Genetic variants at the AMH protein-coding gene showed considerable allelic heterogeneity, with both common variants  and low-frequency variants [rs2385821 ] independently associated with apparently large effect sizes in males, but not females. For all three SNPs, we highlight mechanistic links to AMH gene function and demonstrate highly significant sex interactions (PHet 0.0003–6.3 × 10−12), culminating in contrasting estimates of trait variance explained . Using these SNPs as a genetic proxy for AMH levels, we found no evidence in additional datasets to support a biological role for AMH in complex traits and diseases in men.Anti-Müllerian hormone (AMH) is an essential messenger of sexual differentiation in the foetus and is an emerging biomarker of postnatal reproductive function in females. Due to a paucity of adequately sized studies, the genetic determinants of circulating AMH levels are poorly characterized. In samples from 2815 adolescents aged 15 from the ALSPAC study, we performed the first genome-wide association study of serum AMH levels across a set of ∼9  AMH) and its receptor (AMHR2); however, ∼15% of cases are idiopathic  is an essential messenger of sexual differentiation. In the male foetus, AMH results in involution of the Müllerian ducts, allowing Wolffian ducts to develop into the male reproductive tract under the influence of testosterone. In the female foetus, the absence of AMH allows the Müllerian duct to differentiate into uterine-fallopian internal reproductive structures. Pathological disruption of AMH activity in XY karyotype males leads to the persistent Müllerian duct syndrome, a rare condition in which atypical development of the uterus and sometimes other Müllerian structures occurs ,2. Rare iopathic .In recent years, the development of sensitive assays for AMH has allowed many studies of the role of postnatal AMH levels (which are ∼10-fold lower than in the foetus) as a gonadal marker in both sexes. In pre-pubertal boys, measurement of serum AMH is performed in clinical settings as a reliable indicator of functional testes; its absence supports the diagnosis of primary hypogonadism –5. In woIn epidemiological studies, the association of serum AMH levels with a broad range of cardio-metabolic traits in women has been assessed, with conflicting results suggesting higher levels are associated with increased disease risk ,12, reduAMH locus, which explain a substantial proportion of the population variance in AMH levels in males, but not in females. Following on from this, we completed a phenome scan in both ALSPAC males and deCODE  studies to generate hypotheses around potential causal effects of AMH on a range of phenotypes, which found no evidence for a causal role in over 2500 human disease/traits tested.Here, we report the first genome-wide association study (GWAS) of serum AMH levels in a sample of 1360 males and 1455 females from the ALSPAC birth cohort study. We identified several genetic variants at the Supplementary Material, Table S1). The GWAS for logged AMH levels in all 2815 adolescents  identified a total of 113 variants associated with serum AMH levels beyond the genome-wide significance threshold, all of which were located in/near the AMH protein-coding gene (Table AMH .Natural log-transformed serum AMH levels were higher in 1360 males compared with 1455 females from the ALSPAC study  revealed an additional low-frequency SNP (rs2385821) at genome-wide significance (Table r2 = 0.22) with the lead index SNP, but its addition to a joint model increased the variance explained in serum AMH from 2.7% by rs4807216 alone to 5.2% by both SNPs.Given the large number of variants associated at this locus with a broad range of allele frequencies (MAF 2–40%), we tested for the presence of multiple statistically independent signals at the P rs480726 revealeP = 7 × 10−50). A test for heterogeneity revealed a striking sex interaction for this lead SNP [PHet = 9.3 × 10−22], which was not associated with AMH levels in females (P = 0.67).We next aimed to identify variants with sex-specific effects on AMH by performing two stratified analyses in the subsets of 1360 males and 1455 females. No variants reached genome-wide significance in females; however, a strong signal, represented by the same lead SNP as in the combined analysis, was observed in males . In a joint model, all three SNPs demonstrated significant heterogeneity between sexes , with widely contrasting estimates of the phenotypic variance explained in a model using all three SNPs: 24.5% in males versus 0.8% in females. To examine whether sex differences in AMH levels and/or variability influenced the gene × sex interactions, we examined a sub-sample of 713 boys and girls matched for an identical AMH mean and SD. These demonstrated a very similar pattern of sex-specific associations (results available from authors on request).We repeated conditional analyses in the sex-specific strata and found three independent signals at the es Table , only onWe sought to confirm the identification of these statistically independent signals using an ‘approximate conditional analysis’ methodology implemented in GCTA , run onlAMH function, we assessed publicly available gene expression data from the GTex consortium , in addition to searching for correlated non-synonymous variants. All three SNPs were associated with AMH mRNA transcript levels in multiple tissue types . The lead SNP for AMH protein levels (rs4807216) was also the same lead SNP for the strongest genome-wide signal for AMH mRNA levels ; however, for rs4807216  the mRNA increasing allele was associated with decreased protein levels, despite directionally concordant effects on mRNA across all significant tissues. Two of the three SNPs were correlated (r2 > 0.5) with missense variants in AMH .To identify the potential mechanism(s) linking SNP association to N = 30, P > 0.002; Supplementary Material, Table S2). Nor did we find any evidence of association in deCODE .We performed a ‘Mendelian Randomisation’ analysis to test the likely causal relevance of circulating AMH levels on a broad range of human disease and health-related traits. Using our newly identified SNPs as a genetic proxy for AMH, we found no evidence for a causal relationship between AMH and complex selected available traits in the ALSPAC males .Our study represents the first large-scale effort to elucidate the genetic architecture of circulating AMH levels. As with other sex hormones, progress in identifying genetic determinants has been relatively slow compared with other complex traits, primarily due to a paucity of data. Other studied sex hormones (and their binding proteins) include testosterone ,22, dehy protein . Each ofAside from insight into the genetic regulation of AMH, the identification of associated genetic variants has utility to inform broader biomedical questions. The principles of ‘Mendelian Randomization’ have been widely utilized to model genetic variants as non-confounded proxies for traits of interest –31. NotaGiven the relatively weak genetic effect in females, we were unable to assess what further role circulating levels may have on the tested health outcomes in females. While the phenome scan in deCODE is undertaken in females and males combined (due to our access to these combined summary data only), the results should be interpreted as reflecting a Mendelian randomization study in males only since the genetic instrument explains very little variation in AMH in females. Currently AMH testing is used in a number of diagnostic settings, including for ovarian reserve measurement where it remains a leading predictive biomarker test ,37. BiomWe note a number of limitations of this study. First, due to a paucity of available data, we were unable to replicate our identified genetic signals. However, the highly relevant nature of the gene locus and our closely supporting functional evidence provide confidence that these are real signals for AMH levels. Exaggeration of the true effect sizes due to ‘winners curse’ may be present, and it will be important for future studies to better estimate the true effect in both sexes. However, even if the true effect estimate was half the size observed here, the genetic variants would still explain >10% of AMH variability in males. Second, although two separate statistical approaches revealed evidence for at least three independent effects, it remains possible that a smaller number of untyped causal variants could explain this apparent allelic heterogeneity . This caIn summary, these genome-wide analyses have identified the first genetic variants robustly associated with serum AMH levels. Given their relatively large effects, we were able to use these variants as genetic instruments to infer that variability in AMH levels is unlikely to substantially contribute to complex traits and disease susceptibility in males.http://www.alspac.bris.ac.uk.)  is a longitudinal, population-based birth cohort that recruited 14 541 pregnant women resident in Avon, UK, with expected dates of delivery 1 April 1991 to 31 December 1992 (.ac.uk.) . Since a.ac.uk.) ,43.http://www.bristol.ac.uk/alspac/).Ethical approval was obtained from the ALSPAC Law and Ethics Committee (IRB 00003312) and the Local Research Ethics Committee. The study website contains details of all the data that is available through a fully searchable data dictionary (P > 5 × 10−7) were considered for analysis. We combined 477 482 SNPs genotypes of these subjects with genotype data of a sample of 9048 mothers to allow the use of a large number of duos by the phasing algorithm to increase quality of phased haplotypes and downstream imputation. This resulted in the removal SNPs genotypes with a poor concordance across datasets, which could be completely captured by increasing the missingness filter 5–1% . We also removed a further 321 subjects due to potential id mismatches when assessed using duo data. We estimated haplotypes using ShapeIT (v2.r644), which utilizes relatedness during phasing. We imputed with Impute2 v2.2.2 using the 1000 genomes phase 1 version 3 reference data panel. This gave 8237 eligible adolescents with available genotype data after exclusion of related subjects using cryptic relatedness measures described previously.Within ALSPAC, the index child participants, studied here, were genotyped using the Illumina HumanHap550 quad genome-wide SNP genotyping platform by Sample Logistics and Genotyping Facilities at the Wellcome Trust Sanger Institute and LabCorp (Laboratory Corportation of America) using support from 23andMe. Participants were excluded on the basis of having incorrect sex assignments; minimal or excessive heterozygosity (<0.32 and >0.345 for the Sanger data and <0.31 and >0.33 for the LabCorp data); disproportionate levels of individual SNP missingness (>3%); evidence of cryptic relatedness (>10% IBD) and being of non-European ancestry. EIGENSTRAT analysis revealed no additional obvious population stratification, and genome-wide analyses with other phenotypes indicate little genomic inflation of association estimates in this population. The resulting dataset consisted of 8365 individuals. SNPs with a minor allele frequency of <1% and call rate of <95% were removed. Furthermore, only SNPs that passed Exact tests of Hardy–Weinberg equilibrium  ,44. InteSupplementary Material, Table S1). Association testing was performed using a linear regression model implemented in SNPTest v2.5. The analysis was run three times—in males only, in females only and in all individuals with sex as a covariate. Significance was declared at the genome-wide threshold of P < 5 × 10−8. Independent genetic signals were identified using two approaches—approximate conditional analysis implemented in GCTA using UK10K genotypes as a reference panel; and formal conditional analyses were performed by re-running the GWAS with the inclusion of the tested SNP(s) as covariates.Serum AMH levels were natural log-transformed prior to analysis with outliers ±4 SDs removed, approximating a normal distribution . The number of copies of the reference allele of each of the three AMH-related SNPs identified after association testing were weighted by their adjusted effect size and direction of effect in PLINK (v1.07). SNP rs4807216 reference allele C was weighted by 0.533, SNP rs2385821 reference allele G was weighted by 0.699 and SNP rs8112524 reference allele G was weighted by 0.145. Each individual was thereby scored as a weighted sum of the number of reference alleles for these three SNPs, and the resulting values were used as an independent variable in a linear regression of health-related outcomes.Using our newly identified genetic variants as a proxy instrument for circulating AMH levels, we performed Mendelian Randomization analyses using two complementary approaches. First, male specific analyses were performed across 30 biologically plausible outcomes in the ALSPAC study  and the University of Bristol provide core support for ALSPAC. The work in this paper is funded by a grant from the US National Institute of Health (R01 DK077659). D.A.L., S.M.R. and G.M. work in a Unit that receives funds from the UK Medical Research Council (MC_UU_12013/5) and the University of Bristol. D.A.L. is a UK NIHR Senior Investigator (NF-SI-0611-10196).The This publication is the work of the authors and not necessarily any of the funding bodies who supported the work. Funding to pay the Open Access publication charges for this article was provided by the Medical Research Council and the Wellcome Trust.


