In order to meet future food, feed, fiber, and bioenergy demands, global yields of all major crops need to be increased significantly. At the same time, the increasing frequency of extreme weather events such as heat and drought necessitates improvements in the environmental resilience of modern crop cultivars. Achieving sustainably increase yields implies rapid improvement of quantitative traits with a very complex genetic architecture and strong environmental interaction. Latest advances in genome analysis technologies today provide molecular information at an ultrahigh resolution, revolutionizing crop genomic research, and paving the way for advanced quantitative genetic approaches. These include highly detailed assessment of population structure and genotypic diversity, facilitating the identification of selective sweeps and signatures of directional selection, dissection of genetic variants that underlie important agronomic traits, and genomic selection (GS) strategies that not only consider major-effect genes. Single-nucleotide polymorphism (SNP) markers today represent the genotyping system of choice for crop genetic studies because they occur abundantly in plant genomes and are easy to detect. SNPs are typically biallelic, however, hence their information content compared to multiallelic markers is low, limiting the resolution at which SNP–trait relationships can be delineated. An efficient way to overcome this limitation is to construct haplotypes based on linkage disequilibrium, one of the most important features influencing genetic analyses of crop genomes. Here, we give an overview of the latest advances in genomics-based haplotype analyses in crops, highlighting their importance in the context of polyploidy and genome evolution, linkage drag, and co-selection. We provide examples of how haplotype analyses can complement well-established quantitative genetics frameworks, such as quantitative trait analysis and GS, ultimately providing an effective tool to equip modern crops with environment-tailored characteristics. Unstable environments and increasing climatic fluctuations like extreme heat and drought events have a severe impact on global crop production . In ordeTargeting genetic variants associated with agronomic traits and identifying important underlying candidate genes have become a key area in crop genetic research . BecauseTypically, high-throughput SNP marker arrays or SNPs detected by reduced-representation DNA sequencing are the genotyping methods of choice for crop genomic investigations. However, in the context of GWAS, SNPs have the major limitation that they normally only provide biallelic information at any individual locus. Further, assuming the rare allele model , a signiHere, we review the latest advances in haplotype analyses in crops, highlighting their potential for the improvement of yield stability in the face of increasing abiotic constraints to crop production. We discuss technical aspects of haplotype description using high-throughput genotyping platforms and how these can be useful for genomics-based crop improvement. We also discuss the importance of haplotypes in the context of polyploidy, co-selection, and linkage drag, and give future perspectives on how they can be incorporated in established and emerging quantitative genetics frameworks, such as quantitative trait analysis and GS.r2 . Based on LD criteria, marker-based haplotypes consisting of multiple markers are built and their allelic variation is compared to phenotypic measures for the traits of interest. Subsequently, test lines carrying favorable alleles can be screened and selected for crossings using molecular markers in order to accumulate haplotype variants of interest in breeding lines .Since the advent of highly efficient genotyping technologies, GWAS has become the method of choice for the dissection of complex traits in humans, animals, and plants. Numerous examples have demonstrated the power of GWAS for dissection of agronomically relevant quantitative traits in all major crops . The mosZ. mays L.), for example, O. sativa L.), T. aestivum L.), T. aestivum L.) (Z. mays L.)  (O. sativa L.)  (B. napus L.)  ; maize (mays L.) , rye  , rice (Otiva L.) , triticaosecale) , and oilapus L.) . Paradoxapus L.) .B. napus L.), today the second most important oilseed crop in the world. The recent allopolyploid B. napus arose only recently from a small number of hybridization events between B. rapa and B. oleracea, and wild forms do not exist. Today’s elite breeding pool was narrowed even further by introduction of the essential seed quality traits “low erucic acid” and “glucosinolate content” from just two trait donors, causing another extreme genetic bottleneck (O. sativa L.) (Z. mays L.)   and maizmays L.) . More prmays L.) . Whereasmays L.) .T. aestivum L), cotton (Gossypium arboreum L.), tobacco (Nicotiana tabacum L.), or oat (Avena sativa L.), hybridizations between related species merged genomic information from two or more divergent relatives into a single nucleus. Immediate or subsequent genome restructuring and gene loss (G. arboreum L.), unequal distribution and expression bias of homoeologous genes as a consequence of asymmetric subgenome evolution were found to be associated to fiber development and a wider environmental adaptation  lines found that duplicated homoeologous genes are under purifying selection, implying that a fitness benefit could be obtained by a mutation at any one of the homoeologs and that directional selection likely acted on single advantageous mutations in homeologous chromosome regions (B. napus L.), a GWAS-based haplotype analysis found that duplicated homoeologous haplotype regions in the two subgenomes additively affect leaf chlorophyll content and specific variants have been co-selected in the same direction  (O. sativa L.) (Z. mays L.) (B. napus L.) (Two important genetic features of the variance of complex traits in crops are additive and epistatic effects . While Qivum L.) , rice (Otiva L.) , maize (mays L.) , and rapapus L.) . Since tapus L.) , animalsapus L.) , and croapus L.) . SNP–SNPHordeum vulgare L.) (T. aestivum L.) (B. napus L.) . Using a linear model to estimate pairwise SNP–SNP interaction effects on root biomass, strong positive epistatic interactions were detected among root-associated haplotypes and negative effects were detected for interactions between LD blocks associated to spike and root traits. High-resolution SNP and LD data are an ideal basis for breeders to disrupt linkage in repulsion among valuable traits, particularly (as for root traits) where phenotypic selection is challenging.Different molecular genetic studies have attempted to model the effect of epistasis on quantitative traits. For example, interactions among molecular variants  play a major role in determining the susceptibility of humans to a particular disease. gare L.) , yield iivum L.) , or chloapus L.) . A recenFigure 3). In the retrospective approach, favorable haplotypes that have been selected by breeders for a given crop species are identified by first resequencing the genomes of key genotypes with high importance and related, derived breeding lines which have been evaluated across multiple environments and years, as shown in Figure 3A. This provides retrospective information about selection decisions made by breeders, identifying genomic haplotypes associated with previous breeding success. These can be used to identify causal gene candidates and underlying networks, as well as desired and deleterious genetic variants that cause specific phenotypes. Subsequently, as shown in Figure 3B, molecular markers that define favorable haplotype blocks can be jointly selected to create novel combinations of haplotypes with well-defined trait effects. Haplotype-related markers can also be used to identify lines with novel recombination in chromosomal blocks of interest in order to separate favorable and unfavorable genetic variation. The definition of genome-wide haplotypes by specific functional and genetic relationships differs from classical GS, where genome-wide markers represent anonymous components that are statistically related to phenotypes in a subset of the total breeding population. Instead, O. sativa L.) showed that the prediction accuracies for different traits using classical GS models like ridge-regression best linear unbiased prediction (RR-BLUP) could significantly be improved by a model extension based on upstream GWAS analyses (de novo GWAS model). They showed that extended GS + de novo GWAS models outperformed six other prediction models for various traits. Interestingly, the prediction accuracies of extended GS models outperformed classical models using phenotype data from dry seasons, implying that this approach is particularly suitable for the improvement of drought-resistance in future crop cultivars. Because of their increased information content compared to biallelic SNP markers, fitting haplotypes with statistically significant trait associations to phenotypes as fixed effects in GS models could further improve prediction accuracies. The use of haplotype-assisted GS should more accurately depict the complex relationships between genotypic information and phenotypes than single SNPs alone are able to do; hence, this approach could ultimately help to further increase selection gain per unit of time. Also in horticultural crops, the deployment of haplotype-based approaches holds a great potential for a genetic improvement of future varieties. In cucumber (Holothuria edulis L.) for example, Vitis vinifera L.), TERMINAL FLOWER 1 from Arabidopsis thaliana and found a relationship between haplotype diversity and phenotypic variation for reproductive and inflorescence traits. Solanum tuberosum Andigenum and S. tuberosum ssp. andigenum) species. By analyzing haplotype diversity they could gain further insights into the origin of cultivated potatoes. Combining advanced statistical genetics approaches with ultra-fast crop propagation techniques that allow multiple plant generations per year under greenhouse conditions (Improving the resilience of modern crop cultivars in times of increasing climatic fluctuations is a major challenge for breeders . Althouganalyses , 2016. Unditions  could heLQ, KV-F, and RS conceived the review; LQ, KV-F, AS, and RS conducted the literature survey and drafted the article; LQ and KV-F wrote the manuscript; and LH, CW, and BH contributed additional concepts and carried out critical revision of the manuscript.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.


