DMRT3 is permissive for “gaitedness” across breeds. However, this mutation is nearly fixed in both American Standardbred trotters and pacers, which perform a diagonal and lateral gait, respectively, during harness racing. This suggests that modifying alleles must influence the preferred gait at racing speeds in these populations. A genome-wide association analysis for the ability to pace was performed in 542 Standardbred horses  with genotype data imputed to ~74,000 single nucleotide polymorphisms (SNPs). Nineteen SNPs on nine chromosomes  reached genome-wide significance (p < 1.44 x 10−6). Variant discovery in regions of interest was carried out via whole-genome sequencing. A set of 303 variants from 22 chromosomes with putative modifying effects on gait was genotyped in 659 Standardbreds  using a high-throughput assay. Random forest classification analysis resulted in an out-of-box error rate of 0.61%. A conditional inference tree algorithm containing seven SNPs predicted status as a pacer or trotter with 99.1% accuracy and subsequently performed with 99.4% accuracy in an independently sampled population of 166 Standardbreds . This highly accurate algorithm could be used by owners/trainers to identify Standardbred horses with the potential to race as pacers or as trotters, according to the genotype identified, prior to initiating training and would enable fine-tuning of breeding programs with designed matings. Additional work is needed to determine both the algorithm’s utility in other gaited breeds and whether any of the predictive SNPs play a physiologically functional role in the tendency to pace or tag true functional alleles.Several horse breeds have been specifically selected for the ability to exhibit alternative patterns of locomotion, or gaits. A premature stop codon in the gene  Certain horse breeds have been developed over generations specifically for the ability to perform alternative patterns of movement, or gaits. Current understanding of the genetic basis for these gaits is limited to one known mutation apparently necessary, but not sufficient, for explaining variability in “gaitedness.” The Standardbred breed includes two distinct groups, trotters, which exhibit a two-beat gait in which the opposite forelimb and hind limb move together, and pacers, which exhibit an alternative two-beat gait where the legs on the same side of the body move together. Our long-term objective is to identify variants underlying the ability of certain Standardbreds to pace. In this study, we were able to identify several regions of the genome highly associated with pacing and, within these regions, a number of specific highly associated variants. Although the biological function of these variants has yet to be determined, we developed a model based on seven variants that was > 99% accurate in predicting whether an individual was a pacer or a trotter in two independent populations. This predictive model can be used by horse owners to make breeding and training decisions related to this economically important trait, and by scientists interested in understanding the biology of coordinated gait development. S1 Fig). S1 Fig). However,DMRT3 (an isoform of the doublesex and mab-3 related transcription factor). Subsequent genotyping of additional Icelandic horses revealed that nearly all five-gaited individuals were homozygous for the mutation, compared to only a third of the four-gaited horses. Of even greater interest, when horses of other breeds were genotyped for the mutation, it was found to be nearly fixed in gaited breeds , but absent in non-gaited breeds .[DMRT3 was confirmed in a mouse model, where mice null for DMRT3 exhibited an abnormal gait characterized by an increased stride, prolonged, stance and swing phases of both the thoracic and pelvic limbs, and near absence of coordinated pelvic limb movements. Further, DMRT3 expression was localized to the spinal cord both pre- and postnatally, and null mice had fewer commissural interneurons, suggesting that this gene is important for the development of normal locomotor coordination.[In 2012, a genome-wide association study (GWAS) in four-gaited  and five-gaited  Icelandic horses revealed a strongly associated SNP on equine (ECA) chromosome 23.[DMRT3 mutation appears to be necessary for “gaitedness” in horses it is not sufficient to explain the variation of this trait, as demonstrated by the fact that it is nearly fixed in Standardbreds, although not all individuals exhibit that breed’s alternative gait, pacing.[Although the , pacing. It is no, pacing. It is un−6, as determined by the likelihood ratio test) (Table 1). Seven SNPs were located on equine (ECA) chromosome 17, three on ECA1, two on ECA6, two on ECA31, and one each on ECA2, 9, 19, 23, and 25. The ECA17 SNPs were from two distinct regions, 28.4–41.9Mb (n = 4) and 60.50–60.55Mb (n = 3) (Table 1). Only eight of the genome-wide significant SNPs were found within protein coding genes; all were intronic (Table 1). An additional 37 SNPs on 14 chromosomes reached significance considered to be moderately associated with gait (p < 1 x 10−5) [S1 Table).Horses included in the GWAS cohort n = 542) were genotyped on either the first generation  or second generation  Illumina equine beadchip. After genotype imputation, 73,691 markers were available for analysis; after pruning, 62,901 SNPs were included in the mixed model association analysis. After correction for relatedness and population structure, mixed model association analysis in GEMMA[42 were gWe have previously reported the results of whole-genome sequencing in this cohort. Briefly,ST ≥ 0.35) or a combination of low pool heterozygosity (Hp < 0.1) in one of the groups and high differentiation (FST ≥ 0.30). Some of these regions were contiguous or overlapping, creating larger regions of interest ranging in size from 75-300kb (S2 Table). A total of 1,885 SNPs were called across all regions of interest. Of these, 1,273 were annotated by Ensembl  as intergenic, 184 were located upstream of a gene, 138 were located downstream of a gene, 270 were located within an intron, and 20 were located within an exon (S3 Table).Two pools of genomic DNA  were sequenced at a target depth of 30x. A total of eighty-nine 50kb regions met one of the filtering criteria of either high differentiation between pacers and trotters (FS4 Table). Additionally, 98 ancestry informative markers (AIMs) were included on the assay to help control for population structure during downstream analysis . An additional 1,885 SNPs were identified within regions of interest on 19 chromosomes from the pooled sequencing data. Three hundred three SNPs were included in the final Sequenom assay, including 190 SNPs from the whole-genome sequencing regions of interest  and 113 SNPs from the pooled sequencing regions of interest (hods and ).−4; after correcting for relatedness and population structure, 177 SNPs met this criteria for statistical significance (S5 Table). Pacers were more likely than trotters to carry the derived alleles  (Table 2). Nearly all of the trotters carried only a single copy of the alternate allele in each case, while it was more common for pacers to be homozygous for the alternate allele.Genotyping was performed in 720 individuals . After pruning, 245 SNPs were available for mixed model association analysis in GEMMA. With Bonferroni correction for multiple testing, statistical significance was set at p < 2 x 10Table 3). When the random forest analysis was repeated, the relative importance of these SNPs varied only slightly over multiple iterations. The most important SNPs for classification as a pacer or trotter according to this analysis were located on ECA1, 17, 23, and 30. Ten-fold cross-validation of this data using linear discriminate analysis resulted in a misclassification error of 0.0106.Random forest classification analysis of genotyping data from the Sequenom assay in 659 Standardbreds with racing records  yielded an out-of-box (OOB) error rate of 0.61%, with a total of four misclassified individuals . Interestingly, one of the trotters who was predicted to be a pacer was in fact out of a line of pacing Standardbreds; it is not known whether this horse was trained as a pacer at any point before starting its racing career. There were 21 SNPs with a mean reduction of node impurity score (GINI index) > 5 . For four SNPs, the alternate allele was more common in pacers, and in three SNPs the alternate allele was more common in trotters. In either case, the group with the lower allele frequency included very few homozygotes (Table 4).A conditional inference tree was constructed to determine the hierarchical organization of the most informative SNPs identified by random forest analysis. A tree composed of seven SNPs predicted status as a pacer or trotter among the 659 genotyped individuals with 99.1% accuracy, with only six horses misclassified (three pacers and three trotters). Again, one of these misclassified trotters came from a line of pacers. Considering pacing as the outcome of interest, this prediction model demonstrated a sensitivity of 98.7% (95% CI 96.25% - 99.73%) and a specificity of 99.3% (95% CI 97.97% - 99.86%). The seven SNPs were located on six chromosomes   were genotyped on the same custom Sequenom assay as the discovery cohort. The genotypes for the seven SNPs included in the conditional inference tree were extracted. Two individuals had missing genotypes at one or more of the SNPs and could not be classified. Of the remaining 164 horses, 163 were correctly classified as pacers or trotters, resulting in an overall accuracy of 99.4%. The single misclassified horse was a pacer.DMRT3 which had initially been described as primarily playing a role in gonadal development and sexual differentiation.[DMRT3 nonsense mutation originally reported by Andersson et al. in 2012 [The horse is unique among quadrupeds in that certain breeds have been strongly selected for the ability to exhibit alternative patterns of locomotion as a physiologic adaptation. Beyond giving insight into an economically important trait, improved understanding of the pathways that underlie alternative gaits in the horse may also provide insight into pathways that are dysregulated with disease in other species, as well as basic insight into the underlying neurobiology of locomotion. GWA analysis in our population identified 19 SNP markers that were associated with gait at a level of genome-wide significance. These SNPs defined regions of interest on nine chromosomes that contained more than two dozen named genes. However, a challenge arises in identifying biologically compelling candidate genes for gait because there is still much that is not known about the development of normal limb coordination. It is likely that many genes that play a role in the development of alternative gaits have not previously been associated with any aspect of neurobiology. This is aptly illustrated by ntiation. The DMRTST) and heterozygosity (Hp). Pooled whole-genome sequencing has previously been used to identify genomic regions under selection, and identify candidate variants within those regions, in a number of plant and animal species.[As SNPs are chosen for inclusion in genotyping panels based on their distribution and frequency, rather than on predicted effect, it is unlikely that any of the markers in the GWA analysis play a functional role in gait. Rather, it is more likely that they are “tagging” truly functional variants with which they are in linkage disequilibrium (LD)., 11 Stan species.