The maximum AUC achieved was 0.69  when cell-type proportion was included in the predictor.We conducted DNA methylation association analyses using Illumina 450K data from whole blood for an Australian amyotrophic lateral sclerosis (ALS) case–control cohort (782 cases and 613 controls). Analyses used mixed linear models as implemented in the OSCA software. We found a significantly higher proportion of neutrophils in cases compared to controls which replicated in an independent cohort from the Netherlands (1159 cases and 637 controls). The OSCA MOMENT linear mixed model has been shown in simulations to best account for confounders. When combined in a methylation profile score, the 25 most-associated probes identified by MOMENT significantly classified case–control status in the Netherlands sample (area under the curve, AUC = 0.65, CI Clinical heterogeneity in presentation of ALS12 Indeed, a methylome-wide association study (MWAS) has suggested that neurodegenerative processes in ALS may be associated with DNAm alterations.13 In this study, the authors interrogated the methylation status of genome-wide CpG loci in postmortem spinal cord tissue. Despite the very small sample size , the authors reported 4261 significant differentially methylated positions (DMPs), annotated to 3574 genes. Functional enrichment analyses showed these genes to be highly enriched in biological functions related to immune and inflammation response. However, the presence of confounding factors, and failing to account for these confounders, has been widely recognized as a concern in MWAS,14 because they could lead to spurious association results. For example, Figueroa-Romero et al.13 did not account for the potential confounding of cell-type composition, as there is evidence that these explain much of the observed variability in DNAm.16 Nonetheless, identification of DMPs across the genome that may drive or be driven by ALS pathogenic processes remains of importance, especially for biomarker development.DNA methylation (DNAm), which in mammals is almost exclusively found in cytosine–guanine dinucleotides (CpG), is a widely studied epigenetic modification. Aberrant DNAm patterns can be consequence of environmental exposures, and/or cause or consequence of disease, and have been hypothesized to play a role in neurodegenerative diseases (including ALS).17 However, predicted confounders have inherent classification error, and may only explain a proportion of the variation attributable to the directly measured covariates, which may result in inflated test statistics due to the uncaptured variation of confounders.18 More importantly, recent studies show that correction approaches  widely used in standard MWAS and association studies of other molecular phenotypes may induce bias, which persists for large sample sizes and replicates out-of-sample.19Confounders in the context of DNAm studies need careful consideration. Some confounders such as sex and technical batch effects are usually recorded and can be modeled as covariates. However, other recognized lifestyle confounders may exist, but may not be recorded. Furthermore, there could be confounders that are present, but unknown. Some case–control DNAm differences, driven by cell-type composition, or changes due to environmental exposures, medications, or complications of the disease, may be considered confounders, or alternatively, may be considered of primary interest depending on the context of the scientific question. Some unmeasured confounders can be inferred from DNAm reference-based classification methods, for example the Horvath age predictor or the Houseman algorithm to predict cell-type proportions (CTP).18 implements mixed linear model (MLM) approaches: MLM-based omics association (MOA) and multi-component MLM-based omics association excluding the target (MOMENT). MOA and MOMENT analyses account for trait-associated probes that are highly correlated with other trait-associated probes across the genome, and assume effect sizes are drawn from a normal distribution. MOA assumes a single distribution of effects sizes, while MOMENT allows a different effect size distribution for the most-associated probes. Fewer trait-associated probes are identified in MOA and MOMENT analyses compared to linear regression, but simulations18 show that probes that are significantly associated from these analyses are more likely to be true positives. Briefly, the MOA method fits a random genome-wide DNAm factor per person with variance–covariance matrix (the omics relationship matrix or ORM) between individuals built from genome-wide DNAm sites ; this model is analogous to the MLM association method implemented in EMMAX20 and GCTA21 for SNP data. Extensive simulations showed high false-positive rate (FPR) in standard linear regression MWAS, while both MOA and MOMENT controlled for false discovery with little loss of power.18 However, in some scenarios, the more stringent MOMENT method is needed to control the FPR if a proportion of DNAm sites are much more correlated than the others, at the cost of slightly reduced power. The MOMENT method fits an MLM with two random-effect components for each probe tested (and hence two ORMs between subjects computed from two sets of DNAm sites), with the DNAm sites grouped by their associations with the trait .18 Hence, the MOMENT method is more likely to identify DNAm differences that have a specific role in disease rather than reflect factors that impact multiple DNAm sites across the genome.The OmicS-data-based Complex trait Analysis (OSCA) software95% = [0.58–0.63], p = 5.6 × 10−11. The classification accuracy increased when the effects associated with predicted immune CTP were included .In this study, we applied both the MOA and MOMENT methods to a disease trait (ALS) and compared results with standard linear regression methods. We identified significant differences in predicted immune CTP and one significantly DMP between cases and controls. We used the estimated effect sizes of all DNAm sites, using best-linear unbiased prediction (BLUP) to calculate individual DNA methylation profile scores (MPS) in an independent ALS sample. The MPS classified ALS case–control status with area under the curve (AUC) of 0.61, CI23 Hence, our first analysis was to investigate differences in predicted CTP between cases and controls. We used the Houseman algorithm based on purified cell types from whole blood15 to estimate blood CTP for each individual based on the DNAm data. Using stepwise backward logistic regression models, increased neutrophil proportions were found to be significantly associated with ALS, after Bonferroni correction  , monocytes , B lymphocytes , and natural killer cells  were all significantly associated with ALS .p = 3.1 × 10−7, the number of DMPs passing significance are 476 in a linear model without any covariates; 30 in a linear model with the first 10 PCs, calculated from the ORM as fixed effects added to the model as covariates; 12 in MOA, and 1 in MOMENT , is better controlled using MOA and MOMENT compared to the linear regression models  are still highly correlated  than with MOMENT  in the AU MOMENT analysis, 94 were available in the NL sample; however, none replicated at p < 0.05/94, i.e. 5.3 × 10−4 . Hence, the lack of replication of individual probes may reflect lack of power. Consistent with this conclusion, we found the effect sizes of MOMENT results for the AU and NL samples for these 94 probes were correlated  the To provide quantitative description of the relationship between case–control status and DNAm covariates, we estimated the proportion of variation in case–control status captured by genome-wide DNAm . We also assessed the effect on classification accuracy of MPS derived from estimated effect sizes (from OREML) attributed to each CTP. Indeed, CTP-derived MPS alone were a better classifier than BLUP scores . Classification efficacy was further increased when both BLUP-derived DNAm effect sizes and CTP effect sizes were used together to calculate the MPS .The BLUP model provides jointly estimated effect sizes for each probe, but assumes probe effect sizes are drawn from a normal distribution. The AUC for AU as discovery cohort and NL as target was 0.61 , using all probes with p < 0.5 . However, MPS based on MOMENT results gave higher AUC for all p value thresholds tested, despite fewer probes passing each significance threshold. The maximum MOMENT AUC was 0.65  with probes with p < 1 × 10−4 (m = 25). A model that included MPS calculated with MOMENT-derived effect sizes and CTP effect sizes gave AUC = 0.67 . We note a negative correlation between MOA and MOMENT MPS, despite high correlation of effect sizes  overlapped with brain mQTL regions25 (p < 1 × 10−5) and GWAS SNPs26 (p < 5 × 10−8). We found no evidence for overlap with GWAS signals . The association was not replicated in the independent NL study, but power analyses suggest this may reflect effect size and sample size, reminiscent of early underpowered GWAS for which increasing sample sizes have led to many new (highly replicated) discoveries in the past decade.28 Despite lack of replication of the most-associated probe, out-of-sample classification using effect sizes estimated from the 25 most-associated DNAm sites in the AU sample gave a classification AUC of 0.65 (p = 2.2 × 10−29) in the NL sample. We summarize literature evidence of a functional role for CXXC5 in neurodegeneration and functional annotation of 25 most-associated DNAm sites in a Supplementary Note. We found better out-of-sample classification when using DNAm effect sizes estimated from MOMENT compared to MOA or linear regression results, despite fewer probes detected at each association p value threshold. Our results support the recommendation of Zhang et al.18 to use the MOMENT over MOA model, since MOA results may include more false-positive associations.Using the most stringent MOMENT model, we identified 1 DMP between ALS cases and controls, which is annotated to 95% = [0.66–0.71], p = 4.3 × 10−34). We are careful to use the term out-of-sample classification rather than prediction, because the blood samples available to us in both the AU and NL cohorts were not taken prior to diagnosis, hence the strength of classification may reflect consequences as well as causes of disease. The trans-national out-of-sample classification is a strength of our study, but we recognize that best-practice medication and clinical management are likely shared