Multi-locus genotype data are widely used in population genetics and disease studies. In evaluating the utility of multi-locus data, the independence of markers is commonly considered in many genomic assessments. Generally, pairwise non-random associations are tested by linkage disequilibrium; however, the dependence of one panel might be triplet, quartet, or other. Therefore, a compatible and user-friendly software is necessary for testing and assessing the global linkage disequilibrium among mixed genetic data.mixIndependR” calculates basic genetic parameters like allele frequency, genotype frequency, heterozygosity, Hardy–Weinberg equilibrium, and linkage disequilibrium (LD) by mutual independence from population data, regardless of the type of markers, such as simple nucleotide polymorphisms, short tandem repeats, insertions and deletions, and any other genetic markers. A novel method of assessing the dependence of mixed genetic panels is developed in this study and functionally analyzed in the software package. By comparing the observed distribution of two common summary statistics  with their expected distributions under the assumption of mutual independence, the overall independence is tested.This study describes a software package for testing the mutual independence of mixed genetic datasets. Mutual independence is defined as no non-random associations among all subsets of the tested panel. The new R package “mixIndependR” is compatible to all categories of genetic markers and detects the overall non-random associations. Compared to pairwise disequilibrium, the approach described herein tends to have higher power, especially when number of markers is large. With this package, more multi-functional or stronger genetic panels can be developed, like mixed panels with different kinds of markers. In population genetics, the package “mixIndependR” makes it possible to discover more about admixture of populations, natural selection, genetic drift, and population demographics, as a more powerful method of detecting LD. Moreover, this new approach can optimize variants selection in disease studies and contribute to panel combination for treatments in multimorbidity. Application of this approach in real data is expected in the future, and this might bring a leap in the field of genetic technology.The package “mixIndependR, is available on the Comprehensive R Archive Network (CRAN) at: https://cran.r-project.org/web/packages/mixIndependR/index.html.The R package  Different characteristics, such as mutation rates, deviations, and heterozygosity, make those markers isolated in application. However, due to their specific advantages, such as the higher power of discrimination of STRs, and the important roles of SNPs in application of ancestry informative markers (AIMs) and prediction of physical traits , mixed mBCFTools  and SNPrNPrelate , both ofis (GDA) , which tAnother shortcoming of traditional measures of LD is the way it is assessed, that is to test pairwise linkage disequilibrium. However, due to more accurate conception, non-random associations can be not only pairwise associations, but also triplet, quartet, and higher order associations among all sites, defined as mutual independence. D′ is sometimes used to assess the higher-level associations, but it is time consuming to obtain due to numerous calculations. Therefore, summary statistics become a choice to avoid all these excess and burden.mixIndependR, was developed for testing mutual independence among all sites of the multi-locus genotypes mixed type of genetic markers for the R software. As a larger category of dependency across all over the panel needs to be tested, summary statistics, which are able to give a quick and comprehensive description of the dataset, came into consideration. In an early study [mixIndependR to increase its versatility.A new package, ly study , 10, summixIndependR. In the following example, a sample with 6 STRs and 94 SNPs , based on the genotypes and the reference panel created by Saini et al. [mixIndependR package under the name “mixexample”. mixIndependR is compatible with genotype files in a tabular format  and the variant call format (vcf) [x <- mixexample # This panel with 96 SNPs and 4 STRs are filtered from a reference haplotype panel developed by Saini et al. mixIndependR can be used to estimate basic genetic parameters, such as allele frequencies, tables of heterozygosity and of shared alleles, and to test Hardy Weinberg equilibrium in either Pearson’s.This section presents how a multi-locus genotype panel with mixed genetic markers (SNPs and STR) can be tested for its mutual independence using i et al. . This rei et al. . The thrmentclasspt{minimai et al. , but herat (vcf) . The allAlleleFreq # calculate the table of allele frequencies and return a table with rows of alleles and columns of markers  # calculate the observed genotype frequencies with genotypes in rows and markers in columns.G <- GenotypeFreq # calculate the expected genotype frequencies under Hardy–Weinberg equilibrium (HWE).G0 <- Heterozygous # obtain the table of heterozygosity with rows of individuals and columns of markers, where “1” denotes heterozygous while “0” denotes homozygous  # calculate the observed average heterozygosity or the expected heterozygosity on each marker under the assumption of HWE.H <- AlleleShare # calculate the table of shared alleles of each pair of individuals for each marker with the rows denoting the pairs of individuals and the columns denoting the variants. If the replacement is TRUE, the pairs are formed with replacement randomly and this table includes all possible pairs; if the replacement is FALSE, the pairs are formed without replacement randomly and the number of pairs equals half of the sample size.  # calculate the observed proportions of sharing 0, 1 or 2 alleles on each marker.e <- ExpProAlleleShare(p) # calculate the expected probabilities of sharing 0, 1 or 2 alleles on each marker for any unrelated individuals. This process is according to the functions described by Weirs et al. [e0 <- s et al. HWE.Chisq # test the HWE with Pearson’s Chi-square test and export the p value for each marker.HWE_pvalue <- FreqHetero(h) # calculate the observed distribution of K, exporting the frequencies of K at the values from 0 to total number of tested markers.ObsDist_K <- DistHetero(H) # calculate the expected distribution of K, exporting the probabilities of K at the values from 0 to total number of tested markers.ExpDist_K <- FreqAlleleShare(AS) # calculate the observed distribution of X, exporting the frequencies of X at the values from 0 to 2 times of total number of tested markers.ObsDist_X <- DistAlleleShare(e) # calculate the expected distribution of X, exporting the probabilities of X at the values from 0 to 2 times of total number of tested markers.ExpDist_X <- ComposPare_K #generate comparison data frame for observed and expected distributions. If “trans = F”, the table contains a variable “OvE” denoting the category of “observed” or “expected”, and a variable “Freq” denoting the frequencies. This format is prepared for visualization in “ggplot2”. If “trans = T”, the result is made by two columns- “K_io” and “K_ie” which denoting the observed and expected K for each individual, and the number of rows equals to the number of individuals of the sample.df_K <- ComposPare_X #generate comparison data frame for observed and expected distributions. If “trans = F”, the table contains a variable “OvE” denoting the category of “observed” or “expected”, and a variable “Freq” denoting the frequencies. This format is prepared for visualization in “ggplot2”. If “trans = T”, the result is made by two columns- “X_io” and “X_ie” which denoting the observed and expected X for each pair of individuals, and the number of rows equals to the number of pair of individuals of table of number of shared alleles AS.df_X <- According to the mathematical principles described in previous studies of Chakraborty et al. , 10, theSimulate_DistK #build 500 times of simulations for distribution of K with the sample size equals to the original data for each simulation, under the mutual independence assumption  #build 500 times of simulations for distribution of X with the sample size equals to the number of pairs composed in “AS” table for each simulation, under the mutual independence assumption  # Calculate 500 Chi-square values for K with 1000 times of replicates in each and export the set of p values.x2_K <- Dist_SimuChisq # Calculate 500 Chi-square values for X with 1000 times of replicates in each and export the set of p values.x2_X <- ecdf(x2_K) #Build the cumulative probability of function for the set of Chi-square values. Note: this is the function in the package of “stats”.P1 <- ecdf(x2_X) #Build the cumulative probability of function for the set of Chi-square values. Note: this is the function in the package of “stats”.P2 <- Not only were the visual comparisons made, but statistical tests were also conducted using this package. Considering the expected distributions under assumption of mutual independence follow restricted multinomial distributions with fixed probabilities on each trial, no traditional statistic tests can be applied . Instead, simulations were conducted to obtain null distributions of chi-square values and cumulative probability functions were built to find an accurate critical value.If the significant level is 0.05, the critical value of the chi-square value for each specific expected distribution is the value when cumulative probability equals 95%. In Additional file ms [microsat [ms format. In the single-comparison example, we used the simulated panel with 20 STRs and 10 SNPs for unlinked and fully-linked scenarios and the sample size is 500 in each case. The comparisons of the single-run for