This population was used to investigate whether GS could be enhanced by borrowing information from the genetic basis and genotype-by-environment (G × E) interaction. The results showed that: 1) fitting the top four large-effect SNPs as fixed effects could increase prediction accuracy, including three minor-effect SNPs explaining less than 10% phenotypic variance; 2) the increase of prediction accuracy when fitting large-effect SNPs as fixed effects was related to the decrease of genetic variance; 3) generally, the GS model fitting large-effect SNPs as fixed effects and G × E component enhanced GS. Therefore, we propose fitting large-effect markers as fixed effects and G × E effect for crop breeding projects in order to obtain accurately predicted phenotypic data and conduct efficient selection of desired plants.The popularity of genomic selection (GS) has increased owing to its prospects in commercial breeding. It is necessary to enhance GS to increase its efficiency. In this study, a maize BC Plant quantitative genetics is a burgeoning field, enabling the identification of a great number of quantitative trait locus/loci (QTL) and genes in crops. The QTL or gene information (including its position and effect) should be summarized and transferred to molecular markers to better serve crop breeding , 2. The GS entails the prediction of genomic estimated breeding values (GEBVs) of a validation population based on a training population, for which both phenotypic and genotypic data are available . Factorsy = Xβ+Zu+ε, which is composed of fixed effect β and random effect u. Modifying the fixed and random effects might improve GS models. For example, a simulation study found that fitting major-effect SNPs as fixed effects could enhance genomic prediction [1 plants [Examining of the components of GS models may provide insight into improving the PAs of GS models. In an rrBLUP model, the linear model is ediction , 14. A s1 plants . TherefoThe use of additional random variables might be helpful in enhancing the prediction of GS models. As suggested by a study on wheat, the PA of a GS model including a genotype-by-environment (G × E) effect was higher than that of other GS models . In anot1F3:4 families were constructed using elite inbred lines. Meanwhile, genotypic and phenotypic data of the 481 families were obtained. The objectives of this study were to investigate whether fitting large-effect SNPs as fixed effects could increase the PAs of GS models, and whether modeling G × E interaction could increase the PAs of GS models. Afterward, we assessed the performance of the GS models fitting large-effect SNPs as fixed effects and G × E interaction. This analysis would provide insight into improving the PAs of GS models using available phenotypic and genotypic data.In this study, 481 maize BC1 plants were backcrossed to PH4CV to produce the BC1F1 seeds. Each BC1F1 plant was pollinated with bulked pollens collected from at least ten other BC1F1 plants in the summer of 2014 in Shunyi, Beijing. The offsprings of these BC1F1 plants were defined as bulk-BC1F2. In the summer of 2015 in Shunyi, Beijing, forty-three bulk-BC1F2 families were sown, with each family in a one-row plot. Three plants in each row were self-pollinated to produce the BC1F3 seeds. In the winter of 2015 in Sanya, Hainan, 481 BC1F3 plants from three BC1F2 ears sown and self-pollinated to produce 481 BC1F3:4 families. The flowchart for the construction of materials used in this study was demonstrated in 1F3:4 families were sown in Shunyi, Beijing, and Changji, Xinjiang, in the summer of 2016 and 2017, the four environments were identified as 16BJ, 17BJ, 16XJ and 17XJ, respectively. In each environment, the BC1F3:4 families were planted in a randomized complete design with two replicates. Within each replicate, each family was sown in a one-row plot. The row space was 50cm and the distance between two neighboring plants was 25cm. DA was recorded when 50% of the plants in each plot reached anthesis. The phenotypic data of DA are included in A biparental population was constructed using elite inbred lines Zheng58 and PH4CV. Zheng58 is the female parent of Zhengdan958 and PH4CV is the male parent of Xianyu335. Zhengdan958 and Xianyu335 are popular hybrids in China , 22. The1F3:4 families were estimated following the model:yijm is the phenotype of the ith  genotype in the jth  environment, the mth  replicate effect was nested in each environment. μ is the overall mean, gi is the genotype effect, ej is the environmental effect, geij is the G × E effect, δj)m of the 481 BCage lme4 .H2), all variables were treated as random effects to estimate their variances using the above model, which was fitted using R package lme4 [H2 is [Ne is the number of environments, and r is the number of replicates.To calculate broad-sense heritability on an entry-mean basis , M is the genotype matrix, and pi is the minor allele frequency of locus i [GWAS was performed using the R package sommer  followin formula :K=WW′2∑ locus i .10 (P) value to find the SNPs with the largest effects. The 50 SNPS were fitted in a multiple linear model, from which SSreg and SStol for each SNP were computed. Here, SSreg is the sum of square of each selected SNP, SStol is the sum of square of the linear model. Phenotypic variance explained (PVE) of each SNP was calculated by dividing SSreg into SStol [Considering that flowering time was controlled by a small number of QTL in most biparental populations , we seleto SStol .y is the BLUEs, β is a matrix containing the fixed effects, u is the genetic effect treated as a random effect with ε is the error term with the distribution K was calculated according to a previous report [X and Z are the corresponding design matrixes. The above model was fitted using R package BGLR, Gaussian processes (RKHS) model was used for estimating the variances of random effects. The number of iterations and burn-in were set to 20,000 and 5,000, respectively [The BLUEs were used to test how many large-effect SNPs should be used as fixed effects. PA, calculated as the correlation coefficient between predicted and observed phenotypic data, was obtained by running 100 five-fold cross validations (CVs). The linear mixed model was as follows :y=Xβ+Zus report . X and Zβ included the intercept and the effects of the large-effect SNPs, the genotypic data of the large-effect SNPs were added as columns of the X matrix. Meanwhile, the top SNPs were removed from overall markers when calculating K matrix [t-test analysis was used to test whether fitting one more SNP as fixed effect could increase PA by comparing the 100 