Adverse childhood experiences (ACEs) increase the risk of poor health outcomes later in life. Psychosocial stressors may also have intergenerational health effects by which parental ACEs are associated with mental and physical health of children. Epigenetic programming may be one mechanism linking parental ACEs to child health. This study aimed to investigate epigenome-wide associations of maternal preconception ACEs with DNA methylation patterns of children. In the Center for the Health Assessment of Mothers and Children of Salinas study, cord blood DNA methylation was measured using the Illumina HumanMethylation450 BeadChip. Preconception ACEs, which occurred during the mothers’ childhoods, were collected using a standard ACE questionnaire including 10 ACE indicators. Maternal ACE exposures were defined in this study as (1) the total number of ACEs; (2) the total number of ACEs categorized as 0, 1–3, and > 4; and (3) individual ACEs. Associations of ACE exposures with differential methylated positions, regions, and CpG modules determined using weighted gene co-expression network analysis were evaluated adjusting for covariates.FAM135B gene; q value < 0.05). Five differential methylated regions were significantly associated with the total number of ACEs, and 36 unique differential methylated regions were associated with individual ACEs . Fifteen CpG modules were significantly correlated with the total number of ACEs or individual ACEs, of which 8 remained significant in fully adjusted models . Significant modules were enriched for pathways related to neurological and immune development and function.Data on maternal ACEs and cord blood DNA methylation were available for 196 mother/newborn pairs. One differential methylated position was associated with maternal experience of emotional abuse (cg05486260/Maternal ACEs prior to conception were associated with cord blood DNA methylation of offspring at birth. Although there was limited overlap between differential methylated regions and CpGs in modules associated with ACE exposures, statistically significant regions and networks were related to genes involved in neurological and immune function. Findings may provide insights to pathways linking psychosocial stressors to health. Further research is needed to understand the relationship between changes in DNA methylation and child health.The online version contains supplementary material available at 10.1186/s13148-023-01581-y. Adverse childhood experiences (ACEs) encompass a set of potentially traumatic events that occur during childhood, before age 18 years, and are associated with poor health outcomes during adolescence and adulthood . Of noteACEs are a significant public health issue because they have negative impacts on mental and physical health, education, and job opportunities. During child development, they, along with other social determinants of health, contribute to toxic stress, which can cause neurodevelopmental disruption, epigenetic changes, and reprogramming of stress and immune regulatory systems that affect a child’s developmental trajectory and life course , 6. ThroThere is growing interest in how adverse events experienced by parents affect health outcomes in their offspring. Maternal preconception ACEs have been associated with increased risk of hypertensive disorders of pregnancy, preterm birth, and prenatal depressive symptoms. Maternal psychological challenges have also been shown to increase child behavioral dysregulation . This evChanges in DNA methylation (DNAm) that occur during fetal development and throughout life and offspring inheritance of maternal epigenetic patterns may also confer vulnerability to many pathologic conditions . AssociaIn the Center for the Health Assessment of Mothers and Children of Salinas (CHAMACOS) study, a longitudinal birth cohort from a predominantly Mexican immigrant farmworker population in California , we prevFrom an initial cohort of 601 mother/newborn pairs, 372 had high-quality DNAm data. Mothers’ ACEs were collected using an adaptation of the ACE questionnaire  includinn = 80; 40.8%) had 6th grade or lower education, while 40.3% (n = 79) attained 7th–12th grade education and 18.9% (n = 37) graduated from high school. Eight mothers (4.1%) reported ever smoking while pregnant. Forty-three percent of mothers were married  and 38.8% were living as married (n = 76) at the time of delivery, while 5.1% were separated or divorced (n = 10), and 12.8% were single and had never married (n = 25). The majority of mothers reported Mexico as their country of origin , and having spent ≤ 1 , 2–5 , or 6–10  years in the USA. Slightly fewer than half of newborns were male , and the mean gestational age was 39.1 ± 1.5 weeks.The mean ± standard deviation (SD) maternal age at delivery was 25.7 ± 4.8 years Table . On avern = 101; 51.5%) reported no ACEs, while 26.5% (n = 52) reported 1–3 ACEs, and 21.9% (n = 43) reported 4–10 ACEs , emotional neglect , emotional abuse , parental divorce , and substance abuse in the household . The report of any ACE increased the odds of every other ACE, with pairwise odds ratios ranging from 3.4 for domestic violence and physical neglect : 1.1, 9.9) to 51.4 for emotional and physical abuse   control approach of Storey and Tibshirani [q values ≤ 0.05. CpG-by-CpG results from the EWAS are available at the study’s Open Science Framework (OSF) repository at https://osf.io/ync5t/.Associations with individual cytosine-phosphate-guanine (CpG) dinucleotides in cord blood were analyzed using three complementary approaches to defining maternal ACE exposures: (1) total number of ACEs modeled linearly; (2) total number of ACEs categorized as 0, 1–3, or 4–10, allowing for nonlinear effects; and (3) each of the 10 ACEs in a mutually adjusted model. Models were adjusted for a priori selected confounders or precision variables of newborn sex, gestational age, and cord blood estimated cell type proportions, and maternal parity, pre-pregnancy BMI, age at delivery, educational attainment, smoking during pregnancy, and marital status. Within each model, we adjusted for multiple comparisons  by calculating bshirani . DiffereFAM135B)   Table .Table 2Dp values systematically lower or more significant than the expected under the null hypothesis distribution, was observed for emotional neglect (λ = 1.65), substance abuse (λ = 1.54), and mental illness (λ = 1.40) , physical abuse (λ = 0.89), and parental divorce (λ = 0.67). Deflation was also present for 1–3 versus 0 ACEs in the categorical model of total ACEs (λ = 0.75), although deflation was less evident for 4–10 versus 0 ACEs (λ = 0.97) or 4–10 versus 1–3 ACEs (λ = 1.13)   [p < 0.005) as well as 189 individual CpGs (p < 0.0005) were reported, of which 314 were included in our study. Among these CpGs, 129 were nominally significant  in at least one of our models , although none remained significant after adjusting for multiple comparisons in our EWAS  . The top . The top value < 2.4 × 10–7) [p value < 0.05) in any of our EWAS .Kotsakis Ruehlmann et al. conducted a meta-analysis of maternal prenatal stressors in the Pregnancy and Childhood Epigenetics (PACE) consortium ( × 10–7) . Of the p value ≤ 0.05. DMRs were associated with the total number of ACEs modeled linearly (4 DMRs), the total number of ACEs modeled categorically (1 DMR for 4–10 ACEs vs. 0 ACEs), and individual ACEs in a mutually adjusted model    in cord blood were identified using comb-p with a Šidák multiple testing correction , and sigVWA7), sexual abuse and domestic violence were associated with overlapping DMRs on chromosome 4 (STX18-AS1) with opposite directions of association, and physical neglect and mental illness were associated with a DMR on chromosome 11  with opposite directions of association.There was minimal overlap between DMRs. The total number of ACEs modeled linearly and emotional neglect in the mutually adjusted model were associated with lower methylation of overlapping DMRs on chromosome 6  to 109,576 CpGs. One module, which was composed primarily of probes located on the sex chromosomes, was excluded from further analyses. Information required to reconstruct identified WGCNA modules is available at the OSF repository at https://osf.io/ync5t/. Module eigengenes of the 28 remaining modules exhibited strong representativeness, accounting for 41.0–74.0% of the total variation among probes belonging to each module  were further analyzed using adjusted models  , performp < 0.05) with the total number of ACEs or individual ACEs  . MEs not associated with ACEs were significantly correlated with newborn sex, maternal smoking and age at delivery, and % CD4 + T cells  , Sienna4 (p = 0.006), and Yellow3 (p = 0.002) MEs , consistent with modeling the total number of ACEs linearly. However, estimates of FDRs of linear and categorical associations of total number of ACEs and MEs  were > 0.05   . As with analyses of total number of ACEs, estimated q values of bivariate associations between individual ACEs and MEs were > 0.05 , as well as CpGs in DMRs associated with physical neglect and domestic violence.There was minimal overlap between DMPs, DMRs, and CpGs included in modules associated with ACE exposures. The Blue module (enriched for neurodegenerative disease/cellular anatomy and metabolism) was associated with maternal experiences of emotional abuse and included CpGs in DMRs associated with maternal experiences of sexual abuse, physical neglect, and domestic violence. The Brown module  was associated with maternal experience of emotional abuse and included CpGs in DMRs associated with sexual abuse, emotional neglect, and physical neglect. In addition, the Turquoise module , associated with maternal experience of mental illness in the household, included the DMP associated with emotional-abuse , regions (DMRs), and CpG networks, among mother/newborn pairs who were primarily of Mexican origin and low socioeconomic status . While pFAM135B gene. In agreement with a study of maternal ACEs and DNAm measured in infant blood and buccal epithelial cells [FDR < 0.2 and a biological threshold |Δβ < 0.03|, of which one was significant at FDR < 0.05 [p < 2.4 × 10–7) [p value < 0.05. Although our findings contribute to a growing body of research linking parental stressful or adverse experiences to epigenetic modifications in children, replication of findings across multiple cohorts is necessary to fully establish and understand this relationship. In our look-up approach, we found limited consistency with results from previous studies [We found that emotional abuse experienced by mothers was significantly associated with one DMP in cord blood, cg05486260, annotated to the al