unlinked data and fully-linked data were made and presented in Figs. Both simulation and real data have been tested with this approach. We simulated unlinked and linked data under the Wright-Fisher neutral model using the software ms ; the micmicrosat  from ms p value = 0.26)   and X  at the fully linked STR-SNP panels  Fig. a or X  for the fully linked panel are much larger than the critical values   when the number of markers increases, the power of testing increases  comWhen there is only one pair of genetic markers linked, neither of the two methods detected the dependency effectively. In half-quarter-linked panels, the SNP-biased group has a little higher power than STR-biased group- around 10–40% on K and 6% to 18% on X; and power of the unbiased group is between SNP-biased and STR-biased groups, but none of the three groups present a strong enough power in half-quarter-linked panels. However, for quarter- or higher-levels of linkage both K and X yield power greater than 50% when the number of parkers is no less than 60 in SNP-biased group. In contrast, only the three-quarter of linkage and almost-linkage (one pair of markers not linked) can be detected in the STR-biased group. Only with more than 40 markers can the power of STR-biased panels reach 50% and more. In the unbiased group where the number of linked SNPs and linked STRs are equal, K presented more than 50% power when panel sizes were greater than 32 in half-linked panels and greater than 16 in three-quarter-linked panels; the power of X is not as strong as K, only greater than 50% when panel sizes are over 60 in half-linked panels and over 32 in three-quarter-linked panels. In another direction, the number of shared alleles (X) has a lower power than the number of heterozygous loci (K), but the type-I error is larger for K when the panel size is small . In PCA panel design, this is a threshold for “independent” variants. Refer to the output of p values of mutual independence test were calculated by K and X. Controlling the panel size for easy comparison in later research, panel size was defined as 100. In other words, 100 markers of the 2067 variants were selected randomly as a sample panel to test, and the process of choose and test was repeated in 1000 times.Furthermore, having been used in the tests on simulated panels,  to SNPs , 20, a mp values of K and 19.0% of p values for X are smaller than 0.05, which indicates that the markers of this panel are not mutual independent. In contrast, the number of significant pairwise LDs calculated by GDA is 218 out of 4950 pairs of markers (100 markers were selected randomly in one sample), which is 4.40%. The large difference between the power of X compared to K might result from the fact that majority of the markers are SNPs, the heterozygosity of which data carries more information than number of sharing alleles. In contrast, the pairwise LDs between these markers gave a result of As a results, in the 1000 trials 76.1% of Compared to traditional LD tests , the approaches presented herein appear to become more powerful as the size of the panel increases. In Fig. GDA, a set of p-values for pairwise LD were calculated  is 96.35% on average for K and 23.80% for X. Across four groups with different threshold of On the other hand, the tests of real data panels have also been completed and compared between the pairwise correlation and summary statistics- K and X. With the threshold for .2 Table a. Using ted Fig. b. After Therefore, both in simulation and real data, this approach presented a stronger power on detecting linkage disequilibrium in a manner of testing the linkage more than pairwise of a whole panel, regardless of the types of genetic markers.mixIndependR is available on the Comprehensive R Archive Network (CRAN) at: https://cran.r-project.org/web/packages/mixIndependR/index.html [https://github.com/ice4prince/mixIndependR.git [The R package dex.html  and the endR.git . This pamixIndpendR, dataset to import can be an “. xslx” “.csv” or “vcf” file, with the marker names in the first row, and sample ID in the first column like the example  < 0.2 (2067 variants), < 0.4 (3157 variants), < 0.6 (4278 variants) and < 0.8 (5754 variants), and in each panel there are 47 STRs, 64 STRs, 83 STRs, and 115 STRs, respectively. The LD significant pairs of variants in these groups make up 0.36%, 5.71%, 12.21%, and 21.43% among all variants in each panel, respectively. Furthermore, the pairwise r2 values for each group were exported by plink.Real data was downloaded and filtered from the reference panel of Dr. Saini et al.  using plink 1.90 , 17. Chrmixexample” was filtered from chromosome 4 with the same selection rule but with a threshold 0.1 for The example dataset attached in the package “mixIndependR is made up of two main sections—basic genetic parameters calculation and mutual independence testing. Parameters obtained in the first part can be used in the second section. The software pipeline presented a structure of all the functions , the genotype frequencies or expected genotype probabilities (GenotypeFreq), and the Hardy–Weinberg Equilibrium (HWE.Chisq) [The first part of this package was developed to calculate the basic genetic parameters of a mixed or non-mixed panel, including the allele frequencies E.Chisq) , 27. Dif5 − 1 = 31 free parameters in only pairwise independence testing, not to mention more subsets like triplets and quartets. When tens of loci were imported, the parameters would increase to thousands, where even the sample size might not be that large sometimes.In traditional statistics, non-random associations were tested from pairs. However, mutual independence also included other subsets, like triplets and quartets. As the number of subsets increases, large quantities of free parameters will be generated. For example, for independence of two loci, there would be 3 free parameters if the heterozygosity were chosen as the tested statistics. But for 5 loci where the number of pair comes to 32, there would be 2In order to break the large barrier that the number of free parameters might exceed the relatively small number of observations/subjects for the traditional statistic method when the sample size is not big enough, to avoid numerous calculations, and to reduce time consumption, two summary statistics were designed—the number of heterozygous Loci (K) and the number of shared alleles (X) .Under the assumption of mutual independence, the distribution of these summary statistics follows a restricted multinomial distribution. By comparing the observed and expected distribution, the hypothesis for mutual independence could be tested .For the number of heterozygous loci (K), the distribution follows an appropriate binomial distribution of 0 and 1, with the fixed but different probabilities on each trial. Similarly, the distribution of the number of shared alleles(X) follows a “skewed” multinomial distribution of 0, 1, and 2, where the probabilities are specified on each trial.The number of heterozygous loci (K) is the sum of the number of heterozygous loci for each individual, which was denoted as, a table for heterozygosity was built by Heterozygous. This function exported a table of 0 and 1, where 0 denoted homozygous and 1 denoted heterozygous, with each row for each individual and each column for each marker. With the table of heterozygous status, the function FreqHetero obtained the observed distribution of number of heterozygous loci for the targeted dataset.With the dataset importedThe expected distribution was built according to a recurrence formula with a specially assigned “Start” and “End” . For theRxpHetero in case of Hardy–Weinberg Equilibrium or Disequilibrium with the logic parameter HWE true or false. The heterozygosity was saved into the vector H in the order of loci, and the expected distribution of K was calculated by DistHetero(H).The vector of heterozygosity was calculated with function Similarly, the number of shared alleles (X) is the summation of the number of shared alleles on each locus obtained by comparing each two individuals.AlleleShare, where a logic parameter “replacement” defining the type of “pick pairs” needs to be clarified as TRUE for pairs with replacement or FALSE for pairs without replacement.A table of FreqAlleleShare from the result of AlleleShare. As for the expected distribution, the probability for sharing 0, 1, or 2 alleles on each locus was needed. According to Weir, the expected probabilities of sharing 0, 1, or 2 alleles for two unrelated individuals could be obtained by ExpProAlleleShare, with the allele frequency table from AlleleFreq. On the other hand, for non-ideal samples, the real proportions of sharing alleles were also suitable to use, which could be calculated by RealProAlleleShare. With the probability table, an expected distribution of DistAlleleShare by the principles of multinomial distributionThe observed distribution of ComposPare_K and ComposPare_X. These functions generated expected frequencies from the probabilities and converted the dataset into a form suitable to ggplot2 [plot in R.With the distributions built, two functions were designed for data visualization:  ggplot2  or plot The null hypothesis was that all markers, regardless of which type, are independent from each other. To test the null hypothesis, making comparisons between observed and expected distribution was required. Generally, a multinomial distribution has a fixed probability for each trial. However, in genetics, we cannot predict the distribution of heterozygosity or probability of sharing alleles for an unknown panel under testing. Thus, there were no perfect statistical methods designed for this special problem at this moment.Despite the lack of existed methodology, with the fixed probability, it was not difficult to find the