Understanding cellular structure and organization, which plays an important role in biological systems ranging from mechanosensation to neural organization, is a complicated multifactorial problem depending on genetics, environmental factors, and stochastic processes. Isolating these factors necessitates the measurement and sensitive quantification of many samples in a reliable, high-throughput, unbiased manner. In this manuscript we present a pipelined approach using a fully automated framework based on Synchrotron-based X-ray Tomographic Microscopy (SRXTM) for performing a full 3D characterization of millions of substructures.We demonstrate the framework on a genetic study on the femur bones of in-bred mice. We measured 1300 femurs from a F2 cross experiment in mice without the growth hormone  and characterized more than 50 million osteocyte lacunae (cell-sized hollows in the bone). The results were then correlated with genetic markers in a process called quantitative trait localization (QTL). Our findings provide a mapping between regions of the genome  and observable phenotypes which could explain between 8–40 % of the variance using between 2–10 loci for each trait. This map shows 4 areas of overlap with previous studies looking at bone strength and 3 areas not previously associated with bone.The mapping of microstructural phenotypes provides a starting point for both structure-function and genetic studies on murine bone structure and the specific loci can be investigated in more detail to identify single gene candidates which can then be translated to human investigations. The flexible infrastructure offers a full spectrum of shape, distribution, and connectivity metrics for cellular networks and can be adapted to a wide variety of materials ranging from plant roots to lung tissue in studies requiring high sample counts and sensitive metrics such as the drug-gene interactions and high-throughput screening.The online version of this article (doi:10.1186/s12864-015-1617-y) contains supplementary material, which is available to authorized users. In recent years, sequencing genomes has been accelerated manyfold , 2. WithComplicating the huge time requirements are the importance of reproducibility, which is impossible when too many human elements are involved. Finally management of all the samples, data, and results, which easily exceed the capacities of analysis tools like Excel , R , and MATEven more scalable tools like SQLite are unable to deliver results quickly. Thus, up until now, most large-scale analysis of phenotype on micro- and nanoscale systems has been a gigantic undertaking –10. WhilWe have developed an optimized, reproducible, automated pathway from sample to final results Fig. . We combWe demonstrate the effectiveness of our framework by addressing one of the major challenges of bone biology, understanding bone quality at a cellular scale. Fractures in the femur neck are one of the most debilitating and when surgically treated in the elderly have a mortality rate of 1 in 4 within a year, and require for nearly 1 in 2 cases, additional surgery within 2 years . This boWe found that the heritability criteria >40 %) were met for the following metrics: Cortical Thickness Variation (Ct.Th.R.sd), Canal Density (Ca.Dn), Lacuna Density (Lc.Dn), Mean Lacuna Volume, Lacuna Stretch (Lc.St), and Lacuna Distribution Oblateness (Lc.Dt.Ob) described in  Fig. 2)2). The d0 % were Overlapping markers The table and graphs shown in Table The second focus was to understand properties which are independent of BMD, since BMD has been so well characterized in mice and human populations and is easily measurable. These results are summarized in Table Comparison with previous work The two QTL of highest interest, as mentioned in previous section, are the loci on Chr10 at 10cM and Chr11 at 6cM. The mechanically relevant genes were in both cases from the same work done by Volkmann et al. [Ghrhr. The tag located closest to the Volkmann QTL, D10Mit40 (24.87cM), was located on Chr10 at position 29cM. It was associated with both Ultimate and Post Yield displacement of the femur independent of femur geometry and body weight. The second QTL reported by Volkmann overlapped with the tags D11Mit2 and D11Mit16 located on Chr11 at position 7.3 and 2.94cM respectively.n et al. . In theihttp://www.qtlarchive.org/) and are thus not inherently exhaustive.These tags, while not independent of femur geometry, were associated with predicted modulus, yield load, and stiffness. The QTL located in this study on Chr5 are also of significant interest because they have high LOD scores and do not overlap with previously identified phenotypes possibly indicating a new gene involved only in the microstructure of bone. It is important to reiterate that these QTL are the ones, which have been published in the QTL Archive run by the Churchill Group at the Jackson Laboratory  and spatial distribution, GH plays a significant role and makes inferring the specific differences caused by non-growth-hormone genetic background difficult. This study serves as a proof of concept for the capabilities of high-throughput tomographic X-ray microscopy in combination with a streamlined post-processing and analysis pipeline. While this study only investigated morphological and structural phenotypes of bones, given the high sensitivity of phase contrast to biological materials and the availability of contrast agents, studies investigating more complicated biologically relevant phenotypes are conceivable in the immediate future. In particular studying the interactions between environmental stimulus and different genetic backgrounds could be of high interest and such studies necessitate very large sample sizes.The genetic linkage results confirm loci found by earlier experiments. The mechanically relevant loci found provide the first hints at what microstructural properties might explain the variations in deformation under mechanical load. The results also shed light on several new loci, which might regulate bone structure using previously unidentified mechanisms. Since much is still not known about the modeling and remodeling of bone at the cellular level, these genes might make some of these easier to understand. If we assume the approximate density of genes in the mouse genome is 16 per cM , an inteBeyond biological applications, the framework is applicable to a wide range of high-throughput applications where large sample counts are required to achieve statistical significance. In material science, large numbers of samples measured consistently with detailed quantitative information are required to establish a link between process, structure, and mechanical behavior. Based on our experience with the hundreds of imaging users at the Swiss Light Source, we have noticed a trend in the distribution of time spent preparing experiments and analyzing the results. Much as the genetics community has experienced several years ago, computed tomography measurements and experiments have become manyfold faster and easier. This has shifted much more of the burden on the analysis, with the distribution of work, in many cases being thousands of times longer for the analysis than the experiments themselves.The developments we have made can drastically rebalance the time distribution of scientists examining the structures of complex materials, away from monotonous, repetitive, operator-biased modalities of image processing towards interpretation of vast, rich quantitative results. We think the quality and agility of research can be drastically improved. A faster post-processing pipeline means that study groups and targets can be screened much more easily and a feedback loop can be established so that studies can be tuned in nearly real-time for promising and poor results.Ghrhrlit/J and C57BL/6J-Ghrhrlit/J - were homozygous for a spontaneous mutation in the growth hormone releasing hormone receptor (Ghrhr) causing undetectably low circulating growth hormone (GH) levels [To ascertain the genetic contribution to murine femur cortical microstructure we performed a standard intercross experiment. The two background strains used, C3H/HeJ (C3H) and C57BL/6J (B6), were selected because of their previously shown  strong v) levels . The mic) levels  and deteμm voxel size) using synchrotron-based tomographic microscopy at TOMCAT using automatic sample exchange, alignment, and region of interest identification [The femurs were extracted from four month-old mice and were measured locally in the mid-diaphysis at high-resolution  and radial cortical thickness standard deviation (Ct.Th.R.sd). The radial cortical thickness is calculated using the standard procedure , but whemm3 of calcified bone tissue. Mean Lacuna Volume (Lc.V) is model-free and is calculated by counting the total number of empty voxels inside the given lacuna object. Finally Lacuna Stretch (Lc.St) indicates the anisotropy of the lacuna with a number between 0  to 1 (completely rod or plate-like). Finally Lacuna Distribution Oblateness indicates the type of anisotropy present in the spatial distribution in the spatial distribution: prolate  markers of the at 98 locations distributed among the 19 autosomes. The markers used were MIT, a type of microsatellite marker, that consists of a short sequence with multiple tandem repeats enabling them to be utilized well on these closely related strains. The parental strain for each given allele can be determined by comparing them to genomic DNA. Genotype information was only available for 755 of the 1132 mice; thus for the rest of the study only these 755 will be considered.The genotype probabilities were estimated at intervalsof 2cM and 128 draws were taken to better estimate the actual probabilities at these inter-marker locations. The first activity level for various regions of the genome was estimated by performing a standard single-locus genome scan  for eachhttp://dx.doi.org/10.6084/m9.figshare.726136.The analysis was performed using R (3.0.1)  using R/