Plum pox virus (PPV), agent of Sharka disease, is the most important quarantine pathogen of peach (P. persica L. Batsch). Extensive evaluation of peach germplasm has highlighted the lack of resistant sources, while suggesting the presence of a quantitative disease resistance, expressed as reduction in the intensity of symptoms. Unravelling the genetic architecture of peach response to PPV infection is essential for pyramiding resistant genes and for developing more tolerant varieties. For this purpose, a genome-wide association (GWA) approach was applied in a panel of accessions phenotyped for virus susceptibility and genotyped with the IPSC peach 9 K SNP Array, and coupled with an high-coverage resequencing of the tolerant accession ‘Kamarat’.P. davidiana, allow the identification of allelic variants in promising candidate genes, including an RTM2-like gene already characterized in A. thaliana.Genome-wide association identified three highly significant associated loci on chromosome 2 and 3, accounting for most of the reduction in PPV-M susceptibility within the analysed peach population. The exploration of associated intervals through whole-genome comparison of the tolerant accession ‘Kamarat’ and other susceptible accessions, including the PPV-resistant wild-related species The present study is the first effort to identify genetic factors involved in Sharka disease in peach germplasm through a GWA approach. We provide evidence of the presence of quantitative resistant loci in a collection of peach accessions, identifying major loci and highly informative SNPs that could be useful for marker assisted selection. These results could serve as reference bases for future research aimed at the comprehension of genetic mechanism regulating the complex peach-PPV interaction.The online version of this article (10.1186/s12870-017-1117-0) contains supplementary material, which is available to authorized users. Plum pox virus (PPV) gen. Potyvirus, agent of Sharka disease, is the most devastating viral pathogen of stone fruits, particularly peach (P. persica L. Batsch). Since the first report of PPV infections in Bulgaria [Bulgaria , the virBulgaria . Among sBulgaria .P. armeniaca L.) through a series of linkage and association studies, allowing the development of molecular markers and breeding programmes for the transfer of resistance to novel varieties [P. davidiana and P. dulcis  [. The introgression of resistance through hybrid selections has been unsuccessful so far due to several drawbacks, including the lack of resistance-associated molecular markers. The vast majority of peach accessions are highly susceptible to the PPV-M strain, although genotypes showing lesser symptom severity upon infection have been reported [The identification and exploitation of PPV-resistant sources represents the main eligible strategy for the long-term protection of peach cultivation. Genetic sources of both PPV-M and -D resistance have been identified and characterized in apricot  , 6. The reported , 8. Mostreported . The Itareported  enabled reported .P. davidiana, resistant) progenies suggest a complex pattern of polygenic inheritance [MATH gene [TRAF-like gene family- has been fine-mapped at the PPVRes locus on LG1, although its effect also varies depending on the genetic background [Arabidopsis thaliana, dominant resistance against PPV is also conferred by a MATH gene [eIF(iso)4E gene confers PPV resistance in plum [eIF genes seems to be present within peach germplasm .The range of phenotypic response to virus infection observed in peach germplasm suggests the existence of a quantitative disease tolerance, able to confer a reduction in symptoms intensity rather than absence of the disease. The identification of genetic loci controlling such quantitative tolerance may allow the design of molecular markers to assist breeders in pyramiding favourable alleles and the development of tolerant varieties. However, the genetic architecture of PPV-M tolerance is still unknown in peach and only limited information is available about the resistance alleles present in related species. Linkage mapping experiments in ‘Summergrand’  x ‘clone P1908’  approach is becoming an increasingly powerful tool to identify loci controlling both quantitative and qualitative traits, bearing the potential to improve the power of detection in comparison with classical biparental linkage mapping . This apEvaluation trials have shown an overall high susceptibility of peach germplasm and the absence of resistant accessions  against the PPV-M strain infection. Based on visual assessment (score from 0 to 3), most accessions showed moderate to severe symptoms on leaves  since the first year after inoculum, whereas others became symptomatic only at the third or fourth year   Fig. . The sepCA) Fig. . ToleranCA) Fig. : Fig. S1Y  and skin pubescence controlled by locus G . Based on previous knowledge about the position of causal mutations for both traits [As a proof-of-concept of the statistical power of GWA approach in the considered panel, we analyzed two already characterized Mendelian traits, fruit flesh colour controlled by locus h traits , 35, theh traits  . The inclusion as covariates of either the first two PCs or Q matrix (for K = 3) tend to ameliorate p distribution, although a relevant number of false positives was still present , span a 400 Kb genomic region located at about 9 Mb on chromosome 2. Another locus was identified at about 5.7 Mb on the same chromosome . Similar results were obtained by testing the compressed (CMLM + K) model , different statistical models were tested for detecting associations for PPV tolerance. As expected from the presence of population stratification, strongly inflated p-values of respective QQ-plot .For an approximate estimation of effect size, a logistic regression was fitted at significant SNPs on binary phenotypes. As observed by odds ratio under the assumption of a dominant genetic model, highly significant associations were confirmed for SNP_IGA_366639 (OR = 43.07), SNP_IGA_214703 (OR = 23.53) and SNP_IGA_185608 (OR = 20.66), although with quite large confidence intervals (Table The association of the three SNPs to reduced symptom intensity was further confirmed using 0–3 classes of symptoms intensity in 73 accessions (25 not present in the GWA panel)  belonging to Nodulin-like protein family. WGS data of ‘Kamarat’ and ‘Yumyeong’ showed the presence of an additional A/T polymorphism adjacent to the A/C one tagged by the array, generating two allelic variants AA/TC, respectively , segregating for the partial CT/GA-repeats deletion in the 5′-UTR  and for the 63 nt deletion (heterozygous in ‘Orion’ and absent in SDs) with an expected ratio of 1:2:1 and 1:1, respectively. Four out 70 individuals were classified as resistant , 10 as tolerant  and the remaining 56 as susceptible . Association of the 5′-UTR variant with a reduced disease severity was confirmed in a panel of 73 accessions. As deduced by conceptual translation, PpRTM2-like (encoded by Prupe.2G065600) shares the same functional domains as the Arabidopsis RTM2 protein (AtRTM2), such as the conserved α-crystalline-like domain, a C-terminus transmembrane domain and the coiled-coils regions [P. davidiana. As demonstrated in different studies with P. davidiana hybrids, the peach parent may affect the level of resistance in the progenies, and therefore, the identification of peach determinants could be also important for the introgression of a high level of resistance from related species. The variant found within ENODL-like gene (Prupe.3G291466) cannot be tested, since it is not present in P. davidiana or ‘Orion’ peach background.The estimation of linkage disequilibrium (LD) patterns is critical for mapping resolution and the definition of the window size around the significant SNPs , 47. An  regions   regions , 49, alt regions  and refeENODL-like gene (Prupe.3G291466) or the several aminoacidic substitutions in MYB33/65-like (Prupe.2G050100) represents interesting candidates for future studies. For example, the miR159-regulated MYB33/65 plays a role in disease symptom induction by Cucumber Mosaic Virus in Arabidopsis [Nodulin-like genes in non-nodulating species is still largely unknown, although recent studies highlight their importance in many aspects of plant development and plant-microbe interaction [In our study, the mapping resolution is mainly limited by the panel size, which does not allow the unequivocal identification of candidate gene(s) in the detected intervals. Despite this limitation, the loss-of-function mutation in the bidopsis . The funeraction . ENODL-leraction .In perspective, an improvement of mapping resolution could be achieved by increasing markers density, for example through whole-genome re-sequencing. However, this approach could be advantageous only after the increase of sample size, identifying other tolerant/resistant genotypes and/or transferring the trait in different genetic backgrounds, primary in breeding-derived accessions.The present study is the first effort to identify genetic factors involved in Sharka disease in peach through a GWA approach. The understanding of the genetic basis of peach response to PPV infection is crucial to exploit favourable alleles already present in cultivated peach germplasm, representing a short-term solution for endemic areas and a more feasible approach compared to the introgression from related species. We provide evidence of the presence of quantitative resistant loci in a collection of peach accessions. Although with some limitations due to the small panel size and low number of tolerant individuals, we identified three major loci and three highly informative SNP markers, accounting for most of the phenotypic variability in PPV-M susceptibility that could be useful for marker assisted breeding or selection. Clearly, results should be confirmed by further studies. Biparental populations derived from this set of germplasm may represent a first step of validation and for this purpose, progenies derived from ‘Kamarat’ and ‘Ghiaccio1’ are presently being developed and will be directly evaluated by on-fields trials in endemic areas. Alternatively, the combination of association studies with larger populations and bi-parental linkage mapping could assist the confirmation of the identified loci and also the localization of additional loci or rare variants affecting host susceptibility.. The IPSC peach 9 K SNP array [The panel of accessions used in this study  and composed of 39, 18 and 13 individuals, respectively, were evaluated using the same protocol described above. Each seedling was assigned to a symptomatic class after four years of observations . Phylogenetic tree was build from a pairwise genetic distance matrix between individuals, calculated as 1-IBS similarity, and clustered with UPGMA methods in TASSEL [2 correlation for all pairwise SNPs comparisons on a sliding window with 100 adjacent markers. Intra-chromosomal LD patterns were measured and visualized using HAPLOVIEW v4.2 [Population substructure was inferred in ADMIXTURE v1.22, a model-based clustering algorithm . From SNn TASSEL . Bootstrn TASSEL . LinkageIEW v4.2 .p-values under null hypothesis through quantile-quantile (QQ) plot inspection and considering statistical power against False-Discovery Rate (FDR). A conservative threshold for assessing SNP significance was calculated based on Bonferroni correction for a type I error rate of 0.05. A two-stage approach was also tested, selecting SNP passing the FDR cut-off of 0.1 [p ≤ 0.05).For association analysis, naïve Generalized Linear Model (GLM) and structured GLM using alternatively PCAs or Q matrix  as covariates were performed in TASSEL; Mixed Linear Model (MLM), compressed MLM (CMLM) and Settlement of MLM Under Progressively Exclusion Relationship (SUPER) were conducted in GAPIT R package , involvif of 0.1  and thenf of 0.1 . To reduf of 0.1 . Geneticf of 0.1 . The fitP. davidiana ‘P1908’ were retrieved from NCBI SRA archives  libraries of the accessions ‘Quetta’, ‘GF305’, ‘Yumyeong’, ‘Mayfire’, ‘Jing Yu’, ‘Venus’ and P. davidiana ‘P1908’ x ‘Summergrand’ peach) using a modified CTAB protocol and quantified using Qubit (ThermoFisher). Genomic DNA of the peach accessions listed in Table S4 was extracted using DNeasy Plant kit (Qiagen) following manufacturer’s instructions. The exon II and 5’ UTR variants in Prupe.2G065600, were genotyped through agarose gel-electrophoresis on ethidium-bromide 2% agarose gel. Amplicons were amplified in 10 ul Go-Taq reactions following the same conditions: 95 °C for 2 min, 35 cycles of 95 °C