PAs calculated by fitting top n SNPs with the 100 PAs calculated by fitting top n-1 SNPs (n≧1).When the top large-effect SNPs were fitted as fixed effects, K matrix . Two-tait-test analysis revealed that fitting the top four large-effect SNPs as fixed effects was optimal. To test the effect of adding the four large-effect SNPs on PA, four randomly-selected markers were chosen as fixed effects and PA was calculated correspondingly. This process was repeated for 200 times, then the 200 PAs were compared with the PA calculated using the four large-effect SNPs as fixed effects.The above To calculate the PA of MAS using the top four large-effect SNPs, the four SNPs was fitted in a multiple regression model using the lm function in R. The phenotype was estimated using the predict function . The PAsyi is a vector of phenotypic data in the ith environment, μi is the overall mean, βi is a vector of the marker effect, X is the genotype matrix, and εi is the residual.The SE model can be expressed as:yi is the phenotype in the ith  environment, μi is the overall mean in the ith environment, Xi is the genotype matrix, and εi is the residual error.In this model, the marker effect of each SNP in all environments is assumed to be constant, and supposing that we have n environments , 34, 35,yi and μi were the same as those in the A-E model, marker effect β was decomposed into two parts, a constant main effect β0 and the environment-specific effect βi. The mixed linear model is:In the G × E model, The three environment models were analyzed in the R package BGLR . The codThe variance components were estimated by fitting the full data set to each of the three models . The full data were scaled to standard normal distribution with mean and variance set to zero and one, respectively. In all cases, the number of iterations and burn-in were set to 20,000 and 5,000, respectively.In the SE analysis, prediction accuracy was calculated using 100 five-fold CVs.In the multiple environments GS models (the A-E and G × E models), two different CV schemes , the families flowered earlier in 17BJ  values were selected and fitted using a multiple linear regression model, then PVE of each SNP was calculated. Chr3_159867173, an SNP on chromosome 3, had the largest PVE of 11.88%, followed by Chr2_56238969, Chr9_154782803 and Chr3_23119818, explaining 7.52%, 4.81% and 4.59% of total phenotypic variance, respectively  was calculated to demonstrate the effect of fitting the four large-effect SNPs as fixed effects. For the SE model, it was demonstrated that the PA increased when the four large-effect SNPs were fitted as fixed effects for each environment . We alsoWhen comparing the two multi-environment models (the A-E and G × E models) without fitting any SNP as a fixed effect, the G × E models had better performance than the A-E models in ten of the twelve cases for the CV1 scheme, and in eight of the twelve cases for the CV2 scheme . When coBecause both fitting large-effect SNPs as fixed effects and modeling G × E interaction could increase PA, it was assumed that the best prediction could be achieved using the models including both of the two factors. By looking through each row in With the fast development of genome sequencing technology and the continual decreasing of the genotyping cost, efficient selection is becoming increasingly important for any commercial breeding programme. GS can increase breeding efficiency by making prediction at the seedling stage as soon as DNA of the prediction population was available, thus help breeders to exclude undesired genotypes. GS could also increase breeding efficiency by making the best prediction and selecting the desired plants at the decision-making stage of a GS breeding programme. This study was designed to examine how to make the best use of available genotypic and phenotypic data to make the best prediction by including additional components to the GS models. The analysis in this study suggested that, compared with the use of crude GS models, manipulating existing data using statistical approaches enhanced genomic prediction without increasing any cost.The finding that using known genetic loci as fixed effects could increase PA highlighted the importance of obtaining and assessing these data , 38. Thehttps://www.maizegdb.org/data_center/map). These regions contained consensus QTL according to QTL meta-analysis [Our analysis showed that fitting large-effect SNPs as fixed effects enhance GS. The prerequisite is that each of the large-effect SNPs should be in linkage disequilibrium with a real QTL. The four SNPs were in the chromosome regions of maize bin 3.05, 2.04, 9.07 and 3.04 according to ISU Integrated IBM 2009 Click here for additional data file.S2 FileIn the data file, 1, 0, and -1 represented homozygous PH4CV, heterozygous, and homozygous Zheng58 genotypes, respectively.(ZIP)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.S2 Fig1F3 plant, the proportion of each of the three genotypes  was calculated, generating 481 values for each of the three genotypes. The distribution was plotted using the data of the three genotypes with each containing 481 values.For each BC(TIF)Click here for additional data file.S3 FigP < 0.001 level. P value were determined by two-tailed Student’s t-test.The genetic variance (a) and residual variance (b) for each environment were dissected with or without the four large-effect SNPs as fixed effects. PA was also calculated for each environment with or without the four large-effect SNPs as fixed effects (c). Fixed and Random indicated fitting the four large-effect SNPs as fixed effects and four randomly-selected SNP as fixed effects, respectively. *** on top of gray column indicated significantly different from its left column at (TIF)Click here for additional data file.S4 FigP < 0.001 level. P value were determined by two-tailed Student’s t-test.GWAS was performed using the phenotypic data in each environment and the top four SNPs were identified accordingly. For each environment, PA was calculated with or without the top four SNPs as fixed effects. Fixed and Random indicated fitting the top four SNPs as fixed effects and four randomly-selected SNPs as fixed effects, respectively. *** indicated significantly different at (TIF)Click here for additional data file.S1 TableCV1 and CV2 mean two cross validation schemes, Env1, Env2, ……, Envn means there are n environments, NA means phenotype was not evaluated in the specific environment, N means there are N lines.(DOCX)Click here for additional data file.S2 TableThis table was the summarized according to (DOCX)Click here for additional data file.