The most powerful methods for regional mapping are based on the functional data analysis approach, which assumes that the regional genome of an individual may be considered as a continuous stochastic function that contains information about both linkage and linkage disequilibrium. Here, we extend this powerful approach, earlier applied only to independent samples, to the samples of related individuals. To this end, we additionally include a random polygene effects in functional linear model used for testing association between quantitative traits and multiple genetic variants in the region. We compare the statistical power of different methods using Genetic Analysis Workshop 17 mini-exome family data and a wide range of simulation scenarios. Our method increases the power of regional association analysis of quantitative traits compared with burden-based and kernel-based methods for the majority of the scenarios. In addition, we estimate the statistical power of our method using regions with small number of genetic variants, and show that our method retains its advantage over burden-based and kernel-based methods in this case as well. The new method is implemented as the R-function ‘famFLM’ using two types of basis functions: the B-spline and Fourier bases. We compare the properties of the new method using models that differ from each other in the type of their function basis. The models based on the Fourier basis functions have an advantage in terms of speed and power over the models that use the B-spline basis functions and those that combine B-spline and Fourier basis functions. The ‘famFLM’ function is distributed under GPLv3 license and is freely available at  Despite the massive success of genome-wide association studies (GWAS), a significant part of the heritability of quantitative traits remains unexplained. Studying the role of rare genetic variants in the etiology of complex traits may solve the problem of missing heritability . Rapid pSeveral approaches have been suggested for region-based association analysis of rare variants. The first, simplest of them, employs burden tests based on collapsing rare variants within a region of interest , 4–7. FoThe second approach employs kernel machine regression for regional association analysis –17. ThisIn contrast to collapsing-based methods, kernel-based methods are more resilient to the opposite direction of causal variant effects and the limited proportion of causal variants –19. SeveBoth burden-based and kernel-based approaches have been combined in optimal unified test implemented in SKAT-O  and MONSHowever, burden-based and linear kernel-based approaches, as well as their optimal combination, only partly utilize information about linkage and linkage disequilibrium (LD) of genetic variants. In burden-based methods, the LD pattern may be missing or reduced after collapsing rare genetic variants into a single variable. Linear kernel-based methods utilize only pairwise LD in their kernel matrix. They do not model higher-order LD among the genetic variants .The third approach, based on a functional data analysis (FDA), allows for better utilization of information on LD and linkage in regional analysis of association between rare variants and both quantitative , 28 and The FDA-based method of regional association analysis of quantitative traits has been applied to the independent samples , 28. SimIn this paper, we extend the FDA approach to samples with (sub)structure and implement the method in a computer program. We compare the power of our new method to the burden-based, kernel-based methods, and their optimized combination using Genetic Analysis Workshop 17 mini-exome family data  and a wim genetic variants with known physical locations ti. We order these locations, 0 ≤ t1 <…< tm = T, and scale the region size from  to .Consider a genomic region containing n individuals, let y denote an (n×1) vector of known trait values, X denote an (n×c) matrix of the c covariates such as age and sex, and G denote an (n×m) matrix of genotypes of m variants. Here, Gij is equal to the number of minor alleles of the i-th individual at the j-th variant with the location tj.For a family-based sample of The traditional linear mixed model used to analyze a family-based sample isα is a (c×1) fixed vector of regression coefficients measuring the effects of the c covariates; β is an (m×1) fixed vector of regression coefficients measuring the effects of the m genetic variants; h is an (n×1) random vector of polygene effect values distributed as e is an (n×1) vector of random errors distributed as R and I are (n×n) relationship and identity matrices, respectively. Model  = Xα+Gβ and a covariance matrix Here α is a c× fixed veFor each related individual, we interpret discrete genotypic values of ordered variants in a region of interest as continuous data by using functional linear analysis techniques. Such an interpretation is possible because of the high density of genetic variants, whose genotypes are continuous rather than discrete observations. These techniques have been applied to region-based association analysis for unrelated samples in .n×1) unknown vector of genetic variant functions (GVFs), and t in . In contrast to the functional linear model used in the analysis of independent samples, the proposed model additionally includes a random polygenic effect h.For family-based samples, we introduce a functional linear mixed model asGij,i = 1,…,m, and to define a function tj are represented as an (m×KG) matrix Φ, for which the closest orthogonal matrix is Φ(ΦTΦ)−1. The GVFs may thus be written for t ∈  as in [KG ≤ m).Our goal is to find a functional vector 1] as in , ChapterΦ)−1ϕ(t),where ϕ(Kβ basis functions Kβ×1) vector of model regression coefficients and Similarly, using other (or the same) system of α and β) and random effects (h and e):Φ and the integral are defined, we see that W depends only on the given basis functions and positions of genetic variants in the region.Substituting estimates  and 4)  4) into W can be represented as a product of two matrices W1 and W2, where W1 = Φ(ΦTΦ)−1 of dimension (m×KG), and KG×Kβ). Unlike the matrix W1, the matrix W2 is independent of the real data being analyzed. It is defined only by a selected set of basis functions and is the same for all regions if the number of basis functions is fixed. However, to uniquely and correctly estimate the parameters βF in Model  transition matrix between the vector β in Model  is estimated, using a system of Kβ basis functions:m×Kβ matrix Ψ is constructed analogously to the m×KG matrix Φ in Model TΩ−1(y − Xα) and RSS1 = (y – Xα – GW βF)TΩ−1(y − Xα – GW βF) are the weighted sums of the correlated squared residuals under the null and alternative models, respectively.In a framework of the functional linear Model , we trea− 1, see . HoweverF-statistic for a sample of related individuals, the maximum likelihood estimates of covariance matrix Ω and the vector of regression coefficients α are obtained under the null hypothesis. The vector of regression coefficients βF is estimated under the alternative hypothesis using the obtained values of Ω and α asTo calculate LRT) distributed asymptotically as χ2 with Kβ degrees of freedom and the χ2-distributed score test are used as alternative tests to compare hypotheses H0 and H1.The likelihood ratio test , sequential or parallel calculation, and running time estimation. Any type of relationship matrix (genome- or pedigree-based) can be used. The ‘famFLM’ function is distributed under GPLv3 license and is freely available at http://mga.bionet.nsc.ru/soft/famFLM/.We implemented the new method into the R-function ‘famFLM’ using two common types of basis functions: the B-spline and Fourier bases (see details in h2 = 0.29 under H0 (as in Q2 quantitative trait of GAW17).We used genotypes of the Genetic Analysis Workshop 17 (GAW17 ) family-5 replicas (1.7×108 regions) to obtain the type I error estimates down to the significance level of 2.5×10−6.To estimate the type I error, we analyzed 12,636 genetic variants in 1,702 gene regions that contain more than one polymorphic exome genetic variant of the GAW17 data set. We analyzed 10MAFs ranged from 0.1% to 34.7% with median of 1%). The following scenarios were considered for simulations: 1) proportion of causal variants in the regions 0.05, 0.1, or 0.2; 2) proportion of effects that have the same direction 0.5, 0.8, or 1; 3) for each causal variant, the effect size |β| = log(c)|log10(MAF)| / 2 as in [c being 2, 3, 5, or 7.For power estimation, we selected one region that contains 50 polymorphic genetic variants . Subsequently, we analyzed all rare variants and rare variants after excluding 50% or 80% non-causal variants.To explore the power of different methods for regions with small number of genetic variants, we simulated effects only for rare genetic variants within the region .−6 . The proposed test controls type I error rate correctly over all significance levels. Therefore, it can be used in both candidate gene and exome-wide studies (the model 0-F even in genome-wide studies).We estimated the empirical type I error rates for six significance levels down to 2.5×10−6 . For allEstimates of statistical power for different scenarios are shown in Figs We compared the power of the new method for six functional linear models that differ from each another in type of their function basis used to describe both the GVF and the BSF or the BSF only. The method under 0-F and F-F models demonstrated the highest power for most scenarios Figs  and 2. Hα = 1×10−4 . The matrix W2 is not involved in the models 0-F and 0-B , while the latter uses only 15 functions and W2 is recalculated only for the regions with m < 15. Nevertheless, the running time for the model F-F is smaller than for B-B. This result may be explained by the specific details of B-spline and Fourier basis function computations (see ults see . This me formula ) and the formula . The numions see .m > KG ≥ Kβ, running time increases quadratically with increasing the sample size and linearly with increasing the number of genetic variants in the region  and consequently this model is not equivalent to the 0-B model . The same results were obtained on unrelated samples by Fan et al. . We can To use the FDA approach, we should select not only the types of basis functions, but also the number of these functions. If this number is small, we may miss some important aspects of the smoothing function that we are trying to estimate. It is obvious that the larger the number, the better the fit to the data. However, in this case we risk also fitting noise or variation that we wish to ignore. It is generally unclear how to choose the optimal number of basis functions. Usually two algorithms are used , Chapterm of genetic variants, specifically when m < K, where K is the number of basis functions. Given small m, we automatically limited K in our algorithm and its implementation in the ‘famFLM’ function. In the case when K = m, the functional linear regression model . In this case the FDA-approach is applied to the kernel matrix which describes the similarity of genetic variants’ set in the analyzed region for each pair of individuals [α < 0.01 and this test has less power than the F-test [In the present study, we restricted our analysis by the functional linear models for ividuals . The proe F-test . Even the F-test , its staIntroducing the FDA technique in regional association analysis allows for a more complete use of information on the genetic structure of the analyzed genome regions. All existing methods operate only with a set of genetic variants in the region, whereas the new method also utilizes information about the order of genetic variants and the distances between the variants. This new feature allows us to include pairwise linkage disequilibrium (as existing methods do), as well as information on linkage and higher-order linkage disequilibrium in the model.Previously, the new FDA-based approach was developed only for samples of independent individuals. The present study extends this approach to samples of genetically related individuals. The new method provides a powerful tool in identification of rare variants involved in the control of quantitative traits.S1 FigThe notations of the methods are the same as in (PDF)Click here for additional data file.S2 FigThe notations of the methods are the same as in (PDF)Click here for additional data file.S3 FigThe notations of the methods are the same as in (PDF)Click here for additional data file.S4 FigThe notations of the methods are the same as in (PDF)Click here for additional data file.S1 Note(PDF)Click here for additional data file.S2 Note(PDF)Click here for additional data file.S3 Note(PDF)Click here for additional data file.