across countries. In these historically collected samples we have incomplete records of riluzole use, which was the only approved medication at the time of sample collection. Despite these caveats it is noteworthy that the AUC is much higher for DNAm classification (here AUC = 0.69 from a discovery sample of 782 cases and 613 controls) compared to SNP polygenic risk score prediction . Comparison of genetic and DNAm predictors for some complex traits also found much smaller discovery samples are needed for DNAm predictors.29 However, this will also depend on the underlying (epi)genetic architecture of the trait .The maximum out-of-sample classification was achieved using a score calculated from BLUP-estimated DNAm effect sizes together with effect size estimates for predicted CTP . Differences in CTP between cases and controls is an important contributor to the out-of-sample classification, consistent with reports of aberrant activation of the peripheral immune system in ALS,36 However, blood is an easily accessible tissue which is relevant for generation of biomarkers associated with disease. Biological or environmental interpretation of DNAm associations can be made as downstream analyses after their discovery. Variation between people in DNAm controlled by SNP variation has been shown to have high correlation between brain and blood,37 which provides further support that blood may be an appropriate tissue for the goal of developing early diagnostic biomarkers. A second limitation is that the blood sample available to us from both the AU and NL cohorts had incomplete clinical records, both in relation to time since diagnosis and with respect to clinical management and treatment. Ongoing sample collections in both countries are now collecting such data more consistently.Our study has several limitations. First, a perceived limitation of our study may be that blood is not a relevant tissue for understanding the biological mechanisms underlying ALS, due to the tissue-specificity of most DNAm patterns.In summary, we applied a new OSCA analysis pipeline to DNAm data measured in whole blood in an Australian ALS case–control cohort. The MOMENT method is expected to identify differences in DNAm associated with disease independent of confounding factors such as differences in cell-type proportion or smoking that generate widespread DNAm changes. An MPS calculated from the 25 most-associated probes identified by MOMENT, and an MPS based on cell-type differences both generate significant classification of ALS in an independent sample Fig. , with th38 Control subjects were healthy individuals free of neuromuscular diseases, recruited as either partners or friends of patients with ALS or community volunteers. Those with a recorded family history for ALS (including those recorded as testing positive for known mutations) were excluded as both cases or controls in both AU1 and AU2. Additional controls for the AU2 cohort were monozygotic (MZ) twin pairs aged >65 years contributed from the Older Australian Twin Study (OATS)39 recruited at QIMR Berghofer Medical Research Institute, University of New South Wales and the University of Melbourne. Twin pair data helped in quality control (QC) checks but only one twin from each pair was used in analyses. Written consent was obtained from all individuals enrolled in this study, and the study was approved by the corresponding HREC at the different sites: University of Sydney, Western Sydney Local Health District, Royal Brisbane and Women Hospital Metro North, South Metropolitan Health Service, Macquarie University, QIMR Berghofer Medical Research Institute, University of New South Wales and the University of Melbourne. The mean predicted age,40 predicted smoking scores,29 and sex distribution between cases and controls for the cohorts used in this study can be found in Supplementary Table The Australian ALS cohort (AU) consisted of two cohorts, AU1  and AU2  .42 All ALS cases were diagnosed with definite or probable ALS according to the revised El Escorial criteria,38 and those with a recorded family history for ALS were excluded. All participants gave written informed consent and the institutional review board of the University Medical Center Utrecht approved this study.A cohort from the Netherlands (NL) was available to us for replication analyses, collected under Project MinE.For the AU ALS datasets, bisulfite conversions were performed in 96-well plates using the EZ-96 DNA Methylation Kit . Prior to conversion, DNA concentrations were determined by the Take3™ Micro-Volume Plate on the Epoch™ Microplate Spectrophotometer  and standardized to include 500 ng. Three technical replicates were included in each conversion to assess repeatability. The following DNA samples were obtained from the NIGMS Human Genetic Cell Repository at the Coriell Institute for Medical Research: CEPH NA06997 and CEPH NA07029. Each DNA sample was included as a control on alternating plates. One sample from each run was duplicated on the plate and one sample duplicated from a different plate. DNA recovery after conversion was quantified using the Take3™ Micro-Volume Plate on the Epoch™ Microplate Spectrophotometer . Samples that showed incomplete bisulfite conversion  were not taken forward to the assessment of DNA methylation. Bisulfite converted DNA samples were hybridized to the 12 sample, Illumina Infinium HumanMethylation450 Beadchip  using the Infinium HD Methylation protocol and Tecan robotics. DNAm data for the NL sample were generated under similar protocols.43 The same pipeline for DNA methylation (DNAm) data processing and QC was applied to all samples. AU1 and AU2 samples were processed together . QC threshold parameters (Supplementary Note) determined samples and DNAm sites to exclude prior to normalization  were extracted, decomposed into principal components, and each component regressed against slide, chip column, chip row, and sex to test for batch effects. The association detection p value threshold was set to 0.01. For both datasets technical variation was not completely removed after FN and some known confounders affect DNA methylation. Thus, we perform an additional adjustment step using the normalized DNAm probe values  in linear regression models as response variable and predicted age, sex, chip position, predicted CTP , predicted smoking scores and slide (as random effect) as covariates. The residuals from this adjustment step were used for downstream MWAS analyses. We hypothesized the effect of this pre-adjustment should have a more pronounced effect in standard linear regression MWAS results compared to mixed linear models. Supplementary Fig. −3), compared to both MOA (−3) and MOMENT  effect sizes. Excluding these DNAm sites also reduces the multiple testing burden in MWAS. In all, 160,304 probes remained for analysis in the AU cohort , β is a p × 1 vector of the fixed covariate effects on the phenotype, W is an n × m matrix of m standardized DNAm values, where m is the number of DNAm sites, ui is an m × 1 vector of the joint random probe effects on the phenotype, and e is an n × 1 vector of residuals. The variance of y is var(y) = V=WW′A = WW′/m and A is then the omics-data-based relationship matrix (ORM) and 24 but where variances represent factors that may include both causes and consequences of the phenotype. The baseline variance of the phenotype case–control status in the AU sample is approximated as the binomial variance of P(1−P) = 0.246, where P is the proportion of the sample that are cases (P = 0.56), with the reported Based on extensive simulation and application to real DNAm data, Zhang et al.wi  and bi . We used the 10 principal components estimated from the ORM as covariates.For linear regression MWAS we used models without:We conducted MLM MWAS using both MOA and MOMENT. The MOA MWAS model isW, but this would be computationally very demanding. In this model it is assumed that all probe effects follow a single distribution, which may not reflect the true distribution. In the MOMENT model18 DNAm probe effect sizes are drawn from two effect size distributions for different probes sets, selected according to their association statistics in an initial linear regression model, with each group then fitted as a random-effect:Wj is an n x mj matrix of standardized DNAm probe values in the jth group, and mj is the number of DNAm sites in the group (excluding the DNAm sites in the 100 Kb region centred at the probe being tested). After conducting MWAS, DNAm sites were mapped to the latest GRCh38/hg38 genome build45 and annotated to genes, based on GENCODE v22. We used the rb method25 to quantify the similarity between probe effects, which accounts for sample overlap and errors in the estimated probe effects.In this model, the probe being tested is fitted twice, once as a fixed and also as a random effect, which results in slightly reduced power compared to a  model in which the focal probe is excluded from u from Eq.  were fitted as fixed effects. Classification efficacy of the MPS was evaluated by the area under the receiver-operator characteristic curve (AUC) that relates the false-positive rate (specificity) to the true-positive rate (sensitivity), in logistic regression. We used the R package pROC46 to plot the receiver-operator characteristic curves and calculate AUC for each MPS. To evaluate the possible gain in classification accuracy, we calculated MPS from the fixed effects of predicted CTP, estimated in an OREML analysis (Eq. (MPS were calculated for each individual in the NL sample as the sum of DNAm probe values weighted by their effect sizes estimated in the AU sample (Supplementary Fig. from Eq. , as implFurther information on research design is available in the Supplementary InformationReporting summary