for 30 s, 58 °C for 30 s, and 72 °C for 1.5 min, with a final extension at 72o C for 10 min. The three markers SNP_366639, SNP_214703 and SNP_185608 were scored through an HRMA-based approach. HRM analyses were carried out in an Eco Real-Time PCR System  using 1X EVAGREEN Precision Melt Supermix . The reactions were carried out with the following programs: 2 min at 94 °C, 35 cycles of 30 s at 94 °C, 30 s annealing at 58 °C and 30 s at 72 °C, followed by a melting step over a 70–95 °C gradient with 0.1 °C/s ramp rate. Data were analyzed using EcoStudy software . All primers are listed in Additional file Total genomic DNA was extracted from leaves of ‘Orion’ x ‘SD’ seedlings  to 3 (severe) scale-based scoring method for symptoms intensity (XLSX 26 kb)Additional file 2:List and classification of phenotypic response to PPV-M infection in the evaluated panel of accessions (XLSX 51 kb)Additional file 3: Figure S1.Algorithms used for calculating the kinship matrix: A) Identical-By-State (IBS); B) Balding-Nichols (BN) and C) Van Raden (VR) (TIFF 288 kb)Additional file 4: Figure S2.Scatter plot of the correlation between population structure and binary coded phenotypic values (tolerant vs susceptible) (TIFF 83 kb)Additional file 5: Figure S3Pattern of Linkage disequilibrium decay estimated from SNP array data (TIFF 107 kb)Additional file 6: Figure S4.p-values estimated for fruit flesh colour (top right panel) and fruit pubescence (bottom right panel) traits using FarmCPU algorithm. Red horizontal line indicates the Bonferroni-adjusted threshold based on the effective number of independent tests (−log10 2e-06) (TIFF 339 kb)Manhattan and quantile-quantile plots of the -log10 Additional file 7: Figure S5.Manhattan and quantile-quantile plots of the -log10 p-values estimated for binary (tolerant vs susceptible) coded phenotypic response to PPV infection in the panel of 85 accessions using Generalized Linear Model algorithm adjusted for population structure calculated through A) Q-matrix (for K = 3) and B) the first two principal component (PC1 and PC2). Red circle indicates significant SNP passing the Bonferroni-adjusted threshold  based on the effective number of independent tests (−log10 2e-06) (TIFF 151 kb)Additional file 8: Figure S6.Manhattan and quantile-quantile plots of the -log10 p-values estimated for binary (tolerant vs susceptible) coded phenotypic response to PPV infection in the panel of 85 accessions using A) Compressed Mixed Linear Model adjusted for kinship; B) Compressed Mixed Linear Model adjusted for kinship and population structure (Q-matrix for K = 3); C) SUPER model Red circle indicates significant SNPs passing the Bonferroni-adjusted threshold  based on the effective number of independent tests (−log10 2e-06) (TIFF 223 kb)Additional file 9:Full list of variants annotations and effects  from the WGS libraries assembly of eight accession in the selected regions of chromosome 2 and 3. High-impact variants predicted by SNPEff are highlighted in red (XLSX 1522 kb)Additional file 10: Figure S7.pi) and SNP density for each chromosome, respectively (TIFF 1757 kb)Annotated features of ‘Kamarat’ genome. Red, green and blue smoothed lines indicates gene density, nucleotide diversity Additional file 12: Table S1.List of candidate genes identified on the chromosome 3 region associated to the SNP_IGA_366639 (from 26.2 to 26.5 Mb) (DOCX 10 kb)Additional file 13: Figure S9.Linkage disequilibrium pattern around SNP_IGA_214703 and SNP_IGA_218596 on chromosome 2 (TIFF 374 kb)Additional file 14: Table S2.List of candidate genes identified on the chromosome 2 region associated to SNP_IGA_214703 (from 8.5 to 9.1 Mb) (DOCX 9 kb)Additional file 15: Figure S10.Linkage disequilibrium pattern around SNP_IGA_185608 and SNP_IGA_185721 on chromosome 2 (TIFF 509 kb)Additional file 16: Table S3.Candidate genes identified on the chromosome 2 associated to the SNP_IGA_185608 (from 5.6 to 6.0 Mb) (DOCX 9 kb)Additional file 17:P. davidiana ‘P1908’), evaluated using a 0 (asymptomatic) to 3 (severe) scale-based scoring method for symptoms intensity (XLSX 7 kb)Phenotypic response to PPV-M infection in three pseudo BC1 progenies ‘Orion’ x ‘SD’  (TIFF 97 kb)Box-plots of single marker analysis for the 5′-UTR and the exon II variants inferred by the non-parametric Kruskal-Wallis K-test in 70 individuals from three pseudo BC1 progenies ‘Orion’ (peach) x SD Additional file 20: Table S4.SRA accession number (DOCX 8 kb)Additional file 21: Table S5.List of primers used in this study. (DOCX 8 kb)


In a line or a hybrid breeding program superior lines are selected from a breeding pool as parental lines for the next breeding cycle. From a cross of two parental lines, new lines are derived by single-seed descent (SSD) or doubled haploid (DH) technology. However, not all possible crosses between the parental lines can be carried out due to limited resources. Our objectives were to present formulas to characterize a cross by the mean and variance of the genotypic values of the lines derived from the cross, and to apply the formulas to predict means and variances of flowering time traits in recombinant inbred line families of a publicly available data set in maize. We derived formulas which are based on the expected linkage disequilibrium (LD) between two loci and which can be used for arbitrary mating systems. Results were worked out for SSD and DH lines derived from a cross after an arbitrary number of intermating generations. The means and variances were highly correlated with results obtained by the simulation software PopVar. Compared with these simulations, computation time for our closed formulas was about ten times faster. The means and variances for flowering time traits observed in the recombinant inbred line families of the investigated data set showed correlations of around 0.9 for the means and of 0.46 and 0.65 for the standard deviations with the estimated values. We conclude that our results provide a framework that can be exploited to increase the efficiency of hybrid and line breeding programs by extending genomic selection approaches to the selection of crossing partners. In each cycle of a line or a hybrid breeding program, lines are selected which serve as the parents of the crosses from which the base population of the next breeding cycle is derived. However, not all possible crosses between the superior lines of a cycle can be made and evaluated due to limited resources. The decision which parental lines to cross is therefore an essential factor that determines the selection gain in a breeding program.U = μ + iσgh, where μ is the expectation and σg the standard deviation of the genetic values of the lines derived from the cross, i is the selection intensity [h the square root of the heritability. The potential of this concept was recognized early, its practical application, however, was hindered by the difficulty of obtaining good estimates for the standard deviation σg. The prediction of the segregation variance The usefulness of a cross  is definntensity , and h tented by .h from the equation of the usefulness, the superior progeny value as s = μ + iσg. Their approach was developed for recombinant inbred lines derived by single-seed descent (SSD) and uses additive genetic effects estimated by QTL mapping or genome-wide prediction. Several studies investigated with computer simulations the prediction of the genetic variance within a cross [Bernardo et al.  suggeste Jannink  who defi a cross , 6–8, but generations of intermating, and (3) illustrate the use of the formulas with published data of the nested association mapping (NAM) population in maize [Our objectives were to (1) present an analytical derivation of in maize .s = μ + iσg of the cross of two homozygous lines, we define the random variable Z describing the genotypic values of a population of homozygous lines derived from the cross. The expectation of Z isc sums over chromosomes, j sums over the loci on a chromosome, and j, k sums over all locus pairs on a chromosome. β0 is the intercept in an additive genetic model and the Zj are random variables that describe the genetic effect of the allele at locus j. Zj can either be two times the additive effect of the maternal allele, which we denote by gj, or two times the effect of the paternal allele denoted by hj. The event space of Zj is ωj ∈ Ωj = {gj, hj}. The probability that the random variable Zj takes the value gj or hj isZj isk are gk and hk. For deriving the covariance between the genotypic values at the two linked loci j and kZjZk with event space ωj,k ∈ Ωj,k = {gjgk, gjhk, hjgk, hjhk}. To determine the probability of the four events in Ωj,k, we define the conditional probabilityZk takes the value gk under the condition that Zj takes the value gj, i.e., the probability that the locus k carries the maternal gamete under the condition that locus j carries the maternal gamete. Using qjk, we haveTo derive the superior progeny value 2(gj+hj).The effehk+hjgk).If Eqs (P(A|B) = P/P(B) it follows thatP(Zj = gj) = P(Zk = gk) = 1/2, we can write qjk as a function of the expected LD between the two loci j and k asFrom the definition of the conditional probability s in terms of the expected LD for two linked loci. It can be used for arbitrary mating systems that were used to derive the populations of homozygous lines from the initial cross. Prerequisite is that the expected LD coefficient Djk and, hence, qjk for the mating system is known or can be derived.Eqs 1 (F1-DH), or after t generations of random intermating of the F1, which we denote by (F1)t-DH. SSD lines are derived from the F2, or after t generations of random intermating of the F1, which we denote by (F2)t-SSD. We present results for qjk for the (F1)t-DH and (F2)t-SSD mating systems following the approach of [Two major systems used by plant breeders and geneticists to derive inbred lines from a cross are DH lines and recombinant inbred lines developed by repeated selfing with SSD. DH lines are derived from the Froach of .1-DH population consists of gametes generated by an F1, the probability that such a gamete carries the alleles of one parental line at the loci j and k isrjk is the recombination frequency between j and k. Hence, according to t generations of random mating, the LD coefficient Djk of the F1 population is reduced by the factor (1 − rjk)t [1)t-DH linesAs an F2)t population is the same as in a population of (F1)t-DH lines (2)t-SSD linesruv can be derived from an arbitrary mapping function. For example, using Haldane’s mapping function [Zj and Zk isxj and xk are the map positions of the two loci in Morgan units.The LD coefficient in SSD lines derived from a population in Hardy-Weinberg-Equilibrium is :Djk=DjkDH lines , therefoβ0 and the effects gj and hj are predicted with a genome-wide prediction model. Further, a linkage map of the markers used for the estimation of the genetic effects is required for calculation of the recombination frequencies.For the estimation of the expectation and the standard deviation of a cross with the presented formulas, the parameter www.panzea.org. The data comprised two data sets: an association panel of 282 diverse maize inbred lines and the maize NAM population. The NAM population consists of 25 families of 200 recombinant inbred lines that were derived from crosses of the inbred B73 with 25 lines from the association panel. The 25 parental lines were selected from the association panel to represent its diversity [To illustrate the application of the formulas and to compare our results to results of simulations with PopVar we used publicly available data that was originally generated for the investigation of flowering time in maize , 13–15. iversity , 15. Theiversity . The linui were thus estimated by solving the mixed-model equationμ and For calculating marker effects, the association panel was used as training set. Marker effects were calculated with ridge-regression best linear unbiased prediction (RR-BLUP) . The mar=(1′yZ′y)5Employiμ and μ and In addition to the estimates obtained with Eqs e PopVar . We usedμ and The means and variances estimated with Eqs s = μ + iσg, where μ is the expectation of the genotypic values of the recombinant inbred lines derived by SSD from the cross and μ and σg were defined in terms of αi, which denotes half of the difference between the two homozygous QTL effects at a locus. This parameterization has the advantage that it can be directly applied for effect estimates from QTL mapping in bi-parental populations. In our notation, the absolute value of the αi can be expressed as |gu − hu|/2. Our Duv for F2-SSD lines. Our notation has the advantage that the allele effect estimates from genome-wide prediction approaches can be directly used without re-parameterization to αi, and that the formulas also can be applied when effects for multiple alleles were estimated. This is important for applications in which several SNPs are combined to haplotypes.Zhong and Jannink  suggestes. The situation we investigate is different. Our approach is not restricted to selection of crossing partners from a set of recombinant inbred lines which were derived from a bi-parental cross. Rather, our approach is targeted at choosing the optimal crossing partners from a set of lines that can be selected from multiple families of a certain cycle of a breeding program to be used as crossing parents for the inbred lines of the subsequent cycle.The analogy between  and our As an extension to the approach of , our forDuv can be determined. As an advancement, we provide extensions for DH lines and for an arbitrary number of intermatings before deriving inbred lines by either DH or the SSD. Further, we provide an extension from recombinant inbred lines originating from a single bi-parental cross to sets of inbred lines derived from multiple families from a breeding pool with different parents. We suggest to apply the formulas to select crossing partners from such sets of inbred lines as parents for the subsequent breeding cycle.In summary, in comparison to the approach of , we provBernardo  and a seossovers .