It is believed that almost all common diseases are the consequence of complex interactions between genetic markers and environmental factors. However, few such interactions have been documented to date. Conventional statistical methods for detecting gene and environmental interactions are often based on the linear regression model, which assumes a linear interaction effect. In this study, we propose a nonparametric partition-based approach that is able to capture complex interaction patterns. We apply this method to the real data set of hypertension provided by Genetic Analysis Workshop 18. Compared with the linear regression model, the proposed approach is able to identify many additional variants with significant gene-environmental interaction effects. We further investigate one single-nucleotide polymorphism identified by our method and show that its gene-environmental interaction effect is, indeed, nonlinear. To adjust for the family dependence of phenotypes, we apply different permutation strategies and investigate their effects on the outcomes. Genome-wide association studies (GWAS) have successfully discovered many common variants associated with complex diseases, but the single-nucleotide polymorphisms (SNPs) identified so far account for a small proportion of the total heritability in quantitative traits . IncreasThe commonly applied methods to detect G×E interactions are based on linear or logistic regression models . In partG is the genotype of a SNP, E is the environmental factor, ε is a normally distributed random error, and G, the outcome y is linearly related with E. However, in practice, it is likely that the interaction schemes are more complicated so that the linear model will probably fail to capture the interaction effect. Therefore, there is a pressing need to develop novel statistical approaches for genome-wide G×E interaction studies. Here we propose a nonparametric partition-based approach to detect G×E interactions and conduct a GWAS for hypertension using the real data set provided by Genetic Analysis Workshop 18 (GAW18). For each SNP, both the linear regression model and the proposed method are used to evaluate its interaction effect with each of the 4 environmental factors: age, gender, smoking status, and medicine. We note that, compared with the linear model, the proposed method is able to identify many additional SNPs. We further study the interaction pattern between SNP rs17206492 and medicine, and find that this interaction effect is, indeed, nonlinear. We also investigate different permutation strategies in the presence or absence of pedigree dependence of the phenotype.where The GAW18 data set consists of GWAS data and whole genome sequence data with longitudinal phenotypes for hypertension and related traits from Type 2 Diabetes Genetic Exploration by Next-generation sequencing in Ethnic Samples (T2D-GENES) Project 2. There are 939 individuals in total, and we include in our analysis only the 849 individuals with both phenotype data and imputed sequence information. Each individual has measurements for up to 4 time points. At each visit, systolic blood pressure (SBP) and diastolic blood pressure (DBP) were measured; covariates including age, use of antihypertensive medication, and current tobacco smoking status were also recorded. Gender and pedigree are known for each subject. Genotypes of odd-numbered chromosomes are provided. In our study, we focused on chromosome 3 as suggested by the workshop organizer for the sake of comparison. Although we had access to the answers for the simulated data set, we used only the real data set in our analysis.n independent subjects that can be separated by a partition ∏. An association measure between the outcome Y and the partition ∏ is defined as:Suppose there are i, Y for subjects in partition i, and Y from all subjects. It has been shown that under the null hypothesis ∏ does not have influence on Y, I asymptotically converges to a weighted sum of where ibutions . It has G and an environmental factor E. Suppose G has 3 phenotypes, AA, Aa, and aa , coded as 0, 1, and 2. Suppose E is divided into 3 categories: 0, 1, and 2. Hereby G and E together create 9 partitions for all subjects . Because gender is a binary variable, it partitions all individuals into 2 groups. Although this data set provides longitudinal measurements of age, smoking, and medicine, the records have many missing values . Therefore, for each individual, we summarized these covariates by either the averaged value (for age) or the sum (for smoking and medicine) across different time points from available records and used these summarized quantities in our analysis. Similarly, averaged SBP and averaged DBP were considered as outcomes. Here we created 3 partitions by each of age, smoking, and medicine (Table I (PBI). p Values of LRM were derived from the asymptotic distribution of the regression coefficient p values of PBI were computed from 107 permutations using global, local, or residual permutation procedures. Table p values less than the Bonferroni-corrected significance level (7.9*10−7) for all interactions under consideration. Compared with LRM, PBI identified many additional significant SNPs, especially when testing the G×E interaction effects with medicine. The reason, we believe, is that the interaction modeled by LRM is restricted to the linear form, whereas PBI is able to capture nonlinear and complicated interaction patterns. To confirm our hypothesis, we further analyzed the SNP rs17206492, which was identified by PBI (using any of the 3 permutation strategies) to have strong G×Medicine interaction effect on DBP, but was not selected by LRM. The left panel of Figure PBI.In the GWAS data set provided by GAW18, there are 62,915 SNPs on chromosome 3. For each SNP, we evaluated its interaction effect with each of the 4 environmental factors on both SBP and DBP using the linear regression model (LRM) and the proposed partition-based score p values of PBI, we performed 3 types of permutation: global (GP), local (LP), and residual (RP) permutations. Both LP and RP adjust for familial relatedness between individuals. For SBP, except for the environmental factor age, the results from 3 permutation methods coincide substantially  test and the nonparametric Kruskal-Wallis test indicate that the mean DBP values of different pedigrees are different, whereas the mean SBP values are the same Table . When evPBI to detect G×E interactions, which is nonparametric and model-free. The test statistic is derived from a partition-based measure I, and the interaction information score G×E Iis defined as the difference between the total score T Iand the maximum of the marginal scores. Intuitively, if the genetic and the environmental factors have strong interaction effect, T Iwill be far greater than both marginal scores; hence G×E Iwill be positive and large. If not, T Iwill be no greater than at least 1 of the marginal scores. Therefore, G×E Ievaluates the amount of influence of the G×E interactions on the phenotype.In this paper, we have proposed a partition-based approach PBI identified many more markers than the traditional linear regression method. Because our approach is model-free, it is able to capture complicated interaction patterns that are difficult to detect in linear model. The significance of G×E Iis evaluated by permutation. LP and RP adjust effectively for the family dependence of the phenotype. Despite the fact that the proposed procedure selects more SNPs than linear regression, there is very little experimental evidence of G×E interactions for hypertension in the current literature to verify our findings. Therefore, biological studies will be required to investigate our results. Modifications of PBI have successfully identified gene-gene interactions and constructed genetic networks for breast cancer [PBI can be extended to evaluate the interaction effects between rare variants and environmental factors. Because of the low frequencies of rare variants (<1%), we can apply a gene-based approach by collapsing rare variants in a gene [When applied to the real data set about hypertension provided by GAW18, t cancer  and rheut cancer . Moreoven a gene  and creaThe authors declare that they have no competing interests.SHL and RF designed the study. RF, CHH and SHL performed the study. RF, CHH, IH, HW, TZ and SHL contributed to analysis of the data. RF and SHL drafted the manuscript. All authors read and approved the final manuscript.