DCC, which encodes the netrin-1 receptor and has an important role in the development of the nervous system (p = 4.29 × 10−11 with neuroticism), as well as SARM1, which has been previously implicated in axonal degeneration . We additionally conducted a phenome-wide MR study for each of these 12 genes to assess potential pleiotropic effects on 700 complex traits and diseases. Our findings suggest that genes such as SNX32, which was initially associated with increased risk of Alzheimer disease, may potentially influence other complex traits in the opposite direction. In contrast, genes such as CTSH  and SARM1 may make worthwhile therapeutic targets because they did not have genetically predicted effects on any of the other phenotypes after correcting for multiple testing.Leveraging high-dimensional molecular datasets can help us develop mechanistic insight into associations between genetic variants and complex traits. In this study, we integrated human proteome data derived from brain tissue to evaluate whether targeted proteins putatively mediate the effects of genetic variants on seven neurological phenotypes . Applying the principles of Mendelian randomization (MR) systematically across the genome highlighted 43 effects between genetically predicted proteins derived from the dorsolateral prefrontal cortex and these outcomes. Furthermore, genetic colocalization provided evidence that the same causal variant at 12 of these loci was responsible for variation in both protein and neurological phenotype. This included genes such as  FurtherWe obtained genome-wide summary statistics for seven phenotypes by using findings from GWAS for which summary statistics have been made available: Alzheimer disease,2 < 0.01 with a reference panel consisting of 10,000 unrelated individuals from the UK Biobank study who were of European descent.,Linkage disequilibrium (LD) clumping was undertaken to identify independent pQTL for downstream analyses. This was achieved using PLINKj is the SNP-exposure association and σXj is the standard deviation for the SNP-exposure association for variant j. Instruments with an F-statistic > 15 were selected to reduce the likelihood of weak instrument bias in downstream analyses.where γMR estimates were derived based on the Wald Ratio methodheritability < 0.05) according to analyses undertaken previously by the Neale Lab  oSARM1 and CTSH, for which our initial analysis did not provide evidence of any putative side effects based on Bonferroni corrections. This was undertaken by comparing the estimates from the analysis of these targets on the 700 outcomes with 500 randomly selected pQTL from our initial sample. We then ranked MR effect estimates and calculated permutated p values based on the rank of SARM1 and CTSH effects compared to those of the other 500 proteins. Any effects which provided evidence based on Ppermuted < 0.05 were further subject to the same genetic colocalization analysis as previously undertaken. Lastly, we investigated evidence of genetic colocalization between pQTL and expression quantitative trait loci (eQTL), also derived from brain tissue, based on analyses by Qi et al. .We also performed additional analyses for Applying our selection critieria to identify independent pQTL resulted in 692 proteins which were eligible for analysis . However−05   . To suppThis identified 12 loci which provided evidence of genetic colocalization based on a PPA > 0.8 for the coloc method or a CLPP > 0.01 for eCAVIAR results . Each ofDCC locus, which was associated with neuroticism risk in our analysis (p = 4.29 × 10−11), encodes the netrin-1 receptor, which has been reported to play a role in the development of the nervous system. Similarly, SARM1 was associated with amyotrophic lateral sclerosis risk (p = 1.76 × 10−08) and has been previously reported to influence axonal degeneration.Amongst the results with evidence of genetic colocalization were GWAS loci which harbor genes thought to be involved in neurological functionality. For example, the −08). As such, evidence of genetic colocalization with pQTL derived from a tissue type relevant to these phenotypes can be valuable in terms of prioritizing loci that are yet to be uncovered by GWAS. Two examples of this include FLOT2 (p = 3.97 × 10−05 with intelligence), which encodes the neuronal signaling factor flotillin-2, and SIDT1 (p = 1.34 × 10−05 with insomnia), which is a dsRNA transporter. In contrast, other loci highlighted by our findings are putatively novel trait-associated variants that have not yet reached genome-wide evidence thresholds , along with the same genetic colocalization thresholds used previously, there was evidence of pleiotropy at various loci. For example, based on these criteria, the lead pQTL at SNX32 colocalized with 12 different phenotypes along with Alzheimer disease in the initial analysis (with p = 1.68 × 10−05). As depicted in −05) and body fat percentage (p = 2.51 × 10−05). Further evaluations of this target are necessary to discern whether increased genetic liability toward Alzheimer disease risk is responsible for these predicted effects . Alternatively, genetic variation at this locus may influence these outcomes separately via alternate biological pathways , which may make SNX32 less attractive as a therapeutic target.For each of the 12 loci highlighted by our initial analysis, we conducted a phenome-wide MR analysis to evaluate putative pleiotropic effects on 700 complex traits and diseases . Based oSARM1, which had an effect on amyotrophic lateral sclerosis risk in the initial analysis (p = 1.76 × 10−08), did not provide evidence of an effect with any of the 700 outcomes assessed based on multiple testing corrections . However, this effect was not supported by evidence of colocalization (PPA = 12.7% and CLPP = 2.92 × 10−04), and this effect had an FDR of 0.06.In contrast, there were several genes which did not provide evidence of pleiotropy based on this analysis. For instance, the lead pQTL for rections B. We furCTSH, which encodes the cathepsin H protein, were on standing and sitting height (p = 4.28 × 10−05 and p = 1.49 × 10−05 respectively). However, these effects were not supported by evidence of genetic colocalization. Examples such as SARM1 and CTSH should therefore be prioritized as worthwhile candidates for therapeutic intervention, given that a lack of pleiotropic effects from this analysis using human genetics supports their safety and efficacy.Additionally, the only effect surviving Bonferroni corrections for We have conducted a study to characterize genetic variants associated with neurological phenotypes by harnessing brain-derived protein data. Under the principles of MR, we identified 43 genetically predicted effects across the genome, and this suggested that there may be a shared genetic architecture between neurological phenotypes and the subset of proteins studied. Applying two different genetic colocalization techniques provided evidence that effects at 12 of these loci were driven by a common causal variant. We next undertook a phenome-wide association study for each of these 12 proteins by applying this approach systematically to 700 complex traits and disease endpoints. Doing so elucidated pleiotropic proteins associated with various outcomes, along with protein targets associated more specifically with their corresponding neurological phenotype as identified in our initial analysis.2 = 0.70 between brain and whole blood.ERLIN1 in this study shows no evidence on an effect on this protein in whole blood based on the most comprehensive plasma protein QTL analysis to date by Sun et al.CTSH (rs34593439), although this protein has yet to be linked with Alzheimer disease in whole blood analyses based on evidence from the EpiGraphdb platform  and is responsible for expression of the nectin-1 receptor. Nectin-1 has previously been implicated in various neurological and psychiatric disorders, including schizophrenia and depression.FLOT2, which was associated with intelligence (p = 3.97 × 10−05), encodes neuronal signaling factor flotillin-2, and it has been linked previously with autism and related disorders.PSMB4, which encodes a member of the proteasome B-type family, was associated with depression risk (p = 2.36 × 10−05). Proteasomes have been implicated previously in risk of neurodegenerative disorders.,Among the loci highlighted in our study are various genes which have been previously reported to play a role in brain-related activities. This includes SARM1  and CTSH (p = 5.57 × 10−05 with Alzheimer disease) represent the most promising candidates based on our evaluations. This is because our phenome-wide analyses did not detect strong evidence of pleiotropic effects on non-neurological traits, which may foreshadow adverse side-effects from targeting these genes or their mechanism of action using therapeutics. Evidence from the literature has reported that genetic deletion of SARM1 in mice can block pathological axon degeneration.,SARM1 may therefore be a putatively viable strategy for treating neurodegenerative diseases characterized by axon loss, such as amyotrophic lateral sclerosis.CTSH has also previously been linked with Alzheimer disease, where its expression in the temporal cortices of late-onset Alzheimer patients was shown to be altered.Characterizing GWAS signals using tissue-relevant data can also be valuable for translational purposes such as prioritizing therapeutic targets. In particular, CTSH, KHK, PSMB4, and SNX32,,DCC and RLBP1, which were not analyzed by eQTLGen, and GTEx evaluations suggested that they may not be strongly expressed in whole blood . This limited the number of proteins we were able to instrument using pQTL and also meant we were confined to using single-pQTL instruments. Furthermore, it reduced the overall statistical power of the initial pQTL study, which had downstream implications for our colocalization analysis in terms of the number of signals which met conventional thresholds. Future endeavors which continue to uncover the genetic architecture of the human proteome in disease-relevant tissue types will improve our capability to reliably instrument them under the principle of MR. This will also improve the robustness of evidence from genetic colocalization analyses.We also found that the two genetic colocalization techniques used in this study (the coloc and eCAVIAR approaches) did not always provide corroborating evidence. For example, the loci highlighted in In conclusion, the findings from this study can help elucidate the causal pathway for genetic variants associated with neurological phenotypes and also prioritize candidate targets for therapeutic intervention. Future studies which leverage increasingly large-scale molecular datasets derived from disease-relevant tissues will continue to develop insights into the mechanisms linking genetic variation to complex traits and disease.T.R.G. and C.L.R have previously received research funding from Sanofi. T.G.R. and N.K. have both been previously funded by Sanofi. T.R.G receives research funding from GlaxoSmithKline and Biogen. However, none of these factors contributed to the design or analysis of this study.