–14Of the tens of thousands of SNPs discovered within regions of interest via whole-genome sequencing, only a small fraction could be selected for follow-up. Thus, it is likely that we have not identified any truly functional alleles despite our prioritization process. Indeed, of the top 40 variants from GEMMA analysis of Sequenom genotyping in 720 individuals, only two resulted in amino acid changes. However, given the strength of association of our selected variants with gait in this large population, it is highly likely that one or more of these genotyped variants are “tagging” specific functional alleles, and additional investigation of nearby variants is warranted. It must be noted that given the strong population structure of our cohorts, inherent to the history of this breed which has undergone strong selection for our trait of interest over many generations, it is also possible that one or more of these variants are reflecting some other aspect of population structure unrelated to gait. Future work to address the issue of functionality will include tissue expression profiles of the cerebellum and specific regions of the proximal cervical spinal cord that contain neuronal tracts known to play a role in coordinated locomotion.Random forest classification analysis was selected to help prioritize among the numerous statistically significant variants in our Sequenom assay. In a random forest approach to a binary trait, the predicted probability of an individual expressing or not expressing a trait  is based on the aggregation of a number of decision trees., 16 WithThis study was conducted under the approval of the University of Illinois (protocol #15031) and University of Minnesota (protocol #1111B07193) Institutional Animal Care and Use Committees.S2 Fig).The cohort for the genome-wide association study consisted of 542 Standardbred trotters (n = 366) and pacers (n = 176). All of the pacers and 153 trotters were from North America, while the remaining trotters were from Europe . Horses were classified as pacers or trotters based on race records; if a horse never raced, their gait was assigned based on the race records of the sire and/or dam. Horses that raced as both pacers and trotters were classified as pacers. The North American and European trotters were related to each other. The pacers were genetically distinct from the trotters, with minimal admixture between groups , including the entire GWAS cohort. Horses were classified as pacers or trotters based on race records; if a horse raced at both gaits, it was classified with the gait at which it raced most successfully. Horses without a race record were excluded from downstream analysis, resulting in a final cohort comprised of 659 Standardbred trotters (n = 428) and pacers (n = 231) from North America (n = 374) and Europe (n = 285).Initially, 720 Standardbreds from North America and Europe were genotyped on the custom Sequenom assay  and pacers (n = 83) from North America. Horses were classified as pacers or trotters based on race records. These horses were genotyped on the custom Sequenom assay as described above, and the genotypes at the SNPs included in the prediction algorithm were extracted for analysis. Approximately 10% of the horses in the discovery and validation cohorts had some degree of admixture (between pacer and trotter) found within a 4-generation pedigree.DNA was isolated from whole blood samples using the Gentra Puregene Blood Kit  per manufacturer recommendations. Briefly, RBC lysis solution was added to samples at a 3:1 ratio, incubated, and centrifuged. After discarding the supernatant, Cell lysis solution was added to the white blood cell pellet and the cells were re-suspended, after which protein was precipitated and discarded. DNA was precipitated in isopropanol and subsequently washed in ethanol prior to final hydration. Quantity and purity of extracted DNA were assessed using spectrophotometric readings at 260 and 280nm .Genome-wide genotyping of single nucleotide polymorphism (SNP) markers was performed by Neogen GeneSeek  using an Illumina Custom Infinum SNP genotyping platform. Horses were genotyped at either 54,602 SNPs using the first generation Illumina Equine SNP50 chip (n = 306), or at 65,157 SNPs using the second generation Illumina Equine SNP70 chip (n = 236).The two genotyping platforms used in the GWAS cohort share 45,703 SNPs. As an alternative to losing information from tens of thousands of SNPs by pruning to this shared marker list prior to merging files, genotype imputation may be used. This technique statistically estimates genotypes from non-assayed SNPs based on a comparison of haplotype blocks between one population and a second, more densely genotyped reference population. An established pipeline for imputation of equine genotyping data  was used2 > 0.2; PLINK command—indep-pairwise 100 25 0.2).[−6 based on the effective number of independent tests in our data.[A GWA analysis with gait as the phenotype of interest was performed after genotype imputation using GEMMA  software. A center 25 0.2). All thre 25 0.2). Genome-wour data.We have previously reported whole-genome sequencing in this cohort. For the Data analysis, including quality control, alignment, and variant detection, was carried out following published best practices, 24 withGenomic DNA from 20 pacers and 20 trotters were combined into two pools, each comprising equimolar amounts of DNA from all individuals, for the purpose of whole-genome sequencing. These individuals were selected from the GWAS cohort and were chosen to be as unrelated as possible on the basis of coancestry coefficient generated from the whole-genome genotyping data (PLINK command—genome). Selected pacers had coancestry coefficients <0.06 (no more closely related than first cousins); selected trotters had coancestry coefficients <0.14 .https://broadinstitute.github.io/picard/). SNP and small insertion/deletion calling was performed using the UnifiedGenotyper algorithm of the Genome Analysis Toolkit (GATK) [ST) for the contrast between the two pools and to calculate estimated pool heterozygosity (Hp) within each pool for 50% overlapping sliding windows of 50 kilobases along the genome as previously described.[ST and Hp values were consulted to determine the genomic intervals displaying the most strongly differentiated loci between the pools and the most strongly fixed loci within each pool, respectively. From these distributions we used a strategy where windows fulfilling one of two criteria, (1) FST ≥ 0.35 or (2) FST ≥ 0.30 with the additional criteria of at least one pool showing Hp <0.1, were selected as regions of interest.The two DNA pools were sequenced to 30X average depth of coverage using an Illumina HiSeq2500 sequencer at Uppsala University. The resulting paired reads were subjected to sequencing adaptor trimming and were subsequently aligned to the horse reference genome (EquCab2.1) (bwa samt (GATK) , and thet (GATK) , 24 Numbescribed. DistribuST ≥ 0.35) or a combination of low pool heterozygosity (Hp < 0.1) in one of the groups and high differentiation (FST ≥ 0.30). SNPs discovered via whole-genome sequencing that passed quality control filters were prioritized according to the following parameters: 1) segregation with gait ; 2) not intergenic; 3) non-synonymous, then synonymous changes; 4) if intronic, close to the exon-intron border (preferably < 100bp); 5) coding genes preferred over non-coding; and 6) if upstream/downstream, as close as possible to start/stop codon. Variants from pooled sequencing data were prioritized according to criteria 2–6.A custom Sequenom genotyping assay was designed for high-throughput evaluation of prioritized variants. Variants were selected from top regions of interest identified in the GWA, as well as from regions from the pooled sequencing data with high differentiation between pacers and trotters  were also included in the assay to help control for population structure. These 98Genome-Wide Association (GWA) Analysis. Statistical significance was set at p<0.05 with a Bonferroni correction for multiple testing.Genotyping data from the Sequenom assay were pruned using default parameters in GEMMA . The mixed model included a sex covariate (-c) and a relatedness matrix constructed from the AIMs (-gk 2). All three possible frequentist tests were calculated as described under Sequenom Assay Discovery Cohort) were subjected to random forest classification analysis using the ‘randomForest’ function of the ‘randomForest’ package in R.[n, where n is the total number of variables). SNPs were pruned for missingness <90% prior to analysis. These data were subsequently subjected to 10-fold cross-validation using linear discriminate analysis to estimate misclassification error using the ‘errorest’ function of the ‘ipred’ package in R.[Genotyping data from the Sequenom assay from 659 horses with race records Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.S5 Table(DOCX)Click here for additional data file.S1 Fig(DOCX)Click here for additional data file.S2 Fig(DOCX)Click here for additional data file.


Panicum virgatum L.), an allotetraploid (2n = 4× = 36) perennial C4 grass (Poaceae family) native to North America and a feedstock crop for cellulosic biofuel production, has a large potential for genetic improvement due to its high genotypic and phenotypic variation. In this study, we analyzed single nucleotide polymorphism (SNP) variation in 372 switchgrass genotypes belonging to 36 accessions for 12 genes putatively involved in biomass production to investigate signatures of selection that could have led to ecotype differentiation and to population adaptation to geographic zones.Advances in genomic technologies have expanded our ability to accurately and exhaustively detect natural genomic variants that can be applied in crop improvement and to increase our knowledge of plant evolution and adaptation. Switchgrass  contains supplementary material, which is available to authorized users. A major challenge in crop improvement is to achieve food and energy security by identifying genetic polymorphisms that directly influence traits of economic importance. In switchgrass, we are particularly interested in biomass yield and composition. Next generation sequencing technologies have made accurate detection of genomic variation, including single nucleotide polymorphisms (SNPs), insertions/deletions (INDELs), copy number variants, and presence/absence variants feasible. Association of these variants with agronomic traits via association mapping and/or biparental linkage mapping has greatly facilitated crop breeding and has helped to address the increased global demand for food, feed, fiber, and fuel –8. The aPanicum virgatum L.), a species displaying multiple cytotypes and a wide geographic distribution, constitutes an ideal system for the study of selective pressure associated with environmental gradients, as evidence of local adaptation has been confirmed through numerous agronomic field trials and reciprocal transplant experiments  [st) was calculated on the basis of Nei’s method and its significance was tested using 999 permutations and bootstraps in GenAlEx 6.501 [m) between subpopulations as defined by STRUCTURE was calculated from Gst as Nm = 0.5(1− Gst)/Gst. The significance of subpopulation differentiation defined by STRUCTURE was further investigated by performing a Principal Coordinates Analysis (PCoA) using GenAlEx 6.501. An Analysis of Molecular Variance (AMOVA) implemented in GenAlEx 6.501 was used to investigate the percentage of molecular variability explained by the genetic populations.The SNPs were used to perform a population structure analysis using a Bayesian clustering algorithm implemented in STRUCTURE v.2.3.4 . Ten run[LnP(D)] . At the Ex 6.501 . The estSetaria italica) as standard [n nearest geographic neighbors in order to identify fine-scale patches of lower genetic