Prediction models were used to estimate stem circumference (SC) during the first 4 years of tree development in conjunction with a broad-sense heritability (H2) of 0.60. Applying the model  and kernel method (GB and GK) combinations to the rubber tree data revealed that the multienvironment models were superior to the single-environment genomic models, regardless of the kernel (GB or GK) used, suggesting that introducing interactions between markers and environmental conditions increases the proportion of variance explained by the model and, more importantly, the PA. Compared with the classic breeding method (CBM), methods in which GS is incorporated resulted in a 5-fold increase in response to selection for SC with multienvironment GS . Furthermore, GS resulted in a more balanced selection response for SC and contributed to a reduction in selection time when used in conjunction with traditional genetic breeding programs. Given the rapid advances in genotyping methods and their declining costs and given the overall costs of large-scale progeny testing and shortened breeding cycles, we expect GS to be implemented in rubber tree breeding programs.Several genomic prediction models combining genotype × environment (G×E) interactions have recently been developed and used for genomic selection (GS) in plant breeding programs. G×E interactions reduce selection accuracy and limit genetic gains in plant breeding. Two data sets were used to compare the prediction abilities of multienvironment G×E genomic models and two kernel methods. Specifically, a linear kernel, or GB (genomic best linear unbiased predictor [GBLUP]), and a nonlinear kernel, or Gaussian kernel (GK), were used to compare the prediction accuracies (PAs) of four genomic prediction models: 1) a single-environment, main genotypic effect model (SM); 2) a multienvironment, main genotypic effect model (MM); 3) a multienvironment, single-variance G×E deviation model (MDs); and 4) a multienvironment, environment-specific variance G×E deviation model (MDe). We evaluated the utility of genomic selection (GS) for 435 individual rubber trees at two sites and genotyped the individuals  Hevea brasiliensis) breeding programs are generally characterized by breeding cycles of 25–30 years and include the crosses, evaluation, and selection of field progeny as well as the propagation of selected superior materials , a new approach in which whole-genome molecular markers are used, has the potential to quickly improve complex traits with low heritability, significantly reduce the cost of line and hybrid development and increase yields in reduced amounts of time, allowing improvements to quantitative traits within large plant breeding populations .Genomic prediction combines phenotypic and pedigree data with marker data in efforts to increase the prediction accuracy (PA) for breeding and genotypic values. This method depends on dense genome-wide marker coverage to produce genomic estimated breeding values (GEBVs) from a comprehensive analysis of all available markers.According to Pinus and Eucalyptus  (GB)  interactions must be predicted. UP) (GB)  and the UP) (GB) .A GBLUP model was proposed by A nonparametric and semiparametric method was proposed by via an empirical Bayesian method . Seedlings acquired ong term . The fieong term .via microsatellite markers. The hybrids were selected on the basis of polymorphisms between the parents. GT1 is a male-sterile clone that is classified as a primary clone  at 50 cm above ground level was measured to evaluate the growth of individual trees, where the average per plot was calculated. Growth traits were frequently measured only during the first 6 years, as height and SC are the main selection traits for rubber tree breeding . Measurevia the breedR package  of each genotype used with the following mixed linear model were taken:Analyses of the SC traits were carried out  package  in conjuH2), when the entire data set from both environments (LW and WW) is used, the fixed effects included locale (place where the experiment was performed), block, water, and year. The G × E interaction and genotype were included as random effects in the model. When we considered each environment (LW or WW) separately where y is the adjusted mean phenotypic value (best linear unbiased estimated [BLUES]), × and Z are known incidence matrices, b is the vector of fixed effects , and g is the vector of random effects (genetic effects). In the general model (H2)  was estimated for SC for each water management system (LW and WW) and for every data set:The broad-sense heritability , and sequencing of PR255 × PB217 was performed on the Illumina HiSeq platform.Genomic DNA was extracted according to the methods of via TASSEL 5.0  missing data for the called SNPs. Only biallelic SNPs were maintained, which was performed via VCFtools  calling was performed SSEL 5.0 . Initialsequence  via Bowtsion 2.1 , with thpipeline  and filtpipeline . The folVCFtools . After tsoftware .The genotypic data are available under NCBI accession PRJNA540286 (ID: 5440286) (GT1 × PB235 and GT1 × RRIM701) and accession PRJNA541308 (ID: 541308) (PR255 × PB217).via the mixed model approach.Phenotypic analysis was carried out jointly for all years of evaluation via a relationship matrix-based approach for genomic prediction  schemes. The main objective was to compare the prediction ability of kinship matrices (GB and GK) and the proposed single-environment and multienvironment (G×E) genomic models.The PA was obtained from the correlation between the predicted BLUPs and the observed BLUPs. Four statistical prediction models were fitted to all the data sets to study their PA via the mixed model with breedR software , 5,000 samples were discarded , and every fifth iteration was used to estimate the posterior mean (thin = 5).The PA values were also compared for the single-environment and multienvironment models SM, MM , MDs Ja, and MDesoftware , and allsoftware , in whicUsing the main effect of the genotype, the single-environment model fits data from each environment (LW and WW) separately. Equation (1) shows the matrix representation of this model.y = ’ is the response vector (BLUP), yi is the observation of the ith line  in each environment, µ is the general mean, Zg is the incidence matrix that combines the random genetic effects and phenotypes, and g and e are the random genetic effect and the residual random effect, respectively, for each environment (LW and WW). In SM (1), g is considered to present a multivariate normal distribution with a mean of zero and a covariance matrix g in the jth environment, and where K is a positive semidefinite symmetric matrix that shows the variance–covariance of the genetic values calculated from the molecular markers. Furthermore, the residual error e in each environment is considered to be separate from the homogeneous variance I is the identity matrix and jth environment. Thus, g is an estimation of the true unknown genetic values, and e includes the residual genetic effects that are not elucidated by g more other nongenetic effects that approximate the errors, as described by n x p and p is the number of markers. The entries of the GK are computed as dii′ is the Euclidean distance between the ith and i′th individuals h > 0 is the bandwidth parameter that controls the rate of decay of K values   proposedK=(XX′p) , 2008 fog factor . de los The MM takes into account the main fixed effects of environments, even in the presence of random genetic effects across environments. Equation (2) indicates the matrix representation of this model.y = ’ is the response vector and yj is the vector of line observations  in the jth environment . The fixed environmental effects in the data are models in the XE incidence matrix, where the intercept for each environment (βE) is the parameter to be estimated. The incidence matrix Zg is the other fixed effect that can be incorporated into the model, the matrix Zg combines genotype with phenotype for each environment, and g is the variance in the main genetic effects across environments. The random vector of genetic effects g across environments is considered to follow a multivariate normal distribution with a mean of zero and a covariance matrix of g ∼ g with GB or GK.where ge).The MDs extends the MM to implement the random interaction effect of the environments to incorporate more genetic information of the lines  of the MDe are given by the components of the estimated variance for the data. The kernel matrix K is used in the components of g, while kernel matrix KE is used in the component of gE; both K and KE can be used with GB or GK, as described by The matrix The PA of SM-method combinations was evaluated with the TRN set (which comprised 80% of the hybrids). The TST set comprised 20% of the individuals, and none of the lines to be predicted in the TST set were also in the TRN set, in which 5 random partitions were arranged 5-fold, with 100 random partitions each. This procedure was performed separately for each environment, namely, LW and WW, and the SMs were fitted separately for each environment.The PA values of the multienvironment (LW and WW) model-method combinations were generated using two different cross-validation (CV) designs according to the methods of The parameters of the models, which include the main genetic effects, variance components resulting from residual effects, G×E interaction effects, and environment-specific effects, were reestimated from the TRN data in each TRN-TST partition (50 random), and the models were fitted to the TRN data set. PA was assessed by computing Pearson’s product-moment correlations between predictions and phenotypes in the TST data set within environments.via the breeder’s equation and phenotypic data and with information from the SNPs obtained via GS. The EGG was calculated according to the methods of Expected genetic gain (EGG) was estimated in two ways: the classic method used in rubber tree breeding The EGGs obtained by a classic breeding cycle (EGGcs) were estimated under the assumption that the time for first selection is 10 years. In rubber tree breeding, 3 years are needed from pollination to planting in the field, and as rubber trees usually require 6 years or more to reach tapping girth, there is a wait time of 7–9 years until tapping is started and a long period of 10 to 15 years before production and adaptation can be evaluated in the field  accordinH2, i is the intensity selection, δg is the additive genetic standard deviation, and T is the selection cycle time.where rc is the accuracy of selection, in which the breeding improvement is equivalent to the square root of the via molecular marker information (EGGgs) equation, assuming a time of 3 years for each selection cycle and representing the time required for crossing, seed