Brassica napus) breeding. The primary goal of our study was to examine and compare the potential and the limits of marker-assisted selection and genome-wide prediction of six important seed quality traits of B. napus. Our study is based on a bi-parental population comprising 202 doubled haploid lines and a diverse validation set including 117 B. napus inbred lines derived from interspecific crosses between B. rapa and B. carinata. We used phenotypic data for seed oil, protein, erucic acid, linolenic acid, stearic acid, and glucosinolate content. All lines were genotyped with a 60k SNP array. We performed five-fold cross-validations in combination with linkage mapping and four genome-wide prediction approaches in the bi-parental population. Quantitative trait loci (QTL) with large effects were detected for erucic acid, stearic acid, and glucosinolate content, blazing the trail for marker-assisted selection. Despite substantial differences in the complexity of the genetic architecture of the six traits, genome-wide prediction models had only minor impacts on the prediction accuracies. We evaluated the effects of training population size, marker density and phenotyping intensity on the prediction accuracy. The prediction accuracy in the independent and genetically very distinct validation set still amounted to 0.14 for protein content and 0.17 for oil content reflecting the utility of the developed calibration models even in very diverse backgrounds.Improving seed oil yield and quality are central targets in rapeseed ( The breorldwide –4. The lorldwide , 3, 5. Morldwide –8. All oorldwide –11, and Genomic-assisted crop improvement can either be based on marker-assisted selection  or genomBrassica species, such as B. oleracea and B. juncea [The presence of QTL underlying quality traits in rapeseed has been investigated in linkage and linkage disequilibrium mapping studies , 17–28. . juncea , 30, whi. juncea , 32.The potential and limits of genome-wide predictions have been examined for several major crops, such as barley , wheat , 34–36, Brassica [This study is based on a published dataset from the bi-parental TN DH population comprising 202 DH lines, which has been intensively used to study the genetic architecture of important agronomic traits , 22, 23 Brassica , 53, 54.B. napus denoted as TN DH has been developed, comprising 202 unique lines [1 cross between Tapidor and Ningyou7. The parent Tapidor is a European winter cultivar with low erucic acid and glucosinolate content in the seeds. The parent Ningyou7 is a Chinese semi-winter cultivar with high erucic acid and glucosinolate content in seeds. The TN DH mapping population along with its two parents was grown in 11 winter and semi-winter ecotype environments  and protein content (%), which were separately defined as the percentages of the oil and protein in the total seed dry weight, respectively; three important components of the fatty acid in the seed oil: the erucic acid content (%), the linolenic acid content (%), and the stearic acid content (%); and the content of glucosinolates in the total seed dry weight (µmol/g). The quality traits were determined based on near infrared reflectance spectroscopy measuring three technical and three biological replicates. The details of the phenotyping are outlined in detail in previous studies , 11, 22.B. napus inbred lines were used in this study for validating the prediction accuracy based on the TN DH population. The validation population was developed based on hundreds of crosses between B. rapa and B. carinata accessions [2. Seed oil content and protein content was measured using the same method as that used for the TN DH population.A total of 117 genetically independent cessions , 56. TheThe best linear unbiased estimates (BLUEs) of phenotypic values and variance components were estimated by the following linear mixed model using ASREML-R software :Traits∼E refers to the number of environments, NR is the average number of replications per location, The genotype effects were treated as fixed effects and the other effects were treated as random. To estimate variance components, all effects were treated as random. Broad-sense heritability was calculated as the ratio of genotypic to phenotypic variance:B. napus version 4.1[−20 and mismatch <2 . One hundred and forty-four lines were used as the training set and the remaining 36 were used as the test set. QTL mapping was performed in each training set and estimated QTL effects were used to predict the genetic values of the lines of the test set. The prediction accuracy was defined as the correlation between the predicted and observed phenotypic values standardized with the square root of the heritability.r2>0.95. For BayesCπ, the Gibbs sampling ran 20,000 times, and the first 6,000 cycles were used as burn in. We also implemented an extended GBLUP model denoted as EG-BLUP, which models digenic epistatic effects as well as additive effects [For the genome-wide prediction, four different models were used in this study. We implemented three methods exploiting the additive marker effect: genomic best linear unbiased prediction (GBLUP), ridge regression best linear unbiased prediction (RR-BLUP) , and Bay effects . The acc effects , 42, 65.To evaluate the dependence of prediction accuracy on training set size, we applied cross-validation with randomly selected subsets of n  lines from the full data to form the training set and used the remaining lines as the test set. To evaluate the dependence of prediction accuracy on marker density, we selected subsets of m  evenly distributed markers from the full dataset and applied five-fold cross-validations using all 180 lines. The sampling procedure was randomly repeated 100 times for each scheme, and the prediction accuracies were averaged across the 100 cross-validation runs. We focused in the above outlined analyses of sampling of marker subsets and training set sizes on the traits seed oil content and protein content. The traits were selected because oil content was evaluated in a large number of 11 environments and protein content exhibited a high heritability.We also evaluated the prediction accuracy using an independent validation population. The marker effects were estimated based on RR-BLUP and the TN DH population. Marker effects were used to predict the performance of the 117 individuals of the validation population. The prediction accuracy was again estimated as the Pearson correlation coefficient between predicted and observed values standardized with the square root of the heritability. Heritability was estimated using the variance components estimated for the TN DH population.We combined the information on seed protein content with previously published data for other seed quality traits of the TN DH population. We observed a wide variation of BLUEs approximating a normal distribution for most traits, except for erucic acid content . The anaIn total, 80% of the pairwise trait comparisons were significantly (P<0.001) associated with Pearson moment correlation coefficients ranging from -0.84 between erucic acid content and stearic acid content to 0.66 between erucic acid content and glucosinolate content . InteresB. napus. Phenotypic variance explained by a single putative QTL exceeded 5% for 27 SNPs and reached 45% for a QTL located on chromosome C03 controlling erucic acid content . The average accuracy of MAS ranged from 0.47 for protein content to 0.81 for erucic acid content . These vWe used four different models to investigate the efficiency of genome-wide prediction for the six seed quality traits. Genomic selection significantly showed higher prediction accuracies than MAS for all traits, with the most pronounced differences observed for linolenic acid, oil, and protein content . The aveAs expected for a bi-parental mapping population, a large number of markers were in tight LD and could thus be grouped into genetic bins because of the absence of recombination events. We reduced the co-linearity among markers and removed redundant markers in full linkage disequilibrium, resulting in a subset of 1,527 SNP markers , S2 Fig.Genome-wide prediction based on RR-BLUP performed best on average and, in addition, was computationally efficient. Therefore, we conducted comprehensive analyses on the factors driving the accuracy in genome-wide prediction exclusively based on RR-BLUP. We varied the training population size and marker density and examined the accuracy of genome-wide predictions in our study. The accuracy remained in the range of 0.44 to 0.67 for all traits using only 48 lines as the training set . InteresWe further studied the effects of the number of environments and training population size on the accuracy of genomic selection by focusing on oil and protein content. The traits were selected because oil content was evaluated in a large number of 11 environments and protein content exhibited a high heritability. We randomly selected training sets comprising n = 48, 80, 112, and 144 lines evaluated for oil content evaluated in subsets of environments . The accuracy was estimated as the Pearson moment correlation coefficient between predicted genotypic values and the adjusted entry means of all remaining lines evaluated across all environments. This type of cross-validation allows for the study of the prediction accuracy assuming reduced phenotyping intensity. As the test set was not evaluated in any of the environments, their performance could not be estimated by phenotypic correlations between environments. The prediction accuracies based on phenotypic data from only two environments were 0.73 for oil content and 0.60 for protein content . CompareA panel of 117 diverse lines was genotyped and phenotyped in one environment in order to validate the prediction accuracies of seed oil content and protein content. A total of 1148 common genetic bin markers across the AC genome, were screened for the two populations. Since we observed the highest accuracies for RR-BLUP in the TN DH population, we also used this method for prediction. The prediction accuracy amounted to 0.14 for protein content and 0.17 for oil content based on the genetic bin markers.B. napus [2 populations prior to producing DH populations. Besides of the consistent identified QTL, we also detected several new QTLs accounting for these seed quality traits with minor effects in TN DH population compared to the previous QTL identification in this population [Understanding the genetic basis of seed oil yield and quality is important for efficient rapeseed breeding . PreviouB. napus , 24, 73.B. napus . The QTLB. napus , 19, 75.pulation , 11, 22,r2 >0.8), while the QTLs are reflected by only a limited number of SNPs for erucic acid and glucosinolate content.Previous simulation studies revealed that equal shrinkage of marker effects as applied in RR-BLUP can be inappropriate for traits influenced by QTLs exhibiting large effects , 76. In Epistasis, the interaction between genes , is an aThe successful implementation of genome-wide prediction in rapeseed breeding requires that a certain threshold of prediction accuracy is realized , 79. PreIn accordance with previous studies based on bi-parental populations –85, apprThe number of lines has a greater impact on the prediction accuracy than the number of environments Figs  and 4. TB. rapa and B. carinata accessions [B. rapa/B. carinata. However, the used Brassica 60K-SNP array was developed based on the AC genome sequence of B. rapa, B. olearaca and B. napus. Thus, the lack of unique polymorphisms of B. carinata is expected to impair the prediction accuracies. Taking this into consideration, our independent validation reflects the high quality of the developed calibration models even in very diverse backgrounds highlighting the prospects of genome-wide prediction for routine rapeseed breeding programs.The prediction accuracy within bi-parental populations is of central importance examining the potential to implement genome-wide prediction in breeding programs exploiting the double-haploid technology. Moreover, it is of interest to study the potential to use the prediction model also in unrelated populations. We examined an extreme validation scenario for the prediction of seed oil and protein content using a genetically diverse sample of 117 lines which were based on crosses between cessions , 56. TheS1 Fig10 P-values of the linear regression method. The red lines are the -log10 P-values of the stepwise multiple linear regression method. The expected uniform distribution of negative -log10 P-values is indicated by the diagonal line in blue.The green lines are the -log(PDF)Click here for additional data file.S2 Fig2 values.Within each physical distance class, marker pairs are clustered into five groups with varying r(JPEG)Click here for additional data file.S1 Table(DOCX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.