diversity. Significance levels were estimated through 9999 random permutations of the samples. Analyses were performed for 7 to 14 nearest neighbors (n) to determine the consistency of the observed patterns.To further investigate the differences between the switchgrass genotypes, pairwise Fst and Nei’s genetic distance matrices were calculated using GenAlEx 6.501. All the DNA sequences were concatenated into one contiguous sequence for each switchgrass genotype. Variants detected across the concatenated sequences were used to perform an Unweighted Pair Group Method with Arithmetic mean (UPGMA) tree based on the maximum composite likelihood method with a 500 replicates bootstrap test in the program Mega 6 . Divergestandard . An AMOVstandard  implemenP ≤ 0.05). Accessions for which more than 70% of the genotypes belonged to a specific subpopulation were considered representative for that subpopulation. The molecular variances due to differences between subpopulations, within subpopulations and within individuals were calculated using an AMOVA approach in GenAlEx 6.501. This AMOVA helped us to investigate the percentage of molecular variability explained by the genetic structure, as compared to the earlier described AMOVAs which were based on geographic origin and latitude patterns. In addition, we performed a correlation analysis using the rcorr function under R 3.2.2 [http://www.phytozome.net/). By taking a window of 100 bp, divergence between the subgenomes was investigated for the Phytochrome B (PHYB), Terminale ear (TE), Flowering locus T (FLT), and Phosphoglyceratemutase (PGM) genes.For each contiguous DNA sequence, DnaSP 5.10  was used R 3.2.2  to test . In TE and FLT, 83% (35 SNPs) and 100% (38 SNPs) of the SNPs were located in intron 4, and in the 5’ UTR region, respectively. Sixty percent of SNPs (49 SNPs) located in exons were non-synonymous. Of the non-synonymous SNPs, 65% (32 SNPs) encoded an amino acid that had different properties than the amino acid encoded by the reference allele and were termed non-conservative , the wild-type allele was the most frequent allele.A total of 332 million (M) raw Illumina reads were obtained (average read length: ~ 90 bp) for the 33 amplicons generated from 12 genes. Of these, 166 M mapped to 30 of the 56 selected reference contigs with a minimum of 1 M reads per contig, yielding an average read depth of ~ 8.6× per base per sample. The 30 contigs covered homoeologous regions in the 12 genes . The Bayesian clustering algorithm implemented in STRUCTURE v.2.3.4 combined with the LnP(D) method indicated the presence of three genetically distinct subpopulations C1, C2 and C3  and PI 476290 (tetraploid)  from the C2 and C3 clusters (mostly lowland genotypes). The second axis explained 6% of the genetic variability and separated C2 from C3 , and the lowest was between C2 and C3 (0.167). Similarly, the largest Nei genetic distance (0.359) was noted between C1 and C2, while the genetic distance between C2 and C3 (0.144) was lowest  across the whole sampled region, indicating significant isolation-by-distance. Mantel tests conducted separately on each subpopulation also indicated significant isolation-by-distance within C1, C2 and C3 . Positive FIS values in each subpopulation indicated that individuals were more related than was expected under a model of random mating. This suggested that outcrossing occurred predominantly between close neighbors which, in most cases, were derived from the same accession and genetically similar. In addition, the AMOVA indicated that 15 and 28% of the genetic variation were due to differences in latitude range and accession origins, respectively . All of these individuals were clustered in subpopulation C1 and represented 90 to 100% of genotypes from six accessions . These accessions accounted for 70% of the representative accessions for C1 , but subpopulation C3 displayed a significantly lower Ho index than C1 and C2 (P = 0.003)  across the switchgrass collection. A regression analysis of the percentage of polymorphic loci and latitude revealed that population diversity remained constant with increasing latitude  which had higher levels of variation in subgenome K and PGM which was more polymorphic in subgenome N  were present in the first 1 kb of the 5’ UTR region analyzed. In contrast, 67% of the SNPs identified in subgenome N (14 SNPs) were present in the last 1 kb of the 5’UTR region analyzed. Similar observations were made in PHYB , Vernalization 3  and PHYB (1 amino acid change) (Table Phytochrome C (PHYC), one to a change in the Per-Arnt-Sim (PAS) domain of PHYB, one to a change in the Alkaline-phosphatase-like domain of PGM, one to a change in the Zinc binding domain of Heading date 1 (HD1) and one to a change in the Fibronectin type III domain of VRN3 , PHYC  and GI  were largely in linkage disequilibrium. One haplotype was prevalent in upland accessions (subpopulation C1) while the other haplotype was commonly present in lowland accessions (subpopulations C2 and C3). For the non-conservative and common SNP in HD1, one haplotype was prevalent in subpopulation C2 (lowland accessions) while the other haplotype was commonly present in subpopulations C1 and C3 ; for the non-conservative and common SNPs in VRN3, one haplotype was prevalent in subpopulation C3 (lowland accessions) while the other haplotype was commonly present in subpopulations C1 and C2 . However, some accessions were identified where more than 50% of the individuals had a non-conservative SNP at either the PHYB (accessions PI 315727 and PI 414067), PHYC , GI (accession PI 431575), HD1 (accessions PI 422016 and SPBluff) or VRN3 (accessions PI 642191 and Pasco Co-FL) locus that was different from that expected based on the genetic subpopulation to which these genotypes belonged . A supplementary test of neutrality for this gene with Fu and Li’s F statistic was also significant . Significant positive values of Fu and Li’s F, and Tajima’s D statistics indicated a lack of rare alleles in the PHYB gene. Positive values indicate balancing selection or the presence of population structure. Because it is difficult to clearly distinguish between selection and demographic patterns caused by a population bottleneck or population subdivision [P < 0.05; Fu and Li’s F = − 2.91; P < 0.05) in PHYB (Chr09N) in subpopulation C2, indicating a recent selective sweep  were detected in FLT (Chr07N) in subpopulation C2, indicating balancing selection  and the lowland genotypes grouping into two subpopulations (C2 and C3). The existence of two lowland genetic populations has previously been reported based on SSRs, SNPs identified by exome-capture, and genotyping-by-sequencing (GBS) [P. virgatum is associated not only with ecotype but also with latitude and altitude of origin [Local adaptation is an important process that contributes to population differentiation. Over evolutionary time, biotic and abiotic stresses may exert selection on genomic regions and favor different loci depending on the environment, leading to genotypic and phenotypic divergence among populations. We assessed the natural variation present in 51.5 kb of sequence derived from 12 genes affecting biomass traits across a set of 372 diverse accessions of ng (GBS) , 71. Theng (GBS) . In contng (GBS) , 31, micng (GBS) , 37, 72 ng (GBS) . Considef origin , 74–80. f origin , 81–83. f origin –90.Most of the SNPs in exons were non-synonymous and more than half of them led to non-conservative amino acid changes that, due to changes in charge and/or polarity, might modify the three-dimensional structure of the protein. SNPs differentiating the two ecotypes were mostly fixed in homozygous state in the accessions. This was unexpected as switchgrass is an outcrossing species and previous studies have revealed high levels of heterozygosity in neutral markers , 49. FixThe degree of divergence between upland and lowland switchgrass ecotypes reflects the balance between selection for adaptive traits/drift and gene flow from nearby populations. Gene flow between natural switchgrass populations belonging to different ecotypes has previously been observed . In our PHYB gene in contig13571 (Chr09N) in subpopulation C2, suggesting that this gene may have a key role in switchgrass adaptation. Although most genes are present in two homoeologous copies in the tetraploid switchgrass genome, both copies may contribute differently to environmental adaptation. The PHYB homoeolog on chromosome 9 K carried no non-synonymous SNPs in the region analyzed and did not appear to be under positive selection. Different evolutionary patterns between subgenomes were also seen in PGM and FLT. Regional differences in SNP prevalence in these genes could potentially lead to subfunctionalization of the homoeologous gene copies. In addition, in the case of FLT, Tajima’s test revealed a significant positive value in subpopulation C2 indicating balancing selection in the chromosome 7 N gene copy but not in its homoeolog on chromosome 7 K. However, for both PHYB and FLT, evidence for selection should still be interpreted with caution; the confounding effects of population demographic history can mimic the effects of positive selection [TE and FLT, 83 and 100% of the SNPs (35 SNPs and 38 SNPs) were in intron 4 and in the 5’UTR region, respectively. Previous studies have shown that the upstream region of the FLT gene contained conserved sequences among Brassicaceae species that are putative cis-regulatory elements that are necessary for FLT activation by CONSTANS (CO) in Arabidopsis thaliana [FLT promoter that contributed to the flowering response to the combined effects of photoperiod and ambient temperature in A. thaliana. Terminal Ear1 (TE1) on the long arm of chromosome 3 in maize has been identified as a candidate underlying QTL involved in several traits distinguishing maize and teosinte such as seed number, branching and inflorescence formation [TE1 that encompassed exons 1 to 3, indicating that this region was probably not involved in maize evolution. Terminal ear1 on chromosome 3 L in maize is the ortholog of the TE gene on switchgrass chromosome 5 analyzed here. Our SNP analysis suggests that the first 600 bp of intron 4 may be an important region involved in gene function. It has been previously shown that intronic SNPs can have functional effects on splicing especially in higher eukaryotes [TE gene expression and are responsible for a phenotypic polymorphism or whether they are in linkage disequilibrium with a functional SNP.The relative frequency of SNPs that were predominantly present in a single subpopulation indicated that the three populations had been subjected to varying degrees of selection pressure and/or genetic drift. Non-synonymous SNPs prevalent in C2-C3 (lowland) were present at a low frequency, and were mainly rare whereas non-synonymous SNPs prevalent in C1 (upland) were present at higher frequencies and were more likely to be common and non-conservative. This suggests that C1 has been subjected to higher levels of adaptive constraints and/or genetic drift than the C2 and C3 subpopulations. The degree of selection varied by gene and was likely influenced by its level of involvement in adaptation. Tajima’s test revealed a significant deviation from the null hypothesis of neutrality for the election –69 and selection . The effthaliana , 97. Schthaliana  fine-mapormation . White akaryotes –104. In karyotes . FurtherSetaria were found at a two times higher frequency than ancestral alleles prevalent in C1, suggesting that the lowland ecotype has a higher number of ancestral alleles and that upland switchgrass originated from lowland switchgrass and migrated north. Furthermore, despite the closer geographic proximity