Judgement scores were heritable: 0.21 (0.07)−0.33 (0.09) and were highly correlated. Scores during free jumping were genetically correlated to jump duration: 0.71 (0.15)−0.88 (0.16). Both jump duration and judgement scores were genetically correlated to competition performance: 0.59 (0.13) for jump duration, from 0.60 (0.11) to 0.77 (0.12) for scores. Jump duration and judgement scores can be used as early selection criteria. The advantage of the accelerometric measurement is its objectivity and the ease of recording.The aim of this study was to evaluate the genetic component of the locomotor jumping ability, via a wearable accelerometer sensor, and to estimate the genetic correlation with performance in competition, to introduce such criteria in selection schema. A sample of 1,056 young 3-year-old horses were equipped with a 3-dimensional accelerometer during a free jumping test, in regular breeding shows from 2015 to 2017. Seven variables were extracted from the dorso-ventral acceleration curve for the last three jumps over a double bar obstacle of 1.15 m for the front pole and 1.20 m for the back pole with a 1.20 m spread. Variables were the peaks of forelimbs, hindlimbs, and landing acceleration, the duration between peaks at take-off, the peak of forelimb acceleration and start of jump, jump duration and duration between the beginning of the impact of forelimbs and the peak at landing. During breeding shows, judges scored balance, strength, style, and reactivity for free jumping and jumping tests under saddle. Jumping competition results were recorded by logarithm of the sum of points earned in each competition. All horses in official competitions were included, i.e., 160,257 horses born in 1997 with a total of 649,491 annual performances. An animal mixed model with complete pedigree over four generations  were used with fixed effects of jumping test location and date, morning/afternoon, gender, month of birth, rank of jump for accelerometric data, effect of year of competition, combined with age and gender for competition results. As a result, jump duration was the most heritable and repeatable for jump variables:  Show jumping, consisting of clearing a set of obstacles in a specific order and duration, is one of the most popular equestrian disciplines, with many national and international competitions , young horses aged 3 are routinely inspected for their conformation, gait, and jumping ability (free and under saddle) during breeding shows. For 3 years, from 2015 to 2017, the regional breeding shows with the largest number of horses were retained for measurements . The data included 1,056 horses performing 3,125 jumps. The horses were all 3 years old. There were 58% females, 16% geldings, and 25% males. They were all SF except for 28 with only one SF parent, and 12 crossed foreign sport horses.During regular free jumping tests, all horses were equipped with a gait analysis device (Equimetrix®) fixed with a leather pocket over the caudal part of the sternum at the level of the girth place by means of surcingle . All these components are installed in a small aluminum box: 50 × 25 × 110 mm, with a total weight of 240 g. The moment of the jump was analyzed using the jumping tool analysis of the software Equimetrix® on the dorsoventral acceleration visualization and verified with a video tape recording. Jumps with faults were discarded. Raw data included acceleration recorded at 100 Hz per axis in the dorsoventral, longitudinal and lateral axis of the horse from the forelimbs' last impact in the approach stride, to the forelimbs' first impact at landing. Following Barrey and Galloux , only th- the peak of forelimb acceleration at takeoff (FAT): maximum of acceleration in the increase of dorsoventral acceleration due to the last forelimbs' support before the jump,- the peak of hindlimb acceleration at take-off (HAT): maximum of acceleration in the increase of dorsoventral acceleration due to the last hindlimbs' support before the jump,- the peak of forelimb acceleration at landing (FAL): maximum of acceleration in the increase of dorsoventral acceleration due to the first forelimbs' support after the jump- The logarithm of the ratio between HAT and FAT.- the duration between peaks at take-off (DFH): the time spent between the peak of forelimb acceleration and the peak of hindlimb acceleration,- the duration between peak of hindlimb acceleration at take-off and the start of the jump (DHJ): the time spent between the peak of hindlimb acceleration and the moment when acceleration became negative,- jump duration (DJ): the time spent with negative acceleration, when the horse is in the airborne phase,- the duration between the end of the jump and the peak of hindlimb acceleration at landing (DJL): time spent between the beginning of the impact of the forelimbs, i.e., when acceleration became positive, and the peak of acceleration at the landing.During the free jump test, judgements of (1) balance, (2) strength, (3) style, and (4) reactivity were scored on a scale from 1 (poor) to 20 (excellent), but in practice from 10 to 19. Of the horses recorded for accelerometry, 1,045 obtained judgment scores. Similar scores were recorded during the jumping test under saddle. During the jumping test under saddle, the horse performed on a line with combinations of one obstacle up to 0.50 m, followed by 13.5 m, and a second obstacle, an oxer of 0.90 m for the front pole and 1.00 for back pole with a spread of 1.00 m. The entrance was a trotting gait controlled by the ridder.To estimate genetic correlation between accelerometric variables and judgment in breeding shows, with the results in an official competition in show jumping, all horses that performed in competitions and were born from 1997 were added to the data. There were 160,257 horses and 649,491 annual performances. Performance in a competition was measured and normalized using the logarithm of the annual sum of points earned in each competition. Points allocated to the horse in a competition depended on the technical difficulty of the event and the rank of the horse. Technical difficulty of the event was assessed by the height of the obstacle, the level of the championship , the category of the rider , and the table used to score the horse . These technical levels were in accordance with the ranking of horses and riders provided by the French Equestrian Federation (FFE). The rank of the horse was converted into normal scores depending on the rank and the number of participants in the event. The number of points allocated to the horse was the product of the points allocated to the event and the points allocated to the rank , who are in charge of zootechnical recording of equids for the count of Stud Book of Selle Français (SBSF). Pedigrees ranging across four generations were added for a genetic analysis. Pedigrees were complete up to the second generation and completeness was 98.3% at the fourth generation. The number of horses in the pedigree data was 353,236 when competition performance is included in the analysis and only 6,900 horses when analyzing only accelerometric data and judgment scores.The 1,056 horses with accelerometric data were issued from 274 sires . There were 896 mares (maximum size of progeny 4), 386 maternal grand sires  and 135 paternal grand sires . The mean inbreeding was 0.014 .The model was similar for all measurements:y being the vector of measurement , b being the vector of fixed effects, u being the vector of random effects of genetic values , effect of morning/afternoon (two levels), effect of gender , effect of month of birth , effect of successive number of jumps .- For judgment scores: effect of jumping test location combined with date , effect of gender , effect of month of birth (four levels).- For competition: effect of year of competition combined with age (125 levels), effect of gender Wald F statistics tests for fixed effects were obtained using ASREML software  were certainly involved in this effect. This result means that a sufficient number of horses must be recorded in each jumping test location to estimate this effect. Other effects were not always significant depending on each measurement. The main influence was successive number of jumps and sex. Month of birth and effect of morning/afternoon were significant only twice on duration variables.2) and (r) repeatability between jumps were estimated using univariate analysis  and repeatable variable . The other duration variables had very low heritability (not significantly different from 0) and low repeatability (0.21–0.27).The peaks of acceleration at take-off  were significantly heritable and repeatable among the three jumps. The ratio between hindlimb and forelimb peaks performed similarly. The jump duration (DJ) was the highest significantly heritable . Genetic correlations between scores for the same criteria between the free jumping test and jumping test under saddle were very high: from 0.70 (standard error 0.18) for balance to 0.96 (standard error 0.14) for strength. In contrast, phenotypic correlations were moderate: from 0.25 for balance (standard error 0.03) to 0.31 for strength (standard error 0.03). This can be explained by different teams of judges involved in the two notations, however, the same genetic aptitude was kept.Genetic correlation between judgement scores and accelerometric data are presented in For free jumping, genetic correlations