RRM1 gene), which is known to regulate telomere maintenance in yeast. We also highlight the importance of multivariate approach and the limitations of existing tools for the analysis of TL as a polygenic heritable quantitative trait.Telomere length (TL) regulation is an important factor in ageing, reproduction and cancer development. Genetic, hereditary and environmental factors regulating TL are currently widely investigated, however, their relative contribution to TL variability is still understudied. We have used whole genome sequencing data of 250 family trios from the Genome of the Netherlands project to perform computational measurement of TL and a series of regression and genome-wide association analyses to reveal TL inheritance patterns and associated genetic factors. Our results confirm that TL is a largely heritable trait, primarily with mother’s, and, to a lesser extent, with father’s TL having the strongest influence on the offspring. In this cohort, mother’s, but not father’s age at conception was positively linked to offspring TL. Age-related TL attrition of 40 bp/year had relatively small influence on TL variability. Finally, we have identified TL-associated variations in ribonuclease reductase catalytic subunit M1 ( Accordingly, changes in telomere length (TL) have been linked to development of age-related diseases and cancers9.The terminal regions of linear human chromosomes are composed of telomeres - sequences of tandem TTAGGG repeats normally stretching around 10–15 kb in length. They protect the chromosomes from degradation and end-to-end fusions10, genetic12 and environmental14 factors, and the tissue under study16. Initially, the idea of telomere length dependence on chronological age was based on the fact that in most somatic cells, telomeres get shorter over an individual’s lifespan, mostly due to telomere end-resection that occurs after each round of DNA replication18. However, while telomere attrition is associated with cellular senescence, it’s not completely clear how TL is linked to organismal ageing19. Particularly, inverse correlation of TL with age has been shown to be true for some21, but not for all populations23. Our previous study on South Asian genomes has identified no relationship with age in this population23, confirming previous observations suggesting that age-dependency of telomere length might be population-specific22.TL regulation is a complex phenomenon that depends on a number of variables, such as age12. Single nucleotide variations (SNVs) in several loci, such as telomerase components TERT and TERC, and others  have been linked to TL25. For many loci, however, the identified associations with telomere length are either irreproducible in other cohorts or show population-specificity26. Additionally, a number of environmental factors, such as stress, exposure to oxidative agents, smoking, alcohol consumption and lifestyle, all affect telomere attrition rate14.Genetic factors influencing TL have been identified by multiple genome-wide association studies, both in healthy and in diseased populations27, or mother’s28 TL. Additionally, paternal (PAC) and maternal (MAC) ages at conception also affect TL in the offspring29. This has mostly been shown for PAC, and explained by relatively longer TL in the sperm of older males31. A recent study has simulated this effect across many generations and has suggested this as a mechanism for adaptation to cancer32.Finally, while telomere length regulation and environmental factors affect TL variability in a lifetime of a single individual, TL variability between individuals is also largely explained by inheritance of parental telomeres and variable TLs at birth, with a stronger link between offspring and either father’s25. Involvement of multiple genetic and environmental factors and heritability of TL largely complicates investigation of TL regulation and necessitates multi-factor analysis. We have previously studied TL in the South Asian population, based on whole genome sequencing (WGS) data. In this population, we have identified TL-associated loci in the ADARB2 gene, but did not reveal relation of TL with age23. That dataset, however, did not allow for analysis of TL inheritance patterns. Here, we make use of whole-blood derived DNA sequencing data generated by the Genome of the Netherlands (GoNL) project that involves WGS and SNV datasets from 250 families, comprising trios of a mother, a father and a child. Importantly, this dataset was annotated not only for ages of individuals at the time of data collection, but also for parental ages at conception33. We have measured mean telomere length (MTL) from WGS data using Computel34, and have performed a number of regression analyses to identify age association and inheritance patterns of MTL in the Dutch population, and to reveal MTL-associated genomic loci.Overall, based on their importance in healthy ageing and in regulation of basic cellular functionality, telomeres are being extensively studied for their role in development of age-related diseases, cancers and reproduction33. They had identified a subtle substructure of the population according to geographical origin of the individuals . However, there were no distinct clusters and the first and the second principal components explained very little variation in the genotype data . Therefore, we have performed downstream association analyses with the assumption of a homogenous population.Principal component analysis on SNVs was previously performed by the GoNL consortiumMTL ~Age + Sex) on all study subjects, including the MTL of parents and children, has shown that age is negatively correlated with MTL , with an estimated attrition rate of ~ 40 bp per year, in agreement with prior observations35 , this is likely due to age differences, as women were generally younger than men . Indeed, this difference was gone after adjustment for age by testing the mean difference in MTLs between males and females in each age group .In the studied population, MTL ranged from as low as 1.7 to 12 kbp in length. Multiple linear regression (MLR) analysis , paternal MTL (fMTL), as well as mother’s and father’s ages at conception (MAC and PAC). Pairwise correlation analysis for all these predictors , rs185870422 (non-coding region on chromosome 5) and rs1042858 (RRM1)  Fig. . The curMTL ~Age + mMTL + fMTL + MAC + PAC + SNV. Here each SNV takes on values from 0 to 2, depending on the number of dominant alleles in a child’s genotype. These tests revealed only six SNVs residing within the DSCAM gene, associated with offspring MTL after adjustment for all the variables included in the MLR model. With this model, only two top SNVs from Plink association tests had significant association p values (unadjusted) (rs185870422 (chr5q) and rs1285767 (CCDC88C)). The results for these two SNVs and DSCAM were further confirmed by Plink linear regression test performed on the population of children only. Isolated Plink linear regression tests on the parents’ population did not reveal any significant quantitative loci after multiple comparison test adjustment . Those, however, do not have known roles in telomere length regulation.The next locus identified by Plink-based family tests, as well as by Plink linear regression analysis on parent/children groups was rs185870422, residing in a non-coding region on the q arm of chromosome 5. Interestingly, no individual had a homozygous genotype for the minor allele of this SNV. However, the heterozygotes had consistently lower MTL (by 1000 bp) than homozygotes for the major allele , in contrast to CCDC88C, which had only two SNVs with raw p values < 10−5 , but, it was only identified during Plink family association tests and separate regression tests on parents  that may affect nonsense-mediated decay.The 0−5 Fig. . The rs1nts Fig. . HomozygDSCAM) gene), which encodes an immunoglobulin superfamily member, is involved in axon guidance and is a candidate for Down syndrome and congenital heart disease40. The amount of homozygotes for the minor alleles of these SNVs was low, and their effect on TL was only seen in children. In the MLR inheritance model, the regression coefficient for these SNVs was higher (0.67) compared to all other variables (mMTL had a correlation coefficient of 0.42 after addition of these