of C1 populations to C2 populations, admixed individuals were eight-fold more frequent between subpopulations C1 and C3 than between C1 and C2 and showed a predominantly lowland haplotype. This suggests that the extreme southern area (Florida), represented by the C3 genetic cluster, was probably the source of the northern upland 4× and upland 8× switchgrass populations. Northward migration was a long process characterized by independent recolonization of northern latitudes from southern refugia [P. virgatum at more northern latitudes was tolerance to longer day length [During repeated glaciation events that impacted tall grass prairie and savanna habitats, switchgrass was massively compressed into refuge areas . Multipl refugia , 80, 106y length . Consequy length .P values for 69 individuals. All individuals that were significantly more related to their geographic closest neighbors than to random individuals belonged to subpopulation C1, indicating higher local adaptation within this genetic group. This fine-scale genetic structure revealed several hot-spots of spatial clusters of related germplasm in C1 accessions in the Western US ranging from South Dakota to New Mexico. These locally adapted populations may be the results of differential patterns of selection, gene flow and genetic drift. Subpopulation C2, located mainly in Kansas, Oklahoma and Arkansas, represents the Southern Great Plains lineage described by Zhang et al. [P. virgatum and to reconstruct the patterns of past migrations following glaciation events.Only a single major lineage was identified in the upland tetraploids using SSR markers, cpDNA sequences, GBS and exon capture data , 51, 71.g et al.  that orig et al. . Differeg et al. , 80, 106g et al. . While Zg et al.  identifig et al. . More lig et al.  based onEvolution following migration often begins with divergent selection for locally adapted traits . MutatioPhytochrome B, a gene involved in photoperiod response, was shown to be under positive selection in switchgrass subpopulation C2. Phytochrome B carried a non-conservative amino acid substitution in the PAD domain, which acts as a sensor for light and oxygen in signal transduction. Further analyses are needed to determine whether this SNP plays a role in the differential adaptation of switchgrass ecotypes.SNP variation was assessed in 372 switchgrass genotypes for 12 genes putatively involved in biomass production. Population structure analysis largely grouped upland accessions into one subpopulation and lowland accessions into two additional subpopulations that differed by their local adaptation pattern. Of the 12 genes, Additional file 1:Table S1. List of switchgrass accessions used in the study with their ID and name, number of genotypes, ecotype identification, ploidy level, state of origin, and GPS coordinates [Table S2. Sequences and annealing temperatures of the 33 primer pairs used for PCR amplification of the selected 12 genes. Conserved regions in orthologous exons in Oryza sativa (rice), Sorghum bicolor (sorghum), Zea mays (maize) and Setaria italica (foxtail millet) were used for primer design. Table S3. Sequences of 56 regions of AP13 extracted from the Phytozome database (http://www.phytozome.net/), and used as reference for read mapping and SNP identification. Table S4. Number of amplicon reads mapped to each of the 56 reference switchgrass contigs. Table S5. Summary statistics for the non-synonymous SNPs analyzed in 12 biomass genes. Table S6. Genic regions for which the SNP distribution is different in the K and N subgenomes. The percentage of SNPs and the region in which they are located are given for each subgenome. Table S7. Tajima’s, and Fu and Li’s tests on a per gene basis within each subpopulation. Figure S1. Distance between SNPs. Figure S2. Log probability of data as a function of K. STRUCTURE was run for K ranging from 1 to 10, and 10 repetitions were performed with 100,000 burn-ins and 100,000 runs. K = 3 clusters were retained as the most likely number of genetic clusters in the switchgrass panel analyzed. Figure S3. UPGMA tree performed on the 251 SNPs across the 372 genotypes with a 500 replicates bootstrap test using Mega 6 [Figure S4. Local Indicator of Spatial Autocorrelation Analysis (2D-LSA) on 372 genotypes. Individuals that are consistently significantly more related to their 7 to 14 nearest neighbors than to random individuals are represented as plain blue dots. The number of genotypes is given in parenthesis. Accessions with significant P values for more than 90% of the genotypes are listed; their subpopulation and number of genotypes are indicated. USA Map source: https://upload.wikimedia.org/wikipedia/commons/c/ca/Blank_US_map_borders.svg. Figure S5. Regression analysis of the percentage of polymorphic loci and latitude bins across the switchgrass accessions. Figure S6. Protein structure modeling of an amino acid substitution in the PAS domain of 1D06, a protein with similar PAS domain as PHYB (A) Original structure of protein 1D06; (B) modified structure after two amino-acid changes in the PAS domain (in yellow): one conservative substitution  and one non-conservative substitution . Swiss-Pdb Viewer 4.1.0 [rdinates –116. Tabg Mega 6  based oner 4.1.0  was used


Genetic interactions have been reported to underlie phenotypes in a variety of systems, but the extent to which they contribute to complex disease in humans remains unclear. In principle, genome-wide association studies (GWAS) provide a platform for detecting genetic interactions, but existing methods for identifying them from GWAS data tend to focus on testing individual locus pairs, which undermines statistical power. Importantly, a global genetic network mapped for a model eukaryotic organism revealed that genetic interactions often connect genes between compensatory functional modules in a highly coherent manner. Taking advantage of this expected structure, we developed a computational approach called BridGE that identifies pathways connected by genetic interactions from GWAS data. Applying BridGE broadly, we discover significant interactions in Parkinson’s disease, schizophrenia, hypertension, prostate cancer, breast cancer, and type 2 diabetes. Our novel approach provides a general framework for mapping complex genetic networks underlying human disease from genome-wide genotype data. Genetic interactions may contribute to phenotypic traits but are challenging to decipher. Here, the authors develop BridGE, a computational approach for identifying pathways connected by genetic interactions from GWAS data. However, for most diseases, there remains a substantial disparity between the disease risk explained by the discovered loci and the estimated total heritable disease risk based on familial aggregation5. While there are a number of possible explanations for this “missing heritability”, including many loci with small effects or rare variants4, genetic interactions between loci are one potential culprit6. Genetic interactions generally refer to a combination of two or more genes whose contribution to a phenotype cannot be completely explained by their independent effects7. One example of an extreme genetic interaction is synthetic lethality where two mutations, neither of which is lethal on its own, combine to generate a lethal double mutant phenotype. Thus, genetic interactions may explain how relatively benign variation can combine to generate more extreme phenotypes, including complex human diseases8. Several studies have reported genetic interactions between specific variants in various disease contexts9, and scalable computational tools have been developed for searching for interactions amongst SNPs10. However, systematic discovery of statistically significant genetic interactions on a genome-scale remains a major challenge. For example, a theoretical analysis estimated that ~500,000 subjects would be needed to detect significant genetic interactions under reasonable assumptions5, which remains beyond the cohort sizes available for a typical GWAS study or even the large majority of meta-GWAS studies.Genome-wide association studies (GWAS) have been increasingly successful at identifying single-nucleotide polymorphisms (SNPs) with statistically significant association to a variety of diseases12. Specifically, the mapping and analysis of the yeast genetic network revealed that genetic interactions are numerous and tend to cluster into highly organized network structures, connecting genes in two different but compensatory functional modules  as opposed to appearing as isolated instances13. For example, nonessential genes belonging to the same pathway often exhibit negative genetic interactions with the genes of a second nonessential pathway that impinges on the same essential function . Other existing approaches have also successfully identified interactions by reducing the test space for SNP–SNP pairs, either through knowledge or data-driven prioritization21 (see Methods). However, to our knowledge, no existing method has been developed to systematically identify between-pathway genetic interaction structures based on human genetic data, which is the focus of this study.Here, we present a new method, called BridGE (Bridging Gene sets with Epistasis), that leverages the expected between- and within-pathway structure of genetic interactions to discover them based on human population genetic data. We present results from application of this method to seven different diseases, with significant interactions discovered in six of the seven, along with extensive simulation results establishing the utility of the approach. We note that the method proposed here is broadly similar to previous approaches that have used gene-set enrichment or GO enrichment analysis to interpret SNP sets arising from univariate or interaction analysesWe developed a method called BridGE (Bridging Gene sets with Epistasis) to explicitly search for coherent sets of SNP–SNP interactions within GWAS cohorts that connect groups of genes corresponding to characterized pathways or functional modules. Specifically, although many pairs of loci do not have statistically significant interactions when considered individually, they can be collectively significant if an enrichment of SNP–SNP interactions is observed between two functionally related sets of genes or within a functional coherent gene set Fig. . Thus, w22. Also, in dataset pre-processing, the input set of SNPs is pruned down to a subset of SNPs that are less likely in linkage disequilibrium (LD) with each other to avoid discovery of spurious BPM/WPM structures due to LD. (II) Construction of a SNP–SNP interaction network: BridGE can use any one of four different disease models to compute a SNP–SNP interaction network: additive, recessive, dominant, or combined recessive and dominant. When run in the additive, recessive and dominant mode, BridGE tests all SNP pairs across the two pathways using the same disease model. In the combined recessive and dominant mode, BridGE integrates edges derived from multiple disease models, which allows for SNPs to interact in multiple ways as long as they still connect across the two pathways of interest. Each model encodes different assumptions and will result in a different, overall complementary, set of significant BPM/WPM structures at the end of the pipeline. The additive disease model was implemented as previously described8, with SNP–SNP interaction scores derived from likelihood ratio tests comparing models with and without an interaction term7. Interactions based on recessive and dominant disease models are estimated using a hypergeometric-based metric that directly tests for disease association for individuals that are either