cells  and a stal cells , we did R < 0.05 . A PACE  studies , which mp < 0.05). However, q values, i.e., estimates of FDRs of accepting any bivariate associations of ACE exposures and MEs, exceeded 0.05, suggesting caution in interpreting findings.We found a greater number of associations with DMRs, including significant associations with the total number of ACEs and with emotional abuse, sexual abuse, emotional neglect, physical neglect, domestic violence, substance abuse, mental illness, incarceration, and parent divorce, although there was minimal overlap between the DMRs identified through different analytic models. Previous research has also shown weak associations between total maternal ACEs and correlated methylated regions of infant blood and buccal cells . We alsoPNPO, a protein coding gene involved in the biosynthesis of vitamin B6, which is a co-factor for neurotransmitter synthesis. PNPO deficiency has been linked to neurodevelopmental impairment and epilepsy [CACNA1C. The CACNA1C gene encodes for a transmembrane calcium channel subunit. Genetic variation of CACNA1C has been associated with neurodevelopmental delays and disorders including schizophrenia, autism, and bipolar disorder [CACNA1C has been associated with bipolar disorder [CACNA1C polymorphisms with bipolar disorder, with variant carriers exposed to childhood trauma at greater risk [Downstream effects of adversity experienced by parents in early life include depression, anxiety, post-traumatic stress disorder (PTSD), developmental delay, and behavioral problems in their offspring , 45. Morepilepsy . We alsodisorder –51, and disorder , suggestter risk . In additer risk .HLA-DPB1 gene, a member of the major histocompatibility complex (MHC). DNAm of HLA-DPB1 has previously been associated with PTSD [Dysregulation of the immune system may be another pathway through which adverse experiences impact health , 55, 56.ith PTSD , 58. In q value ≤ 0.05). However, we chose not to correct for multiple comparisons between models as hypotheses were related.Strengths of this study include use of a validated, standardized measures of maternal ACEs, application of an epigenome-wide approach, and multiple modeling strategies. Our study was also strengthened by the use of cord blood samples which allows us to rule out the possibility that associations are due to similar social and environmental exposures between mothers and children after birth, although we cannot rule out possibility of shared exposures while children were in utero. We also employed multiple analytical techniques which allowed us to investigate associations between ACEs and individual methylation loci, differentially methylated regions, and networks of co-methylated CpGs, in addition to analyzing the total number of ACEs linearly, categorized number of ACEs for nonlinearity, and analyzing associations with individual ACEs mutually adjusting for all other ACEs. Although use of multiple models may increase the risk of type-one errors, we adjusted for multiple comparisons within each model and evaluated statistical significance using a false discovery rate approach  [N = 92 and N = 124 for blood and buccal epithelial cells, respectively) [Our small sample size decreased our power to detect associations with small effect sizes, particularly in CpG-by-CpG analyses, although our sample size was larger than that in previous studies of maternal ACEs and offspring DNAm of candidate genes , 31. It N = 896)  while a ctively) . We chosctively) . Howeverctively) , and thectively) , 63, 64.ctively) –74. AlthFuture research should examine the impact of maternal ACEs on children’s DNAm profiles at different points throughout the life course  to evaluate persistence and their role in the sequelae of health outcomes related to ACEs. While our study demonstrates that changes in children’s DNAm possibly reflect maternal adverse experiences prior to conception and birth, prospective, longitudinal cohort studies with repeated measurements may provide opportunities to study how DNAm changes in response to parental ACEs throughout an individual’s life into adulthood. Studies of the impact of maternal ACEs on offspring health or biomarkers in childhood and adolescence must also consider the contribution of the postnatal environment, which may play an important role as a mechanistic pathway or mediator beyond prenatal biological factors. Specifically, maternal anxiety, depression and parenting behaviors have been identified as mediators linking maternal ACEs with children’s internalizing and externalizing symptoms –78. In aIn summary, this study provides further evidence that mothers’ preconception adverse experiences may impact their child’s epigenome at birth. Both gene annotations of DMRs and enrichment analysis of ACE-associated co-methylated modules suggest changes in DNAm related to neurological and immune development and function, pathways previously implicated in response to stressful and adverse experiences. However, larger studies with more diverse populations are needed to fully understand the impact of maternal ACEs on epigenetic markers in children. In addition, further research is needed to investigate how changes in offspring DNAm at birth related to maternal ACEs may affect health later in life.From October 1999 through October 2000, 601 pregnant women with s Valley . Of thesMaternal characteristics included maternal age at delivery, pre-pregnancy BMI, whether the mother smoked at any time during pregnancy, marital status at first interview , educational attainment , and maternal parity.N = 319 (61%) participated in the 18-year follow-up interviews during which data on ACEs were collected using an adaptation of the ACEs questionnaire [Data collection of mothers’ ACEs has previously been described . Of the ionnaire  administWhere possible, gestational age from medical records was calculated based on the self-reported last menstrual period of mothers. In cases where this information was missing or resulted in implausible estimates, ultrasound records were used to estimate gestational age at a weekly resolution. Data on the sex of the children were obtained from physical exams.Cord blood specimens were collected at the time of delivery. DNA was extracted from banked non-heparinized umbilical cord using QIAamp DNA Blood Maxi Kits  following a previously described modified version of the manufacturer’s protocol . Aliquotn = 0); mismatch between recorded sex and sex estimated from DNAm data (n = 8), and replicate samples (n = 1). Functional normalization [minfi (v1.36.0) [ENmix (v1.26.10) [sva package (v3.38.0) [EpiDISH (v2.6.1) [During DNAm data collection, repeats and randomization of samples across chips and plates were used to reduce the chance for artifactual confounding . Qualitylization  was perfv1.36.0)  and norm1.26.10) . The Com1.26.10)  method pv3.38.0)  was used(v2.6.1) .Epigenome-wide association analysis (EWAS), differentially methylated positions (DMPs). A total of 372 samples were retained with high-quality DNAm data, of which 196 with complete paired data on maternal ACEs and covariates were used for EWAS analyses. We performed three complementary EWAS that differed in the definition of maternal ACE exposures: (1) we applied the simplifying assumption that exposure to additional types of adverse experience has homogeneous effects on DNAm, treating the total number of ACEs as a continuous variable modeled linearly; (2) we regarded each additional type of adverse experience as homogenous and categorized the total number of ACEs as 0, 1–3, or 4–10 ACEs, allowing for nonlinear effects; and (3) we regarded each of the 10 indicators for different ACEs as distinct exposures, fitting coefficients for each in a mutually adjusted model. For each exposure definition, we fit linear models on the logit scale  with empirical Bayes adjustment of standard error terms using the package limma (v3.46.0) [a priori based on previously reported associations with cord blood DNAm [p values, coefficients, and standard errors associated with ACE exposure terms.v3.46.0) . In addiood DNAm –74: newbWhile regressing on the logit scale has appealing statistical properties for proportional outcomes , the fitp values from each CpG-by-CpG EWAS via quantile–quantile plots and calculated genomic inflation factors , noting any CpGs as differentially methylated for which a q value ≤ 0.05 was returned. Adjustment for multiple comparisons was performed separately for each specification of ACE exposures : total number of ACEs as a continuous variable, total number of ACEs as a categorical variable, and individual ACEs.We assessed the distribution of bshirani , as implN = 92) were analyzed using correlated methylated regions and individual CpGs not included in the regions [p < 0.005) and 189 individual CpGs (p < 0.0005) were reported, none of which remained significant after an FDR correction. Although this study also investigated associations with infant DNAm measured in buccal epithelial cells, we limited our look-up to results from blood for greater similarity in tissue types. In the second study, associations of maternal stressful life events experienced during pregnancy and offspring DNAm were studied in a meta-analysis of 12 cohorts (N = 5496) conducted by the PACE consortium [p < 2.4 × 10–7), four of which were included in our study. To assess if CpGs associated with maternal ACEs or prenatal stress were also associated with ACEs in our study, we conducted a look-up of reported CpGs in our EWAS results. Replication of was determined by a nominal p value < 0.05.We conducted a look-up of the one DMP using the EWAS Catalog . We also regions . The topnsortium . PrenataDifferentially methylated region (DMR) analysis. We searched for DMRs using a modified comb-p method as provided in Enmix (v1.26.10) [–3 [p value ≤ 0.05.1.26.10) , with ma.10) [–3 . We defiWeighted gene co-expression network analysis (WGCNA). We utilized the R package WGCNA (v1.70.3) [M-values across the epigenome. WGCNA provides a suite of tools for tasks including the identification of non-contiguous network modules of covarying signal loci, identification of central loci in the network , and extraction of summary statistics of module-wide signals such as the eigengene [blockwiseModules function to feasibly calculate unsigned Topological Overlap Matrices for our high dimensional methylation data, then identify covarying modules via hierarchical clustering and dynamic tree cutting algorithms [v1.70.3)  to perfoigengene  , we used the Benjamini–Hochberg FDR estimation, which has higher specificity at low sample sizes but reduced power [q values [p value ≤ 0.05, we assessed the robustness