Tomato quality could be improved under deficit irrigation while maintaining yield. The underlying genetic architecture is polygenic and varies with water availability. Candidate genes related to primary metabolism were identified. Water scarcity constitutes a crucial constraint for agriculture productivity. High-throughput approaches in model plant species identified hundreds of genes potentially involved in survival under drought, but few having beneficial effects on quality and yield. Nonetheless, controlled water deficit may improve fruit quality through higher concentration of flavor compounds. The underlying genetic determinants are still poorly known. In this study, we phenotyped 141 highly diverse small fruit tomato accessions for 27 traits under two contrasting watering conditions. A subset of 55 accessions exhibited increased metabolite contents and maintained yield under water deficit. Using 6100 single nucleotide polymorphisms (SNPs), association mapping revealed 31, 41, and 44 quantitative trait loci (QTLs) under drought, control, and both conditions, respectively. Twenty-five additional QTLs were interactive between conditions, emphasizing the interest in accounting for QTLs by watering regime interactions in fruit quality improvement. Combining our results with the loci previously identified in a biparental progeny resulted in 11 common QTLs and contributed to a first detailed characterization of the genetic determinants of response to water deficit in tomato. Major QTLs for fruit quality traits were dissected and candidate genes were proposed using expression and polymorphism data. The outcomes provide a basis for fruit quality improvement under deficit irrigation while limiting yield losses. Global water scarcity will constitute a crucial challenge in the coming years . AgriculBeyond these concerns, deficit irrigation practices constitute a way to manage fruit flavor by exploiting the morphological, physiological, and molecular changes (referred to as ‘phenotypic plasticity’) occurring in water-stressed plants . The first one consists of computing the effects of a given QTL across the environmental conditions using multivariate QTL mapping models (Solanum lycopersicum L.), QTLs were mapped for fruit quality traits measured under optimal watering conditions using linkage (S. habrochaites and S. pennellii), leading to low mapping resolution  grown under two different watering regimes in two locations and phenotyped for 27 traits; (ii) to identify with a high resolution QTLs and QTL by watering regime interactions in this collection; (iii) to combine the results with those obtained in the bi-parental progeny to draw an accurate picture of the genetic variability and the genetic determinants of tomato response to water deficit; and (iv) to identify candidate genes related to the variation of major fruit quality traits under water deficit by dissecting some of the QTLs.The aims of the present study were (i) to explore the pattern of genotype by watering regime interaction in a GWAS panel with a broad genetic basis . Ten accessions were S. pimpinellifolium  originating from Peru and Ecuador. A total of 110 accessions were S. lycopersicum var. cerasiforme (SLC) originating mainly from South America. Finally, 21 accessions belonged to a mixed genetic group mainly including commercial cherry tomatoes and admixed genotypes between SP, SLC, and S. lycopersicum var. lycopersicum. A description of the accessions and their origin is available in Supplementary Table S1. The genetic groups  are used below in the statistical analysis.The population consisted of 141 accessions (2–46 g FW) encompassing the genetic diversity of the cultivated small fruit tomato. Among these, 105 accessions were previously investigated in ® moisture probes and monitored between 25% and 30% in drought pots. In both experiments, two plants per watering regime per accession were randomized in the greenhouse.The plants were cultivated with the same experimental design as in A total of 27 traits were assessed in the GWA population as described in –1 of FM) and relative to dry matter (g 100 g–1 of DM). Yield (g per plant) was computed by multiplying average fruit FW by average fruit number per plant.Fruit quality measurements were carried out on a minimum of 20 mature fruits per accession per watering regime harvested daily on the third to the sixth truss. All the fruits were weighed  and their firmness was measured with a Durofel device (FIR). Only in Avignon, fruits were pooled in three groups in each watering regime. Half of the fruits of each pool were used to assess dry matter weight , pH, and soluble solid content . From the second half of the fruit replicates, pericarps were crushed in liquid nitrogen and assayed for total vitamin C content (VitCFM) according to the microplate method described in http://solcap.msu.edu/) (Supplementary Table S2).The GWA population was genotyped using the Tomato Infinium Array developed within the SolCAP project . Prior to the ANOVAs and when distributions were skewed, phenotypic data were normalized using Box and Cox transformations. The ANOVAs were performed according to the following model:All statistical analyses were performed using R . BecauseYijkl was the phenotypic value of accession j from genetic group i in watering regime k, µ the overall mean, Gri the fixed effect of genetic group i, Gri(Gj) the fixed effect of accession j nested in genetic group i, Wk the fixed effect of watering regime k, and eijkl the residual error effect. No significant microenvironment pattern was identified and we chose not to include any spatial effect in the model. When the interaction Gr×W was significant, we computed a Tukey’s post-hoc test to compare the means.2G and σ2e) were computed with a second linear model: Yijk=µ+Gri+Gri(Gj)+eijk . Broad-sense heritabilities (H2) were calculated under both watering regimes as the ratio between the genetic variance and the total phenotypic variance: H2=σ2G/σ2Total, with σ2Total=σ2G+1/n×σ2e (with n the number of replicates per accession). Spearman coefficients estimated the correlations between H2 and σ2G under drought and control conditions for the same trait.Then, in both watering regimes, restricted maximum likelihood estimates of the genetic and residual variances (σ∆ki=(Dki–Cki)/Cki, with ∆ki the plasticity value for trait k and accession i, Dki the mean of trait k under drought condition for accession i, and Cki the mean of trait k under control condition for accession i.Average values per accession in each watering regime and location were used for subsequent analyses. Plasticity was computed on the accession means as: Supplementary Table S3 and displayed graphically in Supplementary Fig. S1. A kinship matrix (K) based on identity by state among the 6100 SNPs was estimated.We performed a principal co-ordinate analysis (PCoA) on the genotype matrix. The co-ordinates of the accessions on the first three components are available in Average values for each trait following the transformation giving the least skewed distribution were used in the mapping models. GWASs were performed using correction for population structure (PCoA) and modeling genetic variance with the kinship matrix (K). Two mixed models were implemented.P-value <10–4 were considered as significant. From each test, the percentage of variation explained by the marker  was computed.First, the bivariate multitrait mixed model (MTMM) developed by P-values due to the relatively small size of the population. Models with a maximum of five cofactors all having a raw P-value <10–4 were retained. From the optimal model selected, the percentage variation explained by the selected markers  was computed for each trait.Secondly, the univariate multilocus mixed model (MLMM) developed by For all the QTLs identified, we computed phenotypic effects under both watering conditions as: /2. Among the interactive QTLs, we distinguished between ‘antagonist QTLs’ (effect changing direction according to the watering regime) and ‘differential QTLs’ (effect changing intensity according to the watering regime).r2 estimator implemented in the package ‘genetics’  boundary of the interval as the last marker downstream (upstream) on the chromosome that presented an LD with the significant marker above the ‘critical LD’ threshold. For the QTLs detected with the MTMM procedure, when two markers presented a LD higher than the LD threshold, we considered them as a unique QTL. The number of genes within each interval was identified from the tomato genome (ITAG2.4).To define intervals around QTLs, we used a strategy based on LD between pairs of markers inspired from enetics’  to assesFor the comparison with the QTLs detected in the recombinant inbred lines (RILs) grown under the same conditions and phenotyped for the same traits (http://provean.jcvi.org/seq_submit.php)  .P-values <0.001) compared with the one attributed to the genetic group  and the watering regime , except for leaf length in Agadir and stem diameter in Avignon and Agadir (Supplementary Table S5). For those vigour traits, the watering regime represented 48–61% of the total variation.In the variance analysis, the part of the total variation attributed to the genotype effect was predominant . In contrast, the genotype by watering regime interaction represented 1–19% of the total variation and was significant for all traits, except Flw.Avi, DMW.Avi, pH.Avi, and MalicFM.Avi. Interaction partitioning according to method 1 from rH2=0.80), as