homozygous (recessive and dominant models) or heterozygous (dominant only) for the minor allele at two loci of interest, and compares the observed degree of association to the marginal effects of both loci. BridGE can be run in any of these disease model modes and also implements a combined dominant/recessive mode where interactions among SNP pairs are taken from the maximum (most significant) of the dominant and recessive models. (III) Binarization of the SNP–SNP network: The SNP–SNP network derived from a chosen disease model is thresholded by applying a lenient significance cutoff to all pairwise SNP–SNP interactions to generate a low-confidence, high-coverage network that is expected to contain a large number of false positive interactions, but enables the assessment of significance of SNP–SNP interactions collectively at the pathway level. The binarization threshold is determined by a pilot run that evaluates the SNP–SNP interaction network at a range of cutoffs with a limited number of permutations to establish preliminary significance estimates (see Methods). (IV) Scoring of BPMs and WPMs for enrichment of SNP–SNP interactions: after SNP–SNP network binarization, pathways are defined by curated functional standards25, and these pathways (in the case of WPMs) and pairs of pathways (for BPMs) are tested for enrichment of SNP–SNP pair interactions. The enrichment significance is measured by a permutation test (pperm) derived from randomly shuffling of the SNP-pathway assignment (see Methods). In addition to discovering BPM and WPM structures, our approach also identifies individual pathways that have significantly elevated marginal density of SNP–SNP interactions even where the interaction partners do not necessarily have clear coherence in terms of pathways . In this case, we are not identifying pathway–pathway interactions but simply assessing whether a particular pathway is a highly connected hub and associated with numerous SNP-level interactions. (V) Estimation of false discovery rate based on a hybrid permutation strategy: finally, to correct for multiple hypothesis testing and assess the significance of the candidate BPM, WPM, or PATH interactions, BridGE uses sample permutation to establish an FDR. Specifically, FDR is estimated by measuring the average number of discovered BPMs/WPMs from the random sample labels that achieve a higher significance level than the BPMs/WPMs reported from the real sample labels relative to the total number of discoveries . As the number of hypothesis tests performed for all possible pathways and all possible between-pathway combinations is substantially less than the number of tests for all possible SNP pairs (~105 as compared to ~1011), our power for discovering interactions relative to approaches that operate on individual SNP–SNP interactions is greatly increased. These five steps enabled us to extract statistically significant pathway-level interactions that can be associated with either increased risk of disease when pairs of minor alleles linked to two pathways occur more frequently in the diseased population or, conversely, decreased risk of disease when pairs of minor alleles annotated to two pathways occur more frequently in the control population. The code implementing our approach is available at http://csbio.cs.umn.edu/bridge.Our approach involves five main components, each of which is described briefly below  of the total heritable risk27. The PD-NIA cohort used in this analysis consists of 519 patients and 519 ancestry-matched controls after balancing the population substructure (see Methods). We compiled a collection of 833 curated gene sets 29 representing established pathways or functional modules from KEGG23, BioCarta24, and Reactome25 (Supplementary Data pperm < 4.7 × 10−5) using a combined disease model el Figs. , a 1.5-f3. More specifically, Golgi-associated vesicle biogenesis, Clathrin-derived vesicle budding and the Rac-1 cell motility signaling pathway modules were enriched among the single-locus effects associated with PD at the same FDR applied to the discovery of BPMs  of discovered BPMs were associated with decreased risk for Parkinson’s disease . RAB7L1 itself is not annotated to the Golgi vesicle biogenesis gene set, but we further investigated the individual genes driving the observed between-pathway interaction. The strongest SNP contributing to this pathway interaction was linked to the gene RAB5C, another Rab GTPase that regulates early endosome formation40, for which an isoform (Rab5B) is known to physically interact with LRRK2 (refs. 41). Our result suggests that beyond this known interaction, there are many other combinations of common variants that affect vesicle trafficking involved in genetic interactions associated with risk of PD. BridGE also identified three protective interactions involving the IL-12 and STAT4 signaling pathway, a pro-inflammatory cytokine that has a major role in regulating both the innate and adaptive immune responses42. Specifically, microglial cells both produce and respond to IL-12 and IFN-gamma, and these comprise a positive feedback loop that can support stable activation of microglia44, a hallmark of PD, particularly in later stages45. The prevalence of the FcεRI and IL-12 interactions among the discovered interactions suggests a major role for immune signaling as a causal driver of PD.Aberrant events in the Golgi and related transport processes have also been known to play an important role in the pathology of various neurodegenerative diseases, including Parkinson’s diseaseay Figs.  and 3. Ipperm ≤ 4.7 × 10−5, and FDR < 0.01), Collagen mediated activation cascade , and the HCMV and MAP kinase pathways  . At a stringent FDR < 0.05 cutoff, BridGE discovered two BPM interactions in the PD-NIA cohort, and one of them replicated in the PD-NGRC based on all three significance criteria p = 6.7 × 10−4)  (one-tailed rank-sum test −4) Fig. . Thus, t52 p = 0.0001) while 2 of 7 WPMs discovered from the ProC-BPC3 cohort (FDR ≤ 0.10) could be replicated in ProC-CGEMS . For breast cancer, 6 of 108 significant BPMs (FDR ≤ 0.20) discovered from the BC-MCS-JPN cohort replicated in the BC-MCS-LTN cohort  and the sole significant PATH interaction discovered from the BC-MCS-LTN cohort replicated in the BC-MCS-JPN cohort. For schizophrenia, 1 of 8 significant BPMs (FDR ≤ 0.25) discovered from the SZ-GAIN cohort replicated , and the top significant WPM (FDR ≤ 0.1) also replicated in the SZ-CATIE cohort .Importantly, we were able to successfully replicate genetic interactions discovered for 3 additional diseases beyond Parkinson’s, including prostate cancer, breast cancer and schizophrenia signaling, and insulin regulation pathways. Consistent with our findings, metabolic syndrome has been recently associated with prostate cancer56, and serum insulin levels have been shown to correlate with risk of prostate cancer57. We also identified a replicating interaction associated with decreased risk of prostate cancer between the p38 MAPK signaling and AKAP95 chromosome dynamics pathways. P38 MAPK signaling has been associated with a variety of cancers58, and AKAP95 is an A kinase-anchoring protein involved in chromatin condensation and maintenance of condensed chromosomes during mitosis59 whose expression has been previously implicated in the development and progression of rectal and ovarian cancers60. We also discovered and replicated two WPMs associated with prostate cancer risk. The first involves the antigen processing and presentation pathway (associated with increased risk) and a second involving a gene set associated with activation of ATR in response to replication stress (associated with decreased risk). Both of these pathways have strong relevance to cancer risk62.We also identified and replicated multiple prostate cancer risk-associated interactions that involved DNA repair, 63. Our finding suggests a common genetic basis between risk factors for schizophrenia and host response to the HIV virus, which may help to explain the observed co-morbidity of these diseases. We also discovered and replicated a protective WPM for schizophrenia in the nicotinate and nicotinamide metabolism pathway. Nicotinic acid (vitamin B3) supplements have been pursued as a treatment for schizophrenia dating back to the 1950s64. Interestingly, after an initial series of reports of promising treatments, several follow-up studies had difficulty reproducing the beneficial effects of nicotinic acid65, which could be a result of modifier effects within this pathway. In summary, BridGE was able to detect each of these different types of pathway-level genetic interactions  across several diverse disease cohorts, highlighting the utility of our method and the potential for genetic interactions to underlie complex human diseases.For schizophrenia, we discovered and replicated a BPM interaction comprising a gene set associated with the HIV life cycle and a vitamin and cofactor metabolism pathway. Interestingly, a recent large Danish schizophrenia study reported that schizophrenia patients are at a twofold increased risk of HIV infection, and conversely, that individuals infected with HIV exhibited increased risk of schizophrenia, especially in the year following diagnosisSeveral of our results indicate that the additional power gained by aggregating SNPs connecting between or within pathways is critical for discovering genetic interactions from GWAS, at least based on the cohort sizes analyzed here. To fully explore the limits of our approach, we carried out a simulation study to estimate the statistical power afforded by the BridGE method with respect to sample size, interaction effect size, minor allele frequency, and pathway size, all of which should affect the sensitivity of detection of pathway-level genetic interactions.66 to generate synthetic GWAS datasets with 100 embedded SNP–SNP interaction pairs under different controlled scenarios representing various combinations of different sample size, interaction effect size, and minor allele frequency. Then, we measured the discovery rate of the embedded SNP–SNP interactions. This provides a direct measure of the sensitivity and specificity of the SNP–SNP interaction-level measure that forms the basis of the pathway-level statistics. The statistics on sensitivity and specificity of SNP–SNP interaction detection from this component of our simulations were then used to guide a second set of simulations in which we assessed the sensitivity of BridGE in detecting BPMs with different levels of noise in the SNP–SNP level network. We generated a synthetic SNP–SNP interaction network matching the degree distribution of the network derived from one of the real datasets . Then, a set of non-overlapping BPMs among synthetic pathways of different sizes were embedded into this network, and BridGE was run to measure the rate of detection for each scenario (see Methods for more details on this simulation procedure).We focused our power analysis on the detection of BPMs, which comprise most of our discoveries. Briefly, our simulations involved two components: one in which the discovery rate of individual SNP–SNP pairs was evaluated using a simulated population cohort, and another component that simulated the detection rate of BPM interaction structures across a range of sizes given the corresponding level of false positives in the SNP-level network as determined by the first component. More specifically, for the first component of these simulations, we used GWAsimulatorFor each parameter setting, we measured the minimum cohort size required to detect a pathway-level interaction with the corresponding properties at a fixed FDR FDR < 0.25) . Indeed, we found that each of the