of the association by constructing linear regressions with the ME as outcome, ACE measure as main exposure, and adjusting for newborn sex, gestational age, and estimated nucleated cell-type composition, and maternal parity, pre-pregnancy BMI, age at delivery, educational attainment, smoking during pregnancy, and marital status. For individual ACEs, we additionally assessed the significance of their association with MEs in a mutually adjusted model in which all ACEs were included simultaneously along with the covariates listed above. FDRs were estimated only for bivariate associations to provide an indication of the level of confidence of the probability that associations in our exploratory analyses did not arise by change under multiple testing. FDR estimates were not calculated for adjusted modules, since these estimates had already been subjected to a selection process informed by the same data.To identify modules associated with maternal ACEs, we calculated Pearson correlations between MEs and total ACEs, as well as individual ACEs separately. Analogous to our approach for FDR control in our EWAS analysis, we estimated ed power , 95. Forq values , 96. Forgometh function in the missMethyl package (v1.26.1). This function accepts a vector of CpGs included in each module and a vector of all CpGs used in WGCNA. Enrichment p values were adjusted for prior gene selection probabilities inherent to the Illumina array [We performed KEGG  and GO , 42 pathna array , 98, andAdditional file 1: Table S1. Participant characteristics of mother/newborn pairs with cord blood DNA methylation data (N = 372). Table S2. Weighted correlation analysis (WGCNA) module eigengene representativeness statistics. Table S3. Weighted correlation analysis (WGCNA) module eigengenes (MEs) associated with ACE exposures and pathway summaries. Fig. S1. Flowchart of selection process for mother/newborn pairs included in analyses. Fig. S2. Heatmap of pairwise odds ratios between maternal adverse childhood experiences (ACEs). Fig. S3. Manhattan plot for associations with the total number of maternal adverse childhood experiences (ACEs) modeled linearly. Fig. S4. Manhattan plots for associations with the total number of maternal adverse childhood experiences (ACEs) categorized as 0, 1–3, or 4–10. Fig. S5. Manhattan plots for associations with individual maternal adverse childhood experiences (ACEs) in a mutually adjusted model. Fig. S6. Q–Q plot for associations with the total number of maternal adverse childhood experiences (ACEs) modeled linearly. Fig. S7. Q–Q plots for associations with the total number of maternal adverse childhood experiences (ACEs) categorized as 0, 1–3, or 4–10. Fig. S8. Q–Q plots for associations with individual maternal adverse childhood experiences (ACEs) in a mutually adjusted model. Fig. S9. Correlations of module eigengenes (MEs) with individual maternal adverse childhood experience (ACE) indicators, total number of maternal ACEs, and covariates.Additional file 2: Table S1. Lookup of Moore et al. results including top CpG located in each correlated methylated region (p < 0.005) and individual CpGs (p < 0.0005), and EWAS results from the current study. Table S2. Lookup of Kotsakis Ruehlmann et al. results including CpGs associated with prenatal cumulative stress or individual stress domains in PACE , and EWAS results from the current study.Additional file 3: Table S1. Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways enriched for modules associated with ACE exposures (FDR < 0.05). Table S2. Gene Ontology (GO) pathways enriched for modules associated with ACE exposures (FDR < 0.05).


Here, we report the discovery of a third locus, Dt3, modulating soybean stem growth habit, which was delineated to a ~ 196-kb region on chromosome 10 by a combination of allelic and haplotypic analysis of the Dt1 and Dt2 loci in the USDA soybean Germplasm Collection, genome-wide association studies with three subsets of the collection, and linkage mapping with four biparental populations derived from crosses between one of two elite indeterminate cultivars and each of four semideterminate varieties possessing neither Dt2 nor dt1. These four semideterminate varieties are recessive mutants  in the Dt1/Dt1;dt2/dt2 background. As the semideterminacy modulated by the Dt2 allele has unfavorable pleotropic effects such as sensitivity to drought stress, dt3 may be an ideal alternative for use to develop semideterminate cultivars that are more resilient to such an environmental stress. This study enhances our understanding of the genetic factors underlying semideterminacy and enables more accurate marker-assisted selection for stem growth habit in soybean breeding.Stem growth habit is a key architectural trait in many plants that contributes to plant productivity and environmental adaptation. In soybean, stem growth habit is classified as indeterminate, semideterminate, or determinate, of which semideterminacy is often considered as a counterpart of the “Green Revolution” trait in cereals that significantly increased grain yields. It has been demonstrated that semideterminacy in soybean is modulated by epistatic interaction between two loci, The online version contains supplementary material available at 10.1007/s00122-023-04493-w. Glycine max (L.) Merr.) is the most widely grown oilseed crop in the world, with nearly 129 million hectares (ha) planted in 2021, according to the Food and Agriculture Organization of the United Nations  encoding a phosphatidylethanolamine-binding protein (PEBP) and maintains indeterminate growth at the shoot apex  at a novel locus on chromosome 10, is responsible for their semideterminacy. This study provides a starting point for a more comprehensive understanding of the genetic underpinnings of stem growth habit in soybeans and will aid soybean breeders in marker assisted selection (MAS) for this key trait.There is considerable quantitative variation in degree of soybean stem termination within the three broad phenotypes of determinate, semideterminate, and indeterminate. We wondered whether additional genes influence the range of phenotypic values classified as semideterminate. In this study, we employed allelic analysis of soybeans in the USDA soybean Germplasm Collection and a series of genome wide association studies (GWAS) to further dissect the genetic basis underlying semideterminacy in soybeans. We focused particularly on semideterminate soybeans which did not possess the known stem termination alleles of Dt2 or dt1) are listed in Table 2 lines derived from a cross between the high-yielding indeterminate cultivar HS6-3976 and the semideterminate landrace PI 548406 (Richland). The second consists of 108 F2 lines derived from a cross between the indeterminate cultivar Williams 82 and the semideterminate landrace PI 297520 . The third consists of 108 F2 lines derived from a cross between the indeterminate cultivar Williams 82 and the semideterminate landrace PI 561350B (Yong ji qun zhong da dou). The fourth consists of 153 F2 lines and F3 families derived from a cross between the indeterminate cultivar Williams 82 and the semideterminate landrace PI 597403B (Krasnodar 391–89). The fifth population consists of 50 F2 lines derived from a cross between the indeterminate cultivar Williams 82 and the semideterminate landrace PI 248409 (Subotica).A total of 67 publicly available landraces which were classified as semideterminate according to publicly available phenotypic data from the USDA soybean germplasm collection but which don’t carry known stem termination alleles  and R7 (Full maturity) growth stages and classified as either indeterminate or semideterminate based on, respectively, the absence or presence of a terminal cluster of pods. F2:3 families were planted the following year at ACRE and phenotyped in the same manner for the Williams 82 by Krasnodar 391–89 population. The 67 publicly available accessions were phenotyped in the same manner for two consecutive years in the field at ACRE.Four of the 67 publicly available semideterminate accessions and PI 561350B were selected for crossing once the terminal raceme was visible during R2 (full flowering stage) and crossed to Williams 82 or HS6-3976. Crossing was conducted in the field at the Purdue Agronomy Center for Research and Education (ACRE), with Fdt1 were randomly selected using R. P-values were considered significant at a threshold of 0.05 divided by the population number, n, within each GWAS.Genotypic data was drawn from the Illumina Infinium SoySNP50K BeadChip database  markers polymorphic between the parents were used for genotyping. Linkage analysis calculations were performed according to the Kosambi function using QTL IciMapping. The InDel primers used in this study are listed in Table S9.Dt1 and Dt2 are responsible for the semideterminate phenotype, we selected 990 random accessions  and ss715635425 . A total of 170 semideterminate accessions remained after this filtering process. We then randomly selected 170 accessions classified as indeterminate, paired these with the 170 remaining semideterminate accessions (Table S2), and again conducted a GWAS for stem growth habit. This second GWAS revealed a single major peak on chromosome 18 at the Dt2 locus, with the most significant SNP being marker ss715632223  about 16 kb upstream of the annotated transcription start site for the Dt2 gene . A third GWAS consisting of these 74 semideterminate accessions and 74 randomly selected indeterminate accessions failed to identify any significant loci. Nonetheless, we proceeded to evaluate the 74 lines. Sanger sequencing of the causal SNP sites for dt1 and the SNPs associated with the Dt2 haplotype reported in our earlier study . In the (Williams 82 × Krasnodar 391–89) population, 110 individuals were classified as indeterminate and 43 semideterminate . In the population derived from crossing Williams 82 with Iregi Universal, 40 individuals were classified as indeterminate and 10 were classified as semideterminate . Finally, in the population derived from crossing HS6-3976 with Richland, 199 individuals were classified as indeterminate and 71 semideterminate . These observations suggest that the semidetermancy carried by each of these four semideterminate accessions is likely to be controlled by a single gene, and that, distinct from Dt2-mediated semideterminacy, the semideterminacy in these four accessions was caused by naturally occurring recessive mutations.Three of the 37 semideterminate accessions  were crossed to the indeterminate cultivar Williams 82 and one, Richland, was crossed to the indeterminate cultivar HS6-3976. The Fate Table. In the Dt3.Bulked segregant analysis (BSA) of the four biparental populations revealed overlapping regions on the long arm of chromosome 10 from the semideterminate parents are associated with semideterminacy Fig. a. The reDt2, to Williams 82. We found that 91 F2 individuals derived from the two parent lines were classified as semideterminate and 17 as indeterminate. Instead of a 3:1 (semideterminate to indeterminate) ratio , we observed a 13:3 (semideterminate to indeterminate) ratio . This ratio can be explained by the hypothesis that semideterminacy in PI 561350B is determined by two loci, Dt2 and dt3. As expected, BSA of the (Williams 82 × PI 561350B) F2 population revealed that the semideterminacy in PI 561350B is associated with 37.69–45.32 Mb  on chromosome 10  on chromosome 18. These observations support our hypothesis that PI 561350B carries both the Dt2 and dt3 alleles for semideterminacy.We also crossed PI 561350B, one of the semideterminate lines identified by our screen but which was found to carry the functional allele of dt3 locus, the 153 individual plants of the (Williams 82 × Krasnodar 391–89) F2 population were genotyped (Table S8) using four InDel markers polymorphic between the two parent lines within the region defined by BSA  from InDel 45.111 and 2.39 cM from InDel 45.306  and facilitates the silencing of the floral suppressor FLOWERING LOCUS C (FLC)  and two leguminous crops closely related to soybean, pigeon pea (Cajanus cajan Millsp.) and chickpea (Cicer arietinum L.)  in pigeon pea, chickpea, and tomato, respectively  resulting in stem termination. Our initial screening to remove the dt1 allele suggests that a substantial proportion of those accessions classified as semideterminate actually carry loss-of-function alleles of dt1. These phenotypic classifications may result from the dt1-t alleles which confer determinate growth without reducing height  for the dt3 locus, understand its molecular role in modulating semideterminacy, and evaluate its effect on soybean yields toward the goal of producing optimized soybean shoot architecture.There has long been an interest in modifying soybean stem growth habit to increase yield, although past studies have shown mixed results based upon environment, genetic background, and management conditions Below is the link to the electronic supplementary material.


The resemble between relatives computed from pedigree and genomic data is an important resource for geneticists and ecologists, who are interested in understanding how genes influence phenotypic variation, fitness adaptation, and population dynamics.A matrix) and/or molecular markers (G matrix), with the possibility of building a combined matrix of pedigree corrected by molecular markers (H matrix). Designed to estimate the relationships for any ploidy level, the software also includes auxiliary functions related to filtering molecular markers, and checks pedigree errors in large data sets. After computing the relationship matrices, results from the AGHmatrix can be used in different contexts, including on prediction of (genomic) estimated breeding values and genome-wide association studies.The AGHmatrix software is an R package focused on the construction of pedigree (https://cran.r-project.org/web/packages/AGHmatrix/index.html and also in GitHub at https://github.com/rramadeu/AGHmatrix. It has a comprehensive tutorial, and it follows with real data examples.AGHmatrix v2.1.0 is available under GPL-3 license in CRAN at  Quantitative genetics is a discipline with a distinguished history in multiple biological fields. Geneticists and ecologists have relied on genetic parameters to understand how genes influence phenotypic variation, fitness adaptation, and population dynamics . BreederImportant genetic analyses rely on the estimation of resemblance between relatives. For example, multivariate analyses  are commonly employed to describe the genetic diversity of a population, while linear mixed models are used to predict breeding values and estimate variance components partition. In common, most of these analyses have been carried out in R, one of the most popular statistical programming environments used by breeders and biometricians. Despite its popularity, computing relationship matrices including (i) pedigree records and molecular information, (ii) for diploid and polyploid species, and (iii) using different parametrizations  have not been addressed in the same package using a unique framework. To overcome it, we designed the AGHmatrix R package to compute relationship matrices for a range of scenarios, providing an efficient software to large-scale data sets.AGHmatrix software is an R package to build genetic relationship matrices. The software was initially released for pedigree analyses in outcrossing plants (A matrix) and/or molecular markers (G matrix) with the possibility of building a combined matrix of pedigree corrected by molecular markers (H matrix). The package works for diploid and autopolyploid species, fitting 15 different relationship matrices well-reported in the plant and animal literature (The software is focused on the construction of pedigree (terature . The pacA) after reading pedigree tables recorded in a three-column format, where the first column contains the genotype ID, followed by Parent 1 and Parent 2 IDs. Parent 1 and 2 assignment is arbitrary with no sex distinction, key factor for monoecious breeding. Matrices are built based on the recursive method presented in N, where N is the total number of individuals in the pedigree. Individuals IDs are checked for missing values and for the correct chronological order . If this order is not followed, the algorithm performs the necessary changes to correct it iteratively. After this preprocessing, the second stage relies on matrix algebra to efficiently build A. There is also the possibility to use a prebuilt A and to add new pedigree information (expandAmatrix function), so there is no need to rebuild the A every time new crosses are planned or made.The Amatrix function computes additive relationship matrices . In this case, all seeds will have the same expected relatedness with all the possible parents (1/3) while assuming no inbreeding. Within this function, it is also possible to fix a given parent and mimics the case where the mother is known, and we have equally possible pollen donors (e.g. polycross in sugarcane and other grasses).G) using different approaches  when genotypic probabilities are used as marker input, (ii) genotypic classes are represented as the count of alternative (or reference) alleles over the total read depth for each individual-marker combination (GBS-like technique), (iii) mixed-ploidy populations are provided and a proxy for the additive matrix should be computed, and (iv) for family-pool genotypes . To compute the H matrix, two methods are implemented. The approach described by G matrix toward the A matrix scaling the molecular relatedness by each relationship class. And also, the approach described by A and G matrices are combined using scaling factors, ultimately weighing the importance of pedigree and molecular information when both data are combined. For genomic selection, a valid approach to select the best scaling factor would be testing a grid of values in a cross-validation scheme and checking the impact on predictive ability. The weights can also be managed with the target to build a positive-definite (invertible) H matrix.The last main function implemented in the package is the Hmatrix, which was primarily inspired in animal breeding studies where The AGHmatrix also contains supplementary functions that can help biometricians and breeders organize their pedigree information, filter SNP information, and export the results in different formats. For example, the snp.check function can exclude molecular markers depending on the number of missing data , MAF, heterozygosity (important in the case of breeding lines) and if genetic variants are monomorphic. Simple imputation methods based on the mode or the mean are also available in the same function.Q + K method. While the effects of population stratification and hidden relatedness are an important source of spurious associations, using a polygenic term (G matrix) for controlling population structure is a crucial element in GWAS models. Some packages, including the GWASpoly . They can also be used in a different context. A straightforward implementation is in the so-called “Animal Model” (or ABLUP), which is a mixed model in which breeding values (or the genetic merit) are included as an explanatory variable for a phenotypic trait of interest. Assuming that genetic merits are random effects, the nonindependence between individuals from the same population is accounted for using pedigree information. A simple expansion of this idea is the inclusion of genomic relationship matrices (GBLUP), which makes results applied to genomic selection studies. Various software and packages can read external relationship matrices for prediction breeding values, including asreml-R . AnotherFinally, we reported some benchmarks for using AGHmatrix when computing large pedigree files . The pac