well as the genetic variances (rσ2G=0.99), confirming genotype re-ranking across watering regimes ( Supplementary Table S5).The genetic group by watering regime interactions represented <2% of the total sum of squares for all traits and was non-significant for 12 traits. The eight significant traits were Diam.Aga, Leaf.Avi, Leaf.Aga, Ht.Avi, FW.Avi, FW.Aga, FIR.Aga, and VitCFM.Avi. Tukey’s post-hoc test indicated that these interactions were mainly driven by a singular behavior of the SP group in response to water deficit  see . Howeverr= –0.55, P=2.70 × 10–12; Aga, r= –0.52, P=2.65 × 10–10), as was previously noted in the RILs. This indicated greater FW loss in larger fruited accessions under drought and increased metabolite contents resulting mainly from the reduced amount of water in the fruits. Thus, the differences observed between the populations may mostly reflect differences in fruit size, with larger fruits among the RILs  compared with the GWA accessions . Nevertheless, a larger range of variation was observed among the GWA accessions for ∆Yield.Avi and ∆Nbfruits.Avi compared with the RILs . In particular, 55 accessions exhibited an increased yield under drought in the GWA population against only two among the RILs. No noticeable geographic origin or genetic group was obvious among these 55 accessions of the GWA population .The correlation between fruit FW in control conditions (indicator of fruit size) and ∆FW was strongly negative in the GWA accessions , malic acid, and citric acid contents .When plotting ∆Nbfruits against ∆SSC in regard to fruit size and ∆FW.Avi, the RIL and GWA plants presented different patterns . Among tP-values <10–4 and percentages of variation explained varying from 5.45% to 18.22%  (Supplementary Table S6). A total of 49 associations were ‘constitutive’ irrespective of the watering regime. Among these associations, the most significant were observed for malic acid content, with P-values comprised between 2.40 × 10–6 and 1.33 × 10–13 in the global test (chromosomes 6 and 7) . Four associations were declared ‘interactive’ between the watering regimes, two for Flw.Avi (chromosomes 9 and 11) and two for GlucoseDM.Avi (chromosomes 4 and 5), with P-values ranging from 1.48 × 10–5 to 7.04 × 10–5 (The MTMM mapping approach detected 53 unique associations for 15 out of 27 phenotyped traits in the GWA population with 4 × 10–5 .P <1 × 10–4) for the 27 studied phenotypic traits. Among them, 94 associations were ‘specific’ , 23 ‘interactive’  and seven ‘constitutive’ . The explained percentages of phenotypic variation ranged from 8.16% (one SNP for Leaf.Aga.C) to 63.85% (six SNPs for SSC.Avi.D) . Constitutive and/or specific associations were observed for all the traits. The most significant P-values were associated ith MalicFM.Avi.D (S06_44955568: 1.88 × 10–19), MalicDM.Avi.D (S06_44955568: 1.27 × 10–17), pH.Avi . The 23 interactive SNPs were associated with 11 out of 27 traits. Their P-values ranged from 7.59 × 10–5 (∆Flw.Avi: S06_36868039) to 2.75 × 10–11 .The MLMM approach identified a total of 124 associations (Supplementary Tables S6–S8). Sixteen associations were detected between twice and three times with related traits (‘acid’ and ‘sugar’ traits) and/or for the same trait in the two locations. Thus, a total of 141 different associations were identified, spread unevenly over the genome . Chromosomes carried out six (chromosomes 7 and 8) to 23 associations . Thirty percent of the associations were ‘constitutive’ (44/141), 30% were ‘control specific’ (41/141), 22% were ‘drought specific’ (31/141), and 17% were ‘interactive’ (25/141). Among the interactive associations, 16 showed ‘differential’ effects (effect intensity changing according to watering regime) whereas nine presented ‘antagonist’ effects (effect direction changing according to watering regime). Up to 14, 24, and 28 different associations were mapped for vitamin C, ‘acid’, and ‘sugar’ content in fruit, respectively.When gathering the associations obtained with MLMM and MTMM, 20 associations were detected in common (same trait and same QTL type), resulting in a total of 157 associations for the 27 traits . In the RILs grown in the same conditions .We observed large differences in size and number of underlying genes when drawing confidence intervals around the association peaks. Eighteen QTLs mapped around the weakly recombinant centromeres covered >10 Mbp and included between 410 and 2573 genes, whereas 84 QTLs covered <5.5 Mbp and encompassed between one and 97 genes  and selected in their intervals genes showing expression in the fruits according to the data from the From the 18 dissected QTLs, ‘SSC.Avi_9.1’ (control specific) probably corresponded to the cloned QTL ‘Brix9.2.5’ controlling SSC in fruit and associated with a polymorphism in a cell wall invertase gene (Solyc09g010080: Lin5) . A seconVitCDM.Avi_1.1’, ‘FructoseDM.Avi_4.1’, and ‘FructoseDM.Avi_10.1’), three genes coding for ‘chaperone proteins dnaJ’ were identified  were identified under antagonist and drought-specific QTLs for fructose and malic acid content  and a gene coding for a ‘malate dehydrogenase’ (Solyc07g062650). The PEPC gene presented a non-synonymous polymorphism with a predicted impact on the protein function when comparing the four re-sequenced accessions. The third one  and Lin8 (Solyc10g083300), presenting three non-synonymous polymorphisms between the re-sequenced accessions.Three constitutive QTLs, the first two on chromosome 7 controlling glucose and malic acid content and the third on chromosome 10 controlling fructose content, seemed particularly promising. The first two  had both improved fruit quality and maintained yield (or even improved) under water deficit compared with the control watering regime, although their vigor (measured through leaf length and stem diameter) was decreased. These accessions emphasized the opportunity to increase metabolite content in tomato fruits using deficit irrigation without achieving parallel limitation of the yield. In contrast, no RIL presented such a response to the water deficit treatment, and the increased sugar and acid contents observed reflected mainly concentration effects due to a decreased amount of water in fruit (The large phenotypic variations observed mainly resulted from genotype effects (35–80%) and less from genotype by watering regime interactions (1–19%). The watering regime effect represented a significant part of the total phenotypic variability (up to 40%) only for stem diameter and leaf length. This suggests that tomato plants buffer the negative effect of water limitation by limiting their vegetative growth and reallocating the photo-assimilates to the fruits . With this stringent threshold, we would not have recovered some well-described tomato QTLs, such as, for example, FW11.2 and FW11.3 on chromosome 11  known to encode a cell wall invertase affecting tomato fruit sugar content  and a gene coding for a ‘malate dehydrogenase’. The PEPC gene presented a non-synonymous polymorphism with a predicted impact on the protein function in the four re-sequenced accessions. As the PEPC is catalyzing the carboxylation of the phosphoenolpyruvate arising from glycolysis into oxaloacetate which is then converted into malate by the malate dehydrogenase or enters the Krebs cycle  on data of 6100 SNPs.Fig. S2. Box-plot of the mean distribution for the nine traits that showed a significant genetic group by watering regime interaction in the ANOVAs.Fig. S3. Distribution of the accession means for plant traits in the GWA population grown under two watering regimes..Fig. S4. Distribution of the accession means for fruit traits in the GWA population grown under two watering regimes.Fig. S5. Relationship between plasticity of fruit number and plasticity of vitamin C content in fruit, in view of the fruit FW plasticity, in the GWA and RIL populations, respectively.Fig. S6. Relationship between plasticity of fruit number and plasticity of citric and malic acid content in fruit (relative to FW), in view of the fruit FW plasticity, in the GWA population.Fig. S7. Physical map of the QTLs detected in the GWA and RIL populations.Fig. S8. Example of co-localizations between GWA and RIL QTLs for soluble solid content and fruit FW on the bottom of chromosome 11.Fig. S9. Confidence interval (CI) sizes and numbers of genes underlying the QTLs in the GWA and RIL populations.Fig. S10. Venn diagram representing common QTLs between the RIL population (linkage mapping) and the GWA population (association mapping).Table S1. Genetic and phenotypic description of the accessions in the GWA population.Table S2. Genotypic data in the GWA population.Table S3. Principal co-ordinates analysis in the GWA population.Table S4. Correlations between Avignon and Agadir trials.Table S5. Effect of watering regime (W), genetic group (Gr), genotype nested in genetic group [Gr(G)] and the interactions [Gr×W and Gr(G)×W] on the plant and fruit traits measured in the GWA population.Table S6. QTLs identified under both watering regimes (‘Control’ and ‘Drought’) using the bivariate multitrait mixed model (MTMM) genome-wide association mapping approach.Table S7. QTLs identified under each watering regime (‘Control’ and ‘Drought’) using the univariate multilocus mixed model (MLMM) genome-wide association mapping approach.Table S8. QTLs identified for plasticity data each [(Drought–Control)/Control] using the univariate multilocus mixed model (MLMM) genome-wide association mapping approach.