evaluated parameters  affected the power of our approach Fig. . As expe  and one genetic interaction (between FGF20 and MAOB) reported for Parkinson’s Disease68. Here, we discovered 23 novel pathway-level genetic interactions, emphasizing the potential of our approach to expand our knowledge of the contribution of genetic variation associated with diseases such as PD. Indeed, many of the pathways discovered by our approach have not been previously implicated in these diseases. For example, the median percentage of BridGE-identified pathways for which there was at least one linked SNP reported in dbGaP across the six diseases was 22%  derived from univariate tests applied to GWAS datasets3. There are two key differences between these approaches and the method we propose. First, traditional approaches for GSEA start from univariate statistics of genes or SNPs, while our approach is built on interactions between pairs of SNPs that could have little or no single-locus association with a disease phenotype. Second, approaches for GSEA target the enrichment of single gene/SNP associations in each individual pathway while our approach explores the enrichment of SNP–SNP interactions crossing each pair of pathways (between-pathway model or BPMs).Gene-set enrichment-based approaches applied to loci derived from univariate tests: gene-set enrichment analysis (GSEA) was originally developed for case–control gene expression datasets77. In this study, whole-genome SNPs were first filtered based on their ECML scores78 and only the top 1000 SNPs with the strongest main effects and gene–gene interactions were retained for studying SNP–SNP interactions. Then, a SNP–SNP interaction network was constructed using a logistic regression model, and SNPs were ranked based on their network centrality in this network. Finally, candidate pathways were evaluated using a gene-set enrichment analysis based on pathway members’ rankings. A similar GO enrichment approach was applied to the sporadic Amyotrophic Lateral Sclerosis study17, but SNP interaction strength was first estimated using a multiple dimension reduction (MDR) model and then summarized at a gene level by enrichment analysis. GO annotation enrichment approaches were then applied to these gene-level scores. Again, these studies have not introduced the key concept that motivates our method: that genetic interactions connect coherently across pairs of distinct pathways.Gene-set enrichment-based approaches applied to SNP-level summary statistics from interactions: The gene-set enrichment approach has also been applied beyond loci derived from univariate analysis. Another class of methods first measure genetic interactions based on pairwise SNP analysis, derive summary statistics at the individual SNP level based on specific interaction properties, and follow this with GSEA using pathway-associated SNP (or gene) interaction-based scores. For example, one such approach was recently applied to a bipolar study and a sporadic Amyotrophic Lateral Sclerosis study79. These methods typically employ a filtering step, either data-driven80 or knowledge-driven82, before applying statistical analysis of interactions. Other illustrative examples of this class of approaches are from a recent autism spectrum disorder study where all possible SNPs were tested for interactions with the Ras/MAPK pathway83, and a melanoma risk study where SNP–SNP interactions were studied within the five pathways that are significant based on the traditional individual SNP based-GSEA analysis84. Most studies implementing this approach investigate interactions among a small set of genetic variants (genes or SNPs) that either statistically demonstrate evidence for individual association with the disease phenotype or are known to be relevant to the disease based on prior knowledge. Hence, systematic detection of genetic interactions among novel genes, or genes that show no marginal association will not be detected by these approaches.Methods that use pathways as a prior to study SNP or gene level interactions to reduce the number of hypothesis tests: Another strategy implemented by other existing methods to address the multiple hypothesis testing challenge presented by pairwise SNP analysis is to reduce the number of hypothesis tests, based on a variety of different criteria85, PBA86, and EBLasso87. These methods typically build a regression model using genetic variants (SNPs or pairwise SNPs when considering genetic interaction) from each pathway and use ridge or lasso methods to select a subset of variants. Then, a traditional gene-set enrichment analysis or logistic regression analysis is applied on the chosen genetic variants. Such methods are conceptually different from our proposed method because they do not explicitly search for genetic interactions forming coherent within-pathway or between-pathway structures, which is key foundation of our approach. Furthermore, the methods cited above do not provide evidence for replication of the reported pathway discoveries.Regression methods for pathway-based GWAS studies. A few regression approaches have been previously developed to leverage pathway information to model the relationship between pathway SNPs and disease phenotypes with or without considering genetic interactions, including GRASSFour general directions taken by previous methods for pathway-based analysis that are the most similar to our approach are: (1) gene-set enrichment-based approaches applied to loci derived from univariate tests, (2) gene-set enrichment-based approaches applied to SNP-level summary statistics from interactions, (3) methods that use pathways as a prior to study SNP or gene level interactions or reduce the number of hypothesis tests, and (4) regression methods for pathway-based GWAS studies.In summary, existing approaches are related to the proposed approach in the general sense that they leverage existing knowledge of pathways or other sets of functionally related sets of genes to either perform enrichment on univariate effects or interaction-based SNP summary statistics , or simply use pathways as a prior to reduce the number of SNP pairs tested for interactions. To our knowledge, no existing methods explicitly test for higher-level interactions connecting within or between multiple pathways and are sufficiently powered to perform this systematically across comprehensive pathway databases.88, Wellcome Trust Case Control Consortium or the National Institute of Mental Health (NIMH). Details of each dataset  are summarized in Supplementary Data Twelve GWAS datasets, representing 13 different cohorts covering seven diseases, were used in this paper: Parkinson’s disease , breast cancer , schizophrenia , hypertension , prostate cancer , pancreatic Cancer (.PanC-PanScan: phs000206.v3.p2) and Type 2 Diabetes . These datasets were obtained from three resources: dbGaPWe used the same set of pre-processing steps for all GWAS datasets analyzed in this paper. Each of the steps is outlined in detail in the sections that follow.−6 as the Hardy–Weinberg equilibrium cutoff (--hwe 1e−6).We first controlled data quality using the standard PLINK inclusion procedure with the following parameters: 0.02 as the maximal missing genotyping rate for each individual/SNP , 0.05 as the minimum minor allele frequency (--maf), and 1.0 × 1089 to remove samples that are likely outliers. For these cohorts, duplicate subjects were kept in just one cohort with priority given to PD-NIA over the PD-NGRC cohort, so that we could retain as many samples as possible for the smaller cohort.To identify outlier samples that were not consistent with the reported study population, we mapped SNPs in each GWAS dataset to Genome Reference Consortium GRCh37 and combined the samples with the 1000 Genomes data . We then used PLINK to perform multi-dimensional scaling (MDS) analysis. On the basis of the MDS plot, we removed samples that were not tightly clustered with the corresponding ancestry groups in the 1000 Genomes data. For the two Parkinson’s disease cohorts, we followed the previous studyChecking relatedness among individuals: Relatedness among each pair of subjects was tested by calculating IBD90. For subject pairs with a proportion IBD score greater than 0.2, one was randomly chosen and removed from the data, and the other was kept.Matching population structure between cases and controls: Because spurious allelic associations can be discovered due to unknown population structure91, recent GWAS analyses suggest the use of a procedure to ensure balanced population structure between cases and controls90. Here, all subjects were clustered into groups of size 2, each containing one case and one control that are from the same sub-population , as is implemented in PLINK90.92. The primary concern in developing and applying our current approach was to ensure that population structure was not introducing spurious pathway-level interactions, so we took this relatively conservative approach to adjust for population stratification. More sophisticated approaches could reduce the number of samples lost in filtering based on population stratification and improve the sensitivity of the method.Future extensions of our method could include parameters capturing population structure directly in the model for genetic interactions, for example, as is described in ref. For each dataset, we selected all SNPs that could be mapped to at least one of the 6744 genes in the collection of pathways used in the pathway-level interaction search. A SNP was mapped to all genes that overlap with a ±50 kb window centered at the SNP, and then mapped to pathways to which the corresponding gene(s) were annotated. For the purposes of computing pathway-level statistics, a SNP was only associated once with each pathway, even if it mapped to multiple genes in the pathway.To avoid the discovery of trivial bipartite structures, SNPs in LD need to be removed before between or within-pathway enrichment of SNP–SNP interactions is conducted. Two general approaches can be pursued towards this goal: (1) removing SNPs in LD before calculating pairwise SNP–SNP interactions; and (2) removing structures that emerge as a result of SNPs in LD after calculating pairwise SNP–SNP interactions.16 to condense a yeast SNP–SNP interaction network into an LD-LD network. The algorithm described in that work took the SNP–SNP interaction matrix as input and searched for sets of consecutive SNPs that had a statistically significant number of across-set SNP–SNP interactions based on a hypergeometric test. The algorithm was applied on a yeast SNP–SNP interaction network  with 1977 SNPs, where the LD effect was assumed to be localized to less than 60 SNPs for computational reasons. We attempted to apply this algorithm to the human genotype datasets used in this paper and observed that the algorithm could handle about 1500 SNPs with a threshold of σ below 60, but not beyond. For example, on a dataset with 2000 SNPs, the program did not finish in two days with σ = 100. Given issues with scalability of this approach, we adopted the first alternative, which is to select a subset of SNPs that are not in LD.The first alternative is more likely to miss informative SNP–SNP interactions than the second because it only considers a subset of all SNPs, but is more computationally efficient and scalable. It is worth noting that a biclustering algorithm pursuing the second approach was designed in ref. 90 to select a subset of SNPs that are less likely in LD from each GWAS dataset, specifically “-indep-pairwise 50 5 0.1”. With this procedure, PLINK searches each window of 50 SNPs with a sliding step of 5 SNPs, and selects a subset of SNPs with pairwise r2 below 0.1 within each