χ2 distribution for the number of crossovers on a chromosome and a uniform distribution for the location of the crossovers. This difference in the underlying models is expected to contribute to the differences in the genetic variances predicted with the two approaches in our example data set for traits DTA and DTS (The software PopVar  uses a χ and DTS . Moreove and DTS . This coHowever, the major advantage of analytical approaches compared to simulations is speed. In our example data set, only 325 SNP markers were employed, and the analytical approach was about ten times faster as the simulations. It can be expected that the time advantage will be considerably greater with data sets that comprise a greater number of markers.We conclude that our formulas provide analytical results for the means and variances that are highly correlated to the simulation results, but can be computed more quickly.The accuracy of predicting genetic means and variances obtained when applying our formulas to the flowering time data set is limited by the accuracy of the genetic effect estimates.In addition to homoscedastic ridge regression, we estimated the marker effects also by using heteroscedastic models , but no In data sets from breeding programs, a high marker density is not necessarily required to obtain high accuracies of genomic prediction , 20. ThiThe number of genotypes in the training set seems also low. In contrast to genetically narrow material from a breeding pool, the number of alleles in the diversity panel is expected to be greater. Hence, the number of replications for each allele in the training set is lower in a diversity set than in material from a breeding program.s. With this ranking, a superior fraction of crosses could be identified and further evaluated to determine the crosses with the highest performance in field trials.Despite of these described properties of investigated data set, the correlations between the estimated and observed means of the crosses for DTA and DTS were 0.90 and 0.91, and the correlations of the estimated standard deviations were 0.46 and 0.65 . We thinWe expect that in breeding pools with longer LD stretches and less allelic variation in combination with a higher marker density, a more precise effect estimation can contribute to greater correlations between estimated and observed segregation variances. We plan further investigations with data sets from breeding programs in sugar beet.Due to the comparatively low computation time and versatility with respect to the method of marker effect estimation as well as mating system, the presented formulas can be applied in a wide range of breeding programs. Breeders working in smaller breeding programs for commercially less important crops might consider it a constraint that a linkage map for the markers used for genomic prediction must be available for calculating recombination frequencies. However, the investment might be worthwhile, as a more precise prediction of superior crosses will not only increase selection gain, but also allow for a more efficient allocation of resources.per se performance in line breeding programs, as well as prediction of testcross performance in hybrid breeding programs. On basis of the marker effect estimates from genome-wide prediction models, the means and standard deviations for each cross are predicted.A possible application scheme for our formulas is outlined as follows. In a breeding program the marker genotypes as well as the performance data for lines selected as crossing parents for the next cycle are routinely available. These data can be used to estimate genetic effects for the markers. Areas of application include prediction of line μ and The relative superiority of the crosses would depend on the ratio of means and standard deviations, as was also pointed out by . In plan and σg2 . In thiss = μ + iσg. If we compare two crosses of elite lines with the same expectation μ, the difference in selection gain solely depends on the segregation variance i is applied. However, as the relation between i is a multiplicative one, a cross with a moderately higher genetic variance can result in considerably larger selection gain if the selection intensity is increased. Thus, it makes more sense to invest resources and generate more progeny in crosses with higher segregation variance.The estimation of the genetic variance could also provide a guideline for the allocation of resources to specific crosses. Consider again the superior progeny value In this context, some consideration should be given to the fact that while the magnitude of correlations between estimated and observed means and variances seems reasonable and useful, the estimated standard deviations tended to systematically overestimate the observed values . This miWe still think that it is more efficient to plan the size of the single families within breeding programs based on estimates of the segregation variance than to simply create many small families with the same number of progeny, which is common practice in many plant breeding programs. Open research questions in the field of breeding applications therefore comprise breeding designs that include an optimum family size and selection intensity based on estimated segregation variance. For this goal, the presented approach provides a fast and easy-to-use basis.


Genome‐wide genotype data was available from the Illumina HumanHap550 Quad microarray. Genome‐wide association studies were performed to assess associations with recognition of individual emotions and emotion in general. Exploratory polygenic risk scoring was performed using published genomic data for schizophrenia, bipolar disorder, depression, autism spectrum disorder, anorexia, and anxiety disorders. No individual genetic variants were identified at conventional levels of significance in any analysis although several loci were associated at a level suggestive of significance. SNP‐chip heritability analyses did not identify a heritable component of variance for any phenotype. Polygenic scores were not associated with any phenotype. The effect sizes of variants influencing emotion recognition are likely to be small. Previous studies of emotion identification have yielded non‐zero estimates of SNP‐heritability. This discrepancy is likely due to differences in the measurement and analysis of the phenotype.Emotion recognition is disrupted in many mental health disorders, which may reflect shared genetic aetiology between this trait and these disorders. We explored genetic influences on emotion recognition and the relationship between these influences and mental health phenotypes. Eight‐year‐old participants ( We then used polygenic risk score analysis to predict individual differences in emotion recognition within this cohort, using polygenic risk scores from studies of psychiatric disorders in which emotion recognition is impaired.22.1http://www.bris.ac.uk/alspac/researchers/data-access/data-dictionary/).Participants were drawn from ALSPAC, which has been described in detail elsewhere  as part of the “Focus at 8” assessment, performed when the participants were approximately 8 years old . In brief, 9,912 of the child participants were genotyped on the Illumina HumanHap550 Quad microarray, and the resulting genotypes imputed to the HapMap2 release 22 for autosomes, and HapMap 3 release 2 for the X chromosome using MACH and Minimac, respectively , using MACH‐imputed dosage data  with a nearby (<250 kb) variant with a lower p‐value.Unbiased hit rates for each emotion were arcsine transformed and used as phenotypes in genome‐wide association studies (GWAS) performed in ProbAbel , IQ at assessment, and whether the activities session was the first, second, third, or fourth performed . Further covariates were considered for inclusion, including summary results from each section of the Development and Wellbeing Assessment  was correlated with the phenotypic outcome. This questionnaire is a measure of flexibility and responsiveness to social interactions, and as such may involve the same cognitive processes as the DANVA  were used for polygenic risk scoring. Associations between external traits and specific and general emotion recognition were assessed using the default high‐resolution polygenic risk scoring option implemented in PRSice , and were weighted by their effect size in the external GWAS.Results from external GWAS of schizophrenia  and made up the analyzed cohort.Demographic data for the cohort is displayed in Table 3.2Summed scores for the correct identification of all faces had only a modest internal consistency , and summed scores for specific emotions had poor internal consistency , although this is limited by the small number of items per emotion (Supplementary Table S1). Measurements of skewness and kurtosis suggest that the arcsine transformation of the proportion index was necessary to improve the normality of this measure (Supplementary Table S1). Unbiased hit rates were acceptably normal before transformation, and their normality was largely unaffected by arcsine transformations (Supplementary Table S1). Transformed phenotypes were used to ensure consistency of treatment of all proportional phenotypes. Sensitivity analyses were performed on untransformed hit rates to assess the effect of this transformation.Correct identification of faces differed by emotion. Participants were better at detecting happy faces compared to all other emotions, better at detecting sad faces than fearful or angry faces, and better at detecting fearful faces compared to angry faces Table .3.3p = 5 × 10−8) in any GWAS, but 10 loci reached suggestive levels of significance across the GWAS of individual emotions , with 5 of these loci attaining suggestive significance for general emotion recognition, along with an additional two variants .Sensitivity analyses of the specific emotion GWAS using untransformed hit rates produced results that did not qualitatively differ from those using the transformed phenotypes (Supplementary Table S4). All variants with Post‐hoc power analyses were conducted using Genetic Power Calculator  Figure Spectral decomposition of the optimal scores from the 35 polygenic risk scoring analyses suggested 33.22 effective tests were performed, resulting in an adjusted alpha threshold of 3.01 × 10p < 0.001): autism predicting fear recognition (p = 7.32 × 10−4), anxiety (as a case‐control phenotype) predicting recognition of happy faces (p = 6.72 × 10−4) and anxiety (as a factor score) predicting angry faces . Plots 3.5h2 = 0.0077 (95CI: −0.209–0.224). Similar results were obtained from equivalent analyses in GCTA  is the most interesting candidate. It encodes beta‐chimerin, a rho‐GTPase activating protein involved in the phospholipase C cell signaling pathway, proposed to have a regulatory function in the central nervous system  and near the genes The sample size studied is relatively large for a psychological study; however, it is modest for a GWAS. As such, analyses only had statistical power to detect moderate effect sizes. Studies of psychological and behavioral traits to date suggest emotion recognition is likely to be highly