Nearly half of adults in the United States who are diagnosed with hypertension use blood-pressure-lowering medications. Yet there is a large interindividual variability in the response to these medications. Two complementary gene–environment interaction methods have been published and incorporated into publicly available software packages to examine interaction effects, including whether genetic variants modify the association between medication use and blood pressure. The first approach uses a gene–environment interaction term to measure the change in outcome when both the genetic marker and medication are present (the “interaction model”). The second approach tests for effect-size differences between strata of an environmental exposure (the “med-diff” approach). However, no studies have quantitatively compared how these methods perform with respect to 1 or 2 degree of freedom (DF) tests or in family-based data sets. We evaluated these 2 approaches using simulated genotype–medication response interactions at 3 single nucleotide polymorphisms (SNPs) across a range of minor allele frequencies (MAFs 0.1–5.4 %) using the Genetic Analysis Workshop 19 family sample.The estimated interaction effect sizes were on average larger in the interaction model approach compared to the med-diff approach. The true positive proportion was higher for the med-diff approach for SNPs less than 1 % MAF, but higher for the interaction model when common variants were evaluated (MAF >5 %). The interaction model produced lower false-positive proportions than expected (5 %) across a range of MAFs for both the 1DF and 2DF tests. In contrast, the med-diff approach produced higher but stable false-positive proportions around 5 % across MAFs for both tests.Although the 1DF tests both performed similarly for common variants, the interaction model estimated true interaction effects with less bias and higher true positive proportions than the med-diff approach. However, if rare variation (MAF <5 %) is of interest, our findings suggest that when convergence is achieved, the med-diff approach may estimate true interaction effects more conservatively and with less variability. Hypertension—defined as an average systolic blood pressure (SBP) of 140 mm Hg or higher or an average diastolic blood pressure (DBP) of 90 mm Hg or higher—affects approximately 30 % of American adults, 45 % of whom use antihypertensive medications for blood pressure (BP) control . Broad iTwo complementary gene–environment (G × E) interaction methods have been described in the literature to test G × E interactions such as differential response to antihypertensives resulting from genetic variation. The first method (the “interaction model”) tests for interaction using a gene–environment interaction term to measure the change in outcome when both the genetic marker and environmental factor are present, as compared to when the genetic marker is present but the environmental factor is not . The secCYP3A43 of varying minor allele frequencies (MAFs) with simulated genotype–medication response interactions. We then used TPP to evaluate the power to detect simulated main effects at MAP4  using a 2DF test in each approach. Lastly, we assessed the observed FPPs of each approach across the odd-numbered chromosomes without simulated effect using both 1DF and 2DF tests using publicly available software.Although these methods have been assumed to be theoretically equivalent, no previous studies have directly compared them. Therefore, in this study we aimed to evaluate their performance by comparing both their power to detect simulated interaction effects as well as their false-positive proportions (FPPs) in family-based data from the Genetic Analysis Workshop 19 (GAW19) . This waCYP3A43 with simulated gene–medication interactions in the absence of genetic main effects. We were aware that carriers of these risk variants were assigned to be nonresponsive to the simulated BP treatment effect on SBP of −6.2 mm Hg (βInt = 6.2 mm Hg). Additionally there were 984 SNPs with simulated genetic main effects for SBP explaining between less than 0.1 % and 2.78 % of the phenotypic variance.Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples (T2D-GENES) Consortium Project  genotypi(n = 117) and a subset of 28,156 SNPs were selected for uniform coverage and low mutual linkage disequilibrium (r2 ≤ 0.2). PCs were assigned to all other individuals (n = 959) using estimated PCs from founders and the predict function in R to compute each individual’s PC scores based on the individual’s genotypes (www.R-project.org). We included the top 5 PCs in all association analyses [We accounted for family relatedness using linear mixed models using a Comprehensive Mixed Model Program for Analysis of Pedigree and Population Data (MMAP) , 24. To analyses .p ≥0.05). All G × E analyses were adjusted for age, sex, population structure, and relatedness. We filtered out any SNP that exhibited a minor allele count of less than 2. The characteristics of true-positive findings were investigated at the 3 SNPs in CYP3A43 with simulated gene–medication effects (1DF and 2DF tests), and the only SNP in MAP4 with a simulated genetic main effect  and greater than 80 % estimated power using a 2DF test. The FPP was calculated for the odd-numbered chromosomes using SNPs beyond 500 kb of the simulated effects . Both true and false positives were considered statistically significant using a p value criterion of less than 0.05. Based on the simulated prevalence of medication status and SBP distribution, we estimated the expected TPP using an approximate effective sample size of 80 % of the total sample (n = 849), to account for the nonindependence of relative pairs. Power analyses were conducted using Quanto [Our analysis evaluated simulated SBP at the last time point (t = 3), when both the prevalence of hypertension and use of antihypertensive medications were the highest . We asseg Quanto .p values using MMAP [The interaction between the simulated genotypes and BP medication status on SBP at t = 3 (equation 1) was modeled to calculate the estimated interaction effect, model-based SEs, and ing MMAP . The 1DFing MMAP .Int = 1 when both XSNP and XMed are nonzero, C represents adjustments for covariates , g ~ N(σa2R) is a polygenic random effect to account for familial correlation through a relationship matrix, and e ~ N(σe2I) is the error term. The null hypotheses for X1DF and X2DF are that βInt = 0, and βInt, βSNP = 0 jointly.Where Xr, range across replicates and chromosomes: −0.13 to 0.16), magnitude, SE, and p value of the difference were estimated using EasyStrata [To apply the med-diff approach to BP medication–stratified results Models , b, we msyStrata . The 1DFsyStrata  and AschsyStrata .g and e are as in Model 1. The null hypotheses for Z1DF and X2DF are that βDiff = 0, and βSNP|Med=1, βSNP|Med=0 = 0 jointly.Where C represents adjustments for covariates , and 6 vs. 7.0 × 106’, 2DF: 6.5 × 106 vs. 5.7 × 106).The average age was 48.1 years  with the youngest and oldest participants across all replicates being 18 and 101 years old, respectively. The mean prevalence of BP medication use at the last simulated time point was 32.7 % (range across replicates: 30.2 to 36.4 %). The average change in SBP in individuals who initiated BP medication between the first and last time points was −6.9 mm Hg. The average odd-numbered chromosome-wide convergence was higher for the interaction model than for the med-diff approach  compared to the med-diff approach  with the exception of the least-common SNP (p <0.02), which also did not converge for 30 % of the replicates (59 of 200 replicates).At the 3 SNPs at this locus the same replicates converged in both G × E approaches Table . Nonconvch Table  showing ch Table . Yet at le Table . The TPPp values were comparable between the 2 approaches with TPPs of 100 % (n = 156).At chromosome (chr) 3:48040283, the main genetic effect was overestimated by both the interaction model (−13.1 mm Hg) and the med-diff stratified analysis of nonmedicated individuals (−13.3 mm Hg), whereas the med-diff analysis of medicated individuals underestimated the effect (−7.8 mm Hg). The 2DF joint As shown in Fig. Randall et al.  have argMAP4 using a 2DF joint test of main and interaction effects. Even though we expect that a 1DF test of the main genetic effect would be a more powerful approach than a 2DF test when there is a true genetic main effect, this “true positive” assessment may represent a real world application of a 2DF test, wherein the investigator has no knowledge of the underlying true effects and may be interested in assessing the influence of potential interactions on established genetic loci. Furthermore, unlike the med-diff approach 1DF test implementation, the published 2DF test implemented in publicly available software does not account for the potential for correlation between strata due to relatedness. It is unclear how this may bias the observed 2DF results and methods comparisons made herein. Future work warrants a more thorough investigation of these approaches in family-based and unrelated data sets to detect associations at loci with both true main and interaction effects.The simulated GAW19 data set used in this analysis did not contain any simulated interaction effects at loci with simulated main genetic effects. Thus, using the simulated GAW19 data we were unable to validate a true positive with both main and interaction effects for either approach (2DF test), which may limit the generalizability of our findings. We were however able to compare our ability to detect a strong main effect at CYP3A43 SNP (MAF 0.1 %). At the SNPs examined at CYP3A43 and MAP4 we observed identical convergence between the 2 approaches. Yet we observed lower odd-numbered chromosome-wide convergence for the med-diff approach than the interaction model, because all medication-stratified models must have converged in order to apply the med-diff approach. Second, we observed FPPs for the interaction model less than expected (5 %) for both 1DF and 2DF tests, which was not the case for the med-diff approach. An analytic focus on low-frequency SNPs (MAF 1–5 %) or common SNPs (MAF >5 %) may minimize the observed difference in the FPPs between the 2 approaches.Based on our findings, the use of these G × E approaches on SNPs with less than 1 % MAF may lead to unstable TPPs and FPPs. First, nonconvergence may plague the most moderate samplings of the data, allowing the SEs to appear smaller than they really are and TPPs higher than expected, as we had observed for the least common In this specific simulated example of gene-medication interactions in family-based data the med-diff approach exhibited greater power to detect interaction effects for low-frequency variants (MAF <1 %), whereas the interaction model exhibited greater power for common alleles (MAF >5 %). However, the med-diff method resulted in a stable but greater FPP for low-frequency variants as compared to the interaction method. In summary, both approaches are robust for common variants (MAF >5 %), but become less concordant as MAF decreases. One of the benefits of the stratified analysis of the med-diff approach is that it is less computationally intensive, but may not be appropriate for continuous environmental factors. This indicates that model selection may in part be context-specific. Furthermore if rare variation is of interest in future investigations, our findings here suggest that the med-diff approach may estimate true interaction effects more robustly, with less variability, and with stable FPPs around 5 % as expected; however, if common variants are the focus, the interaction model may be more robust.Future investigations should consider different types of simulated interactions, for example, where genetic effects are in opposite directions in the 2 environmental strata or where genetic effects differ in magnitude between strata . This current study used the GAW19 simulated family-based data to fill a gap in the G × E literature and make quantitative comparisons directly relevant to model choice in future effect estimation (TPP) and discovery (FPP) studies in the field of genetic epidemiology.