selection, and selection of the best individuals via molecular markers. The equation is as follows:The simulation of breeding cycles in which GS was used was based on the EGG rgs is the selection accuracy with GS i is the intensity selection, δg is the additive genetic standard deviation, and T is the selection cycle time.where We started with 435 genotypes, but three genotypes were replicates and thus were merged. We removed 27 individuals that had more than 50% missing SNPs, leaving 411 genotypes. After the data were analyzed, a total of 259.224 million reads of sequence data were obtained, of which 69.8% were high-quality barcoded reads. The overall alignment rate of these reads to the rubber tree reference genome  was 83.7H. brasiliensis reference genome sequence (via low-depth sequencing (approximately 1–2X) of many genotypes.A total of 107,294 SNPs were identified. After markers 1) with more than 20% missing data, 2) with an MAF ≤ 0.05, 3) with more than two alleles were excluded, tags with a minimum depth of six reads were aligned to the sequence . This meAfter the data were filtered, 6.7% were missing. The mean depth ranged from 444 to 521 for GT1 × RRIM701 and GT1 × PB235, respectively, and was 202 for PR255 × PB217 , and the results indicated that the 411 genotypes fell into two major clusters  Table 1 The estimates of the variance components for each of the GS models derived from the full data analysis are presented in The variance components of genetic effects were greater when the GB method was used rather than when the GK method was used in all environments for the SM. Both the genetic variance and the environmental variance were greater when analyzed in the LW Table 2.versus WW) assumed that there was no marker-environment interaction between families tested at the different sites and that there could be an effect between marker effect estimations from families tested at different sites and environments (LW and WW). This should be taken into consideration and should be carefully analyzed in the GK approach when additive vs. additive epistasis is targeted.Compared with exclusion of the interaction term (G×E), inclusion of the term when the MM, MDe, and MDs were used led to a more significant reduction in the estimated residual variance, and for all the environments, the residuals from the GK were smaller than the residuals from the GB for the MM, MDs, and MDe. However, the multienvironment model  and MM-GB  were similar; the genetic variance corresponded to 99% for MM-GB and 96% for MM-GK. The percentage of total variance corresponding to variance components of the genetic main effects of MDs-GK (93%) and MDe-GK (80%) was consistently smaller than that of the genetic main effects of MDs-GB (97%) and MDe-GB (90%) Table 2.The estimated correlations between the phenotypes and predictions obtained from the CV test are shown in The CV2 design can be used only for multienvironment modeling methods  and not single-environment modeling methods (SM). Therefore, a single environment (SM) is analyzed, the random CV is CV1, but it is applied to only one individual environment (LW or WW) Figure 1The results showed that the PA of the SM-GK combination was greater than that of the SM-GB combination under both LW and WW. The SC results were 0.19 under LW for SM-GB and 0.19 for SM-GK, and under WW, the results were 0.27 for SM-GB and 0.28 for SM-GK.In terms of evaluating the PA of a model based on the correlation between the observed and the predicted values, when the PAs obtained by implementing different models  were compared, all the models were most accurate when CV2 was applied. The PA varied considerably between the CV1 and CV2 conditions Figure 1The PA varied very little between the WW and LW Figure 1The investigated alternative rubber tree breeding strategies differed considerably in the number of years required to finish one breeding cycle. For the classic improvement strategy, we considered a minimum duration of 10 years for the beginning of the selection of the best genotypes because 3 years are required from pollination to planting in the field and because rubber trees generally require several additional years (often 6 or more) to reach tapping girth. In the case of GS, we considered 3 years for initial selection (from pollination to field planting).The EGG calculations were performed for all the methods and models and were compared with classic improvements in both environments Figure 2The genetic gains obtained when the information from the G×E interaction was incorporated were much greater gains than those obtained from a single environment. However, the results varied little between methods, with similar values resulting from most of the analyses. Considering the overall LW, the EGG was 0.39 for all models and methods except MDe-GB (0.38). For WW, the EGG was slightly greater than that under LW, and most models and methods had estimated gains of 0.41, with the exception of MM-GB (0.40) Figure 2via the GB and GK methods in conjunction with multienvironment models that evaluated trees under contrasting hydric conditions in different seasons of the year (LW and WW).Incorporating and improving the genomic PA of rubber trees are a challenge for the successful application of GS in breeding programs. In this research, genomic PA was studied in rubber tree data sets Many factors such as genetic architecture, heritability, population structure, and marker density can influence GS . AccordiHevea, which were H2 = 0.32  positively stood out. Using the CBM, via GS. Given this and latex production having greater heritability than circumference growth because the influence of the rootstock is relatively low in production, this feature will be very important in future studies of this population.Trees with rapid SC development may be more productive, and this feature may be a useful way to predict more productive hybrids In GS, G×E interactions can be modeled by a marker × environment interaction and by a linear kernel or a nonlinear GK . Multienvia CV1 under LW.Here, the GK methods presented a small increase in the prediction ability of all single-environment and multienvironment models with CV2, confirming the results of The multienvironment models and the GK method resulted in the best PA. Similar decreases in PA were reported by Considering only random CV2, the PA was slightly greater under WW, ranging from 0.87 (MDe-GK-WW) to 0.82 (MDe-GB-LW), which is consistent with previously published results for forest tree species. via selection of the best stable parents can then be performed to improve hybrid stability and the EGG  and two kernel methods (GB and GK) to rubber tree data sets revealed that the PAs of the models with the nonlinear GK were similar to those of the models with the linear GB kernel. According to Many GS studies of plants have focused on breeding programs that generally evaluate crops in multiple environments, such as in different seasons/years or in geographic locations, to determine performance stability across environments  and to iAdvantages of GS applied to the improvement of forest species have been demonstrated. For example, Using both genetic markers and environmental covariates, GS is expected to increase the accuracy of selection, especially for traits that cannot be measured directly from breeding candidates and for traits with a low heritability , and thiIn the last decade, many statistical models have been proposed for applying GS in plant and animal breeding programs and have received increasing interest from forest tree breeders. Citrus clones .In essence, implementing techniques that reduce the long breeding cycle of trees is urgently needed, and for this purpose, the use of a biparental population was a means of managing the difficulty of obtaining complex families, which can take many years to generate because of the low fecundity of trees and the long duration of the phenotypic evaluation needed. According to In addition, large areas are required for the development of hybrids, which not only increases the costs associated with maintaining plants in the field but also limits the number of genotypes that can be evaluated. GS can minimize these difficulties because selection can be performed on juvenile plants, which reduces the interval between generations and increases the intensity of selection, thus reducing the gain per unit time , significantly increasing the genetic gain relative to that obtained by CBMs. Another advantage of GS compared with phenotypic selection is that more candidate genotypes are generated; therefore, the population size for selection is improved. All of the candidates are genotyped, and those with the best-predicted test cross values are evaluated in the field; this process can be considered a form of indirect selection.According to With declining costs and rapid advances in genotyping methods, even with the costs of maintaining large progeny trials and the potential for increased gains per unit time, we very cautiously expect GS to have excellent potential for implementation in rubber tree breeding programs. However, additional studies examining populations with different structures  are necessary before recommending GS for operational implementation in tree breeding programs.This is the first study to incorporate models for G×E interaction when phenotypic and/or genotypic information was used simultaneously for genetic prediction in the context of GS in a rubber tree breeding program. The results presented here suggest that GS can be useful for rubber tree breeding because this technique can be used to accurately predict the phenotypes and reduce the length of the selection cycle. Thus, GS is a promising tool for improving rubber tree cultivation, and we look forward to exploring the historical phenotypic data collected during 15 years as part of national breeding programs.https://www.ncbi.nlm.nih.gov/bioproject/PRJNA540286 and https://www.ncbi.nlm.nih.gov/bioproject/PRJNA541308Publicly available datasets were analyzed in this study. This data can be found here: LS, FF, PG, RF-N and AS designed the study and performed the experiments; VG and EJ performed the experiments in the field; LS, FF, and RF-N analyzed the data; LS, FF and AS wrote the manuscript. and VG and EJ performed the experiments in the field.The authors gratefully acknowledge the Fundação de Amparo a Pesquisa do Estado de São Paulo (FAPESP) for a Ph.D. fellowship to FF (18/18985-7); the Coordenação de Aperfeiçoamento do Pessoal de Nível Superior (CAPES) for financial support  and postdoctoral fellowships to LS (88887.334728/2019-00); and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for financial support, a postdoctoral fellowship to LS (168028/2017-4), and research fellowships to AS and PG.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.