distribution of the test statistics by large sample simulation.Simulate_DistK and Simulate_DistX built the simulation for K and X, respectively. For each new panel, each new bundle of simulation needs to be built. Via the basic equation of calculating the Chi-square value, a set of Chi-square values were generated by function Dist_SimuChisq. With the set of Chi-square values, a plot of cumulative distribution of In this research, chi square value was chosen as the test statistic since the test was for fit of goodness and the distribution was similar to multinomial distribution. To ensure a good approximation for the chi square distribution, the expected numbers of each category were restricted to no less than five. Functions genetics provides a function LD to test the linkage disequilibrium for all possible pairs of loci in one panel. This function can output D, D′, Pearson’s correlation coefficient, Chi-square statistic for linkage equilibrium (D = D′ = 0) and the p value of Chi-square test for independence. Using the unlinked data and linked data simulated above, a distribution of the proportion of p values smaller than significance level after Bonferroni correction can be obtained. The null hypothesis is that there is no significant LD among all the pairs for unlinked panel, which is p values is larger than 0.05, the null hypothesis would be rejected.The R package Additional file 1: Figure S1. Distribution of number of heterozygous loci (K) for the example dataset. The X-axis is the number of shared alleles from 0 to 100, and the Y-axis is the observed density or expected probability of each K. The red bar is the expected distribution, and the green bar denotes the observed distribution. The red line is the expected spline for probability of K.Additional file 2: Figure S2. Distribution of number of shared alleles (X) for the example dataset. The X-axis is the number of shared alleles from 0 to 200, and the Y-axis is the observed density or expected probability of each X. The red bar is the expected distribution, and the green bar denotes the observed distribution. The red line is the expected spline for probability of X.Additional file 3: Figure S3. Cumulative probability function of Chi-square values for number of heterozygous loci (K) of the example dataset. The Y-axis is the cumulative probability  for the chi-square value at X-axis. In this example, the tested chi-square value of K is 77.417 (blue line), with a cumulative probability of 0.924. In contrast, the critical value for p-value = 0.05 (cumulative probability = 0.95) is 112.9 (red line).Additional file 4: Figure S4. Cumulative probability function of Chi-square values for number of shared alleles (X) of the example dataset. The Y-axis is the cumulative probability  for the chi-square value at X-axis. In this example, the tested chi-square value of X is 62.299 (blue line), with a cumulative probability of 0.778. In contrast, the critical value for p-value = 0.05 (cumulative probability = 0.95) is 115 (red line).Additional file 5: Figure S5. Summary of power tests for simulated data at different linkage levels for K and X- comparison between ‘Bias’. The X-axis denotes the number of markers in each panel, and the Y-axis is the proportion of significant cases whose p-value is smaller than 0.05. The colors present different categories of ‘Bias’- when ‘Bias’ = Both, the types of linked markers are both SNPs and STRs with equal numbers; when ‘Bias’ = SNP, the most or all linked markers are SNPs; when ‘Bias’ = STR, the most or all linked markers are STRs. In Fig. Additional file 6: Figure S6. Comparison of Power for mixed simulated data (‘Bias’ = Both) between number of heterozygous loci (K) and number of shared alleles (X). The X-axis denotes the number of markers in each panel, and the Y-axis is the proportion of significant cases whose p-value is smaller than 0.05. “Linkage on Both” means half of the linked markers are SNPs and the other linked markers are STRs. The solid lines are presented the power trends of K, and the dotted lines are the power trends of X. Different colors are different linkage levels: red lines are half-linked panels (50% markers are linked); green lines are Quarter-Linked panels (25% markers are linked); blue lines are ThreeQuarter-Linked panels (75% markers are linked).Additional file 7: Figure S7. Power and significant level of K and X for simulated SNP panels at different linkage levels. The proportions of significant cases out of 1000 trials along different panel size for simulated SNP panels at different linkage levels. In the “Unlinked” level, all markers in each panel are unlinked; in the “Onepair/Little-Linked” level, only one pair of markers are linked in each panel; in the “HalfQuarter-Linked” level, 12.5% SNPs are linked; in the “Quarter-Linked” level, 25% SNPs are linked; in the “ThreeQuarter-Linked” level, 75% SNPs are linked; in the “Almost-Linked” level, all except one pair of markers are linked; in the “Fully-Linked” level, all markers in each panel are linked. The axis “Panel Size” denotes the number of the SNPs in each panel.Additional file 8: Table S1. Genotypes of example dataset—‘mixexample’. The raw genotypes of the example data. Each row denotes each individual and each column denotes each marker.Additional file 9: Table S2. Table of allele frequency (expected) for example dataset- ‘mixexample’. Each column denotes each marker. The first column lists all alleles appeared at all loci-0, 1, 2, 3, 4, and 5. There is the probability of the allele of this row at the locus of this column.Additional file 10: Table S3. Table of heterozygosity for example dataset- ‘mixexample’. In each cell, the status of heterozygosity -0 (homozygous) or 1 (heterozygous), for the individual of this row at this locus is presented. Column names are markers’ names, and the row names are individuals.Additional file 11: Table S4. Table of shared alleles for example dataset- ‘mixexample’. In each cell, the number of shared alleles -0 or 1 or 2, for the pair of individuals of this row at this locus is presented. Column names are markers’ names, and the row names are pairs of individuals.Additional file 12: Table S5. Simulations for expected number of heterozygous loci (K) for the example dataset- ‘mixexample’. The first row  is the number of heterozygous loci (K) from 0 to 100; and the first column is the index of simulations 1 to 500. Each row denotes each simulation and shows one distribution of K.Additional file 13: Table S6. Simulations for expected number of shared alleles (X) for the example dataset- ‘mixexample’. The first row  is the number of shared alleles from 0 to 200; and the first column is the index of simulations- 1 to 500. Each row denotes each simulation and shows one distribution of X.Additional file 14: Table S7. Summary of power test for simulated mix panels. Full version of Table


Moreover, Meta-QTL (MQTL) analysis of four independent QTL studies for potassium deficiency in bread wheat located 16 MQTL on 13 chromosomes. One locus identified in this study (q5B-1) colocalized with an MQTL (_11MQTL), while the other ten loci were novel associations. Gene ontology of these loci identified 20 putative candidate genes encoding functional proteins involved in key pathways related to stress tolerance, sugar metabolism, and nutrient transport. These findings provide potential targets for breeding potassium stress resistant wheat cultivars and advocate the advantages of multi-locus GWAS models for studying complex traits.Potassium use efficiency, a complex trait, directly impacts the yield potential of crop plants. Low potassium efficiency leads to a high use of fertilizers, which is not only farmer unfriendly but also deteriorates the environment. Genome-wide association studies (GWAS) are widely used to dissect complex traits. However, most studies use single-locus one-dimensional GWAS models which do not provide true information about complex traits that are controlled by multiple loci. Here, both single-locus GWAS (MLM) and multi-locus GWAS  models were used with genotyping from 90 K Infinium SNP array and phenotype derived from four normal and potassium-stress environments, which identified 534 significant marker-trait associations (MTA) for agronomic and potassium related traits: pLARmEB = 279, FASTmrMLM = 213, mrMLM = 35, MLM = 6, FASTmrEMMA = 1. Further screening of these MTA led to the detection of eleven stable loci:  Potassium (K) plays a critical role in plant growth and development, elucidated by its multidimensional capacity of regulating the plant physiological systems such as enzymes activation, membrane potential, osmoregulation, photosynthesis, and osmotic balance . HoweverRecent advances in molecular biology and next generation sequencing along with the discovery of new genome analysis tools have helped identifying high-throughput single nucleotide polymorphisms (SNPs) that are utilized to construct high resolution genetic maps for genome-wide association study (GWAS) . GWAS isIn this study, one single-locus GWAS (SL-GWAS) model and four multi-locus GWAS (ML-GWAS) models were used to identify significant MTA for KUE and agronomic traits in a historical bread wheat diversity panel of Pakistan. Furthermore, a meta-analysis of all the reported QTL studies (related to K-deficiency) was performed to identify consensus loci for K-related traits. These consensus MQTL regions are independent of environment × genotype interaction and population type, and hence along-with the novel associations identified, will help in breeding wheat cultivars for high K efficiency.A historical bread wheat panel of 150 Pakistani spring wheat varieties acclimated to irrigated, arid, and semi-arid climates was selected for sowing. The panel was categorized into four groups on the basis of release time of cultivars: group-I consisted of 20 varieties of pre-green revolution release (1965 or earlier), group-II consisted of 30 varieties of green revolution release (1965-1979), while group-III and group-IV each had 50 cultivars comprised of post-green revolution release and elite cultivars, respectively Table S1Cigar roll method proposed by 2O2 for 5–10 min followed by washing with distilled water before placing in petri dishes for germination. Once germinated, three seeds were transplanted to field in PVC pipes of 2-feet height and 5-inch diameter at the experimental field of Plant Sciences department, Quaid-i-Azam University, Islamabad, Pakistan .Field trials were carried out for three consecutive years from 2016–2018 in triplicated alpha-lattice design for normal K  and low K  conditions, experiments were planted in PVC pipes. Two kg soil (soil to sand ratio of 2:1) was added to each PVC pipe. Random soil samples were tested according to _H) while days to maturity (DM), leaf area (LA), plant height (PH), tiller number (TN), spikelet per spike (SpS), grain yield (GY), thousand kernel weight (TKW), biological yield (BY), and harvest index (HI) for field experiment (_F) were measured according to _14DAG) and 21 days (Chl_21DAG) after germination and at heading stage in field trials. Chlorophyll meter, SPAD-502 Konica Minolta sensing Inc., was used to measure the chlorophyll contents. Scanned root images were used to estimate various root parameters  using GiaRoots software.Agronomic traits such as fresh weight (FW), shoot length (SL), relative water content (RWC), and leaf area (LA) for hydroponic experiment (® (BCR-670) certified reference material (Sigma-Aldrich). Oven dried leaf and grain samples (0.5 g) and certified reference material were digested in separate 50 ml conical flasks by adding 7.5 ml (65%) HNO3 and 2.5 ml (36%) HCl to each sample. The mixtures were subjected to about 270°C by placing the flasks on a hot plate, the mixtures started evaporating as dense yellowish fumes. Once the yellowness of fumes started to disappear, flasks containing mixtures were removed from the hot plate. Distilled water was added to each flask to raise the final volume to 25 ml. K concentration in leaf samples while zinc (Zn) and iron (Fe) concentration in grain samples of both treatments and certified reference material were all analyzed using atomic absorption spectrometer model WFX-210 . No significant variation was observed between the atomic absorption results of Duck weed BCR® (BCR-670) certified reference material, i.e., 0.90 g/kg, 20 mg/kg, and 5.39 mg/kg for Fe, Zn, and K, respectively, and the certified values, i.e., 0.94 g/kg, 24 mg/kg, and 5.79 mg/kg for Fe, Zn, and K, respectively. K utilization efficiency (KUtE) was calculated as a ratio between biological yield  and K uptake. K uptake efficiency (KUpE) was measured as a ratio between K uptake and K available. Finally, the K use efficiency (KUE) was estimated as a product of KUtE and KUpE , resulting in an average of 795 SNP markers per chromosome. Marker density was highest for B sub-genome and relatively lower for the D sub-genome. SNP dataset can be requested via email for further research purposes.DNA was extracted from 25 days old seedlings following CIMMYT manual  and genoDescriptive statistics, correlation among traits, and ANOVA were estimated for all the traits using IBM SPSS Statistics 22. Graphical representation of correlation among traits of interest along with histograms and scatterplots was performed in an R package for data visualization, GGally (an extension to ggplot2), in R 3.6.1.2r value was estimated for pairwise SNPs in a two Mb distance and then averaged across the genome. The LD decay was measured as the distance at which the average 2r between pairwise SNPs dropped to half of its maximum value  for ML-GWAS analysis. Critical threshold of significance was set at P ≤ 0.000001 (Bonferroni significance threshold = P ≤ 0.000047) for SL-GWAS and LOD ≥ 5 form ML-GWAS, normal significant threshold of ML-GWAS model is LOD ≥ 3 since no Bonferroni is applied. Significance of threshold was kept stringent to enhance the precision of candidate genes identification (https://cran.r-project.org/web/packages/RCircos/index.html).GWAS was conducted by both SL-GWAS (MLM) model and the ML-GWAS models for all the agronomic traits assessed in hydroponic and field trials. The MLM model proposed by fication . The lochttp://urgi.versailles.inra.fr/synteny-wheat can be used to identify the genetic  and associated genomic (wheat syntenome and syntenic genes from related grasses) data for a translational research approach.Meta-analysis was performed for four independent studies that had reported QTL for agronomic traits in wheat under K stress . Guo et http://plants.ensembl.org/Triticum_aestivum/Info/Index and the International Wheat Genome Sequencing Consortium (IWGSC) RefSeq v1.1 annotations  between different treatments across field and hydroponic environments. The four groups of genotypes  showed a variation in K uptake. Elite cultivars and post green revolution era cultivars generally had a higher K-uptake, green revolution era cultivars had a moderate K-uptake, while landraces had the lowest K-uptake in most of the treatments. An elite cultivar Punjab-11 had a consistently higher K-uptake across all environments on an average basis, i.e., 142.7625 (mg/kg), 95.9675 (mg/kg), 171.22 (mg/kg), 186.6 (mg/kg), 198.1214 (mg/kg), and 147.3462 (mg/kg) in K_C_H, K_T_H, K_C_2017, K_T_2017, K_C_2018, and K_T_2018, respectively . In stress condition, KUE had a significant positive correlation with CHL, RWC, RL, K, and KUtE . KUtE showed a negative correlation with RL under stress (-0.27), while a highly negative correlation with K in both control and stress treatment . K showed a significant positive correlation with RL in both treatments , while other relationships were either nonsignificant or slightly significant. Correlation analysis for all the agronomic traits in hydroponic experiment are presented in _2017, 0.61 in T_2017, 0.67 in C_2018, and 0.36 in T_2018). Similarly, KUE showed a highly positive correlation with TKW under both control and stress conditions in 2018 (0.53 in C_2018 and 0.35 in T_2018) while a less significant positive correlation with TKW in 2017 (0.14 in C_2017 and 0.16 in T_2017). KUtE had an extremely positive correlation with KUE across all treatments  while a completely reversed relationship with K under both treatments in 2017 and 2018 experimental seasons . K showed significant positive correlation with RL in C_2017 (0.36), T_2017 (0.74), C_2018 (0.21), and T_2018 (0.68). Similarly, K and BY were positively correlated in T_2017, C_2018, and T_2018 with the r values of 0.3, 0.4, and 0.31, respectively. TKW and K showed a highly positive correlation in T_2017 (0.35), C_2018 (0.44), and T_2018 (0.33). The detailed analysis of correlation among all the agronomic and physiological traits across all the field environments is presented in In field experiments, KUE positively correlated with BY across all treatments in years 2017 and 2018 , and markers with MAF ≤ 0.05. Population structure analysis divided the panel into seven subgroups of cultivars, details were provided in our previous report on the diversity panel . The extSL-GWAS method (MLM) identified 661 MTA. Out of these, six MTA with -log10p ≥ 5 were considered as significant and used for further analysis Table S5q1A refers to the stable locus on chromosome 1A, q2B-1 refers to the 1st stable locus on chromosome 2B, while q2B-2 refers to the 2nd stable locus on chromosome 2B, and so on.Among the 534 significant SNPs from both SL-GWAS and ML-GWAS, 54 were detected by at least two different GWAS models Table S7q5B-1) from GWAS resided close to _11MQTL present on chromosome 5B. This SNP was detected by two GWAS models (pLARmEB and FASTmrMLM) with a LOD score of 12.2 and -log10p 13.19 and associated with two K related traits in two environments . All other 10 MTA were novel associations.Genetic maps used for the QTL studies  were projected on to WCGM2017 consensus map, with at least 75% common markers between any single genetic map of linkage analysis (QTL) and WCGM2017. Before doing the meta-analysis of different populations, meta-analysis of each population to identify consensus regions within the population was also conducted. The QTL cluster belonging to two or more different mapping populations was subjected to meta-analysis for the calculation of MQTL. Overall, 130 QTL Table S9RefSeq v1.1 , followed by pLARmEB (57%), mrMLM (56.16%), and FASTmrEMMA (17.62%). Overall, these results suggest the dominance of pLARmEB over the other models used in this study. However, the minimum r2 observed in mrMLM was r2 = 3.9, while the minimum value for all other models was less than 0.01, which indicates that mrMLM can detect major and effective SNPs as compared to other models.Four ML-GWAS models detected 1319 significant SNPs with a logarithm of odds three or higher that were later screened for a more stringent criterion for gene prediction. However, among these four models, pLARmEB detected the greatest number of MTA with 567 MTA that had LOD score ≥ 3 (279 with LOD ≥ 5), FASTmrMLM identified 477 MTA with LOD score ≥ 3 (213 with LOD ≥ 5), mrMLM detected 192 MTA with LOD score ≥ 3 (35 with LOD ≥ 5), while FASTmrEMMA detected the lowest number of 83 MTA with LOD score ≥ 3 (1 MTA with LOD ≥ 5). The highest maximum LOD score was observed in pLARmEB (15.19), while the lowest maximum was detected in FASTmrEMMA (5.3). All methods except FASTmrEMMA had a maximum LOD score of greater than 10 for at least one of the associated SNPs. All these findings were consistent with the study of q5B-1 (IWB38863) was detected in a close proximity to _11MQTL while the other 10 loci were novel associations, eight