Testing the association between multiple phenotypes with a set of genetic variants simultaneously, rather than analyzing one trait at a time, is receiving increasing attention for its high statistical power and easy explanation on pleiotropic effects. The kernel-based association test (KAT), being free of data dimensions and structures, has proven to be a good alternative method for genetic association analysis with multiple phenotypes. However, KAT suffers from substantial power loss when multiple phenotypes have moderate to strong correlations. To handle this issue, we propose a maximum KAT (MaxKAT) and suggest using the generalized extreme value distribution to calculate its statistical significance under the null hypothesis.We show that MaxKAT reduces computational intensity greatly while maintaining high accuracy. Extensive simulations demonstrate that MaxKAT can properly control type I error rates and obtain remarkably higher power than KAT under most of the considered scenarios. Application to a porcine dataset used in biomedical experiments of human disease further illustrates its practical utility.MaxKAT that implements the proposed method is available on Github https://github.com/WangJJ-xrk/MaxKAT.The R package  The advances in high-throughput technology allow researchers to investigate the occurrence, development and treatment of disease from the genetic perspective. Up to now, over ten thousands of disease-associated single-nucleotide polymorphisms (SNPs) have been detected via genome-wide association study (GWAS) based on single trait per variant analysis. However, GWAS suffers from power loss because of weak marginal effects, ignorance of interactions among genetic variants, and strict multiple comparison policy. To make up for these defects, the analysis based on gene sets is a good alternative, where genetic variables are grouped into different sets based on biological knowledge. Many gene-based tests for analysis between a single trait and multiple SNPs have been proposed. For example, There is growing evidence suggesting the wide existence of pleiotropic genetic effects, i.e. many SNPs are prone to be simultaneously associated with several human complex traits, especially those located in one gene or one pathway . For exaDespite its wide usage, KAT is subject to substantial power loss when multiple phenotypes are moderately to strongly correlated. To overcome this drawback, we propose a maximum kernel-based association test (MaxKAT). We first conduct eigenvalue decomposition on KAT and rewrite KAT as a weighted summation of angles between two eigenspaces. By adjusting the weights, we establish a series of tests to describe the association strength at different levels. Since the optimal test is unknown, we choose the most significant one among them as the final test. For convenience of calculation, a generalized extreme value distribution is used to calculate the statistical significance of MaxKAT under the null hypothesis. In addition, the proposed test can accommodate high-dimensional data and yield high power against various alternative hypotheses. Extensive simulation studies show its superior performance over KAT via a wide range of scenarios. And application to a biomedical porcine dataset demonstrates its efficiency in practical situations.n individuals are randomly sampled from a source population. For each individual, data of m SNPs in a target gene or region on a chromosome and n × m and ith individual, respectively, m SNPs are not associated with Suppose n-dimensional column vector with all 1 units.Given two definite kernel functions Then KAT ,b iswheTo overcome the defect of KAT and develop a powerful and robust test, we take another look at KAT. Based on eigenvalue decomposition strategy, we havewhere θ and This indicates that KAT is a weighted summation of angles between two sets of eigenvectors. These angles represent the association strengths between genotypes and phenotypes projected on different coordinate levels, and their weights are determined by the corresponding eigenvalues. This summation, however, may cause information loss when some important information contained in angles corresponding to small eigenvalues is concealed owing to their small weights. To deal with this issue, the relative differences among weights need to be adjusted to ensure that important association information becomes visible in the summation. However, the angles vary across different situations and the optimal weights are difficult to know beforehand. Therefore, we next consider power weights and construct a series of weight-adjusted KATs (abbreviated as wKAT) by changing weights in KAT aswhere θ and m dimensional genotypes) are weakly related, index (such as θ) larger than 1 helps wKAT obtain higher power than KAT does. On the other hand, if elements within multiple variates th element of ijδ. Given ijδ calculates similarity between the ith and jth subjects by integrating their respective similarities with all the other subjects at the level of θ = 2, ith and jth subjects by integrating their respective similarities with all the other subjects measured by the kernel function ijδ, We can write θ and θ and θ and θ and Although θs (those approaching zero) make all the eigenvalues approach one, resulting in almost the same weights for different angles. In contrast, larger θs may highlight angles corresponding to large eigenvalues overly. In order to strike a balance, candidate values for θ and We would like to point out that smaller N), say 1000 times, and plug the permuted N permuted MaxKATs. Then the P-value of the observed MaxKAT is the proportion of all these permuted MaxKATs larger than the observed one.Since the joint distribution of multiple wKATs is complex, we apply the permutation procedure to the significance calculation for MaxKAT. Once calculating the observed MaxKAT using the original data, we simultaneously permute the rows and columns of matrix Z iswhere N permutation replicates obtained above by ζ1, ζ2, and ζ3, respectively. Then by matching them with the three corresponding theoretical moments, we have the following three equations asOn the other hand, since MaxKAT is the maximum over a Gaussian random field th element being y: the autoregressive structure mentioned above and the compound-symmetry structure ρ to be 0.1, 0.5, and 0.9 to indicate diverse association strengths. For the sake of simplicity, parameter matrices xβ and yβ are set to be equal constant matrices, and the values of their elements β are listed in q = 0.3 is the minor allele frequency. The recoded ix and iy are independent. When the alternative hypothesis is true, Since the association strengths between pairs of genotype decrease as their physical distances increase, ΔP-values less than the significance level of 0.05. Given each dataset, we use the inner product-based kernel  are 0.033 (0.043), 0.057 (0.058), 0.043 (0.043), 0.050 (0.055), and 0.046 (0.058), respectively.The type I error rates are presented in tructure , ρ=0.9 am increases, the power gain of MaxKAT relative to KAT increases as well, indicating that the advantage of MaxKAT over KAT is enlarged in high-dimension settings. For example, in m increases. When m = 20, the empirical power of KAT is 0.144, while that of MaxKAT.perm is 0.192. When m = 100, the respective powers of KAT and MaxKAT.perm are 0.278 and 0.579. When m is as large as 500, the powers of KAT and MaxKAT.perm are 0.480 and 0.918, respectively, with the latter having a power gain as large as 0.438. The results in The empirical powers are shown in m and r elements in r being chosen from xβ and yβ are generated from the uniform distribution We also consider situations with different association patterns. The dimensions P-values through the permutation strategy, the number of permutation N increases as the significance level gets more stringent. For example, N = 1000 is sufficient when the significance level is N needs to be no less than P-values for MaxKAT.gev, no matter how stringent the significance level is. We let N choose values from N for MaxKAT.gev to be 1000, to investigate their run time. Dimensions m and As described in Section 2.2, the GEV-based MaxKAT.gev has a computational advantage over MaxKAT.perm and KAT when the significance level is stringent. We conduct simulations to illustrate this point. Since MaxKAT.perm and KAT calculate N gets longer, i.e. as the significance level gets more stringent. And MaxKAT.perm is much more time-consuming than MaxKAT.gev as N increases, demonstrating the advantage of GEV approximation in situations with stringent significance levels. Though KAT is more time-saving than MaxKAT.gev when N is no larger than N is Just as expected, the computational time for KAT and MaxKAT.perm increases as Note that although we use the inner product-based kernel (for genetic data) and Gaussian kernel (for phenotypic data) in the above analysis, other types of kernels can also be used. We conduct simulations to investigate the effect of kernel choice on the performances of different methods. Four types of kernel choice are considered:Apply inner product-based kernel to genetic data, and Gaussian kernel to phenotypic data.Apply IBS kernel to genetic data, and Gaussian kernel to phenotypic data.Apply inner product-based kernel to genetic data, and polynomial kernel to phenotypic data.Apply IBS kernel to genetic data, and polynomial kernel to phenotypic data.Data are generated via Model I. And the powers of different methods for autoregressive Serum lipids are important indicators for health status of humans. Their abnormal concentrations are associated with cardiovascular disease and diabetes. In clinical tests, six blood lipid traits, including total cholesterol (TC), triglycerides (TG), atherosclerosis index (AI), low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein (HDL-C), and the ratio of the HDL-C and LDL-C (denoted as HDL-C/LDL-C), are widely used in risk assessment of cardiovascular disease. Locating genetic variants regulating these traits might be useful for the prevention, identification, and treatment of the disease.Pigs have been used as biomedical experimental materials of human disease research for decades. AssocTests   to the csocTests . Ten prisocTests  is used m1 and m2, respectively) are presented in P-values for all eight SNP intervals are shown in P-values of KAT MaxKAT.perm and MaxKAT.gev are 0.020 and 0.023, respectively, confirming the finding reported in P-value obtained using KAT is 0.065, indicating a failure to detect this association relationship. These results suggest that MaxKAT performs better than KAT in identifying association signals based on SNP regions.MaxKAT and KAT can also be used in association analysis based on SNP regions, such as genes, pathways, and SNP intervals. In the GWAS analysis of Association testing methods being free of constraints on data dimension and data structure are in great demand nowadays in the big data era. The kernel-based approach is a good alternative to this issue and has been generally recommended (P-value, it takes more time to implement MaxKAT in larger sample sizes. However, compared with distributional approximation-based methods, this permutation-based method is free from requirement on the sample size and has high powers even when sample sizes are small. Besides, given that MaxKAT boosts the power in detecting association relationships remarkably, its time cost is acceptable.As MaxKAT relies on a permutation procedure to calculate its MaxKAT which is posted on GitHub https://github.com/WangJJ-xrk/MaxKAT.Although MaxKAT is developed for genetic pleiotropy study, it can also be applied to other areas, such as microbiome data analysis and genomic study, where association analysis between microbiome composition and phenotypes, and between gene expression levels and genetic variants are conducted, respectively. We would like to point out that MaxKAT can also be used to handle data with more complex structures such as tree, network, and image, only if a reasonable kernel is available. The R codes for the implementation of MaxKAT are assembled in the R package named btad291_Supplementary_DataClick here for additional data file.