Arabidopsis thaliana 1001-genomes collection. The high order LD was found to be more prevalent in smaller populations, but present also in samples including several hundred individuals. An empirical example illustrates that high order LD might be an even greater challenge in cases when the genetic architecture is more complex than the common assumption of bi-allelic loci. The example shows how significant statistical epistasis is detected for a pair of markers in high order LD with a complex multi allelic locus. Overall, our study illustrates the importance of considering also other explanations than functional genetic interactions when genome wide statistical epistasis is detected, in particular when the results are obtained in small populations of inbred individuals.A plausible explanation for statistical epistasis revealed in genome wide association analyses is the presence of high order linkage disequilibrium (LD) between the genotyped markers tested for interactions and unobserved functional polymorphisms. Based on findings in experimental data, it has been suggested that high order LD might be a common explanation for statistical epistasis inferred between local polymorphisms in the same genomic region. Here, we empirically evaluate how prevalent high order LD is between local, as well as distal, polymorphisms in the genome. This could provide insights into whether we should account for this when interpreting results from genome wide scans for statistical epistasis. An extensive and strong genome wide high order LD was revealed between pairs of markers on the high density 250k SNP-chip and individual markers revealed by whole genome sequencing in the  The genetic architecture of most biological traits is complex and involves multiple genes, whose effects are often influenced by interactions with other genes and environmental factors. To study the relative contributions by genes, environmental factors and their interactions in segregating populations, statistical genetic approaches are commonly used to partition the genetic variance to additive and dominance variance of individual loci and epistatic interaction variance between them . In prinWood et al . These reduced marker sets are selected with the aim to tag as many of the unobserved functional polymorphisms as possible. The statistical inferences of the underlying genetic architecture made from such reduced sets of markers can, however, be problematic in some cases. For example, multiple unobserved functional polymorphisms can lead to associations to individual markers that do not properly represent the causal variants  using data from the 1001 genomes project . Strong high order LD-r2 was found to be common both within and across chromosomes between pairs of markers from the SNP-chip and the sequencing polymorphisms. The cause of the LD-r2 observed between interchromosomal markers, or distant intrachromosomal markers, is unknown but could either be due random drift or structure due to population genetics processes such as selection or migration. On a genome-wide scale, the number of cases where the combined genotype of the marker pair tagged the genotype of the sequencing markers better than any single marker on the SNP chip was too common for being neglected when interpreting the results from an epistatic association analysis. The risk of falsely inferring genetic interactions between markers on different chromosomes in a two-locus interaction analysis might increase in situations when the underlying genetic architecture is more complex, for example when a single locus contains multiple functional alleles. This is illustrated using an empirical example from a second public A. thaliana dataset  with a functional polymorphism affecting a studied trait, a single-locus association test between the marker and the trait will capture all the phenotypic variance contributed by the functional polymorphism. A basic assumption in genetic association studies is that at least one genotyped marker will be in sufficiently high LD with each functional polymorphism to detect it in this way. In reality, however, not all functional polymorphism will be in such perfect LD with a genotyped marker, and then there is a risk that the joint genotype of two (or more) markers tags the genotype of the functional polymorphism better than any single marker (high-order LD > single-marker LD). This will, as discussed below, influence the significances of the trait-marker associations detected in a genetic association analysis and the inferences made about the genetic architecture of the trait.When an individual marker is in complete linkage disequilibrium  and single targets (here un-genotyped SNP polymorphisms) following  > max (single order LD)). To calculate the high order LD between the two predictors (M1 and M2) and the single target (Q), the two-locus M1M2 genotype is used to create a multi-allelic pseudo marker (P) with four alleles (2) can be calculated for each of the possible ways that M1 and M2 together can tag the genotype at Q  and the four bi-allelic pseudomarkers . For each pair of predictors, the second order LD is then defined as the LD-r2 for the pseudomarker with the highest LD-r2 to the target. Pseudomarkers with higher LD-r2 to the target (Q) than 0.3 are kept for further analyses. The LD-r2 values were computed using the software LdCompare  effects and the additive-by-additive interaction between the loci.In a genetic association study in an inbred or haploid population, two-locus epistasis is typically modeled as:e.g., by Wood et al.  at Q well. However, the causal (blue) allele at Q is, tagged perfectly by one of the two-locus M1M2 genotypes  will be non-zero, illustrating how statistical epistasis can emerge from the second-order LD between M1 and M2 and Q. This example illustrates a scenario similar to what was empirically observed in  from the predictions obtained by the marginal (additive) effects (Alvarez-Castro and Carlborg 2007). However, a non-zero estimate of the interaction term in model [1] does not, as noted ypes ab; , while tA. thaliana . Three types of high order LD are defined based on the locations of the predictors relative to the target. If both predictors are located within 1Mb of the target it is classified as cis-cis. If only one predictor is closer than 1Mb it is classified as cis-trans. If none is closer than 1Mb it is classified as trans-trans. The choice of a 1Mb threshold to define cis vs. trans predictors is arbitrary, but we consider it useful for evaluating how common high order LD is between predictors near  and far  from the target.Here, we evaluate the prevalence and strength of high order LD between pairs of markers selected for genotyping on a 250k SNP chip (predictors) and a third locus revealed by whole genome sequencing (targets) using publicly available datasets in A. thaliana 1001-genomes project has released complete genome sequences for hundreds of wild collected accessions (http://www.1001genomes.org). Here, we used whole-genome SNP data on 728 accessions scored by whole genome re-sequencing . The predictors used in our analysis was a subset of the SNPs selected for the 250k A. thaliana SNP chip  within a randomly selected 6 Mb window on chromosome 2 as well as ii) between three randomly selected windows from different chromosomes . Computa2 > 0.6 to a target were classified as cis-cis/cis-trans/trans-trans. To extrapolate these findings to the genome level, the proportions of all evaluated predictor pairs that displayed these patterns were calculated and then multiplied with the total number of possible cis-cis/cis-trans/trans-trans pairs in the genome (Table S1).The predictor pairs in the evaluated windows in the genome with high order LD-rArabidopsis thaliana accessions were used for a genome wide association analysis. In short, the plants were grown in a controlled environment with 6 biological replicate plants per accession. Analyses by Inductively Coupled Mass Spectroscopy (ICP-MS) provided estimates of leaf molybdenum concentration as described in  without control for population structure. Thereafter, each pair of loci that passed the genome wide significance threshold in the initial scan was fitted in a two-locus epistatic genetic model [1] using hglm function in hglm package  to correct for the possible effects of population structure via the genomic kinship matrix as in (P < 3.2 × 10−10) was defined as a Bonferroni corrected nominal 5% significance threshold. The correction was done for an estimated number of independent association tests assumed to equal the number of independent LD blocks in the A. thaliana genome as described in (−14).A publicly available dataset including 340 Arabidopsis thaliana 1001 genomes project http://1001genomes.org/data-center.html. The 250 K SNP chip data are available as part of the genotype data for the Arabidopsis thaliana Regmap panel  as in (in trans)? How dependent is the prevalence of high order LD and cis vs. trans predictors on the population size? We also present an empirical example where high order LD exists between a cis-trans predictor pair with significant statistical epistasis and a locus displaying strong genetic variance heterogeneity due to independent contributions by multiple linked polymorphisms . When the sample size was smaller  were next explored in three pairs of distant 2Mb windows in the genome (2 than 0.6 to the targets were considered.e genome  to provi2 > 0.6) is low. In the smaller population (n = 100), less than 1 out of 106 evaluated predictor pairs and in the larger population (n = 768) less than 1 out of 107 (Table S1). However, since the total number of evaluated pairs was very large (around 1011), many cases were still detected. Regardless of population size, cis-cis and cis-trans pairs dominated  all have an intermediate molybdenum level in the leaf . It is found to be most common when one predictor is in high LD to  the target, but many cases exist where the LD to the individual predictors is very weak but the high order LD is strong. The choice of target and predictor SNPs in this study is arbitrary and therefore it is difficult to assess how representative they are for the prevalence of high order LD in other populations. However, they do suggest that strong high order LD can be prevalent also in larger populations, indicating that statistical epistasis observed in studies based on reduced representation genotyping (such as SNP-chips) need to be interpreted with caution.High order linkage disequilibrium between combinations of genotyped markers, and unobserved functional polymorphisms, can result in significant statistical epistasis in genome wide association analyses. This was earlier illustrated empirically for linked pairs of genotyped predictor SNPs and ungenotyped target polymorphisms in humans by Wood cis-trans predictor pairs, but also cis-cis pairs are common regardless of population size. The prevalence of trans-trans pairs is high in smaller populations but decreases rapidly as the population size increases. A possible biological explanation for the observation that cis-cis and cis-trans high order LD pairs is relatively prevalent also at larger population sizes would be that the number of, and variation in, the trans located predictors is sufficiently large on a genome-wide basis to complement any imperfection in the tagging of the functional polymorphism by the cis located predictor. Whereas trans-trans high order LD will always result in falsely associated loci, cis-trans and cis-cis high order LD presents an opportunity to identify true functional loci for the trait. The problem in a real data analysis is that statistical epistasis between a pair of predictors can emerge from true interactions or high order LD within and across chromosomes. However, as the sample sizes increase the risk of detecting pairs of predictors where none is located close to the true functional polymorphism decreases. Before concluding that the detected association is due to two interacting loci, further analyses of the associated pair are however recommended.The most prevalent type of high order LD on a genome wide basis is that of A. thaliana leaf. In fact, it is not unlikely that the problem with high order LD between SNP predictors and hidden, complex functional loci will remain a major challenge in the future as the increased number of markers generated by sequencing also increases the chance of finding combinations of cis-cis or cis-trans predictors that tag these functional polymorphisms better than any single marker. To evaluate the extent of this problem one will, however, need a more comprehensive dataset than the one studied here including a more complete scoring