loci were identified on different chromosome from MQTL. These 11 loci from GWAS were critically screened to reduce the possibility of false positives and are thus presumed as true genetic variants. MQTL are also an important target for breeding potential as they reduce the confidence interval by integrating different independent analyses in one place. Narrowing down a QTL confidence interval is a key step towards a precise search of candidate genes.The ultimate goal of all the breeding programs is to achieve a high grain yield in moderate to stress environments . Therefoq2B-1, q2B-2, q2D, q4D, q5B-1, q5B-2, and q5B-3 associated to KUE and KUtE along with other agronomic traits. This provides a compelling evidence that KUE and KUtE have a major influence on the grain yield. Plants invest a greater proportion of photosynthates in the roots and altering the root morphology to enhance exploration of the soil volume (q1D) was associated with RL, HI, and FW, which implicates the role of root architecture in KUE and overall plant growth. Another stable locus q2B-2 (IWB7106) encoded KUtE_C_2017 and CHL_T_2016, which indicate that K plays a key role in photosynthesis , this gene has 4 splicing variants and was annotated for CCAAT-binding transcription factor A. This protein increases grain yield of wheat in low nutrient input cropping systems (q2B-1) encoded TraesCS2B02G201400 and TraesCS2B02G201500 genes responsible for COBRA-like protein which has been reported to increase grain yield in maize . This gene has been characterized in wheat and rye (GLU1B was annotated from TraesCS2B02G599800 present at q2B-2 (IWB7106). Another gene at this locus annotated RING-type E3 ubiquitin transferase, an associated QTL is reported for grain width and weight in rice (q2D (IWB740) associated to KUE_C_2017 and KUE_T_2018 was found in linkage with 3 genes  encoding Bidirectional sugar transporter SWEET. IWA410 at q4D  harbored TraesCS4D02G281600, Calmodulin-binding family protein has been characterized in arabidopsis ortholog of this gene. Calmodulin proteins regulate ion channels such as KCa channel, their expression is enhanced in response to abiotic stresses  Higher Education Commission Pakistan project (HEC NRPU-3825); 2) the Knowledge Innovation Program of Chinese Academy of Agricultural Sciences, Central Public-Interest Scientific Institution Basal Research Fund, the Chinese Agricultural Research System (CARS-13).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


XRCC4 and rs10804247 in XRCC5 was identified for venous thrombosis with a Bonferroni-adjusted likelihood ratio test (LRT) p: 0.0627. A total of 57 interactions were identified from main effect filtering for the cardiac traits G×G (10) and fatty acids G×G (47) at Bonferroni-adjusted LRT p < 0.05. For cardiac traits, the top interaction involved SNPs rs1383819 in SNTG1 and rs1493939 (138kb from 5’ of SAMD12) with Bonferroni-adjusted LRT p: 0.0228 which was significantly associated with history of arterial hypertension. For fatty acids, the top interaction between rs4839193 in KCND3 and rs10829717 in LOC107984002 with Bonferroni-adjusted LRT p: 2.28×10−5 was associated with 9-trans 12-trans octadecanoic acid, an omega-6 trans fatty acid. The model inflation factor for the interactions under different filtering methods was evaluated from the standard median and the linear regression approach. Here, we applied filtering approaches to identify numerous genetic interactions related to cardiac-related outcomes as potential targets for therapy. The approaches described offer ways to detect epistasis in the complex traits and to improve precision medicine capability.Epistasis analysis elucidates the effects of gene-gene interactions (G×G) between multiple loci for complex traits. However, the large computational demands and the high multiple testing burden impede their discoveries. Here, we illustrate the utilization of two methods, main effect filtering based on individual GWAS results and biological knowledge-based modeling through Biofilter software, to reduce the number of interactions tested among single nucleotide polymorphisms (SNPs) for 15 cardiac-related traits and 14 fatty acids. We performed interaction analyses using the two filtering methods, adjusting for age, sex, body mass index (BMI), waist-hip ratio, and the first three principal components from genetic data, among 2,824 samples from the Ludwigshafen Risk and Cardiovascular (LURIC) Health Study. Using Biofilter, one interaction nearly met Bonferroni significance: an interaction between rs7735781 in  As sequencing technology improves, the understanding of genetic variation and their interactions is in high demand to interpret the trigger of complex diseases. Computational approaches to identify epistasis take advantage of improved sequencing technology . PreviouMain effect filtering is a widely used and simple way to reduce the multiple testing burden by selecting suggestive SNPs from GWAS outputs and using them to generate pairwise SNP models for G×G analysis. An alternative method is candidate SNP/gene selection where plausible genetic variants are selected based on relationships between genes published in literature and/or from databases. Biofilter software is a tool which provides a convenient single interface for accessing multiple publicly available human genetics data resources through the Library of Knowledge Integration (LOKI) . It is uThe Ludwigshafen risk and cardiovascular (LURIC) health study is an ongoing study to explore risk factors for cardiovascular diseases and is aimed at the understanding of genes, environments, medications, and their associations with cardiac health . Data weAlongside the use of the main effect filtering from GWAS, we suggest the exploitation of biological knowledge from different databases to generate SNP pairs among genes to limit the number of tests . Many G×The LURIC health study is a prospective cohort study aimed at assessing the genetic and environmental risk factors in cardiovascular diseases for 3,316 Caucasians of German ancestry  between 1997 and 2000 . Pa. Pahttpsclarite) .Var1 and Var2 are the potential SNP predictors of interest, Y is the phenotype, covs are the covariates, and ε is the error. This test evaluates the significance of the interaction between Var1 and Var2 and its contribution above and beyond the main effects of the two individual variates combined.To reduce the high multiple testing burden associated with running pairwise genetic interactions between all genome-wide SNPs, two filtering methods were used for selecting the SNPs based on 1) the main effect from individual GWAS results  and 2) bIndividual GWAS for each cardiac trait and fatty acid phenotype were performed  . The topqchisq of the Chi-square distribution was applied for evaluating the model inflation from the p-values based on the standard median approach and a linear regression approach between the observed values and expected values on R software for G×Gs under each phenotype  plots. A series of referential G×G was performed with the same set of 1000 random selected SNPs  as the reference for comparing the performance of the filtering methods in each variable. A quantile function henotype . The disggplot2 package in R software. The genotypes of the SNPs in top interaction were plotted for the cardiac traits by counting the number of case/control with using the plot3D package in R software.Volcano-like plots were generated from R software for elucidating the associations between the significance and estimated interaction coefficient  against interaction beta-coefficient) for interactions, highlighting interactions with significant adjusted LRT p-values. The distributions of the phenotypes and genotypes for significant interactions were plotted by using igraph package in R software at gene level based on the significant gene-gene interaction with (1) Bonferroni-adjusted p < 0.05 and (2) FDR less than 0.05.The SNPs involved in interactions with the false discovery rate (FDR) less than 0.05 were further annotated with gene by Biofilter using a gene boundary of 5kb. These significant interactions were selected for network plots if both SNPs were located within a gene or locus. Two network plots were generated using XRCC4 and rs10804247 in XRCC5 (uncorrected LRT p = 3.20×10−6 and Bonferroni-adjusted LRT p = 0.0626996) (LOC105375746 (Bonferroni-adjusted LRT p: 0.0104) associated with venous thrombosis or pulmonary embolism. Other top results included SNPs rs1493939 (intergenic) and rs1383819 in SNTG1 (Bonferroni-adjusted LRT p: 0.0228), rs1389542 (intergenic) and rs1383819 in SNTG1 (Bonferroni-adjusted LRT p: 0.0280), and rs1493939 and rs12547263 in SNTG1 (Bonferroni-adjusted LRT p: 0.0286) all for history of arterial hypertension.For the cardiac G×G, one SNP pair was identified through Biofilter modeling associated with venous thrombosis or pulmonary embolism: rs7735781 in 0626996) . The mai0626996) . The topAL121588.1) and rs4923022 in GAS2 , and rs6129232 and rs337459 in GAS2 (Bonferroni-adjusted LRT p: 0.0348). The first two significant interactions for log-transformed 9-trans 12-trans octadecanoic acid involved SNPs rs10829717 (intergenic) and rs4839193 in KCND3 (Bonferroni-adjusted LRT p: 2.280×10−5), and rs10829717 and rs11102365 in KCND3 (Bonferroni-adjusted LRT p: 2.640×10−5). The top significant result for log-transformed trans-palmitoleic acid involved SNPs rs2227016 in HUU95743 and rs351219 in STRA6 (Bonferroni-adjusted LRT p: 0.0078). Another significant interaction for log-transformed trans-palmitoleic acid involved SNPs rs12547615 (intergenic) and rs875979 in GALNT1 (Bonferroni-adjusted LRT p: 0.0453).For the fatty acids G×G, the main effect filtering approach yielded 47 models with a Bonferroni-adjusted LRT p-value less than 0.05, including 