between judgement scores and performances in competition  were ratMost literature, which aims to study jumping technique, is focused on the description of the movement rather than using it as a tool for selection purposes. In most studies analyzing jumping, authors managed small groups of animals with sophisticated technology. Most often kinematics were studied using high-speed cameras, and sometimes, inertial measurements or force plates. Results of these biomechanical studies describe limb coordination and the horse's style in clearing different types of obstacles. Fercher  publisheStudies, which report repeatability of kinematic measurements over jumps in free jumping for the same horse, agree with our results. For free jumping, de Godoi et al.  calculatTo predict the jumping ability of horses in competition from free jumping kinematics, literature very often uses too low a number of horses to calculate genetic correlation and is therefore focused on phenotypic correlation. In several publications . The use of many relatives in a competition, to compute the genetic correlation with accelerometric data, suppressed possible confusion between genetic and environmental correlations. The reliability obtained for the estimated genetic correlation between DJ and jumping performance in a competition was not so high, due to the low number of progeny by stallions, but was sufficient to be significant. Duration of swing phase was also highly heritable in gait analysis according to Sole et al. : 0.37 atLewczuk  estimateHeritability of durations  other than jump duration (DJ) were very low. It can be explained by the short time between each of these events  compared to the duration of the jump. The measured durations were not very accurate, and their standard deviation was too close to the measurement error of the device. Acceleration peaks were heritable and repeatable but were unfortunately not highly correlated to performance in competitions. The most important parameter in free jumping at 3 years old, is perhaps the ability to jump high and far, as measured by DJ, whatever the jumping technique used, measured by the accelerations . The results of this study are not a general observation on jumping technique but only looks at the efficiency of using a free jumping test to select young horses as jumping horses.Many publications have analyzed the kinematics of horse jumping in more detail than we have done. Their results may inspire new variables to be added to our analysis. Of course, accelerometry cannot measure the positions of the anatomical landmarks on the horse. But perhaps some distances from the horse to the obstacle may be translated in duration from the curve of acceleration. Janczarek et al.  suggesteThe process is being automated (Echterhoff et al., a priori knowledge of the judges on the quality of the sires of the horses.This study analyzed free jumping during regular breeding shows of young horses with an accelerometric device. For the first time, estimates of genetic correlation between biomechanical data and performance in a competition were calculated. We found that duration of jump was heritable and genetically correlated to jumping performance in a competition. Judgement scores during free jumping were also heritable and correlated to both performance in competition and jump duration measured by the device. The addition of jump duration measured by an accelerometric device in a selection plan must be further studied to replace or complement judgment scores. The advantage of such a measurement, is to be free from the subjectivity of judgement scores, and the calculated correlation cannot be overestimated by The datasets generated for this study are available on request to the corresponding author.Ethical review and approval was not required for the animal study because Measurement on horses are part of regular competitions and breeding shows. Written informed consent was obtained from the owners for the participation of their animals in this study.AR performed the statistical analyses, critically interpret the data, and wrote the manuscript. BD supervised recording of data and critically interpret the data. SD managed experimental design. EB made substantial contributions to the interpretation of data and edition of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Glycine max (L.) Merr.).Plant architecture-related traits , number of nodes on main stem (NN), branch number (BN) and stem diameter (DI)) and 100-seed weight (100-SW) are important agronomic traits and are closely related to soybean yield. However, the genetic basis and breeding potential of these important agronomic traits remain largely ambiguous in soybean  using 82,187 single nucleotide polymorphisms (SNPs). As a result, we found that a total of 59 SNPs were repeatedly detected in at least two environments. There were 12, 12, 4, 4 and 27 SNPs associated with PH, NN, BN, DI and 100-SW, respectively. Among these markers, seven SNPs  were large-effect markers for PH, NN, BN, DI and 100-SW, and 15 potential candidate genes were predicted to be in linkage disequilibrium (LD) decay distance or LD block. In addition, real-time quantitative PCR (qRT-PCR) analysis was performed on four 100-SW potential candidate genes, three of them showed significantly different expression levels between the extreme materials at the seed development stage. Therefore, These findings shed light on the genetic basis of plant architecture-related traits and 100-SW in soybean, and candidate genes could be used for further positional cloning.The online version contains supplementary material available at 10.1186/s12863-021-00964-5. Glycine max (L.) Merr.] is an important economic and oil crop, providing abundant plant proteins and oil to humans [Soybean [o humans . Researco humans . The effo humans , 4. Plano humans . Plant ao humans , 6. 100-o humans . Moreoveo humans . Given to humans , but thehttp://www.soybase.org), there are 239 QTLs controlling PH in soybean, which are distributed on 20 chromosomes, and 37 QTLs related to NN. For BN and 100-SW, 21 and 297 related QTLs have been reported, respectively. And there were a few reports on the QTL position of DI in soybean. Despite the extensive QTL analysis on plant architecture-related traits and 100-SW of soybean, traditional biparent segregation populations have several disadvantages, including limited genetic variation and mapping resolution [Plant architecture-related traits and 100-SW of soybean are complex quantitative traits influenced by multiple QTLs and are susceptible to environmental factors . Previousolution .Arabidopsis thaliana [With the development of genotyping and sequencing technologies, the pace of genetic research on crop quantitative traits has been accelerated. Comparing with bi-parental QTL mapping studies, the genome-wide association study (GWAS) is a more powerful method for dissecting the QTLs underlying agronomically important traits in natural populations. High density of markers in the GWAS also enables one to predict or identify causal genes . In recethaliana , rice [2thaliana , 23, maithaliana , 25, soythaliana , and foxthaliana . In soybthaliana , 28, sudthaliana , cyst nethaliana , 31, andthaliana , were coDt1, E2, E1, Ln, Dt2, Fan and Fap, as well as 16 unreported loci, which are pleiotropic for different traits [In recent years, association studies have been performed in grain soybean for plant architecture and yield-related traits, and they have achieved great success in identifying loci with high mapping precision . Throught traits . Diers et traits . Associat traits . A totalt traits . By usint traits . Using tt traits . AlthougIn this study, we collected 133 diverse soybean landraces, cultivated them at two locations for 2 years, and phenotyped them for the four plant architecture-related traits  and 100-SW. Using the 180 K AXIOM SoyaSNP array, more than 160 thousand genetic markers were generated. After filtering and quality control, a total of 82,187 high-quality SNPs  were used for association mapping. The endeavor from comprehensive GWAS analyses enabled the identification of the underlying genetic loci and prediction of potential candidate genes for five traits. In addition, candidate genes of 100-SW were initially confirmed by qRT-PCR. The objectives of this study were to reveal the genetic basis of plant architecture-related traits and 100-SW in soybean and provide valuable markers and candidate genes for the molecular breeding of soybean.P < 0.01; Table h2) was calculated for the four plant architecture-related traits and 100-SW  on controlling false associations. For the five traits, the observed P values from the GLM (PCA) and GLM (Q) models greatly deviated from the expected P values assuming that no association existed. The P values from the MLM (PCA + K) and MLM (Q + K) models were similar and close to the expected P values  model, indicating that the MLM (Q + K) model could effectively control false positive associations and avoid false negative associations. Therefore, in the current study, the MLM (Q + K) model was chosen for association mapping.Association mapping for the four plant architecture-related traits and 100-SW were performed to evaluate the effects of population structure (Q), principal component analysis (PCA) and familial relationship  ≥ 3.5) with five traits in at least two environments. Among them, 12, 12, 4, 4 and 27 SNPs were