Arabidopsis thaliana. Here, fine-mapping of this association reveals that the vGWA emerges from the effects of three independent genetic polymorphisms that all are in strong LD with the markers displaying the genetic variance-heterogeneity. By revealing the genetic architecture underlying this vGWA signal, we uncovered the molecular source of a significant amount of hidden additive genetic variation or “missing heritability”. Two of the three polymorphisms underlying the genetic variance-heterogeneity are promoter variants for Molybdate transporter 1 (MOT1), and the third a variant located ~25 kb downstream of this gene. A fourth independent association was also detected ~600 kb upstream of MOT1. Use of a T-DNA knockout allele highlights Copper Transporter 6; COPT6 (AT2G26975) as a strong candidate gene for this association. Our results show that an extended LD across a complex locus including multiple functional alleles can lead to a variance-heterogeneity between genotypes in natural populations. Further, they provide novel insights into the genetic regulation of ion homeostasis in A. thaliana, and empirically confirm that variance-heterogeneity based GWA methods are a valuable tool to detect novel associations of biological importance in natural populations.Genome-wide association (GWA) analyses have generally been used to detect individual loci contributing to the phenotypic diversity in a population by the effects of these loci on the trait mean. More rarely, loci have also been detected based on variance differences between genotypes. Several hypotheses have been proposed to explain the possible genetic mechanisms leading to such variance signals. However, little is known about what causes these signals, or whether this genetic variance-heterogeneity reflects mechanisms of importance in natural populations. Previously, we identified a variance-heterogeneity GWA (vGWA) signal for leaf molybdenum concentrations in  Arabidopsis thaliana. The variance-controlling locus was found to result from the contributions of multiple alleles at multiple loci that are closely linked on the chromosome and is a major contributor to the “missing heritability” for this trait identified in previous studies. This illustrates that multi-allelic genetic architectures can hide large amounts of additive genetic variation, and that it is possible to uncover this hidden variation using the appropriate experimental designs and statistical methods described here.Most biological traits vary in natural populations, and understanding the genetic basis of this variation remains an important challenge. Genome-wide association (GWA) studies have emerged as a powerful tool to address this challenge by dissecting the genetic architecture of trait variation into the contribution of individual genes. This contribution has traditionally been measured as the difference in the phenotypic means between groups of individuals with alternative genotypes at one, or multiple loci. However, instead of altering the trait mean, certain loci alter the variability of the trait. Here, we describe the genetic dissection of one such variance-controlling locus that drives variation in leaf molybdenum concentrations amongst natural accessions of  Arabidopsis thaliana, for example T, X2 = SNPi and i is the index of the SNP whose variance effect we are estimating. β1 and β2 were estimated using maximum likelihood. The model was fitted using the R-package dglm [λ = 0.75 for leaf molybdenum concentration in this population). Here, DGLM was used to i) re-scan the vGWA region on chromosome 2 to identify the SNP with the strongest variance effect in vBLOCK and ii) include evidenced loci as co-factors with mean effect, while redoing the vGWA scan to evaluate whether the loci identified in the GWA led to the vGWA association.analyses , X1 = [age dglm  as suggeage dglm . It shou2) was calculated using an ANOVA y = β0 + accession × βacc + e, comparing within and between line variances.Every accession in our data was grown with at least 6 replicates plants. The broad sense heritability (H2) we fitted a mixed model ZZT = G, where G is the genomic kinship matrix. The intra-class correlation 2, is rH2. In reality, as rH2 ≤ h2 ≤ r. Here, we therefore present the rH2 values, which is the lower bound of h2.To calculate the narrow sense heritability . The fraction of h2 explained by the fixed effects X are then given as X that is additive is calculated as The intra-class correlation MOT1 mRNA in roots of 6 accessions carrying the DUP326 polymorhism, 5 accessions carrying the DEL53 polymorphism and Col-0 as a reference (PP2A or UBQ10 was used. For quantification of MOT1 the following primers were used: forward primer 5’-GGT GGG TGT GTG GCA CTG T-3’ and reverse primer 5’-AGC ACA CCA ACC GGA AAC TT-3’. The cycle threshold (CT) values were determined based on efficiency of amplification. The CT values were normalized against the mean expression of either PP2A or UBQ10 by calculating ΔCT values as CTMOT1–mean(CTPP2A(UBQ10)). The relative change in MOT1 expression versus Col-0 was then calculated for every accession i as ΔΔCTi = ΔCTi—ΔCTCol-0. The fold change in expression for accession i was then calculated as 2−ΔΔCT,i.We quantified the levels of eference  using a 2 > 0.4) surrounding the SNP1 and SNP2 loci. T-DNA insertional alleles, catalogued as homozygous at T-DNA Express , were ordered for all genes where they were available  for this gene was included on every experimental block of plants as a control, along with wild-type Col-0. An experimental block is defined by a cultivation tray containing 9 genotypes (including wild-type Col-0 and mot1-1) with each genotype represented by between 2–12 individuals per block. The tested T-DNA insertional alleles were grown in 8 independent blocks and the molybdenum concentration in leaves of all plants quantified by ICP-MS using the same procedure as used previously [We identified all genes in the LD-region (rvailable  from theeviously .mot1-1 showed significantly lower molybdenum concentrations compared to the wild type Col-0 (p < 0.05) as expected, and in one block, the reduction was significant at (p < 0.1). The mot1-1 mutant in one experimental block of plants showed no difference compared to the wild type Col-0, and the results for the genotypes in this experimental block that were not supported by the results in other experimental blocks were discarded. To combine the data on T-DNA alleles that were replicated on several experimental blocks, we normalized molybdenum concentrations against wild type Col-0 within blocks and jointly analyzed the normalized values using the Wilcox rank test.For every experimental block, we compared the molybdenum concentration in leaves between the replicates of every T-DNA insertion line, versus wild type Col-0, using the non-parametric Wilcox rank test. In 6 out of the 8 blocks, MOT1 gene. The LD is high among these significant markers that define an extended vGWA associated vBLOCK. Visual inspection of the genotype-matrix of this region, sorted by the genotype of the leading SNP in the vGWA analysis Click here for additional data file.S2 Fig2 > 0.4. We measured the mean leaf molybdenum concentrations for available T-DNA insertion lines and compared them to the reference genotype (Col-0). Yellow box = nominally significant difference in leaf molybdenum concentration, deep blue box = no significant difference, light blue = no T-DNA insertion line tested.We identified the genes (colored boxes) in the regions surrounding SNP1 that were bounded by the furthest up- and downstream SNPs with r(TIFF)Click here for additional data file.S3 FigM-, MWT and M+—that have different effects on a hypothetical trait. The bottom panel illustrate the mixture distributions observed in an association analysis to a bi-allelic marker, where one of the marker- alleles tag functional allele MWT, and the other tag both alleles M- and M+. In this situation, no mean difference could be observed between the marker alleles, whereas a large variance difference could be detected via the variance-heterogeneity between the SNP genotypes using a vGWA analysis.The top panel illustrates the hypothetical phenotypic distributions three alleles–(TIFF)Click here for additional data file.S4 FigBlack line illustrates the theoretical distribution of p-values under the null-hypothesis and the blue dots those observed in the two analyses.(TIFF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S1 Text(DOCX)Click here for additional data file.


Puccinia coronata f. sp. avenae) and powdery mildew (Blumeria graminis f. sp. avenae) are among the most important constraints for the oat crop. Breeding for resistance is one of the most effective, economical, and environmentally friendly means to control these diseases. The purpose of this work was to identify elite alleles for rust and powdery mildew resistance in oat by association mapping to aid selection of resistant plants. To this aim, 177 oat accessions including white and red oat cultivars and landraces were evaluated for disease resistance and further genotyped with 31 simple sequence repeat and 15,000 Diversity Arrays Technology (DArT) markers to reveal association with disease resistance traits. After data curation, 1712 polymorphic markers were considered for association analysis. Principal component analysis and a Bayesian clustering approach were applied to infer population structure. Five different general and mixed linear models accounting for population structure and/or kinship corrections and two different statistical tests were carried out to reduce false positive. Five markers, two of them highly significant in all models tested were associated with rust resistance. No strong association between any marker and powdery mildew resistance at the seedling stage was identified. However, one DArT sequence, oPt-5014, was strongly associated with powdery mildew resistance in adult plants. Overall, the markers showing the strongest association in this study provide ideal candidates for further studies and future inclusion in strategies of marker-assisted selection.Diseases caused by crown rust ( Avena sativa L. including both white and red oat (formerly A. byzantina K. Koch) is the main cultivated oat. Several pathogenic fungi can infect oats and drastically reduce its yield including biotrophic pathogens such as powdery mildew  and crown rust (Puccinia coronata f. sp. avenae Eriks). These fungi have very efficient spreading mechanisms, hampering their control by crop management measures such as rotation and the use of resistant varieties is one of the best control alternatives  associated with important agronomic traits using a number of experimental bi-parental oat populations. Examples include vernalization response, flowering, and heading date , qualitysistance , powderysistance , and crosistance . Howeversistance .Association analysis is an alternative approach that overcomes many of the limitations of conventional QTL mapping and has received increasing attention from plant geneticists during the last few years  followinIn recent years, genome wide association studies (GWAS) have identified marker-trait associations for a range of agronomic traits in many crops including maize, rice, sorghum, and foxtail millet . HoweverA. sativa accessions (110 white and 31 red oats) kindly provided by the “Centro de Recursos Fitogenéticos,” INIA, Madrid, Spain, and 36 commercial varieties supplied by the Andalusian Network of Agriculture Experimentation (RAEA) was used. Oat cultivars studied were: Ac1, Acebeda, Adamo, Aintree, Alcudia, Anchuela, Araceli, Brawi, Caleche, Cannele, Chambord, Chappline, Charming, Cobeña, Condor, Cory, Edelprinz, Flega, Fringante, Fuwi, Hammel, Kankan, Kantora, Karmela, Kassandra, Kazmina, Mirabel, Mojacar, Norly, Orblanche, Pallini, Patones, Prevision, Primula, Rappidena, and Saia. Details of the origin of all accessions and of their genetic relationship have been previously reported in For this study, a germplasm collection of landraces consisting of 141 -2 s-1 photon flux density supplied by high-output white fluorescent tubes.Seedlings were grown in 0.5 L pots filled with peat:sand (3:1) in a growth chamber with 20°C, 65% relative humidity (RH) and under 12 h dark/12 h light with 250 μmol mFirst leaves from 40 12-days-old seedlings were harvested, pooled