EVA1A gene, which plays a fundamental role in the MAPK1 signaling pathway. Other identified genes  support results from previous studies, and this gene also contributes to mechanisms of the MAPK1 signaling pathway.The aim of this study was to establish and evaluate a structural equation model to infer causal relationships among environmental and genetic factors on udder health. For this purpose, 537 Holstein Friesian cows were genotyped, and milk samples were analyzed for novel traits including differential somatic cell counts and specific mastitis pathogens. In the structural model, four latent variables (intramammary infection (IMI), production, time and genetics) were defined, which were explained using manifest measurable variables. The measurable variables included udder pathogens and somatic differential cell counts, milk composition, as well as significant SNP markers from previous genome-wide associations for major and minor pathogens. The housing system effect  indicated a small influence on IMI with a path coefficient of −0.05. However, housing system significantly affected production (0.37), with ongoing causal effects on IMI (0.17). Thus, indirect associations between housing and udder health could be inferred via structural equation modeling. Furthermore, genotype by environment interactions on IMI can be represented, i.e., the detection of specific latent variables such as significant SNP markers only for specific housing systems. For the latent variable genetics, especially one SNP is of primary interest. This SNP is located in the  Diseases of the udder are considered as one of the most important clinical infections in dairy cows with strong detrimental effects on farm economy . HoweverAs pointed out in some publications , the cowIn order to fully understand and resolve such complex and various influencing factors and their interrelationships, alternative modeling approaches are needed. Regression analyses are used as a common tool to explore one-way relationships by neglecting possible recursive or mutual associations . StructuThe objective of the present study was to apply SEM to infer causal relationships on IMI based on a detailed recording for differential somatic cell counts and specific mastitis pathogens as well as specifically selected SNP markers. In this regard, a two-step strategy was applied; first, a genome-wide association study (GWAS) was used to detect significant SNPs, and afterwards, in step 2, these SNPs were analyzed using enhanced SEM approaches. Data considered in the present study are based on milk samples from routine milk recording and genotypes used for the official national genetic evaluations. No extra animal experiments were conducted. Thus, following the guidelines of the German animal welfare legislation, a specific ethical approval was not required.Cow milk samples were collected from the individual udders of six Holstein dairy cattle herds located in the German federal states of Hesse and North Rhine-Westphalia for all ongoing studies. The herds for this project were selected based on the criteria for selecting case  and control herds  as defined in the collaborative EU FreeWalk project . The twoAerococcus sp., Aesculin hydrolyzing streptococci, Candida krusei, Enterococcus sp., Escherichia coli, Lactococcus sp., Staphylococcus aureus, Streptococcus dysgalactiae, Streptococcus uberis, mold fungus and Proteus sp. The category MINOR included Coagulase-negative staphylococci and Corynebacterium sp. One udder quarter of at least one pathogen within the defined groups, MAJOR and MINOR, resulted in score = 1 for the respective total group; otherwise, score = 0 was assigned. At cow level, the score = 1 was assigned for the total group  if the respective pathogen was detected in at least one udder quarter; otherwise, score = 0 was applied.For ongoing laboratory milk analyses, we considered milk samples from 2198 udder quarters of these 587 cows. The milk analyses for specific pathogens in the Landesbetrieb Hessen followed the DVG guidelines ,21,22,23Differential cells were counted under the microscope in our own milk analysis laboratory at Justus-Liebig-University, Giessen. Differential cell counting included the cell fractions for lymphocytes, macrophages and polymorphonuclear leucocytes (PMN) in a 50 mL milk sample per udder quarter following official guidelines and protocols ,25. MilkIllumina BovineSNP50 Bead Chip V2. An additional dataset including 273 first parity HF cows was genotyped with the Illumina BovineSNP50 Bead Chip V3. After quality control of the SNP data via the software package PLINK, version 1.9 [p < 0.001) from the Hardy–Weinberg equilibrium. ARS1.2 assembly [Only the significant SNPs from GWAS were included in the ongoing SEM. Genome-wide associations were performed for SNP main effects and SNP x housing system interaction effects. A significant interaction means that the SNP significantly affects udder health in compost-bedded pack barns, but not in cubicle barns. In this regard, we followed SNP data preparation and the statistical methods as outlined in our previous study by Wagner et al. . For thision 1.9 , 43,095 https://jlupub.ub.uni-giessen.de/ (accessed on 20 April 2023). The respective statistical model 1 in matrix notation for the GWAS was defined as follows:snpi = a vector of SNP genotypes; bsnpi = a regression coefficient for the main effect of the ith SNP marker; xinteri = a vector of genotypes for cows kept in compost-bedded pack barns; binteri = a regression coefficient for the SNP x housing system interaction effect of the ith-SNP marker; g = a vector of random additive-genetic effects following N; G = the genomic relationship matrix which was constructed as defined by Yang et al. [2g = additive-genetic variance; Z = incidence matrix for the random additive-genetic effects; e = vector for the random residual effects following N, I = identity matrix; σ2e = residual variance.The algorithm for the estimation of SNP effects and significances is incorporated into our own R package, named GWAInter.R, which can be downloaded at g et al.  by exclu2 value for the main and interaction effects is the ratio of the respective squared regression coefficient divided by the variance of the regression coefficients at 1 degree of freedom. Significance thresholds were defined based on the strict Bonferroni correction with BonfP = 0.05/no. of SNPs and the more relaxed suggestive threshold with suggP = 0.05/number of independent SNPs. The number of SNPs was 43,095, and the number of independent SNPs was 4479. The number of independent SNPs was calculated considering linkage disequilibrium ≤0.15 in chromosomal segments with 500 markers.The estimation for the required additive-genetic and residual variances for MAJOR and MINOR was performed using the model y = Xb + Zg + e, with the effects as stated above for model 1 and applying the software package “gaston” . Our sofThe last step was the annotation of potential candidate gens. The definition of a candidate gene implied at least one significantly associated SNP, which is directly located in the gene or located in a surrounding segment 200 kb up- and downstream. For gene annotations, we used the databases ENSEMBL and NCBI ,33. For A total of 41 SNPs were significant for both SNP main and SNP interaction effects. Based on SEM evaluations for goodness of fit criteria see , 13 SNPsThe package lavaan (version 0.6–9) in R (version 3.6.2)  was usedThe formative measurement Models (3) and (4) were1 = production, η2 = intramammary infection und η3 = genetics); ξ = a vector of exogenous latent variables (ξ1 = time); ζ = indicating the residual variable, since endogenous latent variables are not completely explained by the exogenous latent variables, and the complete impact for factors that were not considered in the model. The coefficient matrices B and Γ show the interdependence relationships B between latent endogenous variables and Γ between latent endogenous and exogenous variables); x and y = vectors representing the indicator variables, as described in ξ and Пη = vectors of multiple regression or weighting coefficients between an (endogenous or exogenous) latent variable and the assigned indicator variables; δ or ε = vectors of the exogenous or endogenous residuals.The reflective measurement Models (5) and (6) were2 goodness of fit test and alternative fit indices. Such applications induce the standardized root-mean-square residual (0.101) (SRMR), the root-mean-square error of approximation (0.135) (RMSEA), the Tucker–Lewis index (0.244) (TLI) and the comparative fit index (0.312) (CFI). Based on these evaluation criteria, failed convergence status and unrealistic parameter estimates when including parity as indicator variable for the latent variable time, we decided to exclude parity as a cow-specific parameter from the SEM. This might be due to the extremely high proportion of first parity cows in our dataset and the strong auto-correlations between parity with other parameters including age at first calving and production traits.The overall goodness fit of the model was assessed by applying a χCompletely standardized estimates of the parameters for the final SEM are shown in According to the measurement models, the overall average somatic cell count of the herd is a weak indicator (0.09) to explain an IMI . In contFor the latent variable production (PROD), all four measurement variables indicate quite a large effect on production . The hig17 = ARS-BFGL-BAC-14274, y18 = Hapmap57340-rs29010501, both located on chromosome 11) indicate quite a strong effect, but the path coefficients of the remaining SNPs are close to zero (The latent variable genetic (GEN) is determined by 13 measured variables, i.e., SNP effects. Two of these SNPs (y to zero .For the exogenous latent variable time (TIME), the path coefficients for average calving interval with 0.96 and the average calving age with 0.87 are quite large . A moderIn the SEM framework, it is evident that the effect of the latent variable TIME on the latent variable IMI is quite small, with a path coefficient of −0.06 . The effIn this