significantly associated with PH, NN, BN, DI and 100-SW, respectively  model to analyze five traits in the different environments. A total of 59 SNPs was significantly associated  where 7 SNPs with large effects markers are located, we found that there is an LD block located in the range of 130.9 kb  on chromosome 5 with the SNP marker AX-90520043, which is only significantly associated with 100-SW. Compared to the candidate region where the marker AX-90520043 is located, the LD block reduces the candidate region (± 119.07 kb) by approximately 107 kb  via qRT-PCR in the seeds from the extreme materials at four developmental growth stages . The genotype of the ZDD06067 (100-SW 24.36 ± 1.67 g) and ZDD20532 (100-SW 4.55 ± 0.94 g) extreme materials at the AX-90520043 locus were AA  and TT , respectively. Among the four potential candidate genes associated with 100-SW, Glyma.05 g127900, Glyma.05 g128000 and Glyma.05 g129000 showed significant differences in expression between ZDD06067 and ZDD20532 at four stages during soybean seed development (P ≤ 0.01)  model was used for a GWAS to examine the four plant architecture-related traits and 100-SW. Fifty-nine stable and significant SNPs were identified, of which 25 were located in QTLs of the reported related traits. Thirty-four novel loci were identified in this study. The three SNPs  that were significantly associated with PH were consistent with the results of Sun et al. (2006) . These SGlyma.05 g030900, Glyma.14 g194100, Glyma.14 g194400 and Glyma.14 g194600) are related to PH. The proteins encoded by Glyma.05 g030900 and Glyma.14 g194400 belong to the pentatrico peptide repeat (PPR) family of proteins, which are involved in the metabolic regulation of RNA, act as binding proteins, and have chloroplasts and mitochondria as their sites of action [Glyma.14 g194100 and Glyma.14 g194600 encode a zinc finger family protein and ATNDI1, respectively. The zinc finger family protein gene is expressed in different developmental stages of different tissues of plants, regulating seed development and germination, and plays an important role in plant growth and development [Glyma.19 g128800 and Glyma.19 g129100, which encode an auxin transporter protein and zinc finger protein, respectively. Glyma.06 g294700, a candidate gene for BN, encodes a GDSL-type lipase that belongs to a large gene family in plants. Plant GDSL lipase plays an important role in plant growth and development, organ morphogenesis and lipid metabolism [Glyma.10 g210500 encodes a GAGA-binding transcription factor protein, whereas Glyma.10 g210600, Glyma.10 g211000 and Glyma.10 g212200 encode auxin response factor 16 (ARF16), a plasma membrane protein and ubiquitin-binding enzyme 19 (UBC19), respectively. Additionally, this study also predicted four candidate genes  that may be related to 100-SW. The results of qRT-PCR analysis indicated that Glyma.05 g127900, Glyma.05 g128000 and Glyma.05 g129000 were differentially expressed in 100-SW extreme materials. Among these genes, Glyma.05 g127900 encode a ribonucleoprotein, its homologous gene is SAD1 in Arabidopsis. Studies have confirmed that SAD1 encodes a polypeptide similar to multifunctional Sm-like-snRNP proteins that are required for mRNA splicing, export, and degradation, the sad1 mutant of Arabidopsis can delay seed germination [Glyma.05 g128000 encode a chlorophyll a/b binding protein, previous studies have shown that the protein can bind to photosynthetic pigments to form a light-harvesting pigment protein complex to participate in light energy transfer and play a role in plant photosynthesis [Glyma.05 g128000. Glyma.05 g128000 may affect the accumulation and transport of soybean dry matter by regulating photosynthetic reaction, and it is likely to participate in the regulation of seed weight in soybean. Glyma.05 g129000 encodes a HMG-box DNA binding protein. At present, the regulatory network of HMG-box DNA binding protein is still unclear. It may be involved in the regulation of genes involved in soybean seed development, and then participate in the regulation of 100-SW in soybean. However, further evidence is needed to functionally validate this hypothesis.Through the functional annotation of genes, the current study predicted a total of 15 potential candidate genes associated with PH, NN, BN, DI and 100-SW. Among these 15 genes, four genes  in 2016 and 2017 and at Dangtu  in 2017 with three randomized replications, with one row per plot, 40 plants per row, 10 cm between plants within each row and 50 cm between rows. 2016JP, 2017JP and 2017DT represent the environments of Jiangpu in 2016, Jiangpu in 2017 and Dangtu in 2017, respectively. The field management was performed under normal soybean production conditions. Five major plant traits, including PH, NN, BN, DI and 100-SW, were investigated. For each of the 2016JP, 2017JP and 2017DT environments, 5 plants were randomly selected for the determination of PH, NN, BN, and DI. In 2017JP and 2017DT, 100-SW determination was performed for each block. Plant height  is the length of the cotyledonary node to the top of the plant. Number of nodes on main stem (NN) indicate the number of nodes from the cotyledonary node to the top of the main stem node. Branch number (BN) indicates the effective number of branches. The stem diameter of the main stem was measured at the third node space with a micrometer . 100-seed weight was obtained by weighing 100 seeds immediately after drying the seeds mixed in each block . The names of the 133 soybean landraces used in this study and the original phenotype data were listed in Additional file σ2g is the genetic variance, σ2ge is the variance due to the G × E interaction, σ2e is the residual error, n is the number of environments and r is the number of replicates within the environment. The estimates of σ2g, σ2ge and σ2e were obtained from ANOVA by considering the environment as a random effect.Statistical analyses of the above five traits were performed using the R software (http:/www.R-project.org) . Analysir2) among SNPs was estimated using E (r2) = 1/ (1 + 4Nec) [c represents the recombination rate of Morgan units and Ne represents the effective population size. The LD decay rate of the population was measured as the chromosomal distance when the average r2 decreased to half its maximum value [The 133 soybean landraces had been genotyped with the 180 K AXIOM Soya SNP array previously . Accordi + 4Nec) , where cum value . The STRum value . A total10(P) were displayed using the observed P values from marker-trait associations and the expected P values from the assumption that no associations exist between the markers and traits. The model with observed P values closest to the expected P values was chosen as the optimal model to control the confounding of population structure. Using the optimal statistical model, association analyses were carried out with 82,187 SNPs for all traits using the mean and BLUP values across multiple environments and within each environment [10(P) ≥ 3.5 was considered significantly associated with target traits.The existence of a population structure and relative kinship in natural populations always results in a high level of spurious positives in association mapping . The popironment . Genome-(http://www.soybase.org/). Based on the soybean genomic annotations, potential candidate genes were predicted.To reduce false positives, we defined the candidate SNPs that had significant associations in at least two environments. We selected significant SNPs with large effects to search candidate genes in their candidate regions. These candidate regions were defined by the average LD decay distance or the LD blocks. The functional annotations of genes located in the candidate regions were obtained from the SoyBase database Gmβ-tubulin was selected as the control gene, and the qRT-PCR assays were conducted three times using a Light Cycler 480 instrument. The relative expression levels of the candidate genes were calculated using the comparative 2−△△CT method [t-test.In addition, for potential candidate genes predicted for 100-SW, qRT-PCR was used to analyze the expression patterns in extreme materials with large phenotypic differences. According to the phenotypic data for 100-SW in the 2017JP and 2016DT environments, the ZDD06067 (24.36 ± 1.67 g) and ZDD20532 (4.55 ± 0.94 g) materials showed stable and large phenotypic differences. Therefore, we chose them as the extreme materials and cultivated in the field. Three replicate biological samples were collected in liquid nitrogen at four stages during soybean seed development (R3 (Pod 5 mm long at one of the four uppermost nodes on the main stem with a fully developed leaf), R5 (Seed 3 mm long in a pod at one of the four uppermost nodes on the main stem with a fully developed leaf), R6 (Pod containing a green seed that fills the pod cavity at one of the four uppermost nodes on the main stem with a fully developed leaf) and R7 ), as defined by Fehr et al. (1971) . Total RT method . StatistAdditional file 1: Fig. S1. Average linkage disequilibrium (LD) decay rate estimated among co-chromosome SNPs.Additional file 2: Fig. S2. Population structure analysis of 133 soybean landraces.Additional file 3: Table S1. Phenotypic data of the four plant architecture-related traits and 100-SW in the 133 soybean landraces.Additional file 4: Table S2. Primer sequences for 100-seed weight candidate genes in soybean.


