long ROH characteristic of recent parental relatedness are also important. We estimated that the increased genome-wide homozygosity that is characteristic of consanguinity results in a reduction of up to 3 cm in the height of the offspring of first cousins compared with the offspring of unrelated parents. Using FROHLD, we then expanded the model to explore possible confounding factors. Firstly, we investigated the possible confounding effects of age-related shrinking. Adult height is the combined effect of growth during childhood and adolescence and loss of height during ageing ROHLD and height remained in both these analyses, suggesting that confounding as a result of the osteoporotic effects of ageing was not a major factor in these samples. The NFBC1966 analysis also suggests that the relationship between genome-wide homozygosity and height is not confounded by the simultaneous improvements in nutrition and living standards over the last century.The strongest association between genome-wide homozygosity and reduced height was observed using FSecondly, we assessed possible confounding by socio-economic status. The association between low childhood SES and reduced adult stature is well established, with the likely mechanism being poor nutrition during childhood While we did not have access to raw intensity data with which to call hemizygous deletions, which can masquerade as ROH, two different studies give us confidence that such copy number variation will only have a very minor effect on our results. First, in the ORCADES population, removing ROH which overlapped with deletions resulted in only a 0.3% reduction in the sum length of ROH across the cohort ped)  and genome-wide homozygosity  in the extreme isolate population of Norfolk Island ped>0, with mean Fped = 0.044. This contrasts with, for example, only 10% of the ORCADES sample having Fped>0, with mean Fped = 0.01 using pedigrees of a similar depth (unpublished data). Although comparable pedigree data are not available for all samples, it is probable that, with the possible exception of NSPHS, all the samples in the present study have lower levels of Fped and genome-wide homozygosity and thus lower power to detect an association with height than is the case in the Norfolk Island sample of descendants of the Bounty mutineers. Cultural attitudes to consanguinity are at best ambivalent in Europe, so marriage between first cousins is rare, even in the nine isolated population samples in our consortium, where inflated levels of parental relatedness are predicted simply as a function of population size and endogamy.Our results are consistent with those of Macgregor and colleagues, who found a significant inverse association between height and both the inbreeding coefficient derived from genealogical data . If this were the case, however, the strongest effects would be observed in the samples with the highest levels of parental relatedness. In fact, we found no correlation between mean sample FROHLD and effect size. We also found evidence of an association after controlling for parental relatedness, suggesting that homozygous genotypes not resulting from recent parental relatedness also contribute to the observed association. The data do not, then, support the hypothesis that the more inbreeding there is in the sample, the stronger the observed effect. We did, however, find a moderate negative correlation between the mean sample FROHLD and the SE of the FROHLD effect estimate, which suggests that the more inbreeding there is in the sample the greater the power to detect an effect and therefore the more precise the estimate of the effect.The present study's analyses provide strong evidence for an association between genomic homozygosity and reduced height; however, there is also strong evidence of heterogeneity. Although we did not find a significant positive association between FROH and FROHLD. The difference in ROH length threshold may contribute to this discrepancy. The 1.5 Mb threshold for FROH was chosen on the basis of an empirical analysis of several European-heritage populations ROHLD measure does not detect ROH arising from common ancient haplotypes in the population because SNPs in LD are removed before the analysis. Any ROH detected using FROHLD are the result of parental relatedness of recent origin. For FROHLD the aim is to maximise the ROH that can be detected by setting a minimum length threshold which is as low as possible. ROH are identified by observing a string of contiguous homozygous genotypes. The greater the number of contiguous homozygous genotypes, the stronger the probability that what is observed is a true ROH , rather than just a chance observation. Because of the reduced number of SNPs, and thus reduced SNP density, in the LD-pruned SNP panels used for the FROHLD analysis, detection of ROH shorter than 1 Mb becomes unreliable: hence 1 Mb was used as the threshold.One puzzling result of this study was the discrepancy in the results of the meta-analyses of FROHLD was very variable across cohorts, but the average was 0.4%. Secondly, by demonstrating that the strongest signal comes from the long ROH characteristic of parental relatedness, we provide evidence that the observed effect is primarily the result of rare, rather than common, recessive alleles. Short ROH (measuring up to 2 Mb) are a common feature of all our genomes The purpose of carrying out this analysis was to investigate possible genome-wide recessive effects on height. These results are important because by showing an association