SNVs). However, addition of these SNVs to the MLR model increased the percentage of explained variation in offspring MTL by only 6%  were all linked and resided within intronic regions of the Down Syndrome cell adhesion molecule  project, which included 250 Dutch family trios with associated meta-information on sex, age, paternal and maternal ages at conception. We have used computational means for estimation of telomere length and have performed a series of regression and quantitative trait association analyses to reveal inheritance patterns of telomeres and to identify genetic variations affecting their length.41. However, whether length inheritance occurs stronger through paternal27 or, as in our case, through maternal line28, is still a controversy.While age plays a role in telomere length variation during a lifetime, our analysis show that its effect is weaker compared to inheritance factors, namely parental telomere lengths, with mother’s telomeres being the strongest predictors of offspring MTL. The observed highly heritable nature of telomeres is in agreement with prior studies performed on twins, showing that lymphocyte telomere length at birth largely determines inter-individual variation, while factors regulating telomeres during lifetime are of less importance29. This association has been explained by positive selection of sperm cells with longer telomeres with increasing age in males31. There is limited evidence on MAC effect on offspring TL due to high correlation between biological ages of partners and the difficulty to assess TL dynamics in healthy female oocytes36. Most studies perform regression analysis to support the hypothesis of PAC association with TL and monitor changes in PAC estimates before and after adjustment for MAC40. Our observation of positive association of MAC with offspring MTL was also confirmed after partial correlation analysis. It is a matter of future investigations to find out the causes for such a link: whether MAC directly affects TL in oocytes or is indirectly involved in TL regulation in the embryo.Our results also show positive association of maternal age at conception (MAC) with offspring MTL. Previous studies have largely linked paternal age at conception (PAC) with offspring TL32, those could also depend on inheritance of genetic factors regulating TL. Identification of telomere-related genetic variants in our cohort was not trivial, due to multiple factors of TL variability that should be accounted for when performing such studies in families. In particular, family association tests implemented in Plink did not allow for inclusion of age as a confounder, while Merlin did not account for heritability of telomeres as quantitative traits. Furthermore, inclusion of genotypes for each SNV into our multiple linear regression model for TL inheritance did not account for family structure. These limitations, along with the small sample size, reduced the statistical power of our tests. Nevertheless, the only consistent hit – RRM1 – was identified by Plink-based analysis, where age was the missing confounder. This once again confirmed the relatively small influence of age on TL variability among other factors.All in all, in the studied population, offspring MTL is positively affected by maternal and paternal MTL and MAC. While these correlations could partially reflect mendelian inheritance of telomeresRRM1 encodes the catalytic subunit of ribonucleotide reductase (RNR), an enzyme essential for dNTP synthesis and DNA replication and repair processes42. In humans, the role of RRM1 in telomere length regulation is not established yet. However, it is known that the yeast ortholog of this gene, Rnr1, is required for telomerase functionality, possibly via facilitation of telomere synthesis via local temporary boosts of dNTPs43. Our data, thus, suggests that RRM1 may also be involved in telomere length regulation in humans. Importantly, it is known that in humans, RRM1 is involved in regulation of cellular proliferation, migration and cancer progression, presumably due to its role in DNA replication44. It is also targeted by certain chemotherapeutics or used as a biomarker to predict their effectiveness46. Furthermore, polymorphisms and altered expression of this gene have been linked to increased susceptibility to certain cancers47. RRM1’s role in cancer, however, is only discussed in terms of its involvement in DNA synthesis, and not in terms of telomere length regulation. This study, thus, may serve as a basis for extending the functional studies on RRM1 to telomeres as well.RRM1 with MTL and prior studies on its ortholog in yeast, suggest possible implications for this gene in telomere biology in humans.All in all, the well-structured and richly annotated dataset provided by the Genome of the Netherlands project has allowed us to reveal several aspects of telomere length inheritance and variability. We have shown that parents’ telomere lengths and mother’s age at conception play an important role in defining telomere length variability among individuals, along with age and genetic factors. Additionally, our results on association of We also highlight the limitations of currently available computational tools for performing genome-wide association studies on heritable quantitative traits in family trio datasets. Development of these tools and emergence of sequencing datasets on family trios from other populations will further allow for delineating common and population-specific factors involved in telomere length regulation.http://www.nlgenome.nl/, European Genome-phenom Archive, EGAS00001000644) previously generated by the Genome of the Netherlands Project (GoNL). The WGS data had been produced on Illumina HiSeq. 2000 platforms with 12x coverage. It consisted of 748 Dutch individuals forming trios of a mother, a father and a child. We also had information about their age and sex, as well as the ages of conception for the mothers and the fathers.We make use of secondary analysis of whole genome sequencing (WGS) data (33.Single nucleotide variation (SNV) data was obtained from the release 5.4 of the GoNL project, where variant calling had been performed on hg19 assembly of the reference genome by the GoNL ConsortiumWe have accounted for SNV data passing the filters with VCFtools version 0.1.14, and have removed SNVs with minor allele frequency <5% , those with missingness values of <10%  and those not passing Hardy-Weinberg equilibrium significance threshold of 0.001  using Plink version 1.9. Overall, genotype information for 5352580 SNVs for 748 individuals were included in the downstream analyses.34. Computel determines MTL by alignment to a special telomeric reference and by comparing the coverage at the telomeric reference to the coverage at the genome reference34. The WGS data contained multiple runs per individual, and we have taken the median MTL per individual across multiple runs.We have calculated mean telomere lengths (MTL) from whole genome sequencing data using Computel version 0.4 with its default parametersMultivariate linear regression analysis was performed to evaluate the correlation between MTL and age and sex in the studied population. Another MLR model was analyzed to study the inheritance of maternal and paternal MTL, as well as the role of MAC and PAC on offspring MTL. Two of the families with missing data for the mother were removed, and two families with discordant age differences at the time of data collection and at conception were also discarded. Overall, MLR were done on 246 families. A set of pairwise regressions on the predictors were performed to estimate dependence between variables, and interaction terms were introduced for correlated predictors. The MLR models were tested by sequential introduction of predictors and interaction terms. The best model was chosen based on maximization of the adjusted R square term: ultimately, from the three best models with similar adjusted R squared values the simplest one was chosen. Partial correlation analyses were performed with R package ppcor and were used to estimate the influence of each predictor when accounting for the rest of the predictors in the model.48 and Merlin 1.1.249, as well as with a series of MLR models. Both, Merlin and Plink use the between/within model implemented in