In phenotype prediction the physical characteristics of an organism are predicted from knowledge of its genotype and environment. Such studies, often called genome-wide association studies, are of the highest societal importance, as they are of central importance to medicine, crop-breeding, etc. We investigated three phenotype prediction problems: one simple and clean (yeast), and the other two complex and real-world (rice and wheat). We compared standard machine learning methods; elastic net, ridge regression, lasso regression, random forest, gradient boosting machines (GBM), and support vector machines (SVM), with two state-of-the-art classical statistical genetics methods; genomic BLUP and a two-step sequential method based on linear regression. Additionally, using the clean yeast data, we investigated how performance varied with the complexity of the biological mechanism, the amount of observational noise, the number of examples, the amount of missing data, and the use of different data representations. We found that for almost all the phenotypes considered, standard machine learning methods outperformed the methods from classical statistical genetics. On the yeast problem, the most successful method was GBM, followed by lasso regression, and the two statistical genetics methods; with greater mechanistic complexity GBM was best, while in simpler cases lasso was superior. In the wheat and rice studies the best two methods were SVM and BLUP. The most robust method in the presence of noise, missing data, etc. was random forests. The classical statistical genetics method of genomic BLUP was found to perform well on problems where there was population structure. This suggests that standard machine learning methods need to be refined to include population structure information when this is present. We conclude that the application of machine learning methods to phenotype prediction problems holds great promise, but that determining which methods is likely to perform well on any given problem is elusive and non-trivial. The phenotype  of an organism is the result of interactions between the organism’s complement of genes (its genotype)  may be genotyped, which opens up the possibility of using statistics/machine learning to learn predictive relationships between an organism’s genotype, environment, and phenotype. Such studies are often called genome-wide association studies (GWAS).The traditional focus of most GWAS has been on the discovery of genetic markers  that are ‘associated’  with a phenotype. However, rather than being true causal mutations, called quantitative trait loci (QTL), these markers are usually correlated to QTLs and serve as proxies. Such single-nucleotide polymorphisms (SNPs) and QTLs are usually in linkage disequilibrium (LD), i.e. within a given population, their alleles are correlated more than would be expected by chance. In GWAS, focusing on a small number of genes has significant biological limitations, as most biological phenotypes result from the interaction of multiple genes and the environment; and the focus on association rather than prediction has statistical limitations, as it makes the objective evaluation of the utility of results difficult.The current trend is therefore towards a more direct and operational approach to phenotype prediction problems: learn a predictive function that, from the input of an organism’s genotype and environment, predicts its phenotype  with standard machine learning methods. We investigate how these methods perform on three very different types of phenotype prediction problem, one from yeast Genomic data has a specific structure that strongly influences the application of machine learning methods. We therefore first briefly describe this structure using standard machine learning terminology—rather than the terminology of statistical genetics which may confuse the uninitiated.Representing genotype. The complete genotype of an organism consists of the linear arrangement of its genes on chromosomes, together with the sequences of all the genes and intergenic regions. Genotype information is normally represented in phenotype prediction problems as ‘markers’, these are discrete attributes that signify that a particular stretch of DNA varies between organisms. Usually, these variations are mutations at a single position (base pair) in a DNA sequence called SNPs. As organisms of the same species mostly share the same DNA sequences, this representation is reasonably concise, but as genomes are large, many thousands of markers are typically needed to characterise an organism’s genome.  In this paper, we utilise this marker representation as it is standard, and it simplifies the application of standard statistical/machine learning methods.In phenotype prediction problems, it is preferable for all the organisms (examples) to have their genotypes fully sequenced, as this provides the maximum amount of information. However, this is not possible in many problems, either because of technical reasons or cost. In such cases, the genotypes are not fully characterised. In this paper we investigate two problems (yeast and rice) where all the organisms are fully sequenced, and another (wheat) where only a subset of markers is known, and the organism’s genome has not yet been sequenced because of its complexity.Environment. Prediction of phenotype is easier if the environment is controlled. However, this is difficult or impossible to do in many cases, for example, in studies involving humans many aspects of the environment are unknown, in outdoor crop studies the weather cannot be controlled, etc. In this paper, we investigate one problem (yeast) where the environment is fully controlled (well-defined laboratory conditions), and another two (wheat and rice) where the environment is partially controlled.Measuring phenotype. Due to the continuing steep fall in DNA sequencing costs in many phenotype prediction problems, the most expensive step is the observation of an organism’s phenotype. This means that in many scenarios the number of attributes is greater than the number of examples. Furthermore, it has also led to new genetic methodologies based on phenotype prediction, an example of which is genomic selection , that was classically studied by Gregor Mendel, is caused by variations (polymorphisms) in a single gene (stay-green)  are formed by meiosis (sex), where parents shuffle their genomes when forming offspring. The mechanisms involved in meiosis are complicated, but, the result is that each of the child cell’s chromosomes consists of a random patchwork of linear sections taken from the two parents Fig. a. This mDue to meiosis populations of organisms typically have complex ancestral (pedigree) interrelationships. These interrelationships take the form of a directed acyclic graph (DAG), with meiosis events being the nodes. However, in many phenotype prediction problems, the structure of the DAG is unknown.  based on genetic changes resulting from meiosis.) Much of classical statistical genetics research has focused on dealing with population structure. For example, the BLUP (best linear unbiased prediction) method encodes genetic similarities between pairs of individuals in a genomic similarity matrix (GSM)  in their sex cells (sperm/eggs), but otherwise have two copies (diploid), one from their father and the other from their mother. This complicates phenotype prediction as it is not clear how the genomes interact to cause phenotype. This complication is related to multi-instance learning problems   greatly exceeds the number of sample points (n), and this is a problem for classical multivariate regression. This is less of a technical problem for some machine learning methods, but of course, basic information-theoretic results imply that the underlying signal needs to be strong enough for machine learning methods to work.Standard off-the-shelf machine learning methods . Finding causal genetic variants is the subject of statistical fine-mapping  to be associated to a particular trait are Saccharomyces cerevisiae. The parent strains differed by 0.5% at the sequence level. The genotypes of the parents and children were determined by sequencing  between a laboratory and a wine strain of the yeast The environment of the yeast strains was modified in 46 different ways Table : the basYeast population growth  was measured under these different conditions. As the data was generated by high-throughput robotics there are many missing values; there are, for example, only 599 readings available for sorbitol. Most traits, however, have upwards of 900 readings, some with two replications (which we average). All the growth measurements are normalised to have a mean of 0 and a variance of 1.0.Using this yeast study, we investigate different aspects of applying machine learning to phenotype prediction data by starting with as clean data as possible, and then gradually artificially degrading it to make it resemble different practical phenotype prediction problems in animals and plants. A complementary motivation for using such clean and complete data is that with improved technology applied phenotype prediction problems will increasingly resemble this clean, comprehensive form.aa, aA and AA alleles, respectively . The wheat lines were evaluated in plots for four phenotypic traits with three replicates (which were averaged): yield (drought), yield (irrigated), thousand kernel weight (TKW) and days to heading . Phenotypic values were once again normalised.The wheat dataset comes from a genomic selection study in wheat involving 254 breeding lines (samples) with genotypes represented by 33,516 SNP markers coded as For the rice data, the Core SNP subset of 3000 Rice Genomes version 0.4 from SNP-SEEK  and agronomic traits evaluated (for wheat and rice) are variables to be predicted.ad hoc fashion. Neither approach is ideal, although lasso’s ability to produce a sparse solution can be a useful feature. The advantage of both these methods is the simplicity of the resulting linear model. We also investigated an array of models that interpolate between ridge and lasso regression through use of an elastic net penalty. We considered 11 values of the elastic net penalty We investigated several variants of penalised linear regression: elastic net (Zou and Hastie entclass1pt{minimap / 3 (where p is the number of attributes) for the number of splitting variables considered at each node, and 5 examples as the minimum node size. For GBM we tuned two parameters via internal train/test split inside each fold: interaction depth and shrinkage. We investigated interaction depths of 1, 2 and 3 and shrinkage of 0.001, 0.01 and 0.1 (in our experience the default shrinkage parameter of 0.001 lead to too slow of a convergence), resulting in a two-dimensional parameter grid. We used 1000 trees, which was enough for convergence for all traits. The optimal number of iterations for predictions was determined via an assessment on an internal validation set within each cross-validation fold. Finally, we used the default value of 0.5 as the subsampling rate.We also investigated the tree methods of random forests Breiman  and gradC and Finally, we investigated support vector machines (SVM) (Cortes and Vapnik For yeast (tenfold CV) and wheat datasets (fivefold CV), during each CV iteration parameter tuning is performed within the training fold comprising 90% (or 80%) of the data. For GBM and SVM, we tune and validate parameters on the 70% and 30% of the training fold, respectively. For lasso, tuning of R . We selR implementation in the rrBLUP package  is a very popular approach in genomic selection, and was the method applied in the original wheat paper . FinallTables entclass1pt{miniman et al. ; Cherlinn et al. ) or simpThe yeast results show that there is at least one standard machine learning approach that outperforms Bloom and BLUP