In particular, two LMM features are lacking in the base version of lme4: the definition of random effects by custom covariance matrices; and parameter constraints, which are essential in advanced QTL models. Apart from applications in linkage studies of related individuals, such functionalities are of high interest for association studies in situations where multiple covariance matrices need to be modeled, a scenario not covered by many genome-wide association study (GWAS) software.Quantitative trait locus (QTL) mapping in genetic data often involves analysis of correlated observations, which need to be accounted for to avoid false association signals. This is commonly performed by modeling such correlations as random effects in linear mixed models (LMMs). The R package lme4qtl as an extension of lme4. First, lme4qtl contributes new models for genetic studies within a single tool integrated with lme4 and its companion packages. Second, lme4qtl offers a flexible framework for scenarios with multiple levels of relatedness and becomes efficient when covariance matrices are sparse. We showed the value of our package using real family-based data in the Genetic Analysis of Idiopathic Thrombophilia 2 (GAIT2) project.To address the aforementioned limitations, we developed a new R package lme4qtl enables QTL mapping models with a versatile structure of random effects and efficient computation for sparse covariances. lme4qtl is available at https://github.com/variani/lme4qtl.Our software The online version of this article (10.1186/s12859-018-2057-x) contains supplementary material, which is available to authorized users. Many genetic study designs induce correlations among observations, including, for example, family or cryptic relatedness, shared environments and repeated measurements. The standard statistical approach used in quantitative trait locus (QTL) mapping is linear mixed models (LMMs), which is able to effectively assess and estimate the contribution of an individual genetic locus in the presence of correlated observations –4. HowevThere has been a notable improvement in computation of LMMs with a single genetic random effect. Both population-based , 5, 6 anlme4qtl R package that unlocks the well-established lme4 framework for QTL mapping analysis. We demonstrate the computational efficiency and versatility of our package through the analysis of real family-based data from the Genetic Analysis of Idiopathic Thrombophilia 2 (GAIT2) project [However, the decrease in computation time comes at the expense of flexibility. In particular, most efficient LMM methods developed for GWAS assume a single random genetic effect in model specification and support simple study designs, for example, prohibiting the analysis of longitudinal panels. We have developed a new  project . More sp project , and finy: n is the number of individuals, yn×1 is vector of size n, Xn×p and Zn×n are incidence matrices, p is the number of fixed effects, βp×1 is a vector of fixed effects, un×1 is a vector of a random polygenic effect, and en×1 is a vector of the residuals errors. The random vectors u and e are assumed to be mutually uncorrelated and multivariate normally distributed, A is a genetic additive relationship matrix and I is the identity matrix. In a general case, the model is extended by adding more random effects, for instance, the dominant genetic or shared-environment components.Consider the following polygenic linear model that describes an outcome Gaston package [lme4 R package, including our lme4qtl package. Of the many existing lme4-based extensions, the closest to lme4qtl is the pedigreemm R package [pedigreemm package is not able to fit many advanced models in comparison with lme4qtl  project consisted of 935 individuals from 35 extended families, recruited through a proband with idiopathic thrombophilia . We condWe considered three models for the analysis of APTT in the GAIT2 data, namely polygenic, SNP-based association and gene-environment interaction.Before conducting the analysis, we organized trait, age, gender, individual identifier id, house-hold identifier hhid variables and SNPs as a table dat. The additive genetic relatedness matrix was estimated using the pedigree information and stored in a matrix mat. A polygenic model m1 was fitted to the data by the relmatLmer function as follows.The proportion of variance explained by the genetic effect (heritability) was 0.56, and its 95% confidence interval, estimated by profiling the deviance , was [0.RLRsim R package [p-value of the test was below 2.2×10−16.We further tested whether the genetic effect was statistically significant by simulations of the restricted likelihood ratio statistic, as implemented in the exactRLRT function of the  package . The p-vFor a single SNP named rs1, the update function created an association model m2 from m1 and the anova function then performed the likelihood ratio test.To automate the GWAS analysis, we created an example assocLmer function with several options such as different tests of association and parallel computation. By using the assocLmer function, we have replicated some loci previously reported for APTT in a larger cohort of 9,240 individuals  , while this option has not been implemented in lme4qtl (6.6 h). When including a widely used lmekin function from the coxme package [lme4qtl also showed the lowest computation time  [If one is interested in more complex models than m1 and m2, our package raction) .ρg and its variance is partitioned among three groups of pairs: male-specific , has three parameters mentclass2pt{minimρg=1) or the variances are equal  . We impl=σg2 . WeNumerical results of the likelihood ratio tests in Additional file lme4qtl computation time depends on the sparse structure of covariance matrices, as the genetic relationship matrices are not necessarily sparse. We used the polygenic model m1 as an initial model (the random effect (1|hhid) was omitted), where the genetic relationship matrix mat has a high proportion of zero values (sparsity) equal to 0.98. We then gradually fill zeros in mat by small non-zero values, thus reducing the sparsity towards 0, and refitted the model m1. We found that the time required to fit the polygenic model increased substantially: it became an order of magnitude greater once the sparsity changed from the GAIT2 level 0.98 to 0.60 .In practice, putation , 4. Of alme4qtl R package enables QTL mapping models with a versatile structure of random effects and efficient computation for sparse covariances.In conclusion, the Additional file 1Supplementary Tables and Figures. Supplementary Note 1: R code to compare lme4qtl and pedigreemm R packages. Supplementary Note 2: Multi-trait and multi-environment linear mixed models. Supplementary Note 3: R code applied to the GAIT2 data. (PDF 1341 kb)


The objective of the present study was to estimate (co)variance components of female fertility traits in Chinese Holsteins, considering fertility traits in different parities as different traits. Data on 88,647 females with 215,632 records (parities) were collected during 2000 to 2014 from 32 herds in the Sanyuan Lvhe Dairy Cattle Center, Beijing, China. The analyzed female fertility traits included interval from calving to first insemination, interval from first to last insemination, days open, conception rate at first insemination, number of inseminations per conception and non-return rates within 56 days after first insemination.The descriptive statistics showed that the average fertility of heifers was superior to that of cows. Moreover, the genetic correlations between the performances of a trait in heifers and in cows were all moderate to high but far from one, which suggested that the performances of a trait in heifers and cows should be considered as different but genetically correlated traits in genetic evaluations. On the other hand, genetic correlations between performances of a trait in different parities of cows were greater than 0.87, with only a few exceptions, but variances were not homogeneous across parities for some traits. The estimated heritabilities of female fertility traits were low; all were below 0.049 . Additionally, the heritabilities of the heifer interval traits were lower than those of the corresponding cow interval traits. Moreover, the heritabilities of the interval traits were higher than those of the threshold traits when measuring similar fertility functions. In general, estimated genetic correlations between traits were highly consistent with the biological categories of the female fertility traits.Interval from calving to first insemination, interval from first to last insemination and non-return rates within 56 days after first insemination are recommended to be included in the selection index of the Chinese Holstein population. The parameters estimated in the present study will facilitate the development of a genetic evaluation system for female fertility traits to improve the reproduction efficiency of Chinese Holsteins. Female fertility traits are the most economically functional traits affecting the efficiency of the dairy industry. Cows with excellent fertility resume cycles soon after calving and become pregnant when properly inseminated . Accordihttp://www.sweebv.info/ba52nycknav.aspx). Furthermore, the results of routine genetic evaluations in Canada (https://www.cdn.ca/) and the United States (http://www.holsteinusa.com/) have shown that the decline in the genetic trend of fertility traits has flattened and even slightly reversed after increasing the weight of fertility traits in the selection index [Although the heritabilities of reproduction traits are relatively low, their additive genetic variances have remained sufficiently high to perform effective selection. Nordic countries  are pioneers in applying fertility traits in dairy cattle breeding and have implemented fertility traits in their selection index since 1994. The Nordic Cattle Genetic Evaluation has shown that the genetic trend for the female fertility index of Holstein bulls has increased by approximately 1% per year since 2000 , days open (DO), interval from first to last insemination (IFL), conception rate at first insemination (CR), number of inseminations per conception (AIS) and non-return rate within 56 days after first insemination (NRR56). For binary traits, CR was coded as 0 (failure) or 1 (success), and NRR56 was coded as 1 when there was no subsequent insemination within 56 days after the first insemination and 0 otherwise. All traits recorded before first calving were considered as heifer traits and were coded as parity 0. Traits measured in first-lactation cows were coded as parity 1, and the same strategy was used for the remaining lactations. Among these traits, ICF and DO were available only for cows. All the remaining traits were measured for both heifers and cows. In this context, h and c were used as suffixes in trait abbreviations to distinguish heifers and cows.Most fertility traits included censored records, as mistakes in recording and some culling events arose during data collection or fertility events were still in progress. The last insemination with a positive pregnancy test result or with the following calving record was considered a verified conception. In the present data, 5.92% of heifers and 13.92% of cow-lactations showed no verified conception from the last insemination. In such cases, the IFL and AIS were calculated according to the last insemination, and the expectation of the