model, the manifest variable housing system shows an effect on three latent variables. However, the respective path coefficient was quite small (0.05) for the latent variable IMI and for the latent variable GEN (0.10). The highest path coefficient from this model was 0.37, i.e., the effect of the measurement variable “housing system” on the latent variable PROD.In the present study, we used a holistic approach, which contributed to a deeper understanding of the mechanisms of udder health in dairy cattle in different housing systems simultaneously considering time, environmental effects and cow effects, combined with a variety of udder health indicators.With regard to the overall measurement models, it is shown that the effect of the average herd somatic cell count is very small (0.09) to explain an intramammary infection. Accordingly, Beaudeau et al.  reportedThe path coefficient for the specific cell fraction of the lymphocytes was negative (−0.63), since this cell fraction predominates, especially in the healthy udder quarter ,42. In cStreptococcus spp. or Staphylococcus aureus. Since our SEM is influenced by both types of pathogens and additional pathogens within the MAJOR and MINOR groups, this may depress individual path coefficients due to different inter-trait relationships of each pathogen, thereby explaining the smaller influence of lactose in our study.The four manifest variables to explain the latent variable PROD indicated a moderate to large effect in a range from −0.44 to 0.91. In this regard, the strongest effect with 0.91 was identified for protein content. Craig et al.  already Staphylococcus aureus and Escherichia coli are different, triggering a cascade of specific genes for specific immune responses [For the latent variable GEN, 13 SNPs were included, but most of them only show a small influence in the SEM when additionally considering a large number of environmental characteristics. Nevertheless, these SNPs were significant for the major and minor pathogens in previous GWAS , but mosesponses .EVA1A. EVA1A is involved in autophagy and the programming of cell death [CHL1 gene [CHL1 in the SEM implied an only small path coefficient of y11 = 0.07. With regard to functional mechanisms and pathways of udder health, CHL1 plays a role in the activation of the MAPK signaling pathway [CTNNA3 was identified, which also intervenes in the MAPK pathway [However, the SNP (ARS-BFGL-BAC-14274) of pathway y17 has a quite strong effect with −0.71. This SNP is located directly in the gene ll death ,49. In all death . The MAPHL1 gene ,51. Howe pathway ,51. In a pathway . In the  pathway .In the SEM, the exogenous latent variable TIME contains four manifest variables. In this regard, the effect of lactation stage was quite small with a path coefficient of −0.02. In contrast, a stronger effect with 0.23 was identified for the age of the cow barn. This variable was integrated in the SEM to consider the experiences of management practices, especially in the context of the quite new compost farming system. Ivemeyer et al.  highlighThe SEM inferred causal relationships among a variety of udder health indicators and respective environmental and cow-associated factors. The direct housing system effect on udder health was quite small (−0.05). However, the housing system moderately affected the latent variable PROD (0.37), implying an indirect housing system effect on IMI through this pathway. Both the housing system and the latent variable IMI were moderately associated with the latent variable GEN. Hence, the SEM also indicates possible genotype by environment interactions, because of the specific reactions of udder health and immune response traits depending on the housing conditions. Overall, the present SEM revealed its potential to depict complex structures of udder health in dairy cows via the modeling of direct and indirect pathways. For the structural equation modeling, we considered the four latent variables IMI, PROD, TIME and GEN and integrated the variable housing system as a formative measurement model in this SEM. Furthermore, we modeled direct and indirect pathways for trait and effect relationships. However, such comprehensive analyses require a broad data structure based on different types of data, i.e., novel cow traits, cow-associated factors, housing characteristics, as well as “classical” environmental effects. Generation of such data structure implies tremendous efforts regarding labor, time and logistics. Consequently, in the present study, we neglected some additional possible environmental effects on an intramammary infection such as the climatic conditions in the barn. Gernand et al.  identifiEVA1A gene, which plays a fundamental role in the MAPK1 signaling pathway. Other identified genes  support results from previous studies, and this gene also contributes to mechanisms of the MAPK1 signaling pathway. Overall, our SEM emphasizes the importance of this pathway for udder health in a very complex modeling context including a larger number of further environmental effects.The applied SEM clearly inferred effects among response variables indicating udder health and environmental and cow-associated factors. Trait and modeling complexity was reduced by considering the latent variables. The direct effect of the housing system on the latent variable IMI was quite small, but the indirect pathway via PROD indicated housing system–IMI associations. For the latent variable GEN, especially one SNP is of primary interest. This SNP is located in the


Genome-wide association studies of complex traits frequently find that SNP-based estimates of heritability are considerably smaller than estimates from classic family-based studies. This ‘missing’ heritability may be partly explained by genetic variants interacting with other genes or environments that are difficult to specify, observe, and detect. To circumvent these challenges, we propose a new method to detect genetic interactions that leverages pleiotropy from multiple related traits without requiring the interacting variable to be specified or observed. Our approach, Latent Interaction Testing (LIT), uses the observation that correlated traits with shared latent genetic interactions have trait variance and covariance patterns that differ by genotype. LIT examines the relationship between trait variance/covariance patterns and genotype using a flexible kernel-based framework that is computationally scalable for biobank-sized datasets with a large number of traits. We first use simulated data to demonstrate that LIT substantially increases power to detect latent genetic interactions compared to a trait-by-trait univariate method. We then apply LIT to four obesity-related traits in the UK Biobank and detect genetic variants with interactive effects near known obesity-related genes. Overall, we show that LIT, implemented in the R package lit, uses shared information across traits to improve detection of latent genetic interactions compared to standard approaches. In particular, recent biobank-sized GWAS collect massive sample sizes and a broad range of phenotypic data to enhance complex trait mapping and augment knowledge of gene functionality. There are two important patterns that have emerged among the multitude of GWAS analyses that have been performed to date. First, the genetic variation of complex traits often involves many thousands of loci . Second,There are many statistical challenges to discovering genetic variants with interactive effects in GWAS . In partWhen there are multiple related traits measured in a study, researchers often apply variance-based procedures on a trait-by-trait (or univariate) basis to detect latent genetic interactions. However, a univariate strategy ignores any biological pleiotropy among traits despite theoretical  and empiThe manuscript is outlined as follows. We first introduce the LIT framework for detecting latent genetic interactions and then evaluate the performance using simulated biobank-sized datasets. We also compare LIT to univariate testing procedures and observe that LIT provides significant power gains to detect interactive effects in GWAS. Finally, we demonstrate LIT using four obesity-related traits in the UK Biobank with over 6 million single nucleotide polymorphisms from 330,868 genotyped individuals. Our analysis identifies multiple loci demonstrating significant interactive effects near known obesity-related genes. We then conclude with a discussion of our results.2.2.1.We provide a brief overview of the LIT framework and leave more technical details to the h common , 36, 37 h common , 38, 39 priori, we maximize the performance of LIT by aggregating the The traditional KDC statistic utilizes the corresponding eigenvectors  and eigenvalues (weights emphasizing eigenvectors) derived from the SQ/CP similarity matrix for inference. In the process, the traditional KDC statistic emphasizes signals explaining the most variation in this matrix. While we show this emphasis is suitable under certain pleiotropy settings, there are other settings where the interaction signal is not captured by the top eigenvectors of the similarity matrix and so the test may not be optimal , 40. Thest (CCT) , which hst (CCT) . We refe2.2.We simulated −3, including when the trait distribution is skewed or heavy trailed  . FurtherThe difference in power between aLIT and Marginal (SQ/CP) is also evident across baseline correlations. Interestingly, the improvement in power of aLIT compared to Marginal (SQ/CP) reduces when the baseline correlation increases from 0.25 to 0.50. This observation agrees with our simulation results. from Overall, while our results suggest that aLIT outperforms Marginal (SQ/CP) for most baseline correlations and sparsity settings under positive pleiotropy, there are some rare cases where Marginal (SQ/CP) has similar (or improved) performance. Meanwhile, under the simulation setting where there is a mixture of positive and negative pleiotropy  or the d2.4We applied the LIT framework to detect shared latent genetic interactions in four obesity-related traits from the UK Biobank, namely, waist