of all types of non-SNP polymorphisms in the genome with potential effect on traits of interest.Whole-genome sequencing provides unprecedented opportunities to genotype most segregating single nucleotide polymorphisms in the genome. Despite this, it is unlikely that these will be able to tag all functional polymorphisms, such as larger structural variants or multi-allelic functional loci due to tandem repeats. Hence, even though the scenario of reduced representation genotyping with SNP-chips or similar will soon be a technology of the past, association analyses will still be challenged by the need to tag hidden polymorphisms with imperfect markers as illustrated in our analyses of the complex locus affecting molybdenum levels in the The prevalence of high order LD is likely to be more of a concern in populations of inbred or haploid individuals. These include, for example, inbred lines derived from bi- and multi-parental crosses of plants and animals, as well as populations of wild collected inbred plants (A. thaliana 1001-genomes collection. The high prevalence of strong high order LD in this dataset suggests that epistatic variance detected between pairs of markers in association analyses, especially in small inbred populations genotyped for reduced representation sets of markers, need to be interpreted with caution. An empirical example is presented where a pair of markers with significant statistical epistasis in a genome wide association analysis is in high order LD with a complex multi allelic locus with large effects on the analyzed trait. As complex functional loci such as this are unlikely to be captured by individual bi-allelic SNP markers, even if millions of them are scored by whole genome sequencing, it is important to evaluate also other explanations of statistical epistasis than underlying genetic interactions in particular when small populations of inbred individuals are studied.Statistical epistasis detected in genome wide association analyses can result from high order LD between genotyped markers and unobserved functional polymorphisms. This study revealed extensive and strong genome wide high order LD between pairs of markers on a high density 250k SNP-chip and individual markers revealed by whole genome sequencing in the


Cenchrus purpureus (Schumach.) Morrone] is used for bioenergy and animal feed. In order to identify candidate genes that could be exploited for marker-assisted selection in elephant grass, this study aimed to investigate changes in predictive accuracy using genomic relationship information and simple sequence repeats for eight traits  linked to bioenergetics and animal feeding.Elephant grass [p < 0.05) was detected for most of the traits evaluated. In general, the overall means for the traits varied widely over the cuttings, which was corroborated by a significant genotype by cutting interaction. Knowing the genomic relationships increased the predictive accuracy of the biomass quality traits. We found that one marker (M28_161) was significantly associated with high values of biomass digestibility. The marker had moderate linkage disequilibrium with another marker (M35_202) that, in general, was detected in genotypes with low values of biomass digestibility. In silico analysis revealed that both markers have orthologous regions in other C4 grasses such as Setaria viridis, Panicum hallii, and Panicum virgatum, and these regions are located close to candidate genes involved in the biosynthesis of cell wall molecules (xyloglucan and lignin), which support their association with biomass digestibility.We used single-step, genome-based best linear unbiased prediction and genome association methods to investigate changes in predictive accuracy and find candidate genes using genomic relationship information. Genetic variability (The markers and candidate genes identified here are useful for breeding programs aimed at changing biomass digestibility in elephant grass. These markers can be used in marker-assisted selection to grow elephant grass cultivars for different uses, e.g., bioenergy production, bio-based products, co-products, bioactive compounds, and animal feed. Pennisetum purpureum Schumach. syn. Cenchrus purpureus (Schumach.) Morrone] is a perennial tropical grass with high photosynthetic efficiency (C4 photosynthetic pathway) that is naturally found in several African countries , and cytogenetic studies have been conducted on these species in order to identify hybrids [Sclerotinia sclerotiorum in Brassica napus [Agrostis stolonifera L.) [Elephant grass is a tetraploid species (2n = 4x = 28) with two genomes (A′A′BB) . Its gen hybrids , 10. Ele hybrids , two stu hybrids , 13, and hybrids  have bee hybrids . For exa hybrids  and used hybrids . Althoug hybrids , resistaca napus , and quaca napus . In genefera L.) .Genomic association studies identify candidate genes and markers linked to important traits. When considering multipurpose traits , the development of selection procedures based on molecular markers can radically streamline and accelerate elephant grass improvement . Appropri) investigate changes in predictive accuracy using genomic relationship information in statistical models, (ii) investigate significant associations between SSR markers and eight traits, evaluated in different cuttings, in a germplasm collection of elephant grass genotypes, and (iii) identify candidate genes linked to these traits with their respective gene annotations. By achieving these goals, we aimed to increase the speed and accuracy of breeding elephant grass for different purposes.In this context, the goals of this study were to (p < 0.05) was detected for seven traits  but not biomass digestibility  for all traits was observed  for height, green biomass, and dry biomass but not for biomass quality traits  (p > 0.05)  for green biomass, dry biomass, dry matter concentration, and lignin  Fig. . There wnin Fig. .H− 1 matrix) ranged from 0.58 (biomass digestibility) to 0.84 . When the model did not include the relationship between the genotypes (simple repeatability plus the genotype by cutting interaction model), the accuracy ranged from 0.59 (biomass digestibility) to 0.89 (dry biomass). Inclusion of the relationship matrix in the ssGBLUP model increased the accuracy of the biomass quality traits  for all SSRs that affected biomass digestibility, while the quantile-quantile (QQ) plot  from those expected.We analyzed 90 elephant grass genotypes that had phenotypic data and SSR alleles available, and identified one allele of the M28 marker (M28_161) that was significantly associated with biomass digestibility. This association was detected only for the first cutting. A Manhattan plot Fig. , right slot Fig. , left dir2 = 0.20) to M28_161, and, in general, its presence was detected in elephant grass genotypes with low values of biomass digestibility. All other r2-values were lower than 0.11, and varied from 0.00 to 0.11.To identify the linkage of all markers, we performed linkage disequilibrium analysis Fig. . In thisSetaria viridis chromosome 3 and Panicum halli chromosomes 5 and 7), M28_161 is close to candidate genes linked to pathways influenced by plant hormones . However, in most cases, M28_161 and M35_202 are associated with candidate genes involved in the synthesis of cell wall components. In P. halli, M28_161 is close to candidate genes involved in lignin biosynthetic processes and cell wall organization (chromosome 7), and in Panicum virgatum, it is close to a candidate gene involved in lignin catabolic processes and oxidation-reduction processes (located on chromosome 8). In S. viridis, both M28_161 and M35_202 were found to have orthologous regions. M28_161 is close to a candidate gene on chromosome 3 that plays a role in xyloglucan biosynthesis, while M35_202 is close to a candidate gene on chromosome 7 that functions in lignin biosynthesis. For Setaria italica, a successful BLAST search was conducted for the M28_161 sequence, but no candidate genes related to digestibility were found. However, for C. americanus, no BLAST results were obtained when using the M28 and M35 sequences.A BLAST search revealed that the two SSR markers (M28_161 and M35_202) are close to candidate genes that have annotated functions in other grasses  revealed by the ssGBLUP analysis does not mean that there was no genetic variability, because the interaction effect may have reduced it. Residual terms were added to the ssGBLUP model to capture nonadditive effects. For crops that exhibit clonal propagation and are not lines (such as elephant grass), nonadditive effects represent epistatic and dominance effects , and addCell component fractions that could affect forage digestibility include cellulose, lignin, hemicellulose, and cell wall proteins . TherefoNone of the agronomic traits  and four of the quality traits  were associated with SSR markers. This was probably related to the low number of SSR markers used  when compared to the genome size of elephant grass, which has recently been estimated as 2.1 Gb . HoweverThe SSR markers used here were previously developed for pearl millet , 29, andS. italica, S. viridis, P. virgatum, P. halli, and C. americanus. These species are closely related to elephant grass [C. americanus genome sequence, which was unexpected because the SSR markers used here were developed from pearl millet [We ran BLAST searches using sequences of the markers M28_161 and M35_202, and the genome of the related C4 grasses nt grass , 31. No l millet  and the l millet , 10. ForS. viridis (Sevir. 3G340800) is orthologous to locus AT2G20370 of Arabidopsis thaliana, and codes for a xyloglucan galactosyltransferase responsible for different functions, including the synthesis of cell wall materials. Xyloglucan, which is a component of the plant cell wall, is a type of hemicellulose that has the ability to bind to cellulose to form a cellulose-xyloglucan network linked through hydrogen bonds (see review by Pauly and Keegstra [One candidate gene annotated on chromosome 3 of Keegstra ). It is Keegstra . HoweverKeegstra . The effP. halli, P. virgatum, and S. viridis genomes, respectively, are useful assets. These candidate genes are orthologous to the loci AT5G48930, AT3G09220, and AT5G48930 in Arabidopsis. AT5G48930 is a hydroxycinnamoyl-Coenzyme A shikimate/quinate hydroxycinnamoyltransferase that is involved in the phenylpropanoid pathway, and plays a role in the production of hydroxycinnamyl alcohols (or monolignols) that serve as the building blocks of lignin [No markers were associated with lignin content. Lignin is the second-most abundant biopolymer on Earth , and is f lignin . The ligf lignin , and canf lignin . In thisf lignin . Howeverf lignin . The molf lignin , 41, 42.P. halli) is orthologous to locus AT5G05190 in Arabidopsis, in which a hypothetical protein is involved in different functions, including responses to fungi [P. halli) has an orthologous locus in Arabidopsis (AT3G05880) that codes for a small and highly hydrophobic protein that is involved in the hyperosmotic salinity response and response to cold. Validating these candidate genes in elephant grass would increase our knowledge of how this species responds to stressors such as spittlebug (Cercopidae) attack and drought or flooding, which are important factors for breeding programs in Brazil [Some candidate genes are associated with plant hormones , the cross-talk of which plays an important role in the molecular responses of plants to stress , and twoto fungi . The cann Brazil .This study showed that, even by using a few SSR markers, it is possible to identify candidate genes associated with biomass digestibility. It also showed that it was possible to increase predictive accuracy in elephant grass by incorporating genomic relationship information. Because there is little genomic information for elephant grass available, our findings may improve elephant grass breeding. For example, marker-assisted selection can be applied, and markers associated with biomass digestibility have the potential to drive elephant grass selection for different uses . Further validation of the candidate genes revealed here may lead to a better understanding of biomass digestibility variation and its genomic basis.