7 models for log-transformed 9-cis 12-trans octadecanoic acid, 38 models for log-transformed 9-trans 12-trans octadecanoic acid, and 2 models of SNPs for log-transformed trans-palmitoleic acid . The topTo check for inflation of results, the distribution of LRT p-values for the referential G×Gs as the baseline and G×Gs under two filtering methods was plotted for each variable Figs  and S4. Volcano-like plots were created based on the interaction beta coefficient in the full model and uncorrected LRT p-value for interactions in cardiac traits and fatty acids under two filtering methods . SeveralPlots of the phenotypic distribution alongside the corresponding genotypes were generated for visualizing the most significant interaction of each phenotype Figs  and 6. TGCNT1 and SCN4B, were involved in multiple significant interactions , PTPRD for omega-6 fatty acid (C18:2n6ct), and LCP1 for trans palmitoleic acid (C16:1n7t).For a global representation of the results, two interaction maps were plotted for the Bonferroni significant at 0.05  and FDR ractions . GCNT1 wThe large demands of computational resources and the multiple testing burden impact our ability to find G×G from genome-wide analyses. In this study, we utilized two filtering methods to reduce the computational impediments and identified a number of significant interactions for cardiac traits and fatty acids in the LURIC Health Study. We compared results when filtering using Biofilter with main effect filtering. In this genetic interaction analysis of cardiac health, we identified 57 SNP-SNP models that were Bonferroni significant using a main effect filter and one SNP-SNP model nearly the Bonferroni significant using Biofilter software.XRCC4 and XRCC5 was generated by Biofilter and identified as a significant interaction for venous thrombosis and/or pulmonary embolism. The proteins expressed by XRCC4 and XRCC5 function together as a DNA ligase complex in facilitating the reparation of double-stranded DNA breaks through non-homologous end joining , but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.”If your commercial affiliation did play a role in your study, please state and explain this role within your updated Funding Statement.b) Please also provide an updated Competing Interests Statement declaring this commercial affiliation along with any other relevant declarations relating to employment, consultancy, patents, products in development, or marketed products, etc. http://journals.plos.org/plosone/s/competing-interests) . If this adherence statement is not accurate and  there are restrictions on sharing of data and/or materials, please state these. Please note that we cannot proceed with consideration of your article until this information has been declared.Within your Competing Interests Statement, please confirm that this commercial affiliation does not alter your adherence to all PLOS ONE policies on sharing data and materials by including the following statement: "This does not alter our adherence to  PLOS ONE policies on sharing data and materials.” :Please provide more details about the main effect GWAS, including Manhattan plots, QQ plots, significance level for the top 100 SNPs etc in Supplements. Please also provide more background for Bilfilter analyses as reviewer 2 suggested.The GxG analyses were performed on a relatively small samples without replication. It is hard to determine if those findings are true positive and can be generated to other populations. Can the authors look at other European ancestry studies for replication evidence? Please estimate statistical power for the GxG analyses.[Note: HTML markup is below. Please do not edit.]Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: YesReviewer #2: Yes**********2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: YesReviewer #2: Yes**********3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.The Reviewer #1: NoReviewer #2: Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: The authors applied two filtering methods to identify genetic interactions related to cardiac related outcomes from data from the Ludwigshafen Risk and Cardiovascular (LURIC) Health Study.The manuscript appears technically sound and the the conclusions drawn are adequate.As stated by the authors not all data underlying the findings in their manuscript are fully available.The manuscript is concise, well structured and comprehensible.Reviewer #2: The study by Zhou et al. identified the SNP–SNP epistatic interactions for a serial of cardiac traits and serum fatty acids in a cohort of 3,316 individuals. It is thought that gene-gene interaction can help to illustrate the genetic etiology of complex disease, but the epistasis identification is impeded by the computational and statistical burden from large numbers of SNP combinations that need to be tested. This study applied two filtering approaches before interaction testing, including main effect filtering based on GWAS and biological knowledge-based modeling through Biofilter. This manuscript is well written and the author clearly illustrated their methods and discussed the potential biological meanings of findings. However, I think the overall goal of this work is a little bit vague and the significances are not well presented. For example, what does the author want to highlight for this study? Is it about the method, or the new findings related to cardiac traits and serum acids?Major Revisions:1. Page 5, lines 94-96 in methods, the authors mentioned the covariates included in models. How does the author decide which covariate should be included? Were they just forced into the model? If so, were they all significant for every trait?2. Page 7, lines 141-143 in methods, the authors mentioned the model for interaction testing also included the first three principal components. How did the author determine the number of PCs? How much variation was explained with the first three PCs?3. Page 7, lines 152, “The top one hundred SNPs were selected from each phenotype’s GWAS.” Choose the top100 seems a little bit arbitrary. How was this selected? And did the author try to include more SNPs?4. Page 7, lines 150-155, section “Main effect filtering and Biofilter filtering”. I would suggest the authors to describe more about how biofilter perform the interaction testing.5. About methods, it would be much more clearly if the authors could add a simple diagram to illustrate the QC and analysis steps.6. As indicated at the beginning, I think more attention should be paid to the biological implications of their findings. In regard to the significance of the findings, is there any replicates? Can these findings be validated in other cohorts? Additionally, were any of the identified interactions that were previously reported? The results would be more meaningful if author could address more about the biological significance of their findings by comparing to existing literatures.7. Page 16, lines 330-332, “Notably, Biofilter-generated models were found to demonstrate larger interaction effect sizes than those found through main effect filtering…”. This is very interesting. Does the author find similar results in other literatures?Minor Revision:The p values can be showed with less digits.**********what does this mean?). If published, this will include your full peer review and any attached files.6. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool,  24 Jul 2020RESPONSE TO REVIEWERSArticle Submitted to PLoS ONEManuscript Number: PONE-D-19-31634Investigation of gene-gene interactions in cardiac traits and serum fatty acid level in LURIC cohortWe would like to thank the reviewers and editors for the time they spent reviewing our paper and the interest that was shown. Below are our detailed responses to reviewers’ comments which are in italics. All revisions in the manuscript have been highlighted in the tracked changes version of the submitted manuscript.Additional Editor Comments:Please provide more details about the main effect GWAS, including Manhattan plots, QQ plots, significance level for the top 100 SNPs etc in Supplements. Please also provide more background for Biofilter analyses as reviewer 2 suggested.Thank you. To provide more details, we have added Manhattan plots from the GWAS, QQ plots, and also result files in the Supplement S1 Figure and Supplement S1 File. Additionally, detail was added to the Methods section.For the main effect analysis, we performed GWAS for each of the phenotypes and selected the top 100 SNPs for each respective phenotype and performed subsequent comprehensive pairwise SNP-SNP interaction analyses for these SNP lists within each phenotype. Due to the fact that power for each phenotype will vary based on differing sample size, we wanted to give equal opportunity to each phenotype to identify genetic interactions. We performed simulation tests to identify an optimal SNP filter amount that yields 80% power for reasonable interaction effect sizes . Greater detail has been added to the Methods section of the manuscript. Finally, we added more details about the Biofilter analysis to the Methods section of the manuscript. Biofilter is a software used to build putative SNP-SNP pairs by referencing publicly available biological database knowledge, including published protein-protein interactions, pathways, and ontological information [1–3]. It has been successfully applied to numerous phenotypes, including cholesterol and lipid levels , efavirenz-containing HIV treatment [7], multiple-sclerosis [8], and cataracts , to identify genetic interactions through knowledge-based filtering, allowing the possibility of identifying SNPs that interact without demonstrating a main effect.The GxG analyses were performed on a relatively small samples without replication. It is hard to determine if those findings are true positive