together, and DNA extracted according to the method stipulated by Diversity Arrays P/L, Canberra, ACT, Australia and described by To remove possible errors and redundancies in markers that may cause false associations in GWAS, data cleaning was performed according to k-value were run. Then, the mean estimate across runs of the log posterior probability of the data for a given k, were plotted to enable the determination of the k-value of the population. As this point is known to be difficult to determine, the Δk, related to the second order rates of change of the likelihood function with respect to k, was also used  isolate Co-04, previously multiplied on the susceptible cultivar Araceli, was used. The virulence of this isolate on an oat differential set collection has been described in -2 (checked by counts made from glass slides laid adjacent to leaves). After inoculation, plants were incubated for 9.5 h in darkness at 100% RH and 18°C, and thereafter at 20°C under a 12 h photoperiod with 250 μmol m-2 s-1 photon flux density. Infection frequency (IF) was determined as previously described in The -2 with one isolate of B. graminis f. sp. avenae race five maintained on seedlings of oat cv. Selma, in a spore proof glasshouse. After inoculation, plants were maintained in the growth chamber for 8 days before assessment of the percentage area covered by powdery mildew on the inoculated leaf. Disease scores were converted into relative values, expressed as the percentage of the susceptible reference cultivar Selma and referred to as the relative disease severity ]) to normalize data and stabilize variances throughout the data range, and subjected to analysis of variance using SPSS software, after which residual plots were inspected to confirm that data conformed to normality. Significance of differences between means was determined by contrast analysis (Scheffe’s). The percentage of variation of each trait explained by the structure was computed through multiple linear regression of the phenotypes on the percentages of admixture using R .p-value for each marker, which is the probability of a greater F-value under the null hypothesis that the polymorphic site is independent of phenotype. All models were assessed for their ability to control for type I error by plotting the distribution of the p-values for the markers, where uniformly distributed p-values indicate proper control for type I errors  to further characterize the most significant markers identified.As many of the DArT markers used here have been previously sequenced , the NCBOf the initial 15,000 DArT markers assessed, 1,587 showed polymorphism in the oat collection. In addition 499 SSR alleles were also polymorphic. From the total 2086 polymorphic markers, 11 markers that showed a call rate lower than 80% and 56 markers that showed a MAF < 0.01 were removed. A total of 476 redundant markers were also merged in 169 groups representing these markers. Following data curation a total of 1,712 markers were used for association purposes in the oat collection of 177 white and red commercial varieties and landraces.Figure 1). Indeed, the correlation between SSR and DArT+SSR results was high with a correlation coefficient of 0.84 (p < 0.001). However, slight modifications of the genotype-cluster assignation and the corresponding percentage of admixture were observed. According to both analyses ∼30% of the accessions showed less than 80% of membership for a particular cluster. The differences of genotype-cluster assignation were always related to these accessions and when they were discarded from the analysis the correlation coefficient increased up to 1. According to STRUCTURE, subpopulation 1 showed the highest degree of admixture with 75.6% of the genotypes with less than 80% of membership to this subpopulation followed by subpopulations 3 and 4 with 18% of genotypes with less than 80% of membership in these groups. Subpopulation 2 in which only 15% of genotypes showed less than 80% membership to the corresponding subpopulation was the subpopulation with lowest admixture.A previous genetic diversity study of the oat collection with only SSR markers revealed a structure of four subpopulations . In the Figure 2). Cluster analysis was implemented on the first four principal components cumulatively explaining ∼50% of the variation with 23.3, 13.8, 8.11, and 4.5% for each of the components, respectively. Although separation between clusters was clear, some accessions were not part of the clusters but formed links between them . The number of lines in each cluster ranged from 33 to 64. The first cluster included mainly the white commercial varieties, cluster 2 the red oats, cluster 3 the white oat landraces characteristic to high altitude locations, and cluster 4 white oat landraces more adapted to low altitude locations.Multivariate analysis based on PCA also revealed a separation of four subpopulations which indicates a high consistency of the data . These relationships between clusters were in agreement with those depicted by the PCA scatter plot . These results suggest that clustering was also efficient in separating the oat types for the germplasm used in this study.As previously stated, PCA showed a separation between clusters but also a clear pair-wise relationship between clusters. Quantitative results for genetic distance (according to Nei’s parameter) between clusters are shown in r2, and the probability . A total of 507,042 pairs of markers showed a significant LD value with an average p = 0.004. From these, 277,920 pairs of markers showed an r2 < 0.1 chosen here as nominal level, according to the studies performed by Identification of disequilibrium between markers is highly useful since it may condition the strength of the association study. Since physical map distances between markers were not available, LD was represented by the disequilibrium matrix visualizing the linear arrangement of LD between polymorphic sites, represented by Figure 4). Means of the 177 accessions assigned to the four subpopulations for the different traits, excluding the admixed accessions were compared (Table 2). Significant differences between subpopulations were observed for all traits. Thus, subpopulation 4 had a significantly lower RIF after rust inoculation than the others (p < 0.005) and showed a high resistant response. Subpopulation 2 had lower RDS to powdery mildew than the others . Powdery mildew was the trait most affected by population structure although the proportion of variance explained by population structure remained under 4% (Table 3).Both traits followed a normal distribution with accessions ranging from highly resistant to highly susceptible . This last model showed almost a perfect fit between the observed and expected p-values except for few of the values, which is the characteristic of a model that sufficiently accounts for the number of false positives. Three additional markers, AM30-178, AME176-3, and oPt-15665 were significantly associated in all GLM models including those accounting for population structure  but not in the MLM models (Table 4).As expected, considerably fewer markers showed a significant association with rust resistance when applying a correction accounting for the population structure than when using GLM alone . The low ability of the GLM alone to account for false positives was confirmed when the distribution of observed e Figure . The dist Figure . Five map-values  and since it was not highlighted by the other models it was not considered to be strongly associated. Indeed, distribution of the p-values in the GLM model corrected with Q indicated also a relative over-abundance of low p-values. Interestingly, the reverse tendency was observed in the MLM with p-values moving down the expected values, indicating a scarcity of low p-values and indicating that the GLM+PCA or GLM+Q+PCA were the best fitted models. This indicated the importance of testing the models in order to help in the selection of the most robust markers.A significant reduction of associated markers with powdery mildew resistance in oat at seedling stage was also observed after correcting for the population structure than when using GLM alone. The low efficiency of the GLM alone in this data set was confirmed by the low fit of the observed and expected distribution of the s Figure . Since t2r < 0.1 .In order to find markers associated with powdery mildew resistance we took advantage of a previous detailed evaluation for powdery mildew adult plant resistance performed in a subpopulation of this collection . In this Figures . AssociaTable 6 show the most significant matches found with BLAST searches (BLASTX) against public databases for associated DArT markers. For most DArT markers, no significant match to specific genic sequences was identified with most significant hits corresponding to repetitive sequences and retrotransposons . However, moderately significant matches to disease resistance genes, including the wheat rust resistance locus Lr21, were seen for a DArT marker flanking MAMA5, oPt-14345  oats. Indeed, in a study by As a first step for the association study, population structure was inferred since it has great implications on the design and analysis of GWAS. The different approaches used here indicated moderate population structure within the germplasm collection evaluated. Thus, four oat groups could be detected albeit they presented a certain degree of admixture according to STRUCTURE software with up to 30% of accessions having less than 80% membership to a determinate group. This was also observed following PCA with several accessions covering “gaps” between clusters. Interestingly the group comprising the commercial varieties showed the highest degree of admixture, most likely due to a sharing of common ancestors in their genealogy as reported by Despite the relative moderate structure of this oat population, it contains a reasonably high genetic diversity, showing ∼10% of polymorphic markers as in the original oat panel . This is2r to 0.15 have been reported to occur within 500 bp  would explain, on average 20% of QTL variance. This is not very different from other self-pollinated cereals such as barley in which LD decay is expected to occur over relatively long map distances compared with allogamous cereals such as maize for which reduction of n 500 bp . Our worThe molecular marker data set in combination with phenotype evaluation was used to examine linkage-related marker-trait associations. Separating the role of population structure and genetic linkage as causes for marker-trait association remains the greatest challenge in association analysis . The fivArabidopsis mutant, atg2-2, has been reported to have enhanced resistance to powdery mildew , mapped onto rice chromosome 9. MAMA5 is reported by Pc38 that cluster with Pc62 and Pc63 . According to stachyon , a powdesome 5BL  and a loand Pc63  also mapand Pc63  together3 (Prq1b . AME176 n mapped . Finallyn mapped  onto chrOverall, the markers showing the strongest association in this study provide ideal candidates for further studies and future inclusion in strategies of MAS.GM-B, NR, and JS-M carried out most of the experimental work and data analysis. DR contributed to the disease resistance aspects. TL, CH, and LM contributed to the genetic aspects. EP designed experiments, and contributed to the interpretation of results and writing of the manuscript. NR, DR, TL, CH, and LM also contributed to critical reading and writing.