the QTDT package50. However, Merlin uses a maximum likelihood variance component model to correct for family structure, while Plink uses a procedure based on permutations.Association of single nucleotide variations (SNV) with MTL was performed with family based association tests for quantitative traits implemented in Plink 1.9We ran Plink with the qfam-total option for identification of quantitative associations with adjustment for sex, and with 100 000 000 permutations to adjust for family structure. One drawback of this approach is that Plink does not handle covariates (other than sex) for family associations, which did not allow to adjust for age. As age was affecting telomere length in our analysis (see Results), we also ran a number of alternative tests.Separate linear regression tests for parents and children were performed with Plink quantitative association tests, using an additive model for variants and treating age and sex as covariates.https://github.com/joepickrell/1000-genomes-genetic-maps). Only the coding SNVs were included in these tests, and those SNVs with mendelian errors were marked as missing. While Merlin accounted for age, it had the disadvantage of not accounting for quantitative trait inheritance, i.e. inheritance of telomere lengths from parents to offspring, as well as being limited to variants for which recombination rate information is available.To perform family association tests accounting for age, we used Merlin. For this, we have downloaded genetic maps of 1000 genomes project variants generated by Hapmap 2 project that involved average recombination rates in three different populations   analysis by incorporating an additive model of child’s genotype for each variant  into the MLR model of telomere length inheritance obtained from MLR analysis described above. While these regression models do not account for variant linkage and thus had lower statistical power, they do consider telomere length inheritance, age and family structure.Supplementary document 1Supplementary datasheet 1Supplementary table S1


Solanum pennellii Introgression Line (IL) population can be exploited to identify favorable alleles that can improve yield and fruit quality traits in commercial tomato varieties. Over the past few years, we have selected ILs that exhibit increased content of antioxidant compounds in the fruit compared to the cultivar M82, which represents the genetic background in which the different wild regions of the S. pennellii ILs were included. Recently, we have identified seven sub-lines of the IL7-3 accumulating different amounts of antioxidants in the ripe fruit. Since the wild region carried on chromosome 7 induces a low fruit production in IL7-3, the first aim of the present work was to evaluate yield performances of the selected sub-lines in three experimental fields located in the South of Italy. Another aim was to confirm in the same lines the high levels of antioxidants and evaluate other fruit quality traits. On red ripe fruit, the levels of soluble solids content, firmness, and ascorbic acid (AsA) were highly variable among the sub-lines grown in three environmental conditions, evidencing a significant genotype by environment interaction for soluble solids and AsA content. Only one sub-line (coded R182) exhibited a significantly higher firmness, even though no differences were observed for this trait between the parental lines M82 and IL7-3. The same sub-line showed significantly higher AsA content compared to M82, thus resembling IL7-3. Even though IL7-3 always exhibited a significantly lower yield, all the sub-lines showed yield variability over the three trials. Interestingly, the sub-line R182, selected for its better performances in terms of fruit quality, in all the trials showed a production comparable to that of the control line M82. A group of species-specific molecular markers was tested on R182 and on the parental genotypes in order to better define the wild genomic regions carried by the elite line R182. In these regions three candidate genes that could increase the level of AsA in the fruit were identified. In the future, the line R182 could be used as pre-breeding material in order to obtain new varieties improved for nutritional traits.The  Solanum lycopersicum L.) is one of the most important and most extensively used crops worldwide and a major component of the Mediterranean diet, even if fruit quality and flavor have deteriorated in recent years  of QTLs (quantitative trait loci) affecting morphology, stress tolerance, plant yield, fruit color and metabolism  carrying a wild region on chromosome 7 and exhibiting high levels of antioxidants and °Brix in the fruit  to understand the effect of the wild alleles mapping in the region IL7-3 on yield and fruit quality traits. Various fruit quality traits and yield performances were here analyzed in the seven different IL7-3 sub-lines in three different experimental fields located in the South of Italy and in two different years. These analyses allowed us to identify one elite sub-line with improved qualitative traits. A group of gene-targeting markers was also tested on the selected sub-line and the parental genotypes in order to better define the wild genomic regions carried by the elite line. Altogether, this work allowed us to identify the genomic region that has major effects on different quality traits and to select one superior genotype that could be used in breeding schemes in order to obtain new varieties with improved nutritional traits, such as higher ascorbic acid (AsA) content in mature fruit.We previously identified one he fruit , 2013. Hhe fruit . Afterwahe fruit . The aimS. pennellii in S. lycopersicum IL7-3 (accession LA4102), previously selected in our laboratory for high content of AsA in the fruit , the he fruit , and sevhe fruit , and fiv−1) was applied to the soil before transplanting. Plowing followed by one or two milling were used as tillage treatments. In absence of rain plants were irrigated as required (2-3 times per week). Levels of N (190 kg ha−1), P (25 kg ha−1), and K (20 kg ha−1) were maintained during cultivation via fertirrigation.For two years (2016-2017), plants at a four leaf-stage were transplanted in open field in three different locations using single rows with plant spacing of 40 cm × 50 cm. Soil texture was classified as sandy-loam in all the experimental fields and details about soil composition are reported in per genotype and 10 plants per replicate was assessed in all the fields. Three plants per genotype were used for measuring traits related to fruit set (FS) and number of flowers/inflorescence (NFL). Data recorded as number of fruit per plant (NFR), fruit weight (FW), and yield per plant (YP) were collected from all the plants of each genotype.Data collected in the year 2016 are related to one field , whereas in the year 2017 data were collected from plants grown in three fields located in the Campania Region . A randomized complete block design with three replicates Tomato fruits were collected at mature red (MR) stage, seeds and columella were subsequently removed, and fruits were ground in liquid nitrogen and stored at −80°C until further analyses.per ripe fruit (six fruits per genotype). The software Tomato Analyzer 3.01 (per genotype to measure the fruit perimeter (FP), fruit area (FA), pericarp area (PA), pericarp thickness (PT), distal (DA), and proximal angles .For each genotype and biological replicate 15 fruits were collected at MR stage to evaluate soluble solids content, firmness, and color. The soluble solids content was measured as °Brix in the homogenized juice from ripe fruit by a refractometer (Hanna), the firmness (FI) of fruit cuticle was measured on ripe fruit by a penetrometer with an 8 mm shore (PCE-PTR200 penetrometer). The color of ripe fruit was assessed as percentage of reflectance (L) and absorbance index (a/b), where a is the absorbance at 540 nm and b at 675 nm, using a Konica Minolta CR-400a, and performing two measures zer 3.01  was used3PO4, 4.6% (w/v) TCA, and 0.6% (w/v) FeCl3] with solution B . The mixture was incubated at 37°C for 40 min and measured at 525 nm by a NanoPhotometerTM (Implen). Three separated biological replicates for each sample and three technical assays for each biological repetition were measured. The