− 1 P2O5 fertilizer applied at planting on December 23rd, 2011. The red-yellow latosol soil at the Embrapa Gado de Leite experimental station in Coronel Pacheco, MG, Brazil  had the following chemical properties: pH (5.4), H + Al (2.31 cmolc dm− 3), P (1.1 cmolc dm− 3), K (23 mg dm− 3), and exchangeable cations Al3+ (0.2 cmolc dm− 3), Ca2+ (1.4 cmolc dm− 3), and Mg2+ (0.7 cmolc dm− 3). The plots consisted of 4-m rows that were planted side by side, 1.5 m apart. Plots were allocated in a 10 × 10 simple lattice design, with two replications. At 30 days after planting, the plots were cut to 0.30-m stubble height (uniformly cut). The number of days to reach each of the six growing seasons (cuttings) started at this time. Maintenance fertilization was made with 300 kg ha− 1 of a N-P2O5-K2O formulation (20:05:20 blended granular fertilizer) after all cuttings. Fertilization was conducted according to the results of a soil analysis.One hundred elephant grass genotypes  was performed at 250 regrowth days, the second  at 250 regrowth days, the third  at 315 regrowth days, the fourth  at 275 regrowth days, the fifth  at 315 regrowth days, and the sixth  at 210 regrowth days. The fourth cutting collected propagation material, i.e., no phenotypic data were obtained at this cutting. We declare that all plant materials in this study represent voucher specimens that have been deposited in a publicly available herbarium (Active Elephant Grass Germplasm Bank) and that comply with institutional, national, and international guidelines for the collection and cultivation of any plant materials.i) height (m) was obtained from the arithmetic mean of the height of three randomly selected plants in each plot, measured from ground level to the curve of the last completely expanded leaf; (ii) green biomass (Mg ha− 1) was obtained from a cutting taken at 7.5 cm stubble height in a 3-m section in the middle of the rows using a gasoline-powered strimmer and that was collected by hand. The 3-m section was immediately weighed in the field to provide estimates of green biomass; (iii) dry biomass (Mg ha− 1) was quantified by multiplying the green biomass by the dry matter concentration (%); (iv) acid detergent fiber (g Kg− 1), (v) neutral detergent fiber (g Kg− 1), and (vi) lignin content (g Kg− 1) were determined following the methodology proposed by Goering [vii) biomass digestibility (g Kg− 1) was determined by the method described by Tilley and Terry [viii) dry matter concentration (%) was obtained by sampling three complete plants from each plot, which were dried in a kiln after weighing (fresh weight) until weight stabilization. The samples were weighed (dry weight) again, and the dry matter concentration was determined by the ratio between dry weight and fresh weight. This trait was used as a common denominator for the estimation of biomass digestibility. For acid detergent fiber, neutral detergent fiber, lignin content, and biomass digestibility, random samples of three complete plants from each plot were collected before cutting the experimental plots. These samples were dried in a forced-air circulation oven at 56 °C for 72 h. After drying, the samples were ground to small particles (1 mm) in a Wiley type grinder and analyzed as described above. For the third, fifth, and sixth cuttings, acid and neutral detergent fiber, lignin content, biomass digestibility, and dry matter concentration were measured using near-infrared spectroscopy (NIRS). Data generated from the first and second cuttings, and from other experiments , were used for NIRS calibration. The phenotypic data are shown in Additional file The plants were phenotyped at first, second, third, fifth, and sixth cuttings for each of the following traits:  bnd Terry ; and (viMi): pi is the allele frequency associated with the presence of a marker at locus i. The algorithm was directly implemented as an R function. After quality control, 87 markers were used. According to previous studies [Eighteen SSR markers were used for genotyping, as described by Azevedo et al. . The all studies , 48, 49,y = Xm + Za + Zg + Wb + Ti + Tr + Qp + ε, where y is the vector of responses across the five cuttings (only using phenotypic data); m is the vector of the effects of the measurement-replication combination (assumed as fixed) added to the overall mean; a is the vector of genetic effects (assumed as random); g is the vector of residual genetic effects (assumed as random); b is the vector of block effects (assumed as random); i is the vector of the genotype by cutting interaction; r is the vector of the residual genotype by cutting interaction; p is the vector of permanent environment effects (random); ε is the vector of residues (random); and X, Z, W, T, and Q represent the incidence matrices for these effects.A mixed model methodology was adopted for statistical analyses using ssGBLUP , 51. TheG is a matrix of genomic additive relationships, I is an identity matrix of appropriate dimensions, Gi is a matrix of genomic interactions (genotype by cutting interaction), The following distributions of random effects were considered: y et al. .G) was used according to Resende et al. [Z∗ = Z − P, in which Z is a matrix containing marker genotypes and P is a matrix with pi elements in column i.An additive relationship matrix structure  was adopted, according to Legarra et al. [A−1 is the inverse of the pedigree relationship for all elephant grass genotypes and A and A22 was an identity matrix for this study because there was no information about the pedigree. To compute the exact inverse of G to compose the H−1 matrix, we used the algorithm G∗ = 0.95G + 0.05A22 [Due to the presence of 10 genotypes that were not genotyped, the inverse of the genomic relationship matrix ; m is the vector of the effects of the measurement-replication combination (assumed as fixed) added to the overall mean; g is the vector of genetic effects (assumed as random); b is the vector of block effects (assumed as random); i is the vector of the genotype by cutting interaction; p is the vector of the permanent environment effects (random); ε is the vector of residues (random); and X, Z, W, T, and Q represent the incidence matrices for these effects.The model was run without considering the relationship (simple repeatability plus G x C interaction model) between the genotypes, as follows: I is an identity matrix of appropriate dimensions and The following distributions of random effects were considered: Reml 4.1 .PEVg is the predictive error variance that was obtained by the diagonal elements inverse of the left-hand side of the mixed model equation for the genetic effect.The accuracy  added to the overall mean; u is the vector of markers (assumed as fixed); a is the vector of genetic effects (assumed as random); g is the vector of residual genetic effects (assumed as random); b is the vector of block effects (assumed as random); ε is the vector of residue (random); and X, M, Z, and W represent the incidence matrices for these effects.The 90 elephant grass genotypes that had been genotyped and phenotyped were used in the genome association study. The R package “sommer” (GWAS2 function ) revealeG is a matrix of genomic additive relationships, I is an identity matrix of appropriate dimensions, and The following distributions of random effects were considered: P − value) up to the false discovery rate (FDR) threshold were considered candidate markers. To compute the FDR, a 0.02 threshold level and p < 0.05 were set.Markers with − log(r2), as described by Hill and Robertson [p(AB) is the frequency of the haplotype AB and p(A) and p(B) are the frequencies of alleles A and B, respectively. Therefore, r2 ranged from 0 (when the two markers were in perfect equilibrium) to 1 . Manhattan plots and QQ plots were obtained using the “sommer” package [We used the LD.Measures function in the R package LDcorSV to compute linkage disequilibrium . A BLAST search of the C. americanus genome was performed on the US National Center for Biotechnology Information website (https://blast.ncbi.nlm.nih.gov/Blast.cgi). For these searches, sequences of the primers M28R (CGAATACGTATGGAGAACTGCGCATC) and M35R (ATCCACCCGACGAAGGAAACGA) were used. For gene annotation, ortholog genes in A. thaliana were searched using the Arabidopsis Information Resource database [A list of candidate genes was assembled by BLAST, with default parameters set, using the plant comparative genomics portal Phytozome  based ondatabase .Additional file 1: Table S1. Genotypes of elephant grass and their respective codes. The genotypes are part of the Active Elephant grass Germplasm Bank (BAGCE) maintained by Embrapa Gado de Leite (Embrapa Dairy Cattle).Additional file 2: Table S2. Phenotyping data for the 100 elephant grass genotypes obtained on five cuttings . Abbreviations used: Cut (cutting day), Gen (genotype - see codes in Table S1), Cut.Rep (concatenation of cut and rep columns), Int (genotype by cutting interaction), Rep (replication), Height (in meters), GB , DB , DM , ADF , NDF , DIG  and LIG .Additional file 3: Table S3. Molecular data for the 90 elephant grass genotypes. “Code” indicates de code of the genotypes (see Additional file


Salix genera) has been of interest for bioenergy but recently also for biofuel production. For a faster development of new varieties molecular markers could be used as selection tool in an early stage of the breeding cycle. To identify markers associated with growth traits, genome-wide association mapping was conducted using a population of 291 Salix viminalis accessions collected across Europe and Russia and a large set of genotyping-by-sequencing markers. The accessions were vegetatively propagated and planted in replicated field experiments, one in Southern Sweden and one in Central Sweden. Phenology data, including bud burst and leaf senescence, as well as different growth traits were collected and measured repeatedly between 2010 and 2017 at both field environments. A value of the plasticity for each accession was calculated for all traits that were measured the same year in both environments as the normalized accession value in one environment subtracted by the corresponding value in the other environment. Broad-sense accession heritabilities and narrow-sense chip heritabilities ranged from 0.68 to 0.95 and 0.45 to 0.99, respectively for phenology traits and from 0.56 to 0.85 and 0.24 to 0.97 for growth traits indicating a considerable genetic component for most traits. Population structure and kinship between accessions were taken into account in the association analyses. In total, 39 marker-trait associations were found where four were specifically connected to plasticity and interestingly one particular marker was associated to several different plasticity growth traits. Otherwise association consistency was poor, possibly due to accession by environment interactions which were demonstrated by the low structure adjusted accession correlations across environments (ranging from 0.40 to 0.58). However, one marker association with biomass fresh weight was repeatedly observed in the same environment over two harvest years. For some traits where several associations were found, the markers jointly explained over 20% of the accession variation. The result from this study using a population of unrelated accessions has given useful information about marker-trait associations especially highlighting marker-plasticity associations and genotype-by-environment interactions as important factors to take account of in future strategies of Salix breeding.The short rotation biomass crop willow ( Salix species and more recently also Populus species have been used in a short rotation coppice (SRC) system with harvests every 3–5 years from the same plants in order to continuously have a high biomass production  mapping have gained more insight into the genetic background of plasticity . The response of a genotype across environments reflect the plasticity of the genotype and its possibility to survive and grow in different environmental conditions . Studyinasticity  and in Ry traits , 2017.To further increase the genetic gain in a recurrent selection breeding program, selection tools using molecular markers could be included in the breeding process . A firstPopulus and Salix species to understand the genetics of different disease resistance traits  and thus 100% outcrossing giving a high genetic diversity and heterozygosity  platform . Sequence reads and polymorphisms were provided at the Genomic Diversity Facility by running the Tassel GBS analysis pipeline v. 3.0.166 . For the 291 accessions for which sampling, DNA extractions, and genotyping were successful, DNA sequence sites showing polymorphisms were identified. The resulting genotype data were merged by Tassel ver. 4.3.7, provided to us as Variant Call Format files (VCF) and is stored at a publicly available repository  and DNA was extracted following a CTAB-protocol described in  3.0.166  using thpository . The polmissing. Assuming an Illumina genotyping error rate of 0.1% this procedure implies a diploid genotype calling accuracy above 97%. The polymorphism data produced by GBS was thereafter merged