trait was added as a penalty. Based on uncensored data, the expectations of IFLh, IFLc, AISh and AISc were 21 days, 43 days, 1.5, and 2.0, respectively. Similarly, for cows without ascertained conception, the penalty for DO was the same as that for IFL. To further reduce the proportion of censored records, we only used data for females with birth years from 1999 to 2013, insemination years from 2000 to 2014, and calving years from 2000 to 2014. To reduce possible selection bias, cows without heifer records were also removed from the data. Moreover, the data in the analysis contained only females inseminated by AI bulls. Other criteria for data editing included age at first insemination between 270 and 900 days, age at first calving between 500 and 1100 days, gestation length between 240 and 300 days, ICF between 20 and 230 days, IFL less than 365 days and AIS less than eight times per parity. Records with values smaller than the lower limit were deleted as outliers, while those with values larger than the upper limit were set as the upper limit.Based on the distribution of records across parities for each trait, only data from heifers and the first three lactations were used in the analysis. After editing, the total number of cows in the final dataset was 88,647, and the total number of records (parities) was 215,632. The numbers of observations available for heifers and the first three parities of cows were 88,647, 60,022, 41,858 and 25,105, respectively. Heifer records comprised 41.11% of the entire dataset.Full pedigree data were provided by the Dairy Association of China , and each animal was traced back as many generations as possible. Unknown parents were assigned into 16 phantom groups, based on sex and birth year. In total, the pedigree included 179,939 females and 4310 males, with birth years from 1930 to 2013. Considering the number of heifers/cows in the present study, the size of pedigree was small. This was determined by the data structure. In the current study, the phenotypic data covered a long period, and the females came from 32 herds during birth year 1999 to 2013. Thus, the phenotypic data already covered a large number of female ancestors . Therefore, the number of animals in the pedigree was only about two times as large as the number of animals with fertility records, even though the heifers/cows were traced back as many generations as possible.Five linear Gaussian animal models were used to estimate the (co)variance components of female fertility traits. First, data across multiple parities were analyzed using a multi-trait model in which the performances of a trait in different parities were treated as different traits. For each of the traits defined both in heifers and cows , a four-trait model was used.For traits only defined in cows (ICF and DO), a three-trait model was used.In addition, cow traits  were further analyzed by pooling data over parities and using a single-trait model treating records in multiple parities as repeated measurements.Correlations between a pair of heifer traits and a pair of cow traits were estimated using a two-trait model. For a pair of heifer traits , the following two-trait model was used:For a pair of cow traits , the following two-trait model was used:yi was the vector of observations  and (2); i = 1, 2 representing fertility traits 1 and 2 in models (4) and (5)); βi was the vector of fixed effects for the ith trait, including age group , herd-year of calving (for ICF and DO) or herd-year of first insemination within parity , year-month of calving (for ICF and DO) or year-month of first insemination within parity , AI technician, sexed semen (coded as 1 for the use of sexed semen and 0 for the use of non-sexed semen), and parity (available only for models (3) and (5); ai was the vector of random additive genetic effects for the ith trait; pei was the vector of permanent environmental effects for the ith trait (available only for models (3) and (5)); and ei was the vector of random residual effects for the ith trait. Xi, Zi and Wi were the incidence matrices connecting βi,ai and peitoyi. It was assumed that In the above models, A is the matrix of additive genetic relationships between individuals in the pedigree; I is the identity matrix; ith trait, respectively; i ≠ j) were the additive genetic covariance, permanent environmental covariance and residual covariance between the ith trait and the jth trait, respectively.In the above distributions, The (co)variance components in the above models were estimated using average information-restricted maximum likelihood (AI-REML) implemented in the DMU package . The asyThe descriptive statistics for female fertility traits regarding heifers and cows are presented in Table Estimates of the variance components and heritabilities of fertility traits using a multi-trait model and a single-trait model are shown in Table The genetic and residual correlations between parities of the performances of a trait using the multi-trait model are presented in Table Table The genetic and phenotypic correlations between cow traits, estimated using data pooled over three parities, are shown in Table This study investigated the relationships among parities and variance components in each parity for female fertility traits in Chinese Holsteins. In addition, the present study estimated genetic and phenotypic correlations between heifer traits and between cow traits. The results obtained from the present study will be useful for genetic evaluations in dairy cattle breeding programs, particularly for developing a routine genetic evaluation system for female fertility traits in Chinese Holstein population.The average performances of fertility traits in the present study were similar to those of other populations in general , 12, 22.The heritabilities obtained in the present study were consistent with the previous estimates for fertility traits in various populations , 12, 24.For traits defined in both heifers and cows, variance components for IFL and AIS differed considerably between heifers and cows, and heritability estimates of the two heifer traits were much lower than those of the corresponding cow traits. These results were consistent with previous observations in Canadian Holsteins , Brown Shttp://www.nordicebv.info).Genetic correlations between the performances of a trait across parities of cows were high (over 0.87) with the exception for CRc, for which the genetic correlation between the first and second parities was 0.66 and between the second and third parities was 0.63 but with a relatively large standard error. The results were consistent with previous literature , 23, 27.Although the genetic correlations among traits varied substantially, moderate or strong correlations were obtained between traits in groups with similar definitions of fertility functions. Therefore, four groups of traits defined based on reproductive biology highly consistent with the patterns of genetic correlations. The first group of traits measured the abilities of the maiden heifers to conceive and maintain pregnancy, including IFLh, CRh, AISh and NRR56h, which had genetic correlations ranging from 0.63 to 0.94 in absolute values. The second trait group measured the abilities of lactating cows to recycle after calving, indicated by ICF in the present study. The third group of traits described the capacities of cows to conceive and maintain pregnancy, including IFLc, CRc, AISc and NRR56c. Most genetic correlations between these traits were moderate to high, ranging from 0.51 to 0.95 in absolute values, except for the correlations of NRR56 with IFLc (−0.15) and CRc (0.31). The fourth group of traits was DO, which measured the combined abilities to recycle, conceive and maintain pregnancy. This grouping of traits is consistent with the current Interbull concepts of grouping fertility traits.The traits IFL, CR, AIS and NRR56 all reflect the ability to conceive and maintain pregnancy. According to the estimated genetic parameters, the expected responses to selection given the same selection intensity can be calculated. Among these traits, selection for IFL would achieve the largest genetic progress in the ability to conceive and maintain pregnancy in both heifers and cows. Since IFL had a very high genetic correlation with CR and AIS, it is not necessary to include CR and AIS in a fertility index that contains IFL. NRR56, which measures the capacity for conception and early embryo loss, had a low genetic correlation with IFL for cows. It would be reasonable to include NRR56 in the fertility index. There is no need to include DO in the fertility index given its component traits, ICF and IFL, are already in the index. Thus, IFL, NRR56 and ICF are recommended to be included in the selection index of the Chinese Holstein population.The present study also estimated genetic and phenotypic correlations between a pair of traits in each parity, using a two-trait model (results not shown). Compared with the results from the analysis using pooled data over parities and treating them as repeated records, the patterns of estimated correlations in each parity were somewhat different from those estimated using the repeatability model (model 5). Moreover, the estimated correlations were not stable across different parities. One possible reason could be bias caused by selection on previous parities, especially the selection for heifer fertility. To avoid this bias, a multi-trait model, which used data from all parities and treated fertility traits from different parities as different traits, was implemented to estimate correlations between a pair of traits for each parity. However, this multi-trait model had difficulty reaching convergence. Therefore, only correlations estimated using data pooled over parities and treating them as repeated records were presented in this study.For traits with binary phenotypes, a linear model was used in the present study due to low computational requirements. The results showed that the heritability estimates of binary traits were generally lower than those of interval traits measuring conception abilities, consistent with previous studies , 8. ManyOne large challenge in genetic evaluations of fertility interval traits is the presence of censoring, which reflects data truncated through culling or fertility events still in progress. Regarding censored data as uncensored or simply excluding them from the dataset would favor bulls with many daughters having censored records , and wouThe parameters estimated in the present study will facilitate the development of a genetic evaluation system for fertility traits to improve the female fertility abilities of Chinese Holsteins. The performances of a trait in heifers and cows were significantly different in genetic and should be considered as distinct but correlated traits in genetic evaluations. In addition, even though high genetic correlations between the performances of a trait in different parities of cows, additive genetic variances and heritabilities differed between the first parity and the later parities, which suggests that the performances of a trait in the first and the later parities should be treated as different traits in genetic evaluations. Generally, the estimated heritabilities of all female fertility traits were low, but selection to improve fertility is promising since the genetic variations are large. IFL, NRR56 and ICF are recommended to be included in the selection index of the Chinese Holstein population.