and can be generated to other populations. Can the authors look at other European ancestry studies for replication evidence? Please estimate statistical power for the GxG analyses.These are excellent points. Unfortunately, for this study we were restricted to only performing analysis on the LURIC cohort. However, we did estimate our power to detect replicating signals in another cohort through power calculations. We included our power simulation in Supplement S3 Figure C-D to show that our study was well powered to detect the gene-gene interactions with betas at 0.2 and higher for logistic model or betas at 0.1 and higher for linear model. We added descriptions of this in the Methods section of the manuscript. The number of published gene-gene interaction studies are limited for the phenotypes we examined in this study, and as such, we did not find any previously reported exact SNP-SNP interactions. However, we added further biological description regarding a gene-gene interaction we identified between XRCC4 and XRCC5 in the Results and Discussion sections of the manuscript. Further, we performed literature searches for the significant individual genes and their associated phenotypes to determine if any of the genes in the gene-gene interaction models had previous associations with the phenotypes and discussed examples of genes involved in multiple gene-gene interactions, including GCNT1, SCN2B, SCN4B, and ASTN2. This has been added to the Discussion section of the manuscript. Major Revisions:1. Page 5, lines 94-96 in methods, the authors mentioned the covariates included in models. How does the author decide which covariate should be included? Were they just forced into the model? If so, were they all significant for every trait?Response: Thank you. We chose to adjust for age, sex, waist-hip ratio, and BMI in this study because these variables have shown to be related to cardiac phenotypes [15]. We also performed ANOVA tests to show the relationships between each phenotype and covariate in S2 Table, which verified the need to adjust for these variables. This has been added to the Methods section of the manuscript.2. Page 7, lines 141-143 in methods, the authors mentioned the model for interaction testing also included the first three principal components. How did the author determine the number of PCs? How much variation was explained with the first three PCs?Response: We calculated all PCs based on individual genetic information. We plotted the distribution of the first 20 PCs and found that the first three PCs explained the majority of the variation (0.2324074%) ). We also included a PCA plot of the samples based on the first two PCs ). This information has been added to the Methods section of the manuscript.3. Page 7, lines 152, “The top one hundred SNPs were selected from each phenotype’s GWAS.” Choose the top100 seems a little bit arbitrary. How was this selected? And did the author try to include more SNPs?Response: As mentioned above, due to the fact that power for each phenotype will vary based on differing sample size, we wanted to give equal opportunity to each phenotype to identify genetic interactions and so we chose to use the top 100 SNPs as a filter rather than a p-value cutoff as the number of qualifying SNPs for this approach will widely vary across the phenotypes. Further, we estimated the power ) prior to implementing our analysis plan and chose to use top 100 as the optimal filtering cutoff. 4. Page 7, lines 150-155, section “Main effect filtering and Biofilter filtering”. I would suggest the authors to describe more about how biofilter perform the interaction testing.Response: Thank you for this comment. We have made changes to add more detail, as described in the response to first comment from the editor above.5. About methods, it would be much more clearly if the authors could add a simple diagram to illustrate the QC and analysis steps.Response: We found this to be a very helpful suggestion. We added a flowchart to show the genotype QC, phenotype QC, and also the interactions to the manuscript .6. As indicated at the beginning, I think more attention should be paid to the biological implications of their findings. In regard to the significance of the findings, is there any replicates? Can these findings be validated in other cohorts? Additionally, were any of the identified interactions that were previously reported? The results would be more meaningful if author could address more about the biological significance of their findings by comparing to existing literatures.Response: Thank you for suggesting this. As only 2,824 people were available after the QC and we had to ensure power to detect interaction signal, we performed a discovery study with the LURIC cohort without replication. As described in the response to the second Editor Comment, we have provided power estimates in S3 Figure that indicate the sample size and number of SNPs needed for replication in future studies. As described in the second Editor Comment, we searched all identified interactions in the gene knowledge databases and also the significant individual genes and their associated phenotypes to determine if any of the genes in the genetic models had previous associations. These details have been added to the Discussion section of the manuscript.7. Page 16, lines 330-332, “Notably, Biofilter-generated models were found to demonstrate larger interaction effect sizes than those found through main effect filtering…”. This is very interesting. Does the author find similar results in other literatures?Response: Thank you very much for this comment; this finding has not been looked into previously, and we appreciate your interest. Upon further investigation of previously published work involving both biofilter and main effect filtering for gene-gene interaction analysis, we found other examples in which the biofilter approach yielded larger interaction effect sizes than main effect filtering, for example, the gene-gene interaction analyses of lipids [5] and type II diabetes [16]. We do not know the reason for this finding at this time, and we would like to investigate this in future research. This has been added to the Discussion section of the manuscript.Minor Revision:The p values can be showed with less digits.Response: We have removed additional digits for the p-values to include only four digits.  Referencehttp://www.ncbi.nlm.nih.gov/pubmed/267762001. Kim D, Lucas A, Glessner J, Verma SS, Bradford Y, Li R, et al. BIOFILTER AS A FUNCTIONAL ANNOTATION PIPELINE FOR COMMON AND RARE COPY NUMBER BURDEN. Pac Symp Biocomput. 2016;21: 357–68. Available: 2. 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Next-generation analysis of cataracts: determining knowledge driven gene-gene interactions using biofilter, and gene-environment interactions using the Phenx Toolkit*. Pac Symp Biocomput. 2015; 495–505. 10. Hall MA, Verma SS, Wallace J, Lucas A, Berg RL, Connolly J, et al. Biology-Driven Gene-Gene Interaction Analysis of Age-Related Cataract in the eMERGE Network. Genet Epidemiol. 2015;39: 376–384. doi:10.1002/gepi.2190211. Zhang Q, Karnak D, Tan M, Lawrence TS, Morgan MA, Sun Y. FBXW7 Facilitates Nonhomologous End-Joining via K63-Linked Polyubiquitylation of XRCC4. Mol Cell. 2016;61: 419–433. doi:10.1016/j.molcel.2015.12.01012. Drouet J, Delteil C, Lefrançois J, Concannon P, Salles B, Calsou P. DNA-dependent protein kinase and XRCC4-DNA ligase IV mobilization in the cell in response to DNA double strand breaks. J Biol Chem. 2005;280: 7060–7069. doi:10.1074/jbc.M410746200https://www.ncbi.nlm.nih.gov/gene/751813. Gene [Internet]. 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Walnut pellicle color is a key quality attribute that drives consumer preference and walnut sales. For the first time a high-throughput, computer vision-based phenotyping platform using a custom algorithm to quantitatively score each walnut pellicle in L* a* b* color space was deployed at large-scale. This was compared to traditional qualitative scoring by eye and was used to dissect the genetics of pellicle pigmentation. Progeny from both a bi-parental population of 168 trees (‘Chandler’ × ‘Idaho’) and a genome-wide association (GWAS) with 528 trees of the UC Davis Walnut Improvement Program were analyzed. Color phenotypes were found to have overlapping regions in the ‘Chandler’ genetic map on Chr01 suggesting complex genetic control. In the GWAS population, multiple, small effect QTL across Chr01, Chr07, Chr08, Chr09, Chr10, Chr12 and Chr13 were discovered. Marker trait associations were co-localized with QTL mapping on Chr01, Chr10, Chr14, and Chr16. Putative candidate genes controlling walnut pellicle pigmentation were postulated. Juglans regia L.) is an economically important edible seed that is diploid 2x = 32 with 16 chromosomes and a genome size of approximately 600 Mbp. In the U.S., the English walnut industry generates 1.5 billion dollars annually with over 99% of production occurring in California  and is formed from maternally derived tissue arising from the inner and outer ovular integuments (Juglans regia L.) pellicle pigmentation can vary significantly between cultivars and developmental stages, and is influenced by environmental stressors. Flavonoids or phenolic compounds synthesized through the phenylpropanoid pathway are localized in seed coats to defend the embryo against biotic stressors , and subjectively by eye using a color chart published by the California Dried Fruit Association (DFA) . Color pHuman perception of color is largely influenced by the number and types of photoreceptors an individual possesses. Differences in the photoreceptors between individuals contributes to variability in the perception of a given color. This forms the basis of subjectivity of human quality assessments within