with genome-wide homozygosity rather than specific individual SNPs, we provide evidence that there is a polygenic recessive component to the genetic architecture of height: i.e. that the observed reductions in height associated with genome-wide homozygosity result from the combined effects of many recessive alleles of individually small effect size, located across the genome. The proportion of the phenotypic variance explained by Fped). Such measures are highly error-prone and cannot account for stochastic variation in the inheritance process. Nevertheless, various studies have found evidence of a significant positive association between blood pressure and FpedpedpedpedThese findings are also important because, if there is a polygenic, rare, recessive component to the genetic architecture of height, this might also be the case for disease-associated QT of biomedical importance, such as blood pressure and lipid levels. Indeed this is more likely, if these traits are associated with fitness. A high dominance variance has been reported in systolic blood pressure (SBP) and LDL cholesterol in the Hutterites Each study had ethical approval for genetic research into the basis of complex traits, approved by the appropriate committees in each country. All participants provided written informed consent. As analyses were performed locally by cohort analysts, no data were shared across national boundaries.This meta-analysis combined data from 21 European or European-heritage population samples: The Estonian Genome Centre University of Tartu (EGCUT), the Erasmus Rucphen Family Study (ERF), the National FINRISK Study (FINRISK) , the Health 2000 Survey (H2000), the Helsinki Birth Cohort (HBCS), the Lothian Birth Cohort 1921 (LBC1921), the Lothian Birth Cohort 1936 (LBC1936) the Carlantino Project (INGI-CARL), Friuli-Venezia-Giulia-Genetic Park (INGI-FVG), Korčula (CROATIA-Korčula), Micro-Isolates in South Tyrol (MICROS), the Northern Finland 1966 Birth Cohort (NFBC1966), the Northern Sweden Population Health Study (NSPHS), the Orkney Complex Disease Study (ORCADES), Queensland Institute of Medical Research (QIMR), the Rotterdam Study (RS), the Study of Colorectal Cancer in Scotland (SOCCS), Split (CROATIA-Split), Val Borbera (INGI-VB), Vis (CROATIA-Vis) and the Young Finns Study (YFS). Most (n = 16) were population-based samples, 4 were birth cohorts and 1 was a case-control sample. Five study populations were Finnish, 4 were Scottish, 4 were Italian, 3 were Croatian, 2 were Dutch, 1 was Estonian, 1 was Swedish and 1 was Australian of NW European heritage. Most of the samples were drawn from genetically isolated populations or populations with increased homozygosity, such as the Finns. The total number of participants was 35,808. All studies were carried out after the appropriate local ethical approval had been obtained. All participants provided written informed consent. Full sample details are given in In all studies apart from SOCCS, height was measured by trained personnel using a stadiometer. SOCCS participants provided self-reported measurements of height. This was validated by measuring height in a subset of the sample by trained personnel using a stadiometer. There was a high concordance between the two measures.All genotyping was performed on the Illumina platform but using four different SNP panels. Seven samples were genotyped using the Illumina HumanHap 300 panel, six using the Illumina HumanHap 370 Duo/Quad panels, five using the Illumina Human 610 Quad panel, one using the Illumina Human 670 Quad panel and one using both the 370 and 610 panels. In order to harmonise the data across samples, SNPs present in the HumanHap 300 panel were extracted and the analysis was conducted using these SNPs only. Quality control procedures were performed on each sample separately, with the minimum requirements as follows. Individuals with more than 5% missing genotypes were excluded. SNPs missing in more than 10% of samples were excluded, as were SNPs failing the Hardy-Weinberg equilibrium test at p<0.0001 and SNPs with minor allele frequency (MAF)<0.01.These were detected using the Runs of homozygosity routine in plink ROHROH were defined as runs of at least 25 consecutive homozygous SNPs spanning at least 1500 kb, with less than a 100 kb gap between adjacent SNPs and a density of SNP coverage within the ROH of no more than 20 kb/SNP. For each individual, an F statistic termed F2 = 0.1). ROH parameters were adjusted to reflect the reduced number of SNPs. The minimum number of consecutive homozygous SNPs constituting a ROH was set at 12 . The minimum length of ROH was set at 1000 kb, with no more than 250 kb gap between adjacent SNPs and a density of SNP coverage within the ROH of no more than 100 kb/SNP. Individual FROHLD statistics were then calculated as described above. This approach yields a more stringent estimate of parental relatedness, as it removes all ROH that are there simply because of parental sharing of long haplotypes that are common in the population. ROH consisting of independent SNPs will be of recent origin and will thus be enriched for rarer haplotypes. Again, this is highly correlated with the pedigree-derived inbreeding coefficient .An alternative approach to deriving an inbreeding coefficient from ROH is to start by pruning the SNP panel of SNPs in strong linkage disequilibrium (LD), in order to remove ROH that are very common due to the high frequency of ancestral haplotypes. SNP panels were pruned using the pairwise option in plink This is defined as the