Six loci were identified; three for HD and three for RCCL. An associated locus at CFA28:34,369,342 for HD was described previously in the same dogs using a conventional mixed model. No loci were identified for RCCL in the previous report but the two loci for ED in the previous report did not reach genome-wide significance using the FarmCPU model. These results were supported by simulation which demonstrated that the FarmCPU held no power advantage over the linear mixed model for the ED sample but provided additional power for the HD and RCCL samples. Candidate genes for HD and RCCL are discussed. When using FarmCPU software, we recommend a resampling test, that a positive control be used to determine the optimum pseudo quantitative trait nucleotide-based covariate structure of the model, and a negative control be used consisting of permutation testing and the identical resampling test as for the non-permuted phenotypes.Hip dysplasia (HD), elbow dysplasia (ED), and rupture of the cranial (anterior) cruciate ligament (RCCL) are the most common complex orthopedic traits of dogs and all result in debilitating osteoarthritis. We reanalyzed previously reported data: the Norberg angle (a quantitative measure of HD) in 921 dogs, ED in 113 cases and 633 controls, and RCCL in 271 cases and 399 controls and their genotypes at ~185,000 single nucleotide polymorphisms. A novel fixed and random model with a circulating probability unification (FarmCPU) function, with marker-based principal components and a kinship matrix to correct for population stratification, was used. A Bonferroni correction at p<0.01 resulted in a P< 6.96 ×10 FBN2, has been directly associated with a hip laxity measurement, the distraction index of HD [Canine hip dysplasia (HD) is a common complex trait affecting dogs of all sizes, with frequencies ranging from 1–75% , 3. The ex of HD . Recent ex of HD , and Gerex of HD . The curex of HD .Elbow dysplasia (ED) in dogs is a group of disorders that affect the articular surfaces of the elbow. The three common abnormalities of ED are fragmented medial coronoid process (FCP), osteochondritis dissecans (OCD) of the medial humeral condyle, and ununited anconeal process (UAP). Adolescent children can develop OCD in the elbow . In LabrRupture of the cranial (anterior) cruciate ligament (RCCL) is the most common cause of acute and chronic, clinically-severe, hind limb lameness in dogs. The majority of dogs with RCCL lack a history of distinct trauma similar to the non-contact type of human anterior cruciate ligament rupture. Up to 50% of dogs affected with RCCL may have bilateral ruptures . Up to oModerate support for genetic susceptibility to non-contact rupture of the anterior cruciate ligament in humans and a predisposition in female athletes has been presented . RuptureHerein, we report the power of a novel fixed and random model circulating probability unification function (FarmCPU), by reanalyzing the genotypes and phenotypes from previous GWAS of HD, ED, and RCCL , and comDogs were admitted to the Cornell University Hospital for Animals for diagnosis of lameness or for genetic screening programs for HD and ED. HD was assessed by the Norberg angle (NA), which measures the relationship between the femoral head and acetabulum on the traditional hip-extended, ventrodorsal radiographic projection. The pelvis of each dog was radiographed following physical maturity. The NA was measured on the Hospital patients by RJT and at the Orthopedic Foundation for Animals by Dr. Gregory Keller. For ED, the diagnosis was based on elbow radiography, computed tomography and exploratory arthrotomy or arthroscopy performed at the Cornell University Hospital for Animals. Ninety-five percent of the dogs had fragmented medial coronoid process (FCP), some had osteochondrosis (OC) or both FCP and OC, and a few had UAP. The controls were over 2 years of age and diagnosed by elbow radiography either at the Cornell Hospital or by the OFA according to routine phenotypic screening for ED. The OFA uses a flexed lateral radiograph taken at 2 years of age or older, and radiologists look for signs of secondary OA, which is a natural sequela to ED .Clinical signs of RCCL included lameness in the affected limb, a positive cranial drawer sign, cranial tibial thrust, synovial effusion, and the presence of a medial proximal tibial buttress. Suspected cases had their stifle(s) radiographed and most of the dogs had arthroscopy or arthrotomy prior to definitive surgical correction. Control dogs were classed as 1 and two classes of affected dogs were used; incomplete ruptures of the ligament (score 2) and complete ligament rupture (score 3). Controls for this trait were over 8 years of age and selected based on orthopedic examination including gait examination, and specifically palpating for normal stifle architecture, stifle stability  and/or stifle radiography .MC1R, and they are black if they have one or two copies of one of the dominant MC1R alleles [MC1R gene is located at CFA5:66,692,398–66,693,344. Color association testing with MC1R was performed on a binary trait defined as yellow versus the others (black or chocolate). The tyrosine related protein 1 (TYRP1) gene, located at CFA11:33,317,110–33,336,030, causes chocolate coat color in black dogs so that when GWAS was performed on a binary trait defined as black versus chocolate, the marker at CFA11:33,326,685 identified the association [One hundred and twenty of the Labrador Retrievers were over 8 years old and were specifically recruited to be used as controls for mapping inherited traits. To test coat color association as a positive control, among 642 Labrador Retrievers (185 of which were represented in this study) were 264 black, 126 chocolate, and 52 yellow dogs in the Cornell Veterinary Biobank. All Labradors are fixed at the K locus. They are yellow if they have two copies of the recessive allele of  alleles , 25. The10.5061/dryad.266k4).DNA was extracted from venous blood collected in Na-EDTA using either phenol-chloroform or the Puregene (Gentra) protocol. All the dogs were genotyped for 185,805 SNPs on the Illumina semi-customized version 2 of the canine HD mapping array . Genotypt test. The bin method was employed to avoid the confounding problem of linkage disequilibrium (LD). The default setting of bin size was used in HD, ED and RCCL association testing.Before statistical analysis, SNPs with minimum allele frequency (MAF) < 0.05 were removed. The top five principal components were included in the model to account for breed effect and population structure in all three traits. The statistical modeling was done with FarmCPU , which cP-value passed the Bonferroni cutoff (P < 0.01) was counted and 100 of 1000 repeats was used as the criterion of a false positive. For false negative testing of the resampling test, the phenotypes were shuffled relative to the genotypes and 100 pseudo phenotype datasets were generated. Then, the resampling test was implemented exactly as for the real data relationships. For false negative testing of the whole population GWAS, the phenotypes were shuffled and 1000 pseudo phenotype datasets were generated. For the false negative threshold, the same criterion was applied i.e. when the cut off was 100 of the 1,000 replicates, the FDR for the permutation test was <0.05, so we used 100 as the cut off.The principle component analysis and LD testing in Q / NQT, and FDR was calculated as: FDR = NF / (NQT + NF), where NQ is number of true positive associations, NQT is total number of QTN, and NF is total number of false positives. The power and FDR calculation were conducted across all the QTNs. All the SNPs within a fixed range around each QTN were treated as loci in the same LD interval (true positives), and the window size of this range was set as 100,000 bp. Simulated phenotypes were generated using GAPIT [In the simulation test, genotype data of all samples was employed to simulate the phenotype value in the three populations . The phenotype value included the additive genetic effect and the residual effect, and both of them follow the normal distribution. The heritability of the three simulated phenotypes was 0.75 (HD), 0.25 (ED) and 0.75 (RCCL), respectively. Heritability based on marker information that was calculated in all three traits was generated from GAPIT . For allng GAPIT . The mixng GAPIT  and compThe Norberg angle (101.8±SD = 9.8°) was averaged over both hips of 921 dogs belonging to 69 pure and 121 mixed breeds. Trait values of the five breeds with the most individuals represented are shown in r2 of 0.3 at an average of 11 kb in all three mapping populations  . The thrCTBP2), a transcriptional co-repressor [TRIM2), an E2 ubiquitin ligase (DPP4), a membrane bound peptidase previously associated with rheumatoid arthritis and OA , the association on CFA8:64,204,398 was below the Bonferroni-adjusted threshold in the GEMMA-based analysis with p = 7.5x10-6. There was no association on CFA7 in the GEMMA-based analysis.We reanalyzed the RCCL trait using the GEMMA  mixed mord et al  BonferroLMN), a brain protein expressed during development (DYN)  , which eMC1R) as expected [TYRP1) gene, located at CFA11:33,317,110–33,336,030 causes chocolate coat color in black dogs so that when GWAS was performed on a binary trait defined as black versus chocolate, the marker at CFA11:33,326,685 was strongly associated as expected , the SNP at CFA5:63,694,334 had the strongest association signal and is located within the melanocortin 1 receptor  asThe negative