concentration was expressed in nmol of AsA according to the standard curve, designed over a range of 0–70 nmol; the values were then converted into mg/100 g of fresh weight (FW).A colorimetric method was used for the AsA determination  with modper sample were analyzed in triplicate.The method reported by t-test was conducted for qualitative and quantitative traits to verify if genotypes were statistically different from the parental line M82. A univariate ANOVA analysis was performed to detect the genotype by environment (GxE) interaction. In order to identify the genotypes with a desirable combination of traits, an evaluation index (EI) was calculated by assigning to each trait a positive (+1) or negative (−1) score depending on its significantly higher or lower value than the control M82. The EI was calculated for yield-related traits and fruit quality-related traits, separately.Data analysis was conducted using the SPSS Software version 23. The Student’s S. lycopersicum (SL3.0 assembly and iTAG3.2 annotation) and the S. pennellii (v2 Assembly) genomes, by investigating the Genome Browser available in the Sol Genomics Network database2. PCR amplification was carried out in 50 μl reaction volume containing 50 ng DNA, 1X of My Taq reaction buffer, 1.0 mM primer and 1 U My Taq DNA polymerase (Bioline). For designing CAPS markers, restriction enzymes suitable to detect polymorphic SNPs between the fragments amplified were found using the tool CAPS Designer available at the Sol Genomics Network2. Amplified and restricted fragments were visualized on agarose gel at different concentrations depending on their expected size.SCAR and CAPS markers were designed in order to estimate the size of the wild region present in the IL sub-line R182. Genomic DNA was extracted from young leaves collected from M82, IL7-3, and R182 using the ISOLATE II Plant DNA Kit (Bioline). Primers for the PCR amplification were designed based on polymorphisms detected in the IL7-3 introgression region between the S. pennellii IL7-3, previously obtained and characterized , but four sub-lines showed levels of FI lower than the two parental lines, and only the sub-line R182 showed a very high level of FI (8.39 kg/cm2). The detection of fruit color in terms of a/b did not show significant differences between M82 and IL7-3, and all the sub-lines showed similar values, except than R176. Differences in the color were detected when measuring the chroma value, which showed a reduction of 12% in IL7-3 compared to the parental genotypes M82. The genotypes R178, R201, and R202 showed chroma values similar to IL7-3  was detected between FA and FW. Also, the micro proximal angle (micro PA) and macro proximal angle (macro PA) were significantly different from M82 in some sub-lines . Only sub-lines R181 and R182 showed all morphological parameters similar to those exhibited by the control genotype M82.Finally, the morphological analysis of tomato fruits evidenced no significant differences for PA and PT , and forFor a general selection of the sub-lines based on all evaluated traits, an EI was assayed, which takes into consideration the scores obtained by each line compared to the control genotype M82. The EI estimated for five productivity and eight fruit quality traits evidenced that the best sub-line in terms of quality and yield score  was R182, which exceeded the control genotype M82 for QS and had the same value for YS, as shown in the scatter diagram of p = 0.657), as well as for NFR (p = 0.359) and YP (p = 0.256). The FW of the genotypes M82 and IL7-3 were significantly different in all the three fields. Differences of FW between the sub-lines and M82 were mainly observed in the Acerra field, where R178, R179, R201, and R202 exhibited a significant reduction compared to M82, confirming data obtained in the year 2016. In all the fields there was around a 50% NFR reduction of IL7-3 fruit compared to M82 . Among the sub-lines, only R179 showed a significant reduction of NFR in all the fields, whereas R181, R182, R201, and R202 exhibited values comparable to M82 in the three environmental conditions tested. Finally, as for yield, IL7-3 showed a significant reduction with respect to M82 in all the fields, whereas the sub-lines R176, R178, R181, and R182 confirmed no differences compared to M82 in all the three trials.In the summer of the year 2017 we restricted the analyses to the most relevant parameters among those measured in the year 2016, with the aim of evaluating them in three different environmental conditions in the South of Italy , 4. As fp = 0.008). Indeed, no differences were observed in Battipaglia, whereas in Acerra four introgression sub-lines showed significantly higher values than M82. As for firmness, the two parental genotypes and most sub-lines showed very similar values in all fields, with a not significant GxE interaction (p = 0.114). The only relevant result was the significantly higher firmness observed in R182 in all cases . Finally, as for AsA, IL7-3 showed significantly higher values compared to M82 in the three fields, whereas most sub-lines showed a high variability, evidencing the presence of a GxE interaction (p = 0.042). Sub-line R182 was the only one showing a higher level of AsA content with respect to M82 in all the three experimental fields. The EI was also estimated on data collected in the year 2017 for the three production  and the three fruit quality traits  evaluated in three different environmental conditions. The scatter diagram   present in this introgression sub-line. The effect on such a different number of traits indicates the great potential of this small introgressed region on chromosome 7. For this reason, the presence of wild/cultivated alleles mapping in this introgressed region was investigated by designing gene-targeting markers, based on the sequencing information deriving from the whole genome of persicum  and S. pennellii , both avosome 7) . In the rphology , it was rphology . OverallS. pennellii introgressed region in R182, a Pyrophosphate-fructose 6-phosphate 1-phosphotransferase (PFP) subunit beta (encoded by the gene Solyc07g049280 corresponding to the S. pennellii ortholog Sopen07g024610) and two Major facilitator superfamily (MFS) proteins (Solyc07g049290/Sopen07g024620 and Solyc07g049310/Sopen07g024640) were identified. These genes could have a role in sugar accumulation affecting °Brix and indirectly also AsA content, being sugars precursors of its biosynthesis (2 and TomExpress3) of these genes, in particular Solyc07g049290, exhibits a typical ripening pattern, with expression increasing until the breaker stage and then decreasing at red ripe stage, indicating as these genes could be active players in processes linked to sugar and AsA accumulation in the fruit.Among the genes mapping in the ynthesis . In partynthesis . MFSs arynthesis . The expRegarding firmness, three genes map in the introgressed region of R182, which are potentially involved in the control of this trait. Genes Solyc07g048085 and Solyc07g048090 encode for the cell wall proteins Fasciclin-like arabinogalactan and the gene Solyc07g049300 encodes for a polygalacturonase, which is a protein potentially involved in cell wall degradation . Furtherpennellii region of 385 Kbp, which exhibit a broad positive effect on nutritional quality and other traits. This result demonstrates that exploiting genetic variation deriving from a wild species could be extremely useful to improve the cultivated tomato, and also that this variation could be rapidly available to plant breeders, since no traits were negatively affected by the wild genomic segment introgressed in the sub-line R182.High-resolution fine mapping investigations in tomato ILs populations were previously carried out to identify loci controlling fruit qualitative traits . For exaRC contributed to metabolic and molecular markers analyses. VR contributed to bioinformatics analysis of the introgressed region. RC and VR drafted the manuscript. AA and FO contributed to growing and evaluating the materials in the fields and in laboratory. MR contributed to the conception of the experiment and critically reviewed the manuscript. AB contributed to the experiment design, to data analysis and interpretation, to draft 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.