number of observed homozygous genotypes per individual, expressed as a percentage of the number of non-missing genotypes for that individual. This measure is less strongly correlated with pedigree inbreeding coefficients than the above r = 0.76 , as it cAll tests were two sided and a p-value threshold of 0.05 was used. In order to account for differences in mean height among population samples, all height measures are expressed as z-scores. Because genetically isolated populations are characterised by high levels of relatedness between individuals, measures of height are not independent and therefore conventional regression techniques are not appropriate. The CROATIA-Korčula, CROATIA-Split, CROATIA-Vis, ERF, FINRISK, HBCS, H2000, INGI-CARL, INGI-FVG, INGI-VB MICROS, NFBC1966, NSPHS, ORCADES and YFS samples were therefore analysed using a linear mixed polygenic model in GenABEL. This programme maximises the likelihood of the data under the polygenic model with specified covariates. It reports twice the negative maximum likelihood estimates and the inverse of the variance-covariance matrix at the point of maximum likelihood Results were combined in a meta-analysis using the inverse variance method to combine effect size estimates from each sample ped = 0.0625 and 0). For each measure of genomic homozygosity we estimated this difference separately in 3 different populations where genealogical and genomic data were available for the reliable identification of the offspring of first cousins. In each population group and for each measure of genomic homozygosity, we estimated the mean difference between the offspring of first cousins and the offspring of unrelated parents. We multiplied this by the effect size estimate from the regression meta-analysis to give a z-score estimate for the reduction in height in the offspring of first cousins compared with the offspring of unrelated individuals. To convert each of these z-scores into cm, we then multiplied them by an estimate of the SD for height across the whole sample, derived by taking the SD for each sample in turn and weighting it by sample size. Two of the three populations used for this analysis were part of the main study (ORCADES and MICROS). The third was a small Irish sample, consisting of members of both settled and traveller communities in Ireland . We repeated this analysis separately in these three populations, partly because of the very small number of first cousin offspring in any single sample in our study and partly to ensure that the observed difference in homozygosity was not simply an artefact of one particular population sample.In order to standardise across the different population samples in this study, we converted height measurements into z-scores. The results of each meta-analysis report a pooled estimate of the change in this z-score associated with a 1% increase in genomic homozygosity. In order to make this easier to interpret, we express this in the text as the difference in height between the offspring of first cousins and the offspring of unrelated parents. The first step in this analysis was to estimate the difference in observed genomic homozygosity between the offspring of first cousins and the offspring of unrelated parents . The plot shows estimated effect sizes (solid squares) for each population, with 95% confidence intervals . Each sample estimate is weighted by the inverse of the squared standard error of the regression coefficient, so that the smaller the standard error of the study, the greater the contribution it makes to the pooled regression coefficient. The area of the solid squares is proportional to the weighting given to each study in the meta-analysis. Effect sizes in z-score units  are: CROATIA-Korčula = −0.03 ; CROATIA-Split = −0.005 ; CROATIA-Vis = −0.03 ; EGCUT = −0.04 ; ERF = −0.09 ; FINRISK = −0.09 ; HBCS = −0.05 ; H2000 = −0.16 ; INGI-CARL = 0.01 ; INGI-FVG = −0.03 ; INGI-VB = 0.001 ; LBC1921 = −0.08 ; LBC1936 = 0.07 ; MICROS = −0.05 ; NFBC1966 = −0.08 ; NSPHS = −0.02 ; ORCADES = −0.02 ; QIMR = −0.06 ; RS = 0.003 ; SOCCS = −0.08 ; YFS = −0.05 .Forest plot of the effect of F(TIF)Click here for additional data file.Figure S2hom on height. Results of a meta-analysis of the association between Fhom and height are shown for twenty population samples. For one sample (INGI-CARL) the polygenic model failed to converge. The model was adjusted for age and sex in all samples. Additionally, it was adjusted for genomic kinship in samples with pairs of related individuals . The plot shows estimated effect sizes (solid squares) for each population, with 95% confidence intervals . Each sample estimate is weighted by the inverse of the squared standard error of the regression coefficient, so that the smaller the standard error of the study, the greater the contribution it makes to the pooled regression coefficient. The area of the solid squares is proportional to the weighting given to each study in the meta-analysis. Effect sizes in z-score units  are: CROATIA-Korčula = 0.03 ; CROATIA-Split = −0.04 ; CROATIA-Vis = −0.09 ; EGCUT = 0.002 ; ERF = −0.2 ; FINRISK = −0.1 ; HBCS = −0.09 ; H2000 = −0.2 ; INGI-FVG = −0.27 ; INGI-VB = 0.02 ; LBC1921 = −0.2 ; LBC1936 = 0.02 ; MICROS = −0.07 ; NFBC1966 = −0.1 ; NSPHS = −0.15 ; ORCADES = −0.06 ; QIMR = 0.09 ; RS = 0.007 ; SOCCS = −0.09 ; YFS = −0.1 .Forest plot of the effect of F(TIF)Click here for additional data file.Table S1Details of genotyping, QC, data analysis and sample characteristics by cohort.(XLS)Click here for additional data file.