with genotype data from 1290 SNPs previously developed for this population (S. purpurea genome was performed by Blast (e < 10-9) whereupon all polymorphic sites were sorted according to increasing chromosome number and position with respect to the reference. The polymorphic sites were then filtered based on data completeness and on minor allele frequency (MAF) depending on intended downstream use. All the above-mentioned processing steps were performed with VCFtools ver.0.1.12b. Furthermore, to reduce the number of sites produced by erroneous merging of paralog or repetitive sequences, all sites for which the frequency of heterozygotes exceeded 70% were removed using a custom perl script. Assuming Hardy–Weinberg equilibrium, even triallelic sites should never exhibit heterozygosity frequencies above 66.7%.For each putative polymorphic site, diploid genotypes were called by finding the maximum likelihood for the observed distribution of haplotype sequence reads . But in pulation . MappingK) for the sample population was estimated in accordance with k) was set to vary from one to ten. The length of the burn-in period was set to 20,000 iterations and the subsequent sample recording period was set an additional 40,000 iterations. For each k, ten replicates were run. Similarly to previous studies using smaller marker sets  for each accession and trait, phenotypic data was subjected to variance decomposition applying linear mixed models (LMM) with the statistics software ASReml 3.0 . All anaijkly is the phenotypic trait value in the ith block for the jth accession located at row k and position l. The overall mean is denoted as μ while b signifies the fixed block effect, c the fixed accession effect, r ×p the random interaction between rows and positions  and e the random residual. Random effects were assumed to be independent except for the spatial term (r ×p) which was restricted to follow a two-dimensional first order autoregressive correlation structure (esy) adjusted for block and spatial environmental effects were obtained from the effect estimates as es,j =  + ĉjy and were used in subsequent analyses.where tructure  across pper se, the (broad sense) accession estimator heritability  BLUE values in Pustnäs subtracted with standardized BLUE values in Svalöv when traits were measured the same year .2r) between closely situated markers (according to the S. purpurea reference) was estimated using a maximum likelihood method  and only one representative marker, having the highest genotype call percentage in that group, were retained for further analysis. Redundant markers were nonetheless kept in a separate accessory marker list to enable future reference. In all, the fully filtered association mapping dataset comprised 19,411 polymorphic markers. Missing marker genotypes were imputed using the LD-kNNi method as implemented by LinkImpute. The number of nearest relatives (k) and the number of SNP markers within a 10 Mb distance that were in closest LD with the marker to be imputed (l), were optimized by LinkImpute and were determined as k = 15 and l = 5.Polymorphic sites used as markers for the association mapping itself were required to be biallelic, have clear genotypic calls for at least 75% of the individuals and MAF > 5%. Furthermore, any adjacently located indel polymorphisms that would cancel each other out  were removed. The LD (d method  implemenesy), a second series of multilocus linear mixed model (MLMM) analyses were performed, again using ASReml 3.0 , q and g are the vectors of fixed population ancestry and SNP genotype effects, respectively, u is the vector of random chip additive genetic effects  and chip additive genetic variance (log(p) values  was selected and during the backward phase, the included SNP with the smallest -log(p) value was eliminated. Forward selections of up to five markers were made and the model with the maximum number of markers all exhibiting Bonferroni corrected p-values of 0.2 or less (p < 1.03 × 10-5) was reported and further analyzed. The percentage variance explained of any marker i added to the model (i (i ((q) as well as all marker genotype effects (g) of stronger statistical significance than marker i in order to discount R2 inflation due to collinearity . Both Genetics R-package.where  effects  linked tS. purpurea genome . The size of the region to check genes were based on LD estimates of S. viminalis , analyses were made were the model component of individual markers (Sg) was excluded.For the association analyses the full model previously presented was used, but in order to estimate other genetic parameters adjusted for ancestral structure such as the chip narrow sense heritability  between traits thereby also assessing the potential occurrence of genotype-by-environment (G × E) interactions, multivariate extensions of the previously described model were made treating each trait-year-environment combination as a separate variate  as:Furthermore, in order to structure adjusted estimate accession correlations  while the remainder 2,468 markers could only be mapped to 569 incompletely integrated sequence in smaller sized scaffolds  indicating G × E-interactions . This wasr-estimates. The structure-adjusted accession correlations between different growth traits were above 0.50 in 50% of the possible correlations in Pustnäs and in 82% of the correlations in Svalöv while correlation magnitudes between the two different phenology traits measured in Pustnäs never exceeded 0.5 (-0.07 to 0.15)  for the number of shoots (Nsh), estimated biomass (SumBA) and fresh weight (FW) both at Pustnäs and Svalöv . For FW to 0.15) . Very fep < 0.2 after Bonferroni correction) were found . The interpretation of the marker S1_361520786 effects also requires some caution because only two rare allele homozygotic accessions constituted the basis for the apparent recessive effect raising the possibility that the effects may be overestimated. Nonetheless the effect cannot be dismissed as a case of cryptic structure because the two homozygotic accessions involved were almost completely unrelated according to kinship estimates (𝜃 = 0.010).When considered individually, trait-associated markers explained from 1.8 to 18.1% of the accession variation but when discounting for association effects dependent on single homozygotes or to the five accessions beyond the Ural Mountains, any single trait-marker association explained up to 9.2% of the accession variation. Taking into account the variation explained by all marker associations for a trait,  in 2017 . With re in 2017  in compa in 2017  althoughA total of four associations were found for plasticity traits. Interestingly, one specific marker on chromosome 12 (S1_246135575) was associated both with the plasticity of number of shoots 2014, SumBA16 and FW17 explaining from 7.4 to 8.6% of the accession variation , S8. In r = 0.35), were between markers whose trait association effects depended on the rare homozygotic accession group originating beyond the Ural mountain range and these were viewed with skepticism anyway. In summary, there was no substantive evidence that the other associations constituted multiple reflections of a lower set of unique associations.In order to know whether the multiple marker-trait associations detected in this study could reflect a smaller set of unique associations, we estimated linkage disequilibrium (LD) correlations between all markers that had significant trait associations. However, such correlation estimates were generally very low indicating no or little LD . Only 14All genes in the region 3000 bp up- and downstream the associated markers are reported in Salix viminalis but recently within the same genera in S. purpurea  and for the number of shoots in 2011 (Nsh11) in Pustnäs, such associated markers explained over 20% of the total accession variation. GWAS in different d traits  that in 2R to be detected with any confidence, the results of this study agree with the notion that biomass and phenology traits are regulated by a multitude of small effect QTL, a concept originally suggested by Populus studies . In line with this result, aggregated biomass traits, such as summed basal area and fresh weight, showed consistently strong accession correlations between years of measurement. For other traits, accession correlations were generally lower and associations were less stable and unique for the trait measurement. Some stable associations were found in the previous candidate gene study  where, fronments . The genIt is notable that the association of SNP S1_361520786 to both FW14 and FW17 in Svalöv was largely dependent on a considerable recessive effect linked to two unrelated accessions that were homozygous for the rare C-allele of the SNP . TherefoSalix. We found no common marker associations between environments for the different growth or phenology traits. This finding could of course be an effect of the statistical power of the analysis being insufficient to detect one and the same association repeatedly but could also be due to G × E-interactions between the Pustnäs and Svalöv. Indeed, the moderate accession correlations between Pustnäs and Svalöv indicate substantial G × E-interactions between the two environments and Populus balsamifera grown in common garden experiments at two locations in Canada, while bud set shared more common associations between locations  and in autumn  temperature, and in soil type but both represent typical environments used for practical cultivation of SRC ocations . These cGiven the observed G × E-interactions in the current study, we estimated the plasticity of each genotype by examining the standardized differences in trait accession BLUEs between Pustnäs and Svalöv and then mapped this difference for associations. One specific marker (S1_246135575) was identified to associate with the plasticity of three different growth and biomass traits  thus being remarkably consistent. This marker explained around 8% of the accession variation suggesting that we have identified an important element of the genetic base for growth trait plasticity. Furthermore, the genotypic effect of this marker showed that the rare C-insert allele produced an increase in biomass traits in one environment while a decrease in the other environment. Interestingly these effects behaved in a largely additive manner . The maiSalix using a GWAS approach with biomass traits, that successfully has identified a set of candidate markers connected to growth and phenology traits as well as to plasticity of traits. Each marker does not explain much of the total phenotypic variation but the effect of the marker may still be substantial. Adding several markers together explain a greater amount of the accession variation. In a breeding perspective these markers and preferably a set of markers with specific allele combinations could be of value and interesting to use in the selection of parents as well for selection of individuals in early stages of the breeding cycle. An early selection of seed plants would reduce the number of plants for field testing and thus also make the breeding more cost effective. Some of the marker-trait associations identified were connected to a homozygote genotypic class with few individuals of large effect, these markers need to be validated through, for example, crossings of heterozygotes and study of the phenotypes in the segregating offspring, i.e., multiple family QTL mapping  of the accession variation although, in concert, associations with budburst and number of shoots occasionally explained about 20%. Associations were generally not repeated across measurement years and environments, due to limited statistical power or to the substantial G × E-interactions observed. Still, one particular association for fresh weight was observed to be consistent across years in the Svalöv experiment and for the plasticity of growth traits between Pustnäs and Svalöv, another association was detected which was consistent across years and traits to a greater degree. Further examination of these associations should contribute to an improved understanding of the genetic architecture of important traits in Salix and facilitate the development of marker-assisted breeding methods for this species.The results from this study using a population of unrelated accessions have given basic information about marker-trait associations that are of importance and could be used for future strategies and breeding of A-CR-W, SB, and MW planned and designed the research. N-EN and A-CR-W performed the field measurements. HH and A-CR-W analyzed the data and wrote the manuscript. All authors read and approved 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.