polygenic, with multiple variants each contributing only a small effect , there are a number of methodological differences that may underlie the differing results. First, there are some demographic differences—Robinson et al. .Table S5. Results from the sensitivity analysis without arcsine transformation for the sentinel SNPs listed in Table p < 5 × 10−6 are shown in bold. Sentinel SNPs from each of the four specific emotion analyses are shown in gray. b: Quantile‐quantile plot shows observed associations between genetic variants and recognition of happy faces (y‐axis) do not deviate from those expected under the null distribution (x‐axis). Lambda median is a measure of genomic inflation. Lambda ≈ 1, indicating minimal inflation due to confounds.Figure S1.Manhattan plot showing associations between genetic variants and recognition of happy faces. Base position of genetic variants on each chromosome are on the x‐axis, ‐log p‐value on the y‐axis. Genome‐wide significance (p = 5 × 10−8) is top line (red), and suggestive significance (p = 5 × 10−6) is bottom line (gray).Figure S2. Manhattan plot showing associations between genetic variants and recognition of sad faces. b: QQ plot showing no deviation from the null expectation for genetic variants and recognition of sad faces.Figure S3. Manhattan plot showing associations between genetic variants and recognition of fearful faces. b: QQ plot showing no deviation from the null expectation for genetic variants and recognition of fearful faces.Figure S4. Manhattan plot showing associations between genetic variants and recognition of angry faces. b: QQ plot showing no deviation from the null expectation for genetic variants and recognition of angry faces.Figure S5. Association of Schizophrenia PRS across seven thresholds  and the optimal threshold. a: Schizophrenia PRS association with response to happy faces. b: Schizophrenia PRS association with response to sad faces. c: Schizophrenia PRS association with response to angry faces. d: Schizophrenia PRS association with response to fearful faces. e: Schizophrenia PRS association with response to facial emotion as a proportion index.Figure S6. Association of Bipolar Disorder PRS across seven thresholds  and the optimal threshold. a: Bipolar Disorder PRS association with response to happy faces. b: Bipolar Disorder PRS association with response to sad faces. c: Bipolar Disorder PRS association with response to angry faces. d: Bipolar Disorder PRS association with response to fearful faces. e: Bipolar Disorder PRS association with response to facial emotion as a proportion index.Figure S7. Association of Major Depressive Disorder PRS across seven thresholds  and the optimal threshold. a: Major Depressive Disorder PRS association with response to happy faces. b: Major Depressive Disorder PRS association with response to sad faces. c: Major Depressive Disorder PRS association with response to angry faces. d: Major Depressive Disorder PRS association with response to fearful faces. e: Major Depressive Disorder PRS association with response to facial emotion as a proportion index.Figure S8. Association of Autism Spectrum Disorder PRS across seven thresholds  and the optimal threshold. a: Autism Spectrum Disorder PRS association with response to happy faces. b: Autism Spectrum Disorder PRS association with response to sad faces. c: Autism Spectrum Disorder PRS association with response to angry faces. d: Autism Spectrum Disorder PRS association with response to fearful faces. e: Autism Spectrum Disorder PRS association with response to facial emotion as a proportion index.Figure S9. Association of Anorexia Nervosa PRS across seven thresholds  and the optimal threshold. a: Anorexia Nervosa PRS association with response to happy faces. b: Anorexia Nervosa PRS association with response to sad faces. c: Anorexia Nervosa PRS association with response to angry faces. d: Anorexia Nervosa PRS association with response to fearful faces. e: Anorexia Nervosa PRS association with response to facial emotion as a proportion index.Figure S10. Association of Anxiety (Case‐Control) PRS across seven thresholds  and the optimal threshold. a: Anxiety (Case‐Control) PRS association with response to happy faces. b: Anxiety (Case‐Control) PRS association with response to sad faces. c: Anxiety (Case‐Control) PRS association with response to angry faces. d: Anxiety (Case‐Control) PRS association with response to fearful faces. e: Anxiety (Case‐Control) PRS association with response to facial emotion as a proportion index.Figure S11. Association of Anxiety (Factor Score) PRS across seven thresholds  and the optimal threshold. b: Anxiety (Factor Score) PRS association with response to sad faces. c: Anxiety (Factor Score) PRS association with response to angry faces. d: Anxiety (Factor Score) PRS association with response to fearful faces. e: Anxiety (Factor Score) PRS association with response to facial emotion as a proportion index.Click here for additional data file.


Both population-based and family-based designs are commonly used in genetic association studies to identify rare variants that underlie complex diseases. For any type of study design, the statistical power will be improved if rare variants can be enriched in the samples. Family-based designs, with ascertainment based on phenotype, may enrich the sample for causal rare variants and thus can be more powerful than population-based designs. Therefore, it is important to develop family-based statistical methods that can account for ascertainment. In this paper, we develop a novel statistical method for rare-variant association studies in general pedigrees for quantitative traits. This method uses a retrospective view that treats the traits as fixed and the genotypes as random, which allows us to account for complex and undefined ascertainment of families. We then apply the newly developed method to the Genetic Analysis Workshop 19 data set and compare the power of the new method with two other methods for general pedigrees. The results show that the newly proposed method increases power in most of the cases we consider, more than the other two methods. There is increasing interest in detecting associations between rare variants and complex traits. Although statistical methods to detect common variant associations are well developed, these variant-by-variant methods may not be optimal for detecting associations with rare variants as a result of allelic heterogeneity as well as the extreme rarity of individual variants . RecentlMeanwhile, quite a few statistical methods for rare-variant association studies have been developed for family-based designs. For any type of study design, the statistical power will be improved if rare variants can be enriched in the samples. If one parent has a copy of a rare allele, half of the offspring are expected to carry it, and, hence, variants that are rare in the general population could be very common in certain families . Therefon pedigrees with ni members in the ith pedigree and a genomic region with M variants. Let yij and gij = T denote the trait value and genotypes of the M variants in the genomic region for the jth individual in the ith pedigree. Let xij = ∑m = 1Mwmgijm denote the weighted combination of genotypes at the M variants, where w = T is a weight function.Consider a sample of yij ∼ N. Using the notation For given genotypes, we assume that RL, the score test statistic for testing the null hypothesis H0 : β = 0 is given bywhere V = wTΣw∑ni = 1yiTΦiyi, Φi is twice the kinship coefficient of the ith pedigree, and Σ = cov is the covariance matrix of the multiple variant genotype of one individual. Σ can be estimated by Tscore is equivalent to the quantitative version of the retrospective likelihood score statistic proposed by Schaid et al [whereid et al .Tscore becomesw, T0(w) reaches its maximum when T0(w) is Because rare variants are essentially independent, following Pan  and Sha σmm is the th element of um is the mth element of u. Under the null hypothesis, TOW-score is asymptotically distributed as a mixture of independent χ2 statistics [TOW-score can be approximated by a Satterwaite approximation for the distribution of quadratic forms [χ2 distribution [TOW-score by a scaled χ2 distribution with the scale δ and degrees of freedom d estimated by the expectation and variance of TOW-score. Note that u ∼ N. We have δ is estimated as d is estimated as where atistics , 19. Altic forms , 20, 21 ribution . We propWe compare the performance of our OW-score with (a) WS-score, the score test given by equation  with weiWe applied our proposed method as well as the WS-score test and famSKAT to the simulated data from GAW19. All tests were conducted on 849 individuals, from 20 pedigrees, that had no missing genotypes or phenotypes. Sex, age, blood pressure medication status, and smoking status were considered as covariates in this study. We were aware of the underlying simulation model.CABP2 because the power of the three tests are essentially the same due to only one variant in this gene. To adjust the effects of the covariates on the phenotype of interest, we first applied a linear model by regressing the phenotype of interest on the covariates: sex, the average of age, the average of blood pressure medication status, and the average of smoking status. The power comparisons based on the 200 replicated data sets are given in Table wm and Wm denote the weights, rescaled to the interval , of the OW-score test and famSKAT for the mth variant. Then, wm > Wm when minor allele frequency (MAF) is less than 0.01; wm ≤ Wm when MAF is in the interval ; wm > Wm when MAF is greater than 0.05. The OW-score test has much higher power than famSKAT for RAI1 and REPIN1 because none of the MAFs of the causal variants in RAI1 and REPIN1 are in the interval .There are two related phenotypes, systolic blood pressure (SBP) and diastolic blood pressure (DBP), at three time points. We considered the average of DBP at three time points as the phenotype of interest in our analysis. We compared the power of the three tests  to detect association between each of the top 14 genes that influence the phenotype of interest. We used the variants between the first functional single nucleotide polymorphism (SNP) and the last functional SNP in each gene in our analysis. We did not consider p value for each replicate and each block. The type I errors of the proposed test were 0.04887, 0.00921, and 0.00131 at significance levels of 0.05, 0.01, and 0.001, respectively. We also considered the average of SBP at three time points as the phenotype of interest, which yielded similar results.We also evaluated the type I error rate of the proposed OW-score test. To evaluate the type I error, we used 1000 blocks (100 variants in each block) from chromosome 5 that are far from causal variants. In each block, we applied the OW-score test to each of the 200 replicates to test association between genotypes and the phenotype of interest. We obtained 1 Next-generation sequencing technologies make directly testing rare variant association possible. However, the development of powerful statistical methods for rare-variant association studies is still underway. In this article, we proposed a novel statistical method for rare-variant association studies based on general pedigrees for quantitative traits. The application to the GAW19 data set showed that the proposed method has correct type I error rate and is more powerful than the other two methods against which our method was compared.We described our method for quantitative traits. For qualitative traits, we can derive a score test similar to that given by equation . HoweverIn this article, we developed a novel statistical method for rare variant association studies in general pedigrees (randomly ascertained pedigrees or ascertained pedigrees). Application to the GAW19 data set showed that the newly proposed method is more powerful than the other two methods in most of the cases. Our new method uses a retrospective view, which allows us to account for complex and undefined ascertainment of families. The GAW19 data is based on randomly ascertained pedigrees. Results of applying our method to GAW19 data showed that the proposed method has correct type I error based on random ascertainment. When random ascertainment is violated and ascertainment is based on trait values, the proposed method is expected to have correct type I error. If pedigrees are ascertained because of extreme trait values, the proposed method is expected to have higher power than methods based on randomly ascertained pedigrees.