sliding window. After this procedure, ~15,000–20,000 SNPs were left in each dataset, and the highest r2 between any pair of SNPs within any window of 1 Mb is lower than the commonly used threshold for controlling LD (r2 < 0.2)94, demonstrating that the LD was effectively controlled. Note that by using a stringent r2 threshold of 0.1, we are undoubtedly ignoring many informative SNPs. However, we chose this conservative approach to minimize the chance that spurious WPMs and BPMs resulted from remaining LD structure. Future work that explores less conservative approaches to handling SNPs in LD would be worthwhile.To accomplish this, we used a procedure in PLINKFor diseases that we tested for replication of discovered interactions on independent cohorts of the same ancestry, to make the discovery and replication analysis consistent for these instances, cohorts were first combined and then processed using the PLINK procedures described above to select the subset of SNPs on which the analysis was run. After selection of SNPs, population stratification and discovery of interactions was then performed independently. We followed this procedure for three of the diseases analyzed, Parkinson’s disease, schizophrenia, and breast cancer. For prostate cancer, our access to ProC-CGEMS and ProC-BPC3 was gained at different times, so SNPs used in ProC-BPC3 were selected based on the CGEMS cohort. A summary of all processed datasets used in this study is included in Supplementary Data 96, Biocarta24, and Reactome25  were collected from the Kyoto Encyclopedia of Genes and Genomes (KEGG)74 to quantify the interaction between two SNPs coded as follows, mm = 2, Mm = 1, MM = 0. In this model, the goodness-of-fit was compared between a standard logistic regression model with an interaction term between the two loci of interest and a standard logistic regression without an interaction term, and the significance of the interaction was measured by a likelihood ratio test74. We refer to this type of SNP–SNP interaction as an additive–additive (AA) model-based interaction. In the dominant model, a SNP is encoded as mm = 1, Mm = 1, MM = 0. In the recessive model, a SNP is encoded as mm = 1, Mm = 0, MM = 0. Because the minor allele could have recessive (R) or dominant (D) contribution to disease at two different loci comprising an interaction, four types of SNP–SNP interactions were examined: recessive–recessive (RR), dominant–dominant (DD), recessive–dominant (RD), and dominant–recessive (DR) model-based interaction for each pair of SNPs. The interactions under these four models can also be estimated by a logistic regression-based model similar to the AA case except with the appropriate encoding of the SNP genotypes. Alternatively, the RR, DD, DR, and RD interactions can be estimated by explicit statistical tests  of the association between a specific genotype combination of two SNPs and a disease of interest, where this association is compared to the association between each of the individual SNPs and the disease . Interactions estimated by logistic regression-based models directly capture non-additive effects between two SNPs considering different combinations of SNP genotypes. In contrast, interactions estimated by explicit statistical tests have the flexibility of specifically testing certain combinations of genotypes for association with the phenotype. We explored alternative approaches both in representing different disease models and in the estimation of SNP–SNP interactions, and found that RR, DD, DR, and RD interactions estimated by explicit statistical tests more likely led to the discovery of significant BPMs/WPMs in the context of our BridGE approach. The measure we developed based on explicit statistical tests, called hygeSSI, is described in detail below. The relationship between hygeSSI and logistic regression-based models is explored in more depth in “Comparison with logistic regression-based interactions” section.MM, Mm and mm are used to denote the three genotypes of each SNP, i.e., majority homozygous, heterozygous, and minority homozygous, respectively. Our method implements multiple disease models, which affect how interactions are estimated at the SNP–SNP interaction level. A minor allele (m) at each locus could be additive, dominant or recessive in the context of different diseases. For the additive model, we used the standard logistic regression-based model implemented in CASSIp-value for a pair of binary-coded SNPs with respect to a case–control cohort is calculated as follows:Sx and Sy are two SNPs; M is the total number of samples; N is the total number of samples in class C; K is the total number of samples that have genotype T; X is the total number of samples that have genotype T in class C.We designed a hypergeometric-based measurement (hygeSSI) to estimate the interactions between two binary-coded SNPs (dominant or recessive). The hypergeometric P1~ and P~1 to represent the individual SNP Sx and Sy’s main effects and P11, P10, P01 and P00 to represent the effects of all pairs of combinations. With a nominal p-value threshold (α = 0.05), we first require a SNP pair to have significant association with the phenotype  ≤ α). In addition, we specifically exclude instances where other allele combinations show significant association with the trait, i.e., we require: P10 > α, P01 > α and P00 > α.We use Sx,Sy) and a binary class label C, the following measure hygeSSI (Hypergeometic SNP–SNP Interaction) was defined to estimate the genetic interaction between two SNPs Sx and Sy :Given a binary-coded SNP pair 97, entropy or information theory98 have been developed to measure genetic interactions. All of these approaches quantify the synergistic effect of SNP pairs by comparing the relative strength of the association between a pair of SNPs and a disease trait with the strength of the associations between two individual SNPs and the disease trait. A few of these alternatives were tested in the context of our method and did not provide the significant results we achieved with the metric above. We designed the above hygeSSI measure because it explicitly captures the interaction between combinations of specific genotypes of two loci.As described in a recent comprehensive review10p-value resulting from the likelihood ratio test. The RR and DD interaction networks were computed based on the hygeSSI metric, and only positive interactions were kept in the network . In addition to the above three networks, we also constructed a hybrid SNP–SNP interaction network in which interactions under recessive and dominant disease model could coexist. To do this, we integrated all four networks  into a single network (RD-combined) by taking the maximum hygeSSI among the four interaction networks for each pair of SNPs.We constructed SNP–SNP interaction networks to serve as the basis for the pathway-level interaction tests based on each of the disease model assumptions. An AA interaction network was constructed by the described logistic regression-based approach, where SNP–SNP edge scores were derived from the –logFor each pair of pathways, we want to test if the number of SNP–SNP interactions between them is significantly higher than expected given the overall density of the SNP–SNP network as well as the marginal interaction density of the two pathways involved. Enrichment analysis based on SNP–SNP interactions is much more computationally challenging, and thus we choose to binarize the hygeSSI values (based on a lenient threshold) to make follow-up computation efficient and scalable. After binarization, we divided the SNP–SNP interaction network into two networks based whether the joint mutation of a SNP pair is more prevalent in the case or control group, which we refer to as the risk and protective networks, respectively.p-value for each pathway–pathway interaction. To do this, we randomly shuffled the SNP-pathway membership , and for a given pathway–pathway interaction (bpmi), we compared its observed p-value.pperm) together with  and locally . Specifically, the marginal density of a pathway is calculated as the SNP–SNP interaction density between the SNPs mapped to the pathway and all other SNPs in the network. We computed a chi-square statistic to test differences from both global and local density, namely chi-square global (i). Specifically, we compared the number of BPMs observed in each real dataset that have better overall statistics than bpmi with the corresponding random expectation estimated from the three null distributions derived from sample permutations  because we observed that in some cases the permutation-based p-value alone did not provide enough resolution to differentiate among top BPMs . p-value, can differentiate among the top-most significant discoveries.Because a large number of pathway pairs  are tested in the search for significant BPMs, correction for multiple hypothesis testing is needed. To estimate a false discovery rate, we employed sample permutations (NP = 10 times) to derive the number of expected BPMS discovered by chance at each level of significance. We randomly shuffled the original case–control groups 10 times while maintaining the matched case–control population structure. For each permuted dataset, the same, complete pipeline for BPM discovery was performed, including calculation of the SNP–SNP interaction network after permutation, which was then thresholded at a fixed interaction density matching the density chosen for the real sample labels. From these sample permutations, we obtained three null distributions  permutation approach mentioned above was used in addition to the SNP permutation strategy to estimate our false discovery rate across all discovered interactions. For each of the 10 sample permutations, we ran the full set of 100,000–200,000 SNP permutations. This hybrid approach provides a robust estimate of significance of the discovered pathway interactions and properly corrects for multiple testing.We also conducted a study to explore the sensitivity of our FDR estimation on the number of sample permutations. Specifically, for the PD-NIA dataset, we performed 1000 sample permutations  to derive an estimate of FDR for discoveries in this dataset  or interaction statistic could be used to discover pathway-level interactions. In this study, we focus on prioritizing a single disease model per disease cohort for full analysis by our pipeline to limit the complexity of data analysis across the 13 GWAS cohorts we explored with our method. Here, we describe the strategy we used to select the disease model to focus on for each GWAS dataset.To prioritize the disease model and SNP–SNP interaction network density threshold for each dataset, we first performed a pilot experiment in which we examined combinations of different disease models and different density thresholds, but with fewer SNP permutations  for each validation cohort, from which we could generate null distributions for pperm in the validation cohort. Given a set of discovered BPMs , we calculated fold enrichment by comparing the number of BPMs discovered from the original dataset that passed the validation criteria to the average number of BPMs that passed the same validation criteria in the random sample permutations. More specifically, given a set of significant BPMs  which were discovered from original cohort, the fold enrichment for replication is defined as:The significant BPMs discovered from one cohort could be evaluated in another independent cohort for replication. To determine whether a discovered BPM was replicated in an independent cohort, we required the BPM to satisfy We also evaluated the significance of the fold enrichment by 10,000 bootstrapped BPM sets. Specifically, we