A genomic selection study of growth and wood quality traits is reported based on control-pollinated Norway spruce families established in 2 Northern Swedish trials at 2 locations using exome capture as a genotyping platform. Nonadditive effects including dominance and first-order epistatic interactions  and marker-by-environment interaction (M×E) effects were dissected in genomic and phenotypic selection models. Genomic selection models partitioned additive and nonadditive genetic variances more precisely than pedigree-based models. In addition, predictive ability in GS was substantially increased by including dominance and slightly increased by including M×E effects when these effects are significant. For velocity, response to genomic selection per year increased up to 78.9/80.8%, 86.9/82.9%, and 91.3/88.2% compared with response to phenotypic selection per year when genomic selection was based on 1) main marker effects (M), 2) M + M×E effects (A), and 3) A + dominance effects (AD) for sites 1 and 2, respectively. This indicates that including M×E and dominance effects not only improves genetic parameter estimates but also when they are significant may improve the genetic gain. For tree height, Pilodyn, and modulus of elasticity (MOE), response to genomic selection per year improved up to 68.9%, 91.3%, and 92.6% compared with response to phenotypic selection per year, respectively.Subject Area: Quantitative genetics and Mendelian inheritance Pinus taeda L.), maritime pine (Pinus pinaster Ait.), Norway spruce (Picea abies (L.) Karst.), white spruce (Picea glauca (Moench) Voss) and hardwood eucalypt species (Genomic selection (GS) is a breeding method that uses a dense set of genetic markers to accurately predict the genetic merit of individuals  and it h species . The non species .Several recent studies show dominance and epistasis may be confounded with the additive effects in both pedigree-based relationship matrix models  and genoSignificant genotype-by-environment (G×E) interaction is commonly observed among the different deployment zones for growth traits in Norway spruce , 2017. LIn all, 1,370 individuals were selected from two 28-year-old control-pollinated (full-sib) progeny trials. The progeny trials consist of the same 128 families generated through a partial diallel mating design involving 55 parents originating from Northern Sweden. Progenies were raised in the nursery for 1 year at Sävar, and the trials were established in 1988 by Skogforsk in Vindeln  and in Hädanberg .A completely randomized design without designed pre-blocking was used in the Vindeln trial (site 1), which was divided into 44 post-blocks based on the terrain. Each rectangular block has 60 trees (6 ×10) with expected 60 families at a spacing of 1.5 m × 2.0 m. The same design was also used in the Hädanberg trial (site 2) with 44 post-blocks. But for the purpose of demonstration, there was an extra block with 47 plots, each plot with 16 trees (4×4) planted in site 2. Based on the spatial analysis, in the final model, the 47 plots were combined into 2 big post-blocks.The tree height was measured in 2003 at the age of 17 years. Solid-wood quality traits including Pilodyn penetration (Pilodyn) and acoustic velocity (velocity) were measured in October 2016. Pilodyn penetration, a surrogate for the trait of wood density, was measured using a Pilodyn 6J Forest  with a 2.0 mm diameter pin, without removing the bark. Velocity, closely related to microfibril angle (MFA) in Norway spruce , was detBuds and the first-year fresh needles from 1370 control-pollinated progeny trees and their 46 unrelated parents were sampled and genotyped using the Qiagen Plant DNA extraction protocol  and DNA quantification was undertaken using the Qubit® ds DNA Broad Range Assay Kit . The 46 parents were sampled in a grafted archive at Skogforsk, Sävar  and in a grafted seed orchard at Hjssjö . Probe design and evaluation are described by The variance components and breeding values (BVs) for the genotypes of each trait in the 2 trials were estimated by using the best linear unbiased prediction (BLUP) method in 3 univariate models that included either additive (A), both additive and dominance (AD) or additive, dominance, and epistasis genetic effects (ADE) as mentioned below. In practice, pedigree-based models (ABLUP) had only 2 models because it is not possible to estimate the epistatic effect in full-sib progeny trials without replicates for each genotype.Five models were used to partition the genetic variance into additive, dominance, and epistatic variances.For the pedigree-based model with additive effect only (ABLUP-A):For the full pedigree-based model with both additive and dominance effects (ABLUP-AD):For the genomic-based model with additive effect only (GBLUP-A):For the genomic-based model with both additive and dominance effects (GBLUP-AD):For the full genomic-based model with additive, dominance, and epistatic effects (GBLUP-ADE):y is the vector of phenotypic observations of a single trait; i is the inbreeding depression parameter per unit of inbreeding, b is the vector of random post-block within site effects, d and X, W, Z, Z1, Z2, Z3, Z4Z, 1, and Z6 are the incidence matrices for f is a vector of genomic inbreeding coefficients based on the proportion of homozygous SNPs. Although Xiang et al. (2016) and fi) in equation (3–5) were excluded in the final model because it is not significant for all the traits. The random post-block effects  in equation [2] were assumed to follow D is the pedigree-based dominance relationship matrix and e was assumed to followwhere where A) and dominance (D) relationship matrices were constructed based on information from pedigrees. The diagonal elements (i) of the A were calculated as D matrix, the diagnonal elements were all one /2 . In the Reml 4.1  or ASRemReml 4.1 . A D relage in R .The genomic-based additive   and trace (tr) . In the a), dominance (d), epistatic effects , and me is the additive main marker-by-environment effect. Therefore, with CS and FAMK structures, the main marker effect (M), M + marker-by-environment interaction effect (A), and A + dominance effect (AD) from the GBLUP-AD and ABLUP-AD models could be estimated. In the CS model, m is the main term for markers and Ψ is a diagonal matrix with diagonal elements referred to as specific variances. In two-trial analyses, K=0, then To compare the predictive ability of models with and without a G×E interaction term in additive effects, a single-site model without specifying the G×E interaction (i.e. ABLUP-AD and GBLUP-AD with DIAG structure for additive + IDEN for dominance) and a MET model (i.e. ABLUP-AD and GBLUP-AD with CS/FAMK for additive + IDEN for dominance) were used. Based on the model comparison, CS were used for additive effects of Pilodyn, velocity, and MOE and FAMK were used for additive effects of tree height. In the MET models, additive effect AG model To compare the relative quality of the goodness-of-fit of the different models, the Akaike Information Criterion (AIC) and the fitted line plot .The expected performance of GS compared to standard phenotypic selection (PS) was evaluated only for the GBLUP-AD model by calculating the response to genomic selection (RGS) as a percentage of the population average as follows:where  average . Responswhere ere used , except ere used .The 6 variance and covariance structures examined for the additive, dominance, and epistatic effects are presented in Table 3M×E effects for the additive or nonadditive effects were considered significant if the AIC values in MET analyses (e.g. under CS and FAMK variance structures) were smaller than the corresponding AIC values in single site (ST) analyses (e.g. under IDEN or DIAG variance structure only) for the same trait or if the Log-likelihood Ratio test (LRT) was significant. All models with CS for additive genetic effects were found performing best, except for the model with FAMK for tree height additive genetic effects . Based oEstimates of variance components, their standard errors (SE), and the variance proportion of each site for tree height and velocity from the 5 genetic models fitted  are shown in l traits . For exace (σa2) , in conte in σa2 . Pilodynh traits . For exaIn the ABLUP-AD model, tree height and velocity dominances showed significant effects based on the AIC  and 3. FEstimates of tree height and velocity narrow-sense heritability from ABLUP-A or GBLUP-A models were larger than those from ABLUP-AD or GBLUP-AD. For example, tree height narrow-sense heritability of 0.12 from ABLUP-A was larger than 0.10 from ABLUP-AD at site 1. Broad-sense heritability estimates were substantially larger than narrow-sense heritability estimates from both ABLUP-AD and GBLUP-AD at both sites for tree height and velocity. For example, tree height broad-sense heritability estimates were 253.8% and 166.7% of the narrow-sense heritability estimates from the GBLUP-AD model at site 1 and site 2, respectively. For tree height, Pilodyn and MOE, GBLUP-ADE produced exactly the same results as GBLUP-AD  because y)  and from ABLUP-A to ABLUP-AD for both sites . For Pilodyn and MOE, R2 was the same from GBLUP-A to GBLUP-AD and from ABLUP-A to ABLUP-AD, which was consistent with the zero estimates of dominance variances for both traits  . The fith traits . The difA comparison of BVs’ precision using the standard errors for the predictions (SEPs) between different models  is shown in A random selection of 10% of the population was used as a validation set. To test the ranking difference of estimated breeding values between 5 models, Spearman’s rank correlations were used . SpearmaThe cross-validation focused on comparing the predictive ability (PA) between GBLUP-AD and ABLUP-AD models and between MET and single-trial (ST) models for all traits; results are shown in Generally, PA was higher in the MET analysis than that in ST analysis for all traits, except for tree height . For PilFinally, we studied the additive M×E effects on the genomic-based estimated breeding values (GEBVs). There was a reduction in tree height PA if M×E was not included in calculating the GEBVs for site 2  for all traits from GBLUP-ADE is not shown in We compared the generation time of GS (ca. 12.5 years) with the generation time of the phenotypic selection (ca. 25 years), as in the traditional breeding program in Northern Sweden . A conseH2) have previously been made in tests of clones selected from commercial nurseries and with an unknown family structure. For example, tree height H2 estimates vary from 0.12 to 0.40 for Norway spruce (h2), which requires a family structure. Using a traditional pedigree-based model, epistasis estimation, on the other hand, requires full-sib family structure plus the replication of genotypes in clonal trials. Existing high-throughput single nucleotide polymorphism (SNP) genotyping technology, such as SNP arrays, re-sequencing, or genotyping-by-sequencing (GBS), allows genotyping larger numbers of SNPs, and therefore is used to study dominance and epistasis in populations without pedigree delineation of full-sib family structure in both animals  was higher than h2 estimated from pedigree-based ABLUP-A and ABLUP-AD (0.10–0.19) (h2 of 0.29 (0.02–1.09) based on 170 field tests with seedlings was higher than the average H2 of 0.18 (0.04–0.50) based on 123 field tests with clonal material  . In a prmaterial , indicatmaterial . The ratus study . The usue traits . It is ah2 from GBLUP-AD and ABLUP-AD when dominance is not zero. For example, tree height h2 estimates decrease by 13%–26%, less than the substantial decrease (50%–70%) reported in hybrid Eucalyptus by Our results show that the inclusion of dominance effects reduces estimates of Eucalyptus  had substantially significant additive M×E and nonsignificant small dominance M×E terms for both height and wood density. In our study, significant but small M×E effects for all traits were found only in additive genetic effects, not for dominance. Recent studies have shown that maximum PA can be reached when the model is based on additive and nonadditive effects . Ly et aIt was found that including dominance could improve PA when a considerable dominance variance in animal  and planPicea sitchensis)  , and eucchensis) . For insP. glauca x engelmannii) (The full model (GBLUP-ADE), which was extended to include 3 first-order interactions, shows almost the same results as GBLUP-AD for all 4 traits based on AIC . This inlmannii) , signifilmannii) , 2018 shEucalyptus. Thus, GS based on genomic-based expected genetic values is ideal for solid-wood quality improvement in Norway spruce.The main advantages of GS are to shorten the length of the breeding cycle and reduce phenotypic evaluation costs in plant and animal breeding . In NortThis is the first paper to study M×E using a different covariance structure for the additive and nonadditive effects and dominance in GS for forestry trees species. We found that M×E and dominance effects could improve PA when they are appreciably large. In a GBLUP-AD model, M×E contributed 4.7% and 11.1% of tree height phenotypic variation for sites 1 and 2, respectively. Dominance contributed 18.1% and 9.8% of tree height phenotypic variation for sites 1 and 2, respectively. The higher PA of the GBLUP-AD model for tree height compared to ABLUP-A and GBLUP-A models suggests that dominance should be included in GS models for genetic evaluations in forestry to improve the predictive accuracy or estimates of genetic parameters. Advanced M×E models could improve PA and should be included in the model fitting. GBLUP-AD could be a more useful model in breeding and propagation when tree breeders want to use the dominance using full-sib family seedlings.Financial support was received from Formas (grant number 230-2014-427), the Swedish Foundation for Strategic Research , and from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 773383 (B4EST project).esz061_suppl_Supplementary_MaterialsClick here for additional data file.