Prunus mume) is an ornamental woody plant that has been domesticated in East Asia for thousands of years. High diversity in floral traits, along with its recent genome sequence, makes mei an ideal model system for studying the evolution of woody plants. Here, we investigate the genetic architecture of floral traits in mei and its domestication history by sampling and resequencing a total of 351 samples including 348 mei accessions and three other Prunus species at an average sequencing depth of 19.3×. Highly-admixed population structure and introgression from Prunus species are identified in mei accessions. Through a genome-wide association study (GWAS), we identify significant quantitative traits locus (QTLs) and genomic regions where several genes, such as MYB108, are positively associated with petal color, stigma color, calyx color, and bud color. Results from this study shed light on the genetic basis of domestication in flowering plants, particularly woody plants.Mei ( Prunus mume) is a woody tree that produces ornamental blossoms which symbolize spring in East Asia. Here, Zhang et al. resequence wild and domesticated mei to reveal considerable admixture and introgression from other Prunus species and identify loci associated with floral traits.Mei ( The flowers of mei are featured for colorful corollas, varying flower types, a pleasant fragrance, and tolerance of temperatures as low as −19 °C2. Being a long-lived woody plant, many mei trees that are hundreds or even thousands of years old in several locations in China, providing a unique set of material to study the genetic processes underlying domestication. Distant hybridization has been extensively conducted between mei and other Prunus species to improve its agronomic traits and environmental adaption, and to understand the genetic diversity of important ornamental traits5. Various types of molecular markers have been developed for mei that provide powerful tools for studying the pattern of genetic diversity within and between populations and for constructing genetic linkage maps aimed to identify QTLs controlling quantitatively inherited traits9. More recently, genome sequencing of mei has made it an ideal model system for the genetic research of woody plants10.P12, floral symmetry13, and flowering time14. Flower pigmentation has also been studied from an evolutionary genetic perspective16. The genetic and molecular bases for the evolution of petal color have been characterized15. However, a systematic study to chart the genetic architecture of these traits in a large population using a genome-wide association (GWA) method has not yet been reported.Flowers have long been a focus of interest in studying this species due to their ornamental value. Mei exhibit an astonishing variety of petal colors, shapes, sizes, petal numbers, and floral bud aperture . Further, other ornamental traits, such as wood color and branching habit, have also received considerable attention. Several studies have investigated the evolution of regulatory networks for transitions in floral organ identityPrunus species, we can begin to study the evolutionary diversification of the Prunus genome.Here, we report the identification of significant QTLs that control floral traits in mei in a GWAS including 348 mei accessions. We further sequenced transcriptomes of flowers with diverse traits to validate the QTLs by biased expression of candidate genes between transcriptomes. The present study has for the first time elucidated the genetic architecture of floral size, color, and structure, in terms of the number of loci, their genomic distribution and the magnitude and pattern of their effects in a woody plant. In addition, by comparing mei with other P. mume cultivars, wild mei, and its close relatives for whole genome sequencing. A total of 348 mei accessions, including 333 landraces and 15 wild mei accessions were sampled and sequenced for the present study  according to classification system of Chinese mei1. Three other close relatives of mei, Prunussibirica, Prunusdavidiana, and Prunussalicina, were also sampled and sequenced in this analysis. The geographic origins of the mostly representative mei accessions analyzed here spanned China, Japan, and France. Each sample was sequenced to ~19.27-fold using the Illumina HiSeq 2000 sequencing platform to generate a total of 16.28 billion raw paired-end reads and 13.71 billion clean reads after filtering  in this population   were also calculated among wild and different cultivar classes  of wild and cultivated mei were estimated to be 2.82 × 10−3 and 2.01 × 10−3, respectively, relatively low compared with crops (Supplementary Table Linkage disequilibrium (LD) values  according to previous study1, and these three classes can be distinguished on the phylogenetic tree . Pink Double and Single Flowered (two varieties of cultivated mei) cultivars showed significant introgression (Z-score < −1.96) from the three Prunus species  and sequencing depth  genes reported in P. mume10 were not present in either the mei or Prunus core gene sets, possibly due to the divergence of blooming time between mei and Prunus accessions.We found that 71.68% and 60.96% of the es Table . These fP. mume genomes and from 8.94 to 25.85 Mb in other Prunus genomes  varied in length from 0.19 to 0.55 Mb in Prunus accessions and three sequenced relatives from the Rosaceae to construct a phylogeny and reconstruct the evolutionary history of Prunus genus. Our results suggested that P. sibirica might be more closely related to mei than is any other Prunus species in the present study, which was consistent with a previous report22. We estimated the divergence times between P. mume and other Prunus species as ~3.8 MYA and between wild and cultivated mei as ~2.2 MYA, which far predated the estimated domestication of cultivated mei  candidate regions on four chromosomes associated with ten traits including petal color, stigma color, calyx color, bud color, staminal filament color, wood color, petal number, pistil character, bud aperture, and branching phenotype  encodes an R2R3 MYB transcription factor and located in the same region on chromosome Pa4 as the petal color-associated SNPs 26 to construct an interactive network of the SEGs identified above  located at an ambiguous nucleotide in this promoter  , a transacting factor that binds specifically to a consensus nucleotide sequence in the AP1 promoter32. A third is PRXR1 , which is involved in the biosynthesis and degradation of lignin32.Our GWAS results showed that wood and staminal filament color were each significantly associated with two regions located on chromosome Pa3  Fig. , a dual-35. PRS is a probable transcription factor that is involved in lateral sepal axis-dependent flower development perhaps by regulating the proliferation of L1 cells in lateral regions of flower primordia37. These two genes could be involved in the control of petal number and pistil character of mei.We identified a region spanning ~3.64 Mb located on chromosome Pa1 (4058003-7693997) that was significantly associated with petal number, pistil character, and bud aperture of mei , have been identified (Supplementary Data 39.A candidate region associated with branching phenotype spanning ~1.15 Mb located on chromosome Pa7 was identified in a hybrid population in a previous studyPrunus mume), a woody plant, and the genetic architecture of its floral traits. We sampled and sequenced 333 mei landraces and 15 individual mei trees from a wild stand, along with three other Prunus species, to reveal the genetic divergence of mei under its domestication. We studied the genetic control of flower color, structure, and shape because these traits directly determine the reproductive behavior, mating system, and domestication process of higher plants40.By using a combined strategy of genome resequencing, de novo assembly and genome-wide association analysis, we address a fundamental challenge for inferring the population diversification of mei  on chromosome Pa4. MYB108, encoding an R2R3 MYB transcription factor, was observed to mediate flower color in plants25. By combining transcriptome data and data from existed database, we further reconstructed a regulatory network related to MYB108, from which the E2F transcription factor 1 (E2F1) that binds a sequence present in the promoter of the S-phase-regulated gene CDC6 was found to activate the expression of MYB108. As a highly conserved gene within Prunus, MYB108 may have played a critical role in modulating the genetic control and evolution of petal color in Prunus.The genetic control of flower-related morphologies of mei was found to be polygenic. For each of the ten floral traits studied, including petal color, wood color, petal number, flower density, branch type, and branching structure, numerous QTLs were identified Figs. , but wit29 and π values for the subpopulations that are dominated by two alternative genotypes at this polymorphism, it was inferred that the QTL for wood color may have been involved in a selective sweep driven by artificial selection30  , a transacting factor that binds specifically to a consensus nucleotide sequence in the AP1 promoter32, and PRXR1 , which is involved in the biosynthesis and degradation of lignin32.We identified two QTLs located on chromosome Pa3, associated with wood color and staminal filament color, respectively Fig. -12. A pon30 Fig. . The QTL02) Fig. , a dual-35 and lateral sepal axis-dependent flower development.Petal number is a key trait that determine the flower structure of mei. One QTL for petal number, as well as for pistil character and bud aperture, was found in a region of chromosome Pa1 , wood color (Pa4), and petal number (Pa1) located in different regions of the mei genome, and their independence suggest that these traits have experienced different routes of evolution. Although many QTLs detected can be annotated, there are also many QTLs that are in previously uncharacterized regions or not associated with any annotated genes. The biological functions of these unknown QTLs deserve further investigation. Taken together, the identification of genetic loci associated with floral and other traits provides more insight into the genetic mechanisms that underlie the domestication of mei and provides opportunities to design strategies for genomic selection to improve the performance of ornamental species.P. mume, and three close relatives of Prunus, including P. sibirica, P. davidiana, and P. salicina . To construct paired-end libraries, DNA samples were fragmented by nebulization with compressed nitrogen gas and treated to create blunt ends before adding an A to each 3′-end. DNA adaptors with a single T 3′-end overhang were ligated to the above products. Libraries with short insert sizes of 500 bp were constructed for each resequencing sample, and extra libraries with long insert sizes of 2 kb were constructed for the core- and pan-genome assembly. All libraries were sequenced on the Illumina HiSeq 2000 sequencing platform, and paired-end reads from each library were obtained. Reads were