The use of a kinship matrix integrating pedigree- and marker-based relationships optimized the performance of genomic prediction in sorghum, especially for traits of lower heritability.Selection based on genome-wide markers has become an active breeding strategy in crops. Genomic prediction models can make use of pedigree information to account for the residual polygenic effects not captured by markers. Our aim was to evaluate the impact of using pedigree and genomic information on prediction quality of breeding values for different traits in sorghum. We explored BLUP models that use weighted combinations of pedigree and genomic relationship matrices. The optimal weighting factor was empirically determined in order to maximize predictive ability after evaluating a range of candidate weights. The phenotypic data consisted of testcross evaluations of sorghum parental lines across multiple environments. All lines were genotyped, and full pedigree information was available. The performance of the best predictive combined matrix was compared to that of models fitting the component matrices independently. Model performance was assessed using cross-validation technique. Fitting a combined pedigree–genomic matrix with the optimal weight always yielded the largest increases in predictive ability and the largest reductions in prediction bias relative to the simple G-BLUP. However, the weight that optimized prediction varied across traits. The benefits of including pedigree information in the genomic model were more relevant for traits with lower heritability, such as grain yield and stay-green. Our results suggest that the combination of pedigree and genomic relatedness can be used to optimize predictions of complex traits in crops when the additive variation is not fully explained by markers. Selection based on dense genome-wide markers has become a revolutionary alternative to traditional genetic evaluations for improving quantitative traits in crops  with quantitative trait loci (QTLs) of interest. Consequently, a major assumption is that the full additive genetic variance can be accurately explained by markers Goddard . When thA) and one depending on a genomic relationship matrix (G). A similar approach based on BLUP integrates pedigree and genomic relatedness into a single matrix. This strategy has been applied in the context of animal genetic evaluations  Moench] is the fifth most important cereal crop worldwide after wheat, maize, rice and barley. Its drought tolerance ability makes it a strategic crop for sustainable grain production in the perspective of climate change and increasing food demand. Early stage breeding of hybrid sorghum involves the development of elite inbred lines, which will be subsequently used as parents of commercial hybrids. The initial selection of superior parental lines is typically based on their additive genetic values estimated from testcross performance trials. Genomic selection could be beneficial for reducing time and field testing resources during the testcross evaluation step, increasing efficiency of hybrid development. Despite the new opportunities offered by GP methods to accelerate genetic progress in sorghum, empirical studies are still limited compared to other crops  or BV of parental lines.The phenotypic records used in this study consisted of 26 testcross performance trials where a total of 646 female lines were tested across 12 locations over a period of 7 years between 2008 and 2014. This trial series comprises a representative sample from a target population of environments covering the main sorghum cropping region in Australia. Phenotypes of 2645 testcross hybrids were used to assess female lines in crosses with one to five different testers. These male parents were chosen to express contrasting levels of yield potential and stay-green capacity . The sequence data generated were then aligned to the most recent version (v3.1.1) of the sorghum reference genome sequence  methodology involving complexity reduction in the genomic DNA to remove repetitive sequences using methylation sensitive restriction enzymes prior to sequencing on next generation sequencing platforms , the ith line × tester hybrid (L × T) and the jth block (B); and random effects for: the kth row (R) and lth column (C). The term f is a smooth function of row (r) and column (c) plot coordinates representing the fitted spatial surface, which simultaneously accounts for global and local trends  of the ith female line crossed with the jth tester in the kth environment, which was fitted by a main line genetic effect (L), a main tester effect (T), a main environmental effect (E) and all possible interactions between these effects. The residual followed eijk ~ N , where R is a diagonal matrix with elements equal to the squared standard errors of each mean yijk estimated by model (1) in the first stage , where R is a diagonal matrix with elements equal to the squared standard errors of genotypic BLUEs from the second stage of phenotypic analysis. This matrix accounts for differences in precision of estimated line means.The prediction models used in our study assume that available SNPs may not explain all additive genetic variances. The general model formulation can be defined as:K is a combined kinship matrix exploiting pedigree and genomic information. This matrix is constructed as K = wA + (1 − w)Gs, where A is the numerator relationship matrix among lines computed from the full pedigree and Gs is a rescaled genomic relationship matrix based on the SNP data (see details below). The weighting factor w represents the fraction of total additive variance G and A are not orthogonal; therefore, the interpretation of w should be considered with caution.Total additive genetic effects were assumed w from 0.1 to 0.8, with increments of 0.1, was explored to assess the impact on predictions. For the sake of comparison, the extreme cases w = 0 and w = 1 were also considered. Note that the latter case corresponds to the traditional pedigree-based model, A-BLUP, which relies only on familial information. Alternatively, assuming w = 0 results in the basic G-BLUP model  and a vector of residual polygenic effects (a), such that g = m + a, with respective variances A and G) to combine pedigree and genomic information, while this information is condensed into a single matrix in K-BLUP; second, under AG-BLUP, the magnitude of w is driven by the data in order to maximize the (restricted) likelihood of the model, as opposed to pre-specified weights used within the K-BLUP method. The performance of AG-BLUP was also compared to that of the best predictive K-BLUP model.An equivalent formulation of the K-BLUP model is as follows:Gs matrix used in our models was rescaled to make it compatible with A in reference to the same base breeding population. The adjustment was based on fitting Gs to A by applying Gs = a + bG, where G is the unscaled genomic matrix as computed with the first method of VanRaden  algorithm as implemented in the mixed model package ASReml-R  were regarded as the realized genetic values of lines and used for validation of prediction models.The quality of predictions from each model was evaluated using a fivefold cross-validation technique. We considered two different strategies for splitting the data into training set (TS) and validation set (VS). These strategies emulate different selection schemes: one based on within-family predictions (W-fam) and one based on among-family predictions (A-fam). In W-fam, 20% of lines from each full-sib family formed the VS, i.e., predicted lines belong to families that were (tested) in the TS. In A-fam, we sampled 20% of whole families to construct the VS, i.e., predicted lines belong to full-sib families that were not present in the TS. With this setting, we examined contrasting levels of genetic relatedness between TS and VS: high for W-fam and low for A-fam. Each splitting scenario was repeated 20 times using the same random seed throughout all models. The line BLUEs from phenotypic analysis (rPA) between predicted additive values yL in the validation set. Bias of predictions was investigated by regressing yL on b = 1 designates an empirically unbiased predictor, while b < 1 indicates inflation of the variance of genotype predictions or overpredictions. The mean squared error of prediction (MSEP) from the linear regression was also measured as an indicator of prediction accuracy, which incorporates concepts of both bias and precision. The evaluation of models was based on average values over the 20 replicates when using within-family or across-family relatedness for prediction. Significance of pairwise differences in predictive ability among prediction models was assessed by the Hotelling–Williams t test (Steiger yL in our case).Model performances were assessed using multiple criteria. In this research, predictive ability was taken as the primary criterion for identifying the best prediction model. However, measures of empirical bias and accuracy were also considered, as they offer complementary information that should be taken into account when evaluating the predictive performance of models. Predictive ability was measured as the Pearson’s correlation  for all traits estimated from BLUP models using only pedigree relationships, using only genomic relationships or combining both sources of information. We also show the influence of scaling the genomic matrix on the estimates of h2. In general, heritabilities varied from relatively low in grain yield to high in the case of plant height. Models using the combined matrix K increased h2 for most traits compared to A-BLUP and G-BLUP. These changes in heritability reflect the ability of the models to capture genetic variation in the breeding population. Note that the weight w used to construct K in each case was defined to maximize the likelihood, being the resulting K-BLUP model equivalent to fitting the model AG-BLUP. Finally, using the scaled genomic matrix Gs in G-BLUP and K-BLUP, increased heritability estimates for all traits relative to the heritabilities obtained using the conventional genomic matrix.Table w) to construct the combined relationship matrix K. Figure w = 0 up to 0.4 ≤ w ≤ 0.6. The use of higher weights caused decreasing trends in rPA for both traits. The largest relative increases in predictive abilities were observed for GY, with K-BLUP achieving 7% and 8% of improvement compared to G-BLUP (w = 0) for within- and among-family predictions, respectively. For PH and FT, rPA was generally maximized by using lower weights (w ≤ 0.2) in both prediction scenarios. Any further increase in w slightly changed rPA within families and was clearly detrimental for among-family predictions. Using a combined pedigree–genomic matrix provided more limited benefits for PH and FT, representing less than 2% of relative gains in rPA over using only marker information.In both prediction scenarios, predictive ability for GY and SG improved as the weight placed on pedigree information increased from w = 0). Moreover, the addition of genealogy information was more effective in reducing inflation of predictions when these were based on among-family relatedness. The only exception was observed for FT, where higher values of w gave more biased among-family predictions.In most cases, placing increasing weights on pedigree relationships reduced bias of predictions relative to predictions based on genomic relationships alone . However, the rescaling did affect the scale of genomic variances, and thus changed heritability estimates . In addition, K-BLUP is likely to produce more stable results when using small training sets since fewer variance components have to be estimated. We applied relatively simple prediction models, but differences in computational burden and stability between AG-BLUP and K-BLUP are prone to increase when more elaborate models are used. For instance, when prediction models include interactions of genotypes with environmental factors or when multi-trait prediction is aimed. Finally, the use of a blended matrix prevents from potential convergence problems resulting from collinearity between pedigree-estimated genetic effects and genomic effects when A and G are fitted separately, which may also deteriorate the quality of predictions  should also be considered when searching for the best predictor. For instance, inflation of genomic predictions can be detrimental for genetic gain since the genetic merit of new genotyped lines is overestimated when compared to older lines that have undergone testcross field evaluations. Our results revealed that including pedigree information through the blended matrix K always caused the largest reductions in the inflation produced by G-BLUP. Reduced bias of predictions obtained by increasing the weight on familial relationships has also been reported in animal genomic evaluations . This reflects the capacity of marker information to capture populational LD, which becomes particularly relevant when predictions rely on more distant genetic relatedness (Habier et al. We evaluated model performance when within-family or across-family information was used for prediction. For all models, predictions were clearly better when full-sib relationships were exploited. The value of using information from close relatives for prediction in structured populations is consistent with the previous studies in animal and plant breeding (e.g., Wientjes et al. This paper provides a first empirical evidence based on sorghum breeding data that the use of genomic relationships alone, even with relatively low marker density, can give better predictions of parental BVs than the pedigree-based model. We also investigated how the use of different combinations of pedigree and genomic information affected prediction quality. Our results showed that using a kinship matrix integrating both sources of information yielded better predictive performance than G-BLUP for different traits and prediction scenarios. Identification of the optimal weighting factor used to combine familial- and marker-based relationships was driven by the search for maximizing predictive ability. Under this approach, the weight that optimizes predictions differed between traits. These weights were generally consistent with the weights that optimized model fitting to the entire dataset. The impact of including genealogy information to improve genomic predictions was stronger for traits with lower heritability, such as grain yield and stay-green. Findings of this paper might be relevant for other breeding programs with limited genotyping resources and when lowly heritable traits are the main targets of selection.