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The method was compared with five commonly used methods: Bayes A, Bayes B, Bayes C, Bayesian Lasso and GLUP.A method for estimating genomic breeding values (GEBV) based on the Horseshoe prior was introduced and used on the analysis of the 162) (up to a constant). It has an infinite spike at zero and heavy tail that decay by β-2 (slower than the Laplace or the Student-t). The implementation of all methods (except GBLUP) was done using a MCMC approach, where the relevant parameters defining the prior distributions were jointly estimated from the data. The GBLUP was done using ASREML.The main difference between the methods is the prior distribution assumed during the estimation of the SNP effects. The distribution of the Bayesian Lasso is a Laplace distribution; for Bayes A is a Student-t; for Bayes B and Bayes C is a spike and slab prior combining a proportion of SNP without effect and a proportion with effect distributed as a Student-t or Gaussian for Bayes B and C, respectively; for GBLUP is similar to a ridge regression. The distribution for the Horseshoe prior behaves like log(1+1/βThe accuracy for all methods ranged from 0.74 to 0.83, representing an improvement of 44% to 78% over the traditional BLUP evaluation. GEBV with the highest accuracy were obtained with Bayes A, Bayes B and the Horseshoe prior. The Horseshoe tended to select smaller number of SNP and assigning them larger effects, while strongly shrinking the remaining SNP to have an effect closer to zero.The Horseshoe prior showed a different shrinkage pattern than the other methods. While for this specific dataset, this has little impact on the accuracy of the GEBV, it may prove a good property to discriminate true effect from noise, and thereby, improve overall prediction under different scenarios. Genomic selection can be described as the use of high dense genotyping for the evaluation of individuals to increase the accuracy of their estimated breeding values (GEBV) . SeveralIn this study the Horseshoe distribution ,5 is proth QTLMAS workshop organisers, consisted of 3,000 individuals across three generations (G1-G3) phenotyped and genotyped for about 10,000 SNPs on five chromosomes of equal length. The phenotypes  resembled three milk production traits, given as individual yield deviations, and generated in order to mimic two yields and the corresponding content. Additionally, 1020 genotyped individuals from the fourth generation were used as the validation set to estimate GEBV.The dataset, provided by the 16The model for all methods is the following:n is total number of SNP; y the vector of phenotypic observation; zi the vector of genotypes at SNP i; βi indicates the allelic substitution effect for SNP i.where, spike-and-slab' prior )approach ,13 similapproach .The parameters defining the prior distribution of the SNP effect were also estimated in the analysis . Bounded flat priors were used for all these parameters.For each analysis, a MCMC chain was run and the first 50,000 cycles were discarded as burn-in period. Following this, 50,000 realisations were collected, each separated by 50 cycles between consecutive realisations . The posterior mean was used as the estimate for each parameter of interest. Genetic variance for all genomic selection methods (except GBLUP) was calculated from the GEBV using an approximation based on the infinitesimal model theory. Assuming that GEBV for all training individuals have the same prediction error variance (PEV), the genetic variance is calculated as the sum of the variance of the GEBV plus the mean PEV for all training individuals  ranged between 0.74 and 0.83, across all methods and traits, representing an improvement between 44% and 78 % compared with the accuracies obtained with the traditional BLUP evaluation Table . Across Although the overall GEBV obtained with the Horseshoe prior, Bayes A and Bayes B were very similar, the differences on the individual estimated SNP effects were large, suggesting differences in the shrinkage properties of the methods. Figure The accuracy of the GEBV from the different genomic selection methods ranged between 0.74 and 0.83, representing an improvement of 44% to 78% over the traditional BLUP evaluation. The highest GEBV accuracies were observed with the Horseshoe, Bayes A and Bayes B methods. Although they yielded very similar GEBV, the route for estimating them was different. The Horseshoe prior tends to assign greater effect to fewer SNPs, while strongly shrinking smaller effect. This property may prove beneficial in situations using much denser SNP genotyping or whole sequence data.The author declares that they have no competing interests.Pearson correlation between GEBV obtained with the different methods of genomic selection.Click here for file


Genetic variants that predispose adults and the elderly to high blood pressure are largely unknown. We used a bivariate linear mixed model approach to jointly test the associations of common single-nucleotide polymorphisms with systolic and diastolic blood pressure using data from a genome-wide association study consisting of genetic variants from chromosomes 3 and 9 and longitudinal measured phenotypes and environment variables from unrelated individuals of Mexican American ethnicity provided by the Genetic Analysis Workshop 18. Despite the small sample size of a maximum of 131 unrelated subjects, a few single-nucleotide polymorphisms appeared significant at the genome-wide level. Simulated data, which was also provided by Genetic Analysis Workshop 18 organizers, showed higher power of the bivariate approach over univariate analysis to detect the association of a selected single-nucleotide polymorphism with modest effect. This suggests that the bivariate approach to longitudinal data of jointly measured and correlated phenotypes can be a useful strategy to identify candidate single-nucleotide polymorphisms that deserve further investigation. High blood pressure is a common disorder in adults and the elderly and is associated with increased risk of cardiovascular diseases and many other morbidities . It is aIn multivariate longitudinal data, multiple response variables are jointly measured over time from the same individuals. Other environmental variables can also change over time and could have been recorded. To understand the relationship between independent and multivariate dependent response variables, we need to take into account the correlation between multivariate responses measured over time. In GAW18 data, the phenotypic data, namely systolic blood pressure (SBP) and diastolic blood pressure (DBP), as well as some environmental data, were measured over time and these phenotypic data from the same individuals are likely to be correlated as they might be regulated by the same genes or common environments. Therefore, we used a bivariate linear mixed-effect model approach to test the association of genetic variants with bivariate phenotypic values adjusting for environmental factors.Details about sample recruitment can be found in Hunt et al . For GAWp value ≥10−3 and subjects with genotyping call rates ≥0.95. We applied these criteria to those 142 individuals using PLINK.We analyzed genome-wide association studies (GWAS) data from chromosomes 3 and 9. There were 65,519 single-nucleotide polymorphisms (SNPs) on chromosome 3 and 42,177 SNPs on chromosome 9. We restricted our analysis to common SNPs  with genotyping call rates ≥0.95 and Hardy-Weinberg equilibrium k, suppose i n× 1) vector of the trait values for ip independent variables with We applied a bivariate linear mixed model framework  in oressed as ,4kth trait with i n× q) design matrix, usually a subset of i n× 1) vector of the stochastic processes (within subject errors over repeated times) with realization t with variance s and t, 0 i n× 1) vector of random errors, where where That is, t and covariance matrix t and s, B is a B have negative real parts and matrices C and ymmetric . We haveAfter the quality control filtering, we had only For the bivariate linear mixed-effect model fitting for each SNP, genotype  of a SNP was the independent variable of interest. Besides, we a priori selected to include 3 covariates, namely, measurement time in years at an examination since enrollment (which is 0 for the first year of enrollment), baseline age (at enrollment), and repeatedly measured antihypertensive medication use in the model. We also included sex and repeatedly measured smoking status in the model because keeping them, each separately or together, resulted in a better fit  of the bivariate model for the 20 SNPs from chromosome 9 selected for model fit assessment (modeling techniques description given in a successive paragraph). We considered autoregressive order-1 ver time ,5. The AThere were missing follow-up data on blood pressure and other repeatedly measured covariates, where data from 97 subjects were missing in the fourth enrollment period. The available data for the fourth period were not used because discarding them resulted in much better fit for each of those 20 SNPs. Next, 2 subjects had missing data on medication use and smoking in all 3 examinations. Thus, the effective sample size was 131 for real data analysis. No attempt was made to use imputation.A binary variable "BPTYPE" (blood pressure type) was defined as BPTYPE = 1 for SBP and = 0 for DBP for a subject at a measurement time. Finally, equation (2) was fitted for each SNP, where the repeatedly measured bivariate blood pressure (a maximum of six possible measurements for two phenotypes at three examinations for a subject) was regressed against genotype and the covariates specified above  using MIXED procedure in SAS . The SNP had the effect sizes, β1 = −1.4951 (variation explained β2 = −2.3810 (variation explained = 0.0143%) in simulated SBP and DBP, respectively, per copy increase in minor allele. We used data from 141 subjects as genotype data was missing for the SNP in 1 subject. We employed the same regression analysis model and modeling technique, and assessed the same hypothesis using F α = 7.2 × 10−8 to be consistent with real data analysis.We assessed the statistical power of the bivariate linear mixed effect model using 200 simulated longitudinal data sets provided by GAW18 organizers. However, we considered the data from only 142 unrelated subjects who had genotypic data and phenotype and covariate information from all 3 examinations. We chose to assess power to detect the association of a common SNP, In our sample data, the mean age (standard deviation) at enrollment was 53.7 (16.0) years, where subjects were 20.3 to 94.2 years old when enrolled. In a graphical inspection, the SBP and DBP data at each and all 3 examinations looked approximately normal.p values for all SNPs are shown in Figures p values using p value by rs9632874 was smaller by 1.98E-10 [results not shown]). Three SNPs, rs12634258, rs7647249, rs4533619 from intergenic region on chromosome 3, and 4 SNPs rs9632874, rs12335766, rs10122040 from gene TTC39B and rs7864652 from gene BNC2 on chromosome 9, appeared to be significant at genome-wide level.Table rs6442089 jointly on SBP and DBP; whereas the separate univariate linear mixed model analyses had only 30.5% and 45.0% power to detect of effects of the same SNP on SBP and DBP, respectively at α = 0.05, using 141 unrelated subjects. At α = 7.2 × 10−8 the association of SNP was detected in 5 (2.5%) of simulated data sets in the bivariate analysis, but the corresponding univariate analysis did not detect the association with either of the phenotype in any simulated data set. The univariate analysis produced the smallest p value of 1.6 × 10−5 for SBP and that for DBP was slightly bigger  and UN, AR(1) had a similar or somewhat smaller AIC. However, it assumes that measurements were made at an equal interval over time for each and all phenotypes [UN assumption is more flexible, consequently, we employed it our bivariate analysis. A detail investigation of the properties of bivariate method in many realistic scenarios via extensive simulation is warranted before we draw a general conclusion about the usefulness of the bivariate method for the correlated repeatedly measured phenotypes.However, we wish to underscore the limitation that our simulation study was not extensive; we just compared the power of the bivariate approach with that of the univariate approach for only 1 SNP. We did not assess the type I error rate of the bivariate method, which could be inflated, especially for a small data set. In fact, the Q-Q plot (see Figure enotypes ,5. But tA bivariate approach to test associations of genetic variants with multiple phenotypes jointly measured over time from the same individuals could be a useful strategy to identify genetic variants that deserve further investigation as it can exploit the correlation structure between phenotypes at a time and the same phenotype over time.The authors declare that they have no competing interests.JB and BN designed the analysis plan. BN conducted the statistical analyses, and drafted the manuscript. JB assisted in drafting, and critically revised the manuscript. Both authors read and approved the final manuscript.