firstly filtered to obtain high-quality sequences for mapping and assembly by eliminating: (i) reads containing ≥10% ambiguous bases, (ii) reads with low-quality data  for 65% of bases for short inserts libraries (<2 kb) or 80% of bases for long inserts (2 kb), (iii) reads containing 10-bp adaptor sequences, (iv) reads with >10 bp overlaps between two ends of short-insert reads, and (v) reads with identical sequences at both ends.We collected leaves from 333 representative mei landraces, 15 wild 42 and used for cDNA library preparation. RNA was first assessed by capillary electrophoresis on an Agilent BioAnalyzer 2100 . Polyadenylated RNA isolated using oligo (dT)-attached beads was fragmented and reverse transcribed to cDNA. Paired-end libraries, with 500 bp in length, generated from each sample were then sequenced separately. RNA-seq were performed on the Illumina Hiseq 2000 platform. A total of 483.58 Mb raw data were produced by transcriptome sequencing of six samples and details were mentioned in Supplementary Table We performed RNA-seq for fresh flowers from two mei landraces (MDL vs. WYY) with three replicates for each were collected in April, 2016. Samples were immediately fixed in liquid nitrogen after collection and stored at −80°C. Total RNA was isolated using a modified CTAB protocol43. SNP calling was then performed following best practices for the GATK44 (v3.1) pipeline . We further filtered SNPs with more than 10% samples with missing genotypes, or deviated from Hardy-Weinberg principle in some downstream analysis. Structural variants (SV) were identified using BreakDancer45, which cataloged deletions, insertions, inversions, and intra-chromosomal translocations.All reads were mapped against the mei reference genome using BWA46, where the distance between two individuals i and j was defined as:L represented the length of the SNP region, where at position 1, dij would be equal to 0 or 1 if genotypes were identical or different between two individuals, and dij would be equal to 0.5 for other scenarios. A matrix of genetic distance was then used to generate a Neighbor-Joining tree using PHYLIP (v3.69)47. Linkage disequilibrium values for wild and cultivated mei, and populations with particular traits were calculated using Haploview48 with filtration parameters “-minMAF 0.05 -hwcutoff 0.01.” LD decay was then estimated as the relationship between the distance between each pair of SNPs and their corresponding correlation coefficient (r2) value. The distance that the LD decays to half of the highest value was then calculated. Principle Component Analysis were taken by EIGENSOFT49 software using genome-wide SNP.Genetic distance was estimated using genome-wide SNPsPrunus varieties were subjected to deep sequencing (~70.1×) using a single paired-end library and a mate-paired library with insert sizes of 500 bp and 2 kb, respectively, using the Illumina HiSeq 2000. All reads from each sample were processed and assembled using SOAPdenovo50(v2.04), followed by gap closing using GapCloser (v1.12) from the SOAPdenovo package. Both homology-based and ab initio prediction of protein-coding genes was then performed using P. persica, P. mume, Fragaria vesca51 and Pyrus × bretschneideri52 gene sets as references, and final gene prediction results for each genome were generated using GLEAN53. The core-genome was established by: (1) aligning all 12 assembled genomes plus the P. persica reference genome to the P. mume reference genome, using pairwise alignment software NUCmer from the MUMmer package;54 (2) filtering alignment results with identity <90%, map_len_min = 100 bp, query_seqs <500 bp and coverage <0.8; and finally (3) extracting and retaining core-genome sequences for nine mei and 13 Prunus species under different ratio.Nine mei and three Prunus genomes analyzed here during the establishment of the core- and pan-genome. Then these previously unaligned sequences were realigned to the reference genome using BLAT55 and unaligned sequences with identity <95% and length >100 bp were extracted. Finally, sequences generated from each assembly above were aligned to any other assemblies to identify any sequences specific to individuals . For validation of the PAVs and identification of population-specific PAVs, we mapped all paired-end reads from the 351 resequenced samples and calculated coverage for each PAV. From this set, PAVs covered by more than 90% of the samples with coverage and identity over 90% were excluded. To investigate population pattern of PAVs, a total of 93 PAVs were selected and their distribution among all samples was displayed on heatmap using R/pheatmap56. PAVs specific to the P11 subpopulation were then identified and average coverage was calculated in the genomic vicinity of each PAV. The ggmap57 package in R was used to visualize the distribution of PAVs across these locations.PAVs in each genome assembly were identified in a stepwise manner. First, unaligned sequences were collected after aligning all mei and 12. The generation-time hypothesis, which suggests that shorter generation times could accelerate a species’ molecular clock58, might explain differences in the divergence rates in molecular clocks. Firstly, we used MUSCLE59 to align the predicted proteins of single-copy genes. Then the protein sequences were reverse-transcribed into coding DNA sequences (CDS) based on the alignment results. Fourfold degenerate sites in each alignment were identified and concatenated into a single supergene for each species. A phylogenetic tree was then constructed using PhyML60 or MrBayes61. The fourfold degenerate sites were used to estimate the neutral substitution rate per year and divergence times among species.The phylogenetic tree for mei and other chosen plant genomes was constructed using single-copy orthologous genes identified using the clustering program OrthoMCL62 package. The Markov Chain Monte Carlo (MCMC) process in MCMCTREE program was run 800,000 times, with a burn-in of 80,000 iterations. Four independent runs were performed to check convergence.The models “Correlated molecular clock” and “JC69” were chosen to calculate species divergence times using the MCMCTREE program from the PAML64, we describe the measured value yi of a trait for individual i using a regression modelμ is the overall mean, Xi refers to the subpopulation of individual i, β is the effect for subpopulation, a and d are the additive and dominant effect of SNPs, respectively, ξi and ζi are the indicator vectors of the additive and dominant effects of SNPs for individual i, and ɛi is the residual error. The J-th elements of ξi and ζi are defined asH0 corresponds to the reduced model and H1 corresponds to the full model. The test statistics for testing the hypothesis is calculated as the log-likelihood ratio (LR) of the full over reduced model. LR can be viewed as being asymptotically χ2 distribution with different df. Level of significance is adjusted by Bonferroni method.In this GWAS studyHowever, in GWASs, a number of traits are either discrete or continuous. The discrete traits are categorized into binary, multinomial, and ordinal. Traits such as white or red flowers or calyx color due to pigment phenotypes are classic unordered categorical variables. This study used three different methods to detect relationships between genotypes and phenotypes based logistic regression model for discrete traits. (1) General linear model (GLM): GLM was used to test the associations based binary logistic regression link function for the binary variable. (2) Multinomial logistic model (MLM): MLM was used that the dependent variable is nominal with more than two levels and no intrinsic ordering. (3) Ordinal logistic regression (OLR): OLR was used to test the associations between markers and multiple ordered levels. For the continuous traits, linear regression model was used to test association.Besides, we used two models to analyze the data, considering effects of population structure or kinship. The first is the Q model that adjusts for the population structure of mei varieties, and the second is the Q + K model that correct for population structure and the kinship, i.e., the most probable identity by state of allele between varieties. The degree of kinship was calculated through correlation analysis using marker data. The model that better fits the data was assessed and chosen according to the Q−Q plot, in conjunction with the inflation factor estimated from the median of the test statistics for all the markers. Optimal model for each trait and Q−Q plot with results generated from both models were presented in Supplementary files , and Kyoto Encyclopedia of Genes and Genomes (KEGG) databases. By comparing with the background of all genes in mei genome using hyper-geometric distribution, enrichment analysis provides all terms (GO term and KEGG pathway ID) that are significantly enriched in the target genes. Computer code used to perform population genomics and GWAS is available from the corresponding authors upon request.PRJNA352648). All other relevant data supporting the findings of the study are available in this article and its Supplementary files, or from the corresponding authors upon request.The sequence data of mei genome resequencing involved in this study have been deposited in NCBI with the accession number SRP093801 (BioProject: Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10Supplementary Data 11Supplementary Data 12Supplementary Data 13Supplementary Data 14Supplementary Data 15Supplementary Data 16Supplementary Data 17Supplementary Data 18