on all but 6 and 5 traits, respectively. In addition, the mean advantage of the Bloom (BLUP) method on these 6 (5) traits is marginal: 1.8% (0.4%), with a maximum of 4.1% (1.5%), whilst the mean advantage of the standard machine learning techniques is 5.0% (5.5%), with a maximum of 14.2% (27.5%)—for SVM (GBM) on tunicamycin . , so there is no significant difference between the two closest performing methods, SVM and BLUP.The results for the wheat dataset paint quite a different picture: SVM performs the best for all traits , followed closely by genomic BLUP. Both of the tree methods underperform compared to SVM and BLUP. The weakest method overall is lasso. The Friedman test returns a p-value of On the rice dataset, SVM performs best for 6 of the 12 traits, genomic BLUP outperforms all other methods on 4 of the 12, and on a trait each, lasso and ridge perform best , and the complexity of their interactions have an important impact on the ability to predict phenotype. We investigated how the mechanistic complexity of a phenotype impacted on the prediction results for the different prediction methods applied to the yeast dataset. Without a full mechanistic explanation for the cause of a phenotype, it is impossible to know the number of relevant attributes. However, in our yeast phenotype prediction data, which has no interacting environmental attributes, a reasonable proxy for the number of relevant attributes is the number of non-zero attributes selected by lasso regression Fig. . This apTo investigate the relationship between the number of markers chosen by the lasso and variance explained by the models we split the data into test (30%) and training (70%) sets, counted the number of non-zero parameters in the model fitted to the training set, and compared it to the model’s performance on the test set. We observed that the environments with a higher proportion of variance explained tend to have a higher number of associated non-zero attributes. Notable exceptions to this are the three  in the top-left part of the graph, which has an unusually high We also wished to investigate how the complexity of the interactions of the attributes  affected relative performances of the models. Figure Finally, we noted optimal tuning parameters chosen for GBM in each CV fold for each trait. Scrutinising optimal tuning parameters might help us understand what makes a particular model suitable for a particular regression problem. In particular, we recorded tree interaction depth most frequently chosen across the 10 cross-validation folds . Overall 1, 3 and 7 splits  were chosen for 9, 18 and 19 traits, correspondingly. Looking closer, we noted that traits for which Bloom did not identify interacting attributes favoured stumps and shallow trees, while those with 2 or more interactions favoured deeper trees (7 splits)—in fact, 7 splits were identified as the optimal tree depth for all traits with more than two interactions. We conclude that optimal GBM tree depth might help draw conclusions about the structure and complexity of the underlying data.There is a great deal of noise in many real-world phenotype prediction problems. By noise, we mean both that the experimental conditions are not completely controlled, and the inherent stochastic nature of complex biological systems. Much of the factors affecting experimental conditions are environmental , and this cannot be investigated using the yeast dataset. However, in many phenotype prediction problems, there is also a significant amount of class noise. To investigate the importance of such class noise, we randomly added or subtracted twice the standard deviation to a random subset of growth phenotype. We sequentially added noise to 5%, 10%, 20%, 30%, 40%, 50%, 75% and 90% of the phenotypic data for each trait and assessed performances of the statistical/machine learning methods on a test set (with training-testing split of 70%–30%). We repeated the procedure 10 times, each time selecting a different random subset of the data to add noise to. Figure The algorithm underlying GBM is based on recursively explaining residuals of a model fit at the previous step, which might explain why it fares worse than RF under noise addition. For all the methods and traits, there seem to be very rapid deterioration in accuracy even for relatively small noise contamination . Figure The relative insensitivity to marker deletion across most traits and methods is not surprising given high linkage disequilibrium (correlation) between SNPs in the dataset see Fig. a, which The steepest dropping line in plots for lasso, ridge, GBM, and RF corresponds to cadmium chloride; this is most likely because only a handful of important markers are likely to be governing the trait see Fig. .For each yeast strain, the marker data enabled us to recover the genomic structure formed by meiosis. We observed blocks of adjacent markers taking the same value, 1 or 0 Fig. , we alsoThe second way we investigated the fusing of blocks of markers was to group markers in genes and their flanking regions. To do this, we divided the genome into regions, each of which contained one gene together with half of the two regions between it and the two neighbouring genes. Partially overlapping genes were treated separately, but genes contained entirely within another gene were ignored. Markers lying within gene regions formed in this manner were fused according to the dominant value within this gene. This produced an alternative set of 4383 binary attributes.We observed that the performance of the two alternative sets of genotypic attributes matched that of the full attribute set with the mean pairwise difference between any two attribute sets performance for each of the five ML methods, apart from ridge, not exceeding 0.5%. Ridge regression’s accuracy for some traits suffers considerably  when the reduced attribute sets were used. This indicates that most of the markers in blocks are in fact redundant as far as RF, GBM, SVM, and lasso are concerned.In phenotype prediction studies, there is often a shortage of data as it is expensive to collect. Traditionally obtaining the genotype data was most expensive, but increasingly data cost is being dominated by observation of the phenotype—with the cost of observing genotypes decreasing at super-exponential rate. To investigate the role of the number of examples, we successively deleted 10%, 25%, 50%, 60%, 70%, 80% and 85% of all sample points and assessed performance of the six statistical/ML models (again on a test set with a train-test split of 70%–30% and 10 resampling runs). Figure Lactate, lactose, sorbitol, and xylose: four sugar-related phenotypes with relatively high pairwise correlations (0.6–0.8).Lactate, lactose, sorbitol, xylose, ethanol, and raffinose: six sugar-related phenotypes with medium to high pairwise correlations (0.42–0.8).Grouping these traits makes sense given yeast biology: xylose, sorbitol, lactose, and raffinose are all sugars, and plausible environments for yeast to grow in; ethanol is a product of yeast sugar fermentation; while lactate participates in yeast metabolic process. Hence, it is not surprising that the six traits enjoy moderate to high pairwise correlations.Rather than regarding the yeast dataset as 46 separate regression problems with 1008 sample points in each, in the spirit of multi-task learning one might consider it as a single large regression problem with 46 Caruana . Most ofCombining several phenotype prediction problems into one results in each individual (yeast sample) having several entries in the input matrix and output vector—one for each trait. Additionally, we introduced an extra attribute, a categorical variable indicating which trait each sample corresponds to. We applied GBM and RF to this grouping approach. We show only random forest results, as GBM considerably underperformed compared to RF, and we did not apply SVM due to it being too computationally extensive for such a large problem. The performance was assessed by evaluation on a test set (30% of the data), which was an aggregation of test sets of individual traits used throughout the paper; this made comparing the new results to reference results obtained by training on separate traits easier.a) and (b)  benefited greatly from grouped learning (blue and orange bars) whilst predictive accuracy for the two additional traits in group (b) (ethanol and raffinose) are substantially lower than reference. Moreover, adding these two traits reduced predictive accuracy for 3 out 4 of the original traits in group (a) (orange bars). Overall accuracy across all traits was 61% for group (a) and 52% for group (b).We assessed the performance of RF on the two groups of traits above as well as on the group comprising all 46 traits. The three models were assessed for overall prediction accuracy as well as for prediction accuracy for each trait. We compared the latter values to reference fits, models trained and tested on each trait separately. Figure For any pair of traits in groups (a) and (b), the RF model trained on one of the traits has at least one of its top (as assessed by permutation OOB permutation tests) markers highly (or perfectly) correlated with one of the markers highlighted as important by RF model trained on the second trait. Likewise, RF models trained on groups (a) and (b) highlight highly (or perfectly) correlated markers. Models trained on combined traits, therefore, benefit from larger datasets to learn common genetic variants affecting these phenotypes.a) and (b). It, therefore, seems that while combining multiple traits into a single regression problem indiscriminately might not, on the whole, improve overall or individual trait prediction accuracy, grouping carefully chosen traits with high pairwise correlation (perhaps advised by the organism’s biology) can be advantageous.For the full multi-task set-up using all 46 traits .One important form of phenotype prediction problem that we have not studied is human disease associations studies. These problems typically differ from the problems investigated here in several ways: there exists complex but unknown population structure, the environment of the examples is poorly controlled, and the phenotype investigated is a disease that may have a partly understood mechanism. Compared to the problems investigated here these properties make such problems in some ways easier, and some ways harder. We hypothesise that just as for the yeast, wheat, and rice datasets, the performance of off-the-shelf machine learning methods will compare favourably to those obtained from state-of-the-art classical statistical genetics methods.There are a number of ways that machine learning methods could be developed for phenotype prediction problems. As mentioned in the introduction, the use of markers to describe genotypes is inefficient as it ignores their linear ordering, the type of sequence change, etc. One way to capture this information would be to use a relational representation  that new examples (organisms) are produced.To conclude, there is relatively little communication between the machine learning and statistical genetics communities. This is unfortunate. Statistical genetics suffers from lack of access to new developments in machine learning, and machine learning suffers from a source of technically interesting, and societally important problems. We, therefore, hope that this paper will help bridge the differences between the communities and encourage machine learning research on phenotype prediction problems.http://genomics-pubs.princeton.edu/YeastCross_BYxRM/, wheat data at https://dl.sciencesocieties.org/publications/tpg/abstracts/5/3/103, and rice data at http://snp-seek.irri.org/_download.zul. Custom R code used to analyse the datasets can be found at: https://github.com/stas-g/grinberg-et-al-evaluation-of-ML-code.The original yeast data can be found at