control tests were conducted in two ways. One was performed to determine the significant cutoff for the resampling test; the other was the permutation test for the whole population in the GWAS. For the resampling test, if 100 of 1000 repeats was employed as the cutoff, the resampling test would pass the permutation test significant level of 0.05 on all three traits. For the whole population permutation test, the false positive proportion were 1.2% (HD), 0.8% (ED) and 0% (RCCL) respectively, which are all lower than the significance criterion of 5%.The statistical power difference of FarmCPU and the mixed linear model was evaluated through a simulation test in the three populations. The heritability of these three traits was 97.1% (HD), 20.4% (ED) and 100% (RCCL) respectively, which was calculated using the genotypes. Thus the heritability of HD and RCCL in current population sample is much higher than in the natural population. Accordingly, the heritability of the simulated phenotype was set as 75% (HD), 25% (ED) and 75% (RCCL), respectively. The power of FarmCPU was better than the mixed linear model in the HD and RCCL population samples and slightly worse than mixed linear model in the ED sample. These results coincided with the respective model analyses of the real traits. Under the scenario of low heritability, FarmCPU will be identical or similar to GLM because few of the possible QTNs could be captured and treated as fixed effects in the model. As such, the statistical power of MLM may be higher than FarmCPU in those traits with low heritability in a GWAS population sample. The breeds, phenotypes, and genotypes are in accompanying et al.[et al. [A GWAS of these three orthopedic traits on this population of dogs using the same genotypes and phenotypes based on a linear mixed mapping model implemented in GEMMA v. 0.94 has been previously reported , 23. Her.[et al. . Our conFalse positives in a GWAS can be effectively controlled by a fixed and a random effect mixed linear model that incorporates population structure and kinship among individuals to adjust the effect of a marker association. However, the adjustment for occult population structure can penalize the number of true positive associations. The FarmCPU approach extends previous mixed linear models into two separate stages. The fixed effect component tests each SNP, one at a time, with multiple associated markers (pseudo quantitative trait nucleotides) as covariates to control false positive associations. To avoid model over-fitting, the effect of the associated markers is then estimated as a random effect in the second stage by using them to define kinship. Previously, both real and simulated data analyses demonstrated that FarmCPU improved statistical power compared to current methods, while still controlling inflation . Here weIt is important when mapping complex traits in veterinary medicine to maximize power, as proffered through the FarmCPU software, because financial constraints limit the number of individuals that can be phenotyped and genotyped for GWAS. Yet, we remained concerned about controlling false positive associations and so we set the Bonferroni-adjusted, genome wide p value to <0.01 instead of the standard <0.05 level. When only three PCs were used as covariates in the model, we found 2 spurious associations with coat color yet the QQ plot showed a lack of inflation in p values in the lower part of the curve (data not shown). By using five PCs as covariates, the spurious associations were removed . A seconet al. [The validity of these associations requires replication in an independent sample of pure and mixed breed dogs and sequencing of the candidate genes . Haywardet al. , demonstet al. . Here, wCX3CR1 [HOXB9 [UFSP2) [Comparative mapping and candidate gene screening of cognate complex traits in dogs and people may lead to discovery of common molecular genetic etiologies. Both the human ,31 and cCX3CR1 , a patte1 [HOXB9 , 34, 35, [UFSP2)  have beeCTBP2) contains the marker associated with HD at CFA28:34,369,342 in this report and in Hayward et al., [Ctbp1_+/-_;Ctbp2_-/-_ mouse embryos fail to form normal musculoskeletal structures like vertebral bodies, distal ribs, and skeletal muscle [Ctbp1 and Ctbp2 are expressed in the ventral sclerotomal somitic domain, and later in the myotome and dermatomyotome, that give rise to skeletal muscles and distal ribs [Wnt), Notch, and bone morphogenetic protein (Bmp) signaling. Wnt, together with Bmp signaling, controls the patterning of the dorsal and ventral muscles in the developing limb bud [CtBP1 and 2 are both expressed in canine hip joint capsule and round ligament of the femoral head (data not shown).C-terminal binding protein 2 , an E2 ubiquitin ligase. Mutations in E2 cause Charcot-Marie-Tooth disease type 2R characterized by muscle weakness, atrophy, and axonal degeneration [et al. [The marker associated with HD at CFA15:51,083,415 is ~40 kb from tripartite motif-containing protein 2 , which is a plasma membrane peptidase that selectively cleaves an N-terminal dipeptide from peptides with a proline or alanine residue [DPP4 are associated with several diseases including rheumatoid arthritis and OA [DPP4 could influence hip conformation but it is possible that secondary hip OA could be affected by DPP4 function because its cytokine and growth factor cleavage products will influence tissue inflammation. It is conceivable that separate mutations can influence the primary heritable HD defect and the secondary organ response to the disorder [The marker at BICF2P1242852 on CFA7 is ~55 kb from dipeptidyl peptidase-4 . Calmin is a developmentally-regulated brain protein with calponin-homology domains [DYN) [DYN mutations cause delayed endoplasmic reticulum to Golgi trafficking [The closest candidate gene for RCCL in the region of CFA8:64,204,398 is calmin  –59, the fficking . There hfficking .FBN2) [VEGFA), kinase insert-domain receptor (KDR) [COL1A1 [DCN), aggrecan (ACN), biglycan (BGN), LUM (lumican) [COL5A1 [COL5A1 and COL12A1 have been associated with rupture of the anterior cruciate ligament in people, especially in female athletes, but none of these genes were associated with RCCL in our study.Polymorphisms in fibrillin 2 (FBN2) , vasculaor (KDR) , COL1A1  [COL1A1 , decorinlumican) , COL5A1  [COL5A1 , and intet al.[Our report is the first to apply FarmCPU, a novel statistical association method, to canine complex trait mapping. We confirmed the previous association on CFA28 with HD and identified 5 further associations. We confirmed a further association using the linear mixed model applied in the Hayward et al. analysiset al., 67. SimCornell Institutional Animal Care and Use Committee approval numbers were 2005–0151  and 2006–0187 (Hip Dysplasia and Osteoarthritis Genetics).S1 Fig(A) Radiographic images of a dog with normal hip joints and a dog which is severely affected with osteoarthritis secondary to hip dysplasia (B). (C) Radiographic images of a dog which has a normal stifle joint and a dog which is severely affected with osteoarthritis secondary to rupture of the cranial cruciate ligament (D). (E) Radiographic images of a dog which has a normal elbow joint and a dog which is severely affected with osteoarthritis secondary to elbow dysplasia (F).(DOCX)Click here for additional data file.S2 FigMC1R. (b) The tyrosine related protein 1 (TYRP1) gene, located at CFA11:33,317,110–33,336,030, causes chocolate coat color in black dogs so that when GWAS was performed on a binary trait defined as black versus chocolate, the marker at CFA11:33,326,685 was strongly associated. Note the Y axis scale denoting the strength of the association is different for the two color traits.Dashed line is Bonferroni adjusted genome wide p < 0.01. (a) When GWAS was performed on a binary trait defined as yellow versus the others (black or chocolate), the SNP at CFA5:63,694,334 had the strongest association signal and is located within (DOCX)Click here for additional data file.S3 FigFor the permutation, the real phenotype data of these three traits was shuffled and, for the resampling test, 80% of the individuals were sampled each time. This process was repeated 1,000 times and the most frequently associated loci were collected and their frequency displayed in the Box Plots (a) and the cumulative distributions for each trait . Black dashed line  refers to the cutoff of 100 that we used in real trait-genotype resample testing. Note the Y axis scale denoting the frequency of each replicated association is different for each panel.(DOCX)Click here for additional data file.S4 FigThe vertical axis is the statistical power of 50 different randomly sampled causal loci and the horizontal axis is the false discovery rate (FDR) of different causal loci. The window size of each locus in both the power and FDR calculations was defined as 100,000 bp.(DOCX)Click here for additional data file.S1 TableHip dysplasia was measured as the Norberg angle. Elbow dysplasia was scored as present or absent based on physical examination and radiography, computed tomography and/or surgery. Rupture of the cranial cruciate ligament was assessed by physical examination, radiography, and surgery, and scored as control  or case, which could be a partial rupture (score of 2) or a complete rupture (score of 3) based on surgery.(DOCX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Tabledatadryad.org, doi:10.5061/dryad.266k4) through the common IDs.This data can be linked to the genotypes in Dryad ((XLSX)Click here for additional data file.