randomly selected the same number of BPMs and used the above procedure to evaluate the fold enrichment, and we repeated this for 10,000 times to generate a null distribution for the fold enrichment scores in the validation cohort. We then evaluated the significance of the fold enrichment score for our discovered BPM set based on this empirical null distribution. All replication results can be found in Supplementary Data For the BPMs that replicated in an independent cohort, we further checked if the SNP–SNP interactions supporting the discovered pathway-level interactions were similar between the cohort used for discovery and the independent cohort used for replication. For example, we used the BPMs discovered from PD-NIA (FDR ≤ 0.25) and for each BPM replicated in PD-NGRC, we computed the number of SNP–SNP interactions in common between the PD-NIA and PD-NGRC interaction networks as supporting interactions for the BPM. We used the same permutation approach as that described in the “Correction for multiple hypothesis testing” section for BPM-level validation except that the SNP–SNP interactions supporting each BPM were compared between the discovery and validation cohorts by a hypergeometric test. This was done for the real validation cohort PD-NGRC first and then repeated 10 times under sample permutations of the validation cohort to estimate a null distribution. A Wilcoxon’s rank-sum test was then used to evaluate the significance of the SNP–SNP interaction overlap between the replicated BPMs in the real validation cohort and in the random sample permuted validation cohorts Fig. .Due to the fact that many of the curated gene sets overlap, we needed to control for redundancy in the discovered BPMs. To do this, in reporting total discoveries, we filtered BPMs based on their relative overlap in terms of SNP–SNP interactions using an overlap coefficient. The overlap coefficient between two BPMs is defined as the number of overlapping SNP pairs divided by the number of possible SNP pairs in the smaller BPM.For the significant BPMs discovered, we computed all pairwise overlap coefficients and used a maximum allowed similarity score of 0.25 as a cutoff. We reported the number of unique BPMs based on the number of connected components. For visualization purposes Fig. , we sele14 . All of the measures and procedures described above for BPMs apply directly to the WPM case, only we specifically look at SNP pairs connecting genes within the same pathways/gene sets instead of between-pathway pairs. For WPMs, the false discovery rate and validation statistics were computed separately from BPMs. All WPM discovery results can be found in Supplementary Data In addition to the between-pathway model (BPM), we also tested for enrichment of genetic interactions within each pathwayDpath) in the SNP–SNP interaction network. We then applied a one-tailed rank-sum test (Upath) to compare each pathway-associated degree vector with the non-pathway-associated degree vector (Dnon_path) to see if the PATH-associated SNPs exhibited significantly more interactions than the entire set of SNPs. PATH discovery and validation is then done by repeating the same steps as BPM/WPM discovery but replacing the Upathp-value . All PATH discovery results can also be found in Supplementary Data Since both “between-pathway model” and “within-pathway model” analysis have been designed to avoid discoveries caused by the higher marginal interaction density of the individual pathways, pathways that are frequently interacting with many loci across the genome  are less likely to appear in our pathway–pathway or within-pathway interactions. However, such pathways may also be disease relevant as they reflect pathways that modify the disease risk associated with a large number of other variants, so we also report pathways exhibiting these characteristics with BridGE (we refer to these as “PATH” discoveries in BridGE output files). For PATH discovery, the procedure is similar to that for BPMs and WPMs, with a minor modification to the scoring of each pathway. Specifically, each pathway is represented by a vector of pathway-associated SNPs’ degrees (p ≤ 0.05) in logistic regression-based tests, and (2) if the significant BPMs discovered from a hygeSSI interaction network show significance (pperm ≤ 0.05) based on SNP–SNP interactions estimated from logistic regression. This analysis revealed that among the top 1% hygeSSI interactions, 93% are significant based on a logistic regression-based test for interaction. And for the significant BPMs (FDR ≤ 0.05), 100% of them are also significant if only SNP–SNP interactions also supported by a logistic regression model are considered. These data suggest SNP–SNP interactions captured by hygeSSI do represent non-additive interactions as defined based on a logistic regression model. Detailed results from this comparison can be found in Supplementary Data We examined if the interactions captured by hygeSSI were non-additive as measured through a standard logistic regression-based interaction measure. We applied the logistic regression model on the PD-NIA data and computed RR, DD, RD, and DR interaction networks (binary encoding as described earlier). We also integrated these four logistic regression-based networks to form an RD-combined network. Then we checked (1) if the top SNP–SNP interactions based on hygeSSI were significant  for three different disease models: (1) recessive; (2) dominant, and (3) a combination of recessive and dominant, in which each SNP were tested for both recessive and dominant disease models and the more significant one assigned to each SNP. We then used Wilcoxon’s rank-sum test to check if a pathway was enriched for SNPs with higher association than the background . With 10,000 sample permutations, we computed FDR for each individual pathway (both risk and protective associations) by using same procedure described in “Correction for multiple hypothesis testing” section. The results are summarized in Supplementary Data 67 . Based on the GWAS catalog, the numbers of genes linked to known risk loci (p ≤ 2.0 × 10−5) in each disease are: 143 , 1009 , 134 , 71 , 249 , and 294 . For each disease, we summarized all pathways that were discovered by BridGE (FDR ≤ 0.25) and identified pathways that were implicated by individually associated SNPs reported in the GWAS catalog (a SNP mapping to a single gene in a given pathway was assumed to implicate the corresponding pathway). For context, for each disease, we also summarize the total number of genes implicated by GWAS-identified SNPs, how many these map to the 833 pathways we used in our study, and how many of them can be linked to the significant pathways identified by BridGE. These results are presented in Supplementary Data To check if previous singly associated SNPs also appear in our discovered pathway-level interactions, we compared our BridGE-discovered pathways with pathways that could be linked to disease risk loci reported in NHGRI-EBI GWAS catalog99 would be worthwhile.While we tested multiple disease models , the most significant discoveries for the majority of diseases examined were reported when using a dominant or combined model as measured by our SNP–SNP interaction metric. The relative frequency of interactions under a dominant vs. a recessive model may be largely due to our increased power to detect interactions between SNPs with dominant effects compared to recessive effects. More specifically, individuals with both heterozygous and homozygous  genotypes at two interacting loci would be affected under a dominant disease model, while only individuals with homozygous  genotypes would be affected in a recessive disease model. The number of individuals homozygous at two interacting loci can be quite small depending on the allele frequency, which limits our power to discover them. Thus, the larger number of discoveries based on a dominant model assumption relative to a recessive model is likely a reflection of difference in statistical power and not an indication that genetic interactions among alleles with dominant effects are contributing more strongly to disease risk. We observed that interactions derived from an additive disease model provided the fewest significant discoveries when used in the context of BridGE based on the pilot experiments  and a range of interaction effects 66. We also varied the number of samples (genotypes) in the simulation . In all simulations, we specified the disease prevalence to be 0.05, dominance effect for all disease SNPs with PR1 = 1 (see GWAsimulator for more details)66. Under different scenarios , we embedded 100 SNP pairs and measured the percentage of SNP–SNP interactions that were identified by our pairwise SNP–SNP interaction measure, hygeSSI at a 1% network density   of the significant BPM discoveries across all GWAS cohorts (FDR ≤ 0.25) as the discovery significance cutoff for the simulation analysis.The SNP–SNP level power statistics (sensitivity) were complemented with a second set of simulations in which we directly assessed the sensitivity of BridGE in detecting BPMs with different levels of noise in the SNP–SNP level network (derived from the process described above). To characterize the statistical power of our approach as a function of pathway size, we first generated a synthetic interaction network with the same degree distribution as the PD-NIA DD network at 1% density. Then, we embedded a set of non-overlapping BPMs into this SNP–SNP interaction network while retaining the same degree distribution and density of the network. Each set had 90 BPMs at 9 different sizes ; and 10 different background densities 0.01, 0.012, 0.014, 0.016, 0.018, 0.02, 0.025, 0.03, 0.04, and 0.05. We applied 150,000 SNP-pathway membership permutations to assess the significance of these embedded patterns. The SNP permutation-derived s = 0.025, 0.05, and 0.1) which corresponds to the biological density of genetic interactions crossing each pair of truly interacting pathways. This represents the fraction of all possible SNP–SNP pairs crossing the pair of pathways of interest for which the combination of variants actually has a functional deleterious impact on the phenotype. This quantity is expected to be relatively small, but is difficult to estimate, which is why we have explored three scenarios . For a given BPM of a specific size , from the 2nd simulation, we identified the corresponding BPM density (DensityBPM) needed for it to rise to the level of statistical significance required for a 25% FDR based on the PD-NIA cohort. We then scaled the required density by the parameter, s, and based on the 1st set of simulation results, identified the minimum sample size required under each scenario  to support the discovery of the corresponding BPM: Sensitivity × s ≥ Densitybpm. Results are summarized in Fig. We derived power estimates for each combination of parameter settings by integrating the results from the two simulation studies above. More specifically, we estimated the minimum sample size needed to discover significant BPMs at different pathway sizes under each of the scenarios . To connect the two simulation studies, we require a scaling parameter  are included in the Supplementary Fig. Simulation results for additional scaling parameters (Further information on research design is available in the Supplementary InformationPeer Review FileReporting SummaryDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10Supplementary Data 11Supplementary Data 12Supplementary Data 13Supplementary Data 14Supplementary Data 15Supplementary Data 16Supplementary Data 17Supplementary Data 18Supplementary Data 19Supplementary Data 20Supplementary Data 21Supplementary Data 22Supplementary Data 23