Genomic selection (GS) is a promising approach for decreasing breeding cycle length in forest trees. Assessment of progeny performance and of the prediction accuracy of GS models over generations is therefore a key issue.Pinus pinaster) with an estimated effective inbreeding population size (status number) of 25 was first selected with simulated data. This reference population (n = 818) covered three generations  and was genotyped with 4436 single-nucleotide polymorphism (SNP) markers. We evaluated the effects on prediction accuracy of both the relatedness between the calibration and validation sets and validation on the basis of progeny performance. Pedigree-based  and marker-based (genomic BLUP and Bayesian LASSO) models were used to predict breeding values for three different traits: circumference, height and stem straightness. On average, the ABLUP model outperformed genomic prediction models, with a maximum difference in prediction accuracies of 0.12, depending on the trait and the validation method. A mean difference in prediction accuracy of 0.17 was found between validation methods differing in terms of relatedness. Including the progenitors in the calibration set reduced this difference in prediction accuracy to 0.03. When only genotypes from the G0 and G1 generations were used in the calibration set and genotypes from G2 were used in the validation set , prediction accuracies ranged from 0.70 to 0.85.A reference population of maritime pine  contains supplementary material, which is available to authorized users. The use of genome-wide DNA markers to predict genomic estimated breeding values (GEBV), first proposed by Meuwissen et al. , has radIn forest tree breeding, the duration of a single cycle of selection-recombination is driven by the time at which flowering first occurs (e.g. 7–8 years in maritime pine) and the age at which early indirect selection for mature properties can be carried out . A full cycle therefore generally lasts more than two decades. In addition, the low–to-medium heritabilities of most complex traits, such as growth, stem form, and branching characteristics, limit the response to selection, and, thus, the expected genetic gain. GS may overcome these limitations, by decreasing breeding cycle duration and improving selection efficiency/intensity for traits with a low heritability, thereby increasing the efficiency of breeding strategies. Preliminary studies on major plantation forest trees  have given encouraging results , 10, witPinus pinaster) is a major forest tree species in south-western Europe. A breeding program based on a recurrent selection strategy was initiated in France in the 1960s [Maritime pine (he 1960s . A base he 1960s . A prelihe 1960s . In thisa priori on the basis of genotyping constraints) to maximize the expected genomic prediction accuracy.The reference population was designed in two steps, as summarized in Fig. S, an estimate of effective population size). This procedure resulted in the selection of 2038 G2 trees. Pedigree recovery with 63 SNP markers was carried out on these trees to identify the paternal parent and to check the maternal genotype  and 27,265 G2 trees. Breeding values based exclusively on maternal pedigree  were estimated for height, stem circumference at breast height and stem straightness, in a mixed model framework. Two criteria were used to select a subset of G2 trees: i) an index combining the best linear unbiased predictions (BLUP) for volume and stem straightness  to select the best half-sib family, ii) a maximum of 40 half-sib families with a maximum contribution of a single founder (G0) of 0.15, to prevent the over-representation of a few founders and to give a limited status number . In the first method, G2 trees were selected at random (the random method). The second method was based on sampling within the largest maternal half-sib families, with equal numbers of individuals selected from each half-sib family (the HS method). In the third method, G2 trees were sampled from the largest full-sib families, with a maximum of two individuals selected per family (the FS method). For the fourth method, we maximized the mean generalized coefficient of determination (CD method) , 34. TheS, ) was estp < 0.01) and between circumference and stem straightness  were moderate. A weaker correlation was observed between height and stem straightness  for three different traits — circumference and height at 12 years of age and stem straightness at 8 years of age — were obtained from a meta-analysis based on the TREEPLAN framework . The corP. pinaster composite map [P. pinaster unigene [The DNA extraction method and the Illumina Infinium array used to genotype the reference population have been described elsewhere . SNP clusite map  was dete unigene . The numr2 with R software and expressed as a function of the genetic distance between markers. The effect of selection (differentiation between generations), resulting in changes in allele frequencies between generations, was assessed by calculating a fixation index (FST) [pegas [The intra-chromosomal LD between markers was calculated as ex (FST)  with the) [pegas .synbreed [ggplot2 package [Data for genomic prediction models were handled in the R 3.2.2 environment  with thesynbreed  and BGLRsynbreed . The res package .A) based on pedigree were derived. The first, AP, used only data for the maternal parents and corresponds to polymix breeding, in which only the maternal parents are known. For the second (AF), the full pedigree was used. G0 plants were considered to be unrelated and no population structure was identified [G) was also calculated, as described by Van Raden [n  × p (number of markers). i for all individuals. Use of the matrix of minor allele frequency scales Kinship coefficients between individuals of the three-generation pedigree were estimated from pedigree and genomic data. Two expected additive genetic relationship matrices  random selection of G2 trees (random), ii) selection of G2 trees from the same half-sib families, to obtain a low level of relatedness between the calibration and validation sets (S1), iii) sampling of G2 trees from different full-sib families, to obtain a high level of relatedness between the calibration and validation sets (S2). For each sampling strategy, two types of calibration sets were used to evaluate the effect of pedigree depth. The first was the remaining 80 % of the G2 population and the second was the remaining 80 % of the G2 population plus all progenitors (G0 and G1). Model fit statistics were obtained for 100 replications for each scenario.In addition to subset validation (different sampling approaches applied to G2 trees), we performed progeny validation to evaluate the prediction accuracy of GS models over generations. The individuals of the G0 and G1 generations were used as the calibration set and the individuals of the G2 generation were used as the validation set. This second validation method was used to assess the accuracy of genomic prediction models across generations, with the model trained on ancestral generations  and validated on progeny generation (Gn + 1). The prediction accuracy of GS models was estimated as the coefficient of correlation between the genomic estimate breeding values (GEBV) of the validation set and the EBV obtained by TREEPLAN evaluation. The prediction bias was calculated as the slope of the regression line between EBV and GEBV. A slope of b > 1 indicates deflation and a slope of b < 1 indicates inflated predictions.AF) substantially increased the prediction accuracy of GS models (p < 0.05) over that for the partial pedigree based only on maternal information  were achieved by using GBLUP rather than AFBLUP. For example, for the HS selection method, the mean accuracies of genomic predictions were 0.53 for AFBLUP and 0.56 for GBLUP . This value was significantly higher than those for the HS (19.8), FS (20.7) or Random (20.4) methods , use of the full-pedigree information  and only a few marker pairs (0.5 %) had r2 values greater than 0.4. Most of the markers concerned (96.5 %) were physically linked (on the same contig) or genetically linked (less than 5 cM apart on the composite map). The remaining markers displaying high levels of LD (2.5 %) probably reflected a bias in composite linkage map construction rather than true long-distance LD, as suggested by their positions on component maps. Changes in allele frequencies were observed between G0 and G1, with an FST value greater than 0.05 for 19 SNPs, mostly located on chromosomes 5, 6, 9 and 12  or environment. No clear trend was observed for the relationship between accuracy and trait heritability. Using a large number of traits, resulting in a wider range of heritability, Resende et al. [R2 = 0.79) between predictive ability and narrow-sense heritability. Compared to a previous study on maritime pine with a broader genetic basis [S = 25), than in a previous study (NS ≈ 100) and the inclusion of multiple generations might account for the higher prediction accuracies in this study. Indeed, effective population size, which is directly related to level of LD and relatedness in populations, is known to be an important factor determining GS accuracy [Eucalyptus with contrasting effective population sizes: Ne = 11 and Ne = 51.Our reference population was specifically designed to maximize prediction accuracy given the available genetic material. By contrast to previous GS studies on forest trees, we used simulation to select individuals on the basis of an explicit criterion maximizing the expected prediction accuracy for the population. As a result, we obtained medium-to-high prediction accuracies for all three traits studied 0.52 to 0.91), consistent with published results for forest tree species  and high (S2) levels of relatedness. Our findings are consistent with previous results for white spruce  and miceaccuracy .Given all the possible mechanisms separating genomic variants, such as SNPs, from phenotype expression and the efforts required to identify them, one of the main issues in GS studies is demonstrating the predictive value of markers relative to conventional BLUP. In this study, regardless of the scenario used, the model using pedigree information (ABLUP) had a higher prediction accuracy than marker-based models. The marker density (2.4 SNPs per cM) used to predict GEBV may account for this difference. Indeed, simulation studies have suggested that there may be a positive asymptotic relationship between marker density and prediction accuracy , 22, 56.This study is novel because, unlike previous empirical studies on forest trees, we assessed the predictive value of markers across generations, rather than splitting a single population in two for model development and validation . GS in fCryptomeria japonica trees generated over a period of 60 years showed that GS outperformed phenotypic selection only if the GS model was updated [When progenitors (G0 and G1) of the G2 population were included in calibration models, differences in prediction accuracy between low (S1) and high (S2) levels of relatedness were less than 0.03. Moreover, a slight increase in prediction accuracy was observed for all scenarios, highlighting the importance of genotyping the ancestral populations, which are generally conserved in tree breeding programs, to increase prediction accuracy. Simulation studies have also highlighted the importance of including multiple generations in the calibration set, to update the prediction equation , 66. Ind updated . Sallam  updated  reportedEucalyptus [The maritime pine breeding program follows a recurrent selection scheme, with breeding value estimated from polycross and bi-parental progeny trials. The genetic gain achieved in the released varieties over the first two generations was estimated at 30 % for both growth and stem straightness. The improved varieties generated by this program in the future will need to be adapted to predict changes in climate, pest and disease outbreaks and the demand for diversified wood-based products. The major challenge faced in this breeding program will therefore be the integration of new traits to deliver suitable varieties. With the rapid decrease in genotyping costs and the promising results obtained for forest trees Table , GS coulcalyptus  and whitcalyptus . These tcalyptus , 74, butS = 25) and a marker density of 2.5 SNPs per cM, for assessment of the prediction accuracy of GS models within and across generations. We studied three major traits used in maritime pine breeding: circumference, height and stem straightness. These three traits have low heritabilities, from 0.17 to 0.32. Prediction accuracies of up to 0.85 were obtained with progeny validation, confirming the potential of GS to predict progeny performance for low-heritability traits. However, the pedigree-based model had prediction accuracies similar to or greater than that of marker-based models. The optimization of current breeding strategies based on polymix breeding will therefore be required to enhance the potential of the GS approach in the maritime pine breeding program.We selected a reference population covering three generations, with a limited status number (NST, Fixation index; G, realized genomic relationship matrix; G0, G1 and G2, generations of the breeding program; GEBV, genomic estimated breeding value; GS, genomic selection; HS, half-sibs; LD, linkage disequilibrium; Ne, effective population size; NS, status number; QTL, quantitative trait lociA, expected additive genetic relationship matrix; B-LASSO, Bayesian least absolute shrinkage and selection operator; BLUP, best linear unbiased prediction; CD, coefficient of determination; EBV, estimated breeding value; FS, full-sibs; F