Autism Spectrum Disorders (ASD) are heterogeneous neurodevelopmental disorders with a complex genetic architecture. They are characterized by impaired social communication, stereotyped behaviors and restricted interests and are frequently associated with comorbidities such as intellectual disability, epilepsy and severe sleep disorders. Hyperserotonemia and low melatonin levels are among the most replicated endophenotypes reported in ASD, but their genetic causes remain largely unknown. Based on the biochemical profile of 717 individuals including 213 children with ASD, 128 unaffected siblings and 376 parents and other relatives, we estimated the heritability of whole-blood serotonin, platelet N-acetylserotonin (NAS) and plasma melatonin levels, as well as the two enzymes arylalkylamine N-acetyltransferase (AANAT) and acetylserotonin O-methyltransferase (ASMT) activities measured in platelets. Overall, heritability was higher for NAS (0.72 ± 0.091) and ASMT (0.59 ± 0.097) compared with serotonin (0.31 ± 0.078), AANAT (0.34 ± 0.077) and melatonin (0.22 ± 0.071). Bivariate analyses showed high phenotypic and genetic correlations between traits of the second step of the metabolic pathway  indicating the contribution of shared genetic factors. A better knowledge of the heritability of the melatonin synthesis variability constitutes an important step to identify the factors that perturb this pathway in individuals with ASD. Large-scale genetic studies revealed a complex genetic architecture, involving combined effects of multiple low risk common variants, rare and de novo deleterious mutations4. Endophenotypes are measurable markers with potentially reduced genetic heterogeneity compared to the disease itself and they can be used to overcome the genetic and phenotypic heterogeneity. They facilitate the stratification of patients into more homogeneous subgroups5, increase the power of quantitative genetic analyses to detect variants, genes or pathways associated with the disease of interest and they reveal underlying biological mechanisms.Autism Spectrum Disorders (ASD) are complex neurodevelopmental disorders characterized by deficits in social communication/interaction as well as restricted interests and repetitive patterns of behaviors. Although ASD are highly heritable disorders10. A recent meta-analysis including 739 patients and 868 controls estimated an elevated whole-blood serotonin in 28.3% of the patients with ASD compared to 5% of controls11. Low melatonin levels in urine, plasma and pineal gland have also been described in ASD individuals15. Melatonin derives from serotonin, which is successively converted into N-acetylserotonin (NAS) and melatonin by the enzymes arylalkylamine N-acetyltransferase  and acetylserotonin O-methyltransferase . Melatonin biosynthesis essentially occurs in the pineal gland, following a marked circadian rhythm with a maximal secretion at night. A global disruption of this pathway was observed in patients compared to relatives and controls, including hyperserotonemia, deficits in AANAT and ASMT platelet activity, increased platelet NAS and melatonin deficit15. These alterations were also observed to a lesser extent, in the relatives of patients with ASD, compared to controls15, but familial correlations and heritability have never been assessed for both steps of the melatonin synthesis pathway in families with ASD.Hyperserotonemia is one of the most replicated endophenotypes in ASD17. NAS is an agonist of melatonin receptors and activates TrkB in mice, a receptor of the brain-derived neurotrophic factor (BDNF), in a selective and circadian manner19. Melatonin is a pleiotropic neuroendocrine molecule essential for synchronizing circadian and seasonal rhythms, as well as sleep/wake cycles, but also displays antioxidant, neuroprotective, or immunomodulatory effects22. Biochemical alterations of this pathway could thus be related to the core symptoms of autism or the comorbidities such as cognitive problems, epilepsy, sleep and gastrointestinal disorders observed in ASD25.Serotonin is involved in a wide range of central processes, such as brain development, emotion, learning, memory or cognitive functions2), defined as the ratio of total genetic variance  to phenotypic variance, or high narrow sense heritability (h2), reflecting only the additive part  of the genetic contribution to the phenotypic variance (Supplementary Note). Several studies in humans and in animal models have demonstrated relatively high heritability for serotonin28 and melatonin32. In humans, serotonin narrow sense heritability estimates range from 0.2 to 0.5133 and urinary melatonin narrow sense heritability estimate was 0.53 in families with acute intermittent porphyria32. To our knowledge, NAS, AANAT and ASMT heritability have never been investigated. In this study, we estimated the narrow sense heritability of all five quantitative traits  in 717 individuals including 213 children with ASD, 364 parents, 128 unaffected siblings and 12 other relatives   for each biochemical parameter: hyperserotonemia, increased platelet NAS, and deficit in platelet ASMT, platelet AANAT and plasma melatonin  with a mean age of 31.3 years and 59.3% males (425/717). As frequently observed in ASDRegarding the distribution of the biochemical traits within pedigrees, different categories of families could be determined Fig. . We obseWe first calculated the correlation coefficients for parent-offspring (P-O), sibling-sibling (S-S) and father-mother (F-M) pairs Table . When alWe then estimated the heritability of each trait. When all individuals were taken into account, the narrow sense estimates of heritability (reflecting additive effects) were all significant , as previously reported15. When only children with ASD were included, these phenotypic correlations were significantly different from 0  . Regarding genetic correlations, two negative genetic correlations were significantly different from 0 in children with ASD  and in unaffected children, only one genetic correlation was significant (NAS-ASMT: ρG = −0.90)  and for ASMT-melatonin (ρE = 0.48) in children with ASD  Fig. . For una90) Fig. . These gASD Fig. . In concASD Fig. .Figure 336. These processes are closely related to light-dark cycle39 and their regulation might depend on environmental factors, such as sleep-wake cycle and artificial light exposure. Thus, synchronization could be observed between parents that share daily habits and life rhythms.Very few heritability estimates for serotonin and melatonin are available for humans in the literature Table  and thiset al.27 in an inbred founder population of Hutterite families. They found respectively 0.51 and 1.0 for narrow and broad sense heritability, suggesting a very strong genetic influence with both additive and dominance components. Our estimation of serotonin narrow sense heritability was lower (0.31) than the one reported by Abney et al., but very similar to the one obtained in a large cohort of 866 monozygotic and 878 dizygotic unaffected twin pairs  ranged between two previous estimates32. Wetterberg et al. (1983) estimated melatonin heritability to 0.53 in 107 families with acute intermittent porphyria32. In contrast, a twin study measuring late night plasma melatonin in nine monozygotic and 11 dizygotic twin pairs, reported a high monozygotic correlation (rMZ = 0.928) and a high dizygotic correlation (rDZ = 0.867)31. Using these correlations and the Falconer’s formula (H2 = 2(rMZ - rDZ)), the heritability for melatonin would be 2(0.928-0.867) = 0.12.We then estimated the heritability of the five traits. In the literature, the first estimate of blood serotonin heritability was obtained by Abney  lower 0.1 than thAll the five traits studied here are not expected to be independent since they belong to the same metabolic pathway. Using a bivariate approach, we estimated pairwise phenotypic, genetic and environmental correlations in samples including only children with ASD or only unaffected children. In both groups, phenotypic correlations appeared to be particularly high for the last step of melatonin biosynthesis pathway  Fig. . Therefo40. Another limitation is the absence of analyses in the pineal gland. Finally, our estimations for unaffected children might not reflect the heritability the melatonin synthesis variability in the general population. Nevertheless, for serotonin and melatonin, our heritability estimates are very similar from those obtained in previous studies  at the Institut Pasteur in Paris (France) approved the study. Methods were performed in accordance with the relevant guidelines and regulations. Written informed consents were obtained from all participants. For the patients who were unable to consent for themselves, a parent or legal guardian consented to the study on their behalf.10. All the subjects were recruited into the Paris Autism Research International Sib-pair (PARIS) study. The ASD diagnosis was based on clinical expert assessment including the Autism Diagnostic Interview – Revised (ADI-R)45 and the Autism Diagnostic Observation Schedule (ADOS)46. Intellectual Quotient (IQ) was measured using an age-appropriate Wechsler scale. For the most severe and/or non-verbal patients, the Raven’s Standard Progressive Matrices and the Peabody Picture Vocabulary test were used.Clinical evaluations of patients with ASD, their relatives and control subjects have been detailed previously14. Subjects were asked to avoid food with high content of tryptophan and/or serotonin two days before blood sampling and individuals receiving exogenous melatonin were not included in this study. Melatonin was measured in plasma using a radio-immunoassay  according to the manufacturer’s instructions. Whole-blood serotonin  was measured by high-performance liquid chromatography47. NAS, as well as enzyme activities of AANAT and ASMT were determined in platelets by radio-enzymology48. Patients who were receiving melatonin for treatment of sleep disorders were not included in the analyses. Only pedigrees with both parents and at least one child were included in the following analyses. The overlap between the biochemical data for serotonin, AANAT, NAS, ASMT and melatonin is illustrated in Supplementary Fig. 15.Blood samples were collected in the morning, between 8:30 and 10:30 as described previously49. Because some of the studied traits were not normally distributed, nonparametric statistical tests (Wilcoxon rank-sum test) were preferred to compare groups of individuals. For familial correlation and heritability analyses, serotonin, ASMT and melatonin values were logarithmically transformed in order to conform more closely to a normal distribution  7.2.5 55, when their effect as covariates  were significant at the threshold of P < 0.1. Individuals at more than three standard deviations (SD) from the mean were considered as outliers and were removed. Depending on the biochemical trait and the subgroup considered, the number of outliers was always very low, ranging from 0 to 7  and R software56. For each relative pair types available in the sample pedigrees, FCOR calculates sibling-sibling (S-S), parent-offspring (P-O) and father-mother (F-M) familial correlations with their asymptotic standard errors. S.A.G.E then tests the difference of the correlation coefficients from 0 using Fisher’s z-transformation.Parent-offspring (P-O), sibling-sibling (S-S) and father-mother (F-M) correlations were measured for the five biochemical traits using the Family Correlations (FCOR) module of the Statistical Analysis for Genetic Epidemiology (S.A.G.E.) 6.3 software package Narrow sense heritability was estimated using the variance component-based program SOLAR 7.2.5 with a maximum likelihood estimation method and polygenic models. When the effect of the covariates  was significant (P < 0.1), relative proportion of variance explained by known covariates was estimated and they were included in the model.57. The trait pairs included all pairwise combinations and the same covariates (age and sex) significant at the threshold of P < 0.1 were used. Three parameters were estimated for each pair of traits: the additive genetic correlation (ρG), the shared environmental correlation (ρE) and the total phenotypic correlation (ρP) (Supplementary Note).SOLAR can extend the variance component model to a bivariate analysis that maximizes the model for two dependent traitsFamilial correlations and univariate heritability analyses were first performed on all individuals, including parents and their affected children as well as their unaffected children (Supplementary Fig. Supplementary Information