A large number of clinical studies have shown that interleukin-18 (IL-18) plasma levels are positively correlated with the pathogenesis and development of type 2 diabetes mellitus (T2DM), but it remains unclear whether IL-18 causes T2DM, primarily due to the influence of reverse causality and residual confounding factors. Genome-wide association studies have led to the discovery of numerous common variants associated with IL-18 and T2DM and opened unprecedented opportunities for investigating possible associations between genetic traits and diseases. In this study, we employed a two-sample Mendelian randomization (MR) method to analyze the causal relationships between IL-18 plasma levels and T2DM using IL18-related SNPs as genetic instrumental variables (IVs). We first selected eight SNPs that were significantly associated with IL-18 but independent of T2DM. We then used these SNPs as IVs to evaluate their effects on T2DM using the inverse-variance weighted (IVW) method. Finally, we conducted sensitivity analysis and MR-Egger regression analysis to evaluate the heterogeneity and pleiotropic effects of each variant. The results based on the IVW method demonstrate that high IL-18 plasma levels significantly increase the risk of T2DM, and no heterogeneity or pleiotropic effects appeared after the sensitivity and MR-Egger analyses. Type 2 diabetes mellitus (T2DM) is a complex metabolic disease and accounts for more than 90% of diabetic cases. Its pathogenesis involves both genetic predisposition and unhealthy living habits . The disAmong the known risk factors, inflammation has been identified as a potential cause of T2DM as well as other obesity-associated diseases, such as atherosclerosis and fatty liver . InflammMendelian randomization, greatly facilitated by the development of genome-wide association studies (GWASs), is a method for establishing causal effects between genetic traits and diseases by building instrumental variables (IVs) based on the information about single nucleotide polymorphisms (SNPs), i.e., phenotype-associated genetic variants . For MR In this study, we verified the assumption that T2DM is caused by high IL-18 levels. Next, we estimated the causal effect of IL-18 levels on T2DM by the MR method.We extracted summary-level data from GWAS datasets and processed the data by removing the SNPs not suitable for establishing IVs. We then calculated the Wald ratio of each IV, and we used the inverse-variance weighted (IVW) method to predict the causal effects of high IL-18 serum levels on T2DM. Upon completing the MR analysis, we evaluated the heterogeneity and pleiotropic effects of each variant, using the sensitivity analysis and the MR-Egger method, respectively .P < 5 × 10−8), using the GWAS data from the Cardiovascular Health Study (CHS) and a prospective population-based cohort study called InCHIANTI  consortium1. The odds ratio (OR), SE, and P-value of T2DM per allele were extracted. The P-value established for screening genotypes (P < 5 × 10−8) independent of type 2 diabetes is specifically referenced to a number of similar studies; the most authoritative of which is “Estimating the causal influence of body mass index on risk of Parkinson disease: A Mendelian randomization study,” which was published in PLOS Medicine in 2017.The GWAS data used for this study were obtained from the 2 to remove the interfering SNPs  (P < 0.05) were removed to meet the conditions for the MR analysis, making the IL-18-associated variants independent of the disease.Due to the potential linkage disequilibrium (LD), the IVs were chosen independent of each other to avoid over-precise estimates in subsequent analysis caused by genetic pleiotropy. According to the application principles of MR analysis, the study is based on Mendel’s second law of inheritance: the separation and combination of gene pairs controlling different traits do not interfere with each other; in the formation of gametes, the paired genes are separated from each other, and genes that determine different traits are randomly distributed between two gametes. When two genes are not completely independent, they will show a certain degree of linkage; this situation is called LD, and it greatly affects the exclusiveness of the variable tool to phenotypic inheritance, leading to subsequent calculation bias, generally called “over-precise estimates” . Althougistance) . Next, tX, Y, and Z to be IL-18, T2DM, and IVs, respectively, and the Wald ratio (XYβ) of IL-18 to T2DM through a specified variant can be calculated as follows:Mendelian randomization is a method applied by pooling Wald ratios of the IVs to verify the causal relationship between exposures and diseases . The WalZY represents the per-allele log(OR) of T2DM from summary-level data of Morris et al.  of IL-18 from summary-level data of Walston et al.  were calculated from the SE of each Wald ratio. Then, these data were pooled to estimate a weighted average of the causal effect by the IVW method. This method is one of the most commonly used methods for meta-analysis of fixed effects models. It summarizes effect sizes from numerous independent studies by calculating the weighted mean of the influence sizes, taking the inverse variance of individual studies as weights. The meta-analysis model for the point estimate is on the basis of the heterogeneity of the pooled data. The fixed effect model is applied for the case of no significant heterogeneity, while the random-effect model is used for others (where r others .Q-test and the I2 statistic were applied. Cochran’s Q-test applies a χ2 distribution with (k-1) degrees of freedom, where k is the number of variants for analysis; I2 = [Q - (k - 1)]/Q × 100% ranges from 0 to 100%. P < 0.01 and I2 > 50% are defined as significant heterogeneity  and no association with T2DM (P > 0.05) or LD effect  satisfied all conditions, including strong associations with IL-18 phenotypes /1.14] to 0.009 [(1.1505–1.14)/1.14]. This means that the causality effects we obtained from MR were supported by most of the individual SNPs, demonstrating that no single SNP dominated the IVW point estimate, and there was no heterogeneity in the variants .P = 0.044); the intercept size was 0.011 , suggesting that all variants were valid. There is no alternative pathway leading to the disease, and the IVW was applied under no pleiotropic effect.The pooled causal effects from the MR-Egger regression analysis are consistent with the IVW results: an estimated bate of T2DM per SD higher IL-18 plasma level was 0.122 . Additionally, the sensitivity analysis and the MR-Egger regression analysis also provided adequate evidence that the results were not due to heterogeneity or pleiotropic effects of any single variant.In this study, we conducted an MR analysis to explore the causal effect of IL-18 plasma levels on the risk of T2DM. The estimated causal impact resulting from the IVW method was 1.14 , and γ-interferon, and cause islet cell function defects and diabetes . The queFinding a solution for the high IL-18 levels may be a lengthy task. For instance, Schrezenmeir et al. used probiotic oligosaccharides to reduce the production of pro-inflammatory cytokines in intestinal cells and effectively reduced the burden of self-immunity . The useInevitably, this study has some minor limitations. When studying a single phenotypic variable, other phenotypes become confounding factors, so we introduced the MR concept, based on Mendel’s second law, the “law of independent assortment,” to solve this problem and to control genetic factors of different traits. We can insulate other pathway effects by linking genetic loci that control a single phenotype to the disease. But, as stated, the possibility of “non-isolation” still exists for some phenotypes that have not yet been completely described and which may be regulated by the same set of genetic loci. However, with the rapid updates and development of the databases, we expect this issue will be solved soon, e.g., by methods such as link prediction  or artifHZ wrote the manuscript. JH and LC carried out the experimental method design. S-LL did the supervision and modification of the article.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.