circumference (WC), hip circumference (HC), body mass index (BMI), and body fat percentage (BFP). After preprocessing, there were 329,146 unrelated individuals that have measurements for all traits and 6,186,503 SNPs . The corIn each implementation of LIT, after filtering for LD and significant SNPs, the genomic inflation factor of wLIT and ULIT was 1.14 . While tractions .Using the aLIT ost loci . Althoug (SQ/CP) . Thus, iA concern in this analysis is whether statistical significance is due to a nearby SNP with a large additive effect and/or trait scaling issues. To address the latter, first note that the LIT framework not only detects latent interactions, but also departures from linearity due to dominance or misspecification of the trait scale. Therefore, to be conservative and help distinguish interactive effects, we removed the non-linear genetic signal within a locus by fitting a two degree of freedom genotypic model . After rFTO gene is a known obesity-related gene that is associated with type 2 diabetes , it was also close to GRB14  which has been associated with body fat distribution and may be involved in regulating insulin signaling [MC4R; [LYPLAL1; [KLF14; [After evaluating the significant SNPs found by aLIT, we focused on ten lead SNPs that remained significant after accounting for LD and dominance/scaling issues. Using the Variants to Genes (V2G) measure on Open Targets Platform , we assie, e.g., –47). Whiignaling –50. Otheg [MC4R; ), adiposLYPLAL1; , 53), an [KLF14; , 55).KLF14, GRB14, and LYPLAL1 [We then searched for evidence of known interacting variables using the significant SNPs identified by aLIT. Previous work has found sex-specific effects of variants in  LYPLAL1 , 55, 56.3.It is challenging to identify, observe, accurately measure, and then detect genetic interactions in a GWAS study. While there are methods to infer interactions that do not require specifying the interactive partner(s) , 22–24, There are some caveats when interpreting the significance results of LIT or, more generally, any approach that does not require observing the interactive variable(s). Type I error rate control is impacted by loci with large additive effects and trait scaling issues. To address the former issue, we performed inference using all SNPs in LD with the lead SNPs. While it is possible that the true causal SNP is not tagged, it is unlikely in this work since there is dense coverage with the imputed genotypes. We also assessed model misspecification due to an incorrect trait scaling by fitting a genotypic model to flexibly capture non-linear genetic signals. Interestingly, we found that our significance results were primarily impacted at loci located on chromosome 6 (outside the MHC). While this strategy can help identify the extent of genome-wide inflation due to dominance/scaling, it cannot determine whether the latent interactive effects are an artifact of the scale, even though our simulations suggest that detections by LIT are robust to deviations from normality. When presented with traits that follow a non-Normal distribution, an inverse-Normal transformation is typically applied so a trait “appears” as a standard Normal distribution. However, for detecting latent interactions, we recommend against such practice as it does not correct for the mean-variance relationship and can lead to invalid inference . In geneThere are also several important considerations when applying LIT to genetic data. Importantly, in this work, we assume that individuals are unrelated and traits follow a multivariate Normal distribution. While LIT assumes the data follows a multivariate Normal distribution, our simulation study suggests that it is robust to violations of this assumption. In general, the computational time of LIT increases as the number of traits and sample size increases . TherefoFor many complex traits, there is strong discrepancy between GWAS-based estimates of heritability (which explicitly assume additive effects of genetic variation) and family-based estimates (which may incorporate non-additive effects and higher-order interactions). With recent biobank-sized datasets, we can begin to identify loci with non-additive genetic variation that contribute to this missing heritability while understanding its role in the etiology of complex traits. As biobank-sized datasets become more prevalent, we anticipate that computationally scalable approaches that leverage information across multiple traits, such as LIT, will become increasingly important to discovering non-additive genetic loci.4.4.1.Consider the trait Under the above model assumptions, the latent GxE interaction will induce differential trait variance and covariance patterns that differ by genotype. Without loss of generality, assume the environmental variable has mean zero with unit variance. In genotype , but cann ϕk′≠0; . These r4.2.Our strategy builds from the above observations and estimates the ITV and ITC to detect latent genetic interactions. To derive estimates of these quantities, we first remove the additive genetic effect from the traits to ensure that any variance and covariance effects are not due to the additive effect. Let us denote the trait residuals as ectively . Thus, wOur inference goal is to assess whether the SNP, To address these issues, we develop a new multivariate kernel-based framework, Latent Interaction Testing (LIT), that captures pleiotropy across the ITV and ITC terms to increase power for detecting latent interactions. There are three key steps in the LIT framework :Regress out the additive genetic effects and any other covariates from the traits. Additionally, adjust the traits and genotypes for population structure.Calculate estimates of the ITV and ITC for each individual using the squared residuals and the cross products of the residuals, respectively.Test the global null hypothesis of no latent interaction by comparing the adjusted genotype(s) to the ITV and ITC estimates.We expand on the above steps in detail below.Step 1: In the first step, LIT standardizes the traits and then regresses out the additive genetic effects, population structure, and any other covariates. This ensures that any differential variance and/or covariance patterns are not due to additive genetic effects or population structure. Suppose there are The above approach only removes the mean effects and does not correct for variance effects from population structure which can impact type I error rate control . A stratStep 2: The second step uses the residuals, Step 3: In the last step, we test for association between the adjusted SNP and the squared residuals and cross products (SQ/CP) using a kernel-based distance covariance framework [ramework –33. Specramework –38). TheSince our primary application is biobank-sized data, we use a linear kernel so that LIT is computationally efficient. The linear similarity matrix is defined as ionships , 35.Once the similarity matrices  large T , 38, 60.For the linear kernel considered here, we implement a simple strategy to substantially improve the computational speed of LIT. We first calculate the eigenvectors and eigenvalues of the SQ/CP and genotype matrices to construct the test statistic. Since the number of traits, t manner –63. This4.2.1.We explore an important aspect of the test statistic in In summary, there are two implementations of the LIT framework. The residuals are first transformed to calculate the SQ and CP to reveal any latent interactive effects. We then calculate the weighted and unweighted eigenvectors in the test statistic which we refer to as weighted LIT (wLIT) and unweighted LIT (uLIT), respectively. We also apply a Cauchy combination test (CCT)  to combi4.2.2.We can extend LIT to assess latent interactions within a genetic region  consisting of multiple SNPs. In the first step, we regress out the joint additive effects from the multiple SNPs along with any other covariates and population structure. In the second step, we calculate the squared residuals and cross products using the corresponding residual matrix. Finally, in the last step, we construct the similarity matrices and perform inference using the HSIC: the linear similarity matrix for the Compared to the previous section, this extended version of LIT is a region-based test for interactive effects instead of a SNP-by-SNP test. A region-based test is advantageous to reduce the number of tests compared to a SNP-by-SNP approach. However, in this work, we demonstrate LIT on SNP-by-SNP genome-wide scan to demonstrate the scalability.4.3.We evaluated the performance of LIT using simulated data with the following assumptions. Let the individual-specific minor allele frequencies of We transformed the components in the model using the function In our simulation study, we also varied the proportion of traits with an interaction term. For 4.4.The UK Biobank is a collaborative research effort to gather environmental and genetic information from half a million volunteers 40–69 years old in the United Kingdom. The data was collected across 22 assessment centers from 2006 to 2010 where participants were given a general lifestyle and health questionnaire, a physical examination, and a blood test that provided genetic data , 65. See−5), and an INFO score of >0.9. The traits were adjusted for age and the top 20 principal components provided by the UK Biobank to account for ancestry. We removed individuals with measurements that were four standard deviations above the average and then standardized the traits by sex. After filtering, there were 329,146 individuals and 6,186,503 SNPs in our analysis.We applied LIT to four obesity-related traits, namely, waist circumference, hip circumference, body mass index, and body fat percentage. We restricted our analysis to unrelated individuals with British ancestry and removed any individuals with a sex chromosome aneuploidy. Using the imputed genotypes (autosomes only), SNPs were filtered in PLINK  with the4.5.In the The second challenge is that an incorrect scaling of the trait, or a scaling where the polygenic assumption does not hold, will induce a variance effect , 24. Thi1