a color perception dataset. As such, color(s) quantified by human perception can be an unreliable source for obtaining quality data , howeverUsing traditional scoring, walnut pellicle color is labor intensive to measure, strongly influenced by environmental variation, and is a polygenic trait  was used for QTL mapping with a range in tree age of 8 – 12. Trees in this study were planted across eight blocks; five of them were across the same field location and all trees were spaced six feet apart and irrigated with micro-sprinklers. Blocks consisted of trees planted in row plots with multiple family crosses made in one year. A full-sib family had between 10 and 50 individuals with 31 unique parents. Most male parents were only used once, with a few male parents used 2-4 times, one male was used for 13 different crosses, and two males were used reciprocally as females.At least 30 nuts per tree were hand harvested as each tree reached fruit maturity (hull-split) during August and September of 2015, 2016, and 2017. These were hung in polypropylene mesh bags, air-dried for two weeks, and then stored at -4° until measurements were taken. Walnut kernels were placed on commercial scoring trays obtained from the Dried Fruit Association of California which contain 100 wells each. Each tray held ten kernels from each of 10 distinct trees, and 10 kernels were evaluated. When kernels were being evaluated for color, they were kept at 0° for short-term storage, and kernels were kept at - 4° for long term storage.Qualitative color scoring by eye was done by examining each kernel for its separation into color category 1 - 4, according to the Dried Fruit Association (DFA) scoring sheet , Safe F, in accoa; LITE = light, 2b; LAMB = light amber, 3c; AMBR = Amber, 4d , a* (red/green color), and b* (yellow/blue color). The data produced contains each color scores for every pellicle measured. Details on system and method was modified from  which mounts over an enclosed dome encircled with four (D65) light emitted diodes (LED) tubes of 18W  which provided consistent illumination. Custom algorithms were developed for calibration and image acquisition of the computer vision system . Briefly, The calibration macro written in FIJI 1.52 software lk is the interaction between family and year, aijk is the effect of age on color measurement for the i-th genotype, j number of measurements in the k-th year, and εijkl is the random error term with mean 0 and variance σ2ε.Multi-year phenotypic data collected for DFA scores and the CVS scores were analyzed with ANOVA using R packages ‘car’, ‘agricolae’, ‘lme4’ with equation (1) for the model,i is the effect on color measurement of the i-th genotype, βk is the effect on color measurement of the k-th year, (αβ)ik is the interaction between genotype and year, and εijk is the random error term with mean 0 and variance σ2ε. For the larger dataset of the 31 full-sib families, breeding values (BV) per individuals were estimated using ASReml-R v4 (τ is a (p × 1) vector of fixed treatment effects (block and year), X is an (n × p) design matrix, u is the (q × 1) vector of random effects (pedigree), Z is an (n × q) design matrix, e is the (n × 1) vector of residual error. The pedigree utilized in the model was reconstructed to identify corrected kinship relationships from the original UC Davis Walnut Improvement Program pedigree using the Axiom J. regia 700K SNP array  for linear model,scanone and ‘Haley Knott’ regression  and 100 imputations. A multiple QTL model was then fitted with the function fitQTL where both trait QTL identified in scanone were added in the model. The function refineQTL was applied and adjusted if the new positions in the ANOVA the model had a greater fit . The Bayesian credible interval for 5% error rate was implemented as the confidence QTL interval.Quantitative-trait loci mapping was performed using the genetic maps (File S5) of the bi-parental population ‘Chandler’ × ‘Idaho’ described in (gression . Signifigression . When muJ. regia 700K SNP array as described in (The whole population was genotyped using the Axiom ).Principal components of SNP markers were obtained by running the mixed linear model (MLM) algorithm in GAPIT. The first component explained 9.39% variation, the second PC explained 6.97% variation, the third PC explained 5.31%, the fourth PC explained 3.41%, and the fifth PC explained 2.63%. The number of principal components (PCs) to include as covariates in the models was defined based on the screeplot . This model was set to perform 10 iterations, with four to six PC’s added as covariates, depending upon the goodness of fit in the QQ-plots for each color phenotype, a minor allele frequency threshold of 5%, and the default parameters for bin size. A 5% Bonferroni threshold (2.29 × 10−7) was used to assess significance, and Q-Q plots and Manhattan plots were inspected for evidence of inflation. A multiple corrections test (−6).Genome-wide associations were conducted using the Fixed and Random Model Circulating Probability Unification (FarmCPU) algorithm . The MLM2 between 100-120 kb. Within these genic regions the predicted mapped genes and functional annotation as described in  respectively. Output tables from ANOVA in the GWAS population provided in File S4. ‘Chandler’ and ‘Idaho’ genetic maps with phenotypic data are available in supplemental (File S5). Estimated breeding value phenotypes and principal components used in GWAS analysis are available in supplemental . Supplemental data file S8 contains raw color score data for both the GWAS population and ‘Chandler’ x ‘Idaho’ population. Supplemental material available at figshare: P < 0.0) factors were family, year of harvest, family × year interaction, individual, and age; however age was not a significant factor in the linear models for DFA and L* phenotypes (File S8). For the calculation of adjusted means with ‘Chandler’ × ‘Idaho’ dataset, all terms and their interactions were significant (P < 0.0001) (File S4).In general, ‘Chandler’ produces kernels with an extra-light pellicle color, while Idaho’s kernels are light amber ; these differences are consistently observed in both the DFA and CVS analyses. For the ANOVA linear models significant . ‘Scharsch Franquette’, a selection made in California which is genetically identical to ‘Franquette’, a French variety, is a founder of the UC Davis Walnut Improvement Program, displayed the highest breeding value (47.35) for the lightness L* score. Families that possessed multiple individuals with top L* score breeding values included 10-024 (03-001-977 × ‘Ivanhoe’), 11-030 (04-003-107 × ‘Ivanhoe’) and 09-25 (95-026-16 × 94-019-85) along with founder ‘Waterloo’, and ‘Chandler’ (Table S1).Pellicle color measurements acquired using the new image-based phenotyping method yielded values of the narrow-sense heritability similar to the DFA scoring system  .Principal component analysis revealed four to six principal components which explained SNP variation for the 31 full-sib families in the Walnut Improvement Program, excluding ‘Chandler’ × ‘Idaho’ . See 2 = 0.37) and with SNP associated with the a* score on Chr16 (r2= 0.63). Pairwise LD measures between these SNPs associated with DFA and L* scores and SNPs associated with DFA and a* scores are visualized to show close proximity to each other 16.29 kb and 213 kb respectively  respectively (Table S2).Similarly, (CAD), which is associated with the b* score. Lastly, the third gene function which lies on Chr01 encodes tryptophan synthase (TRP), which is also associated with the b* score. One gene function (transcription factor MYB1) associated with the DFA score was identified on Chr07. For the a* score, on Chr10 flavonol synthase/flavanone 3-hydroxylase (FLS) was identified to be associated with a SNP, as well as on Chr11 chorismate mutase (CM). Two putative gene functions were identified on Chr12; the first of these genes was associated with both an L* and b* score, and encoded 4-coumarate—CoA ligase while the second gene encoded flavonoid 3′-monoxygenase, was associated with a DNA score. Four gene functions were identified to be associated with SNPs on Chr13; the first gene function is anthranilate phosphoribosyltransferase (PAT) which was associated with a b* score, the second gene function was also associated with a b* score and encoded caffeic acid 3-O-methyltransferase (COMT), and the final two gene functions on Chr13 both encoded FLS genes, were both associated with L* scores  putative candidate genes were identified within 100 kb windows surrounding the significant SNPs (Table S3). These putative candidate genes are predicted to have functions related to abiotic stress, pathogen resistance, hormone signaling and the biosynthesis of pigmented metabolites , indicating that these genes may contribute to a slight reddish/brown pigmentation. CM is involved in the biosynthesis of phenylalanine and tyrosine as well as their derivatives, the phenylpropanoids, lignins, flavonoids and anthocyanins, most of which are pigmented . FLS/F3H is a bifunctional enzyme , suggesting that these genes promote yellow color. PAT and TS both act in the biosynthesis of tryptophan, a light yellow AAA and its yellow/orange derivative tryptamine , suggesting that these genes are associated with a pigmentation of the pellicle; bifunctional FLS/F3H- FLS desaturates dihydroflavonols to yield yellow/brown flavonols (F3′H was associated with the DFA score (2.2), indicating a possible diversity of colored pigments. F3′H hydroxylates flavanones, dihydroflavonols, flavones and flavonols to increase the diversity of each of the aforementioned categories of yellow flavonoids  markers from the most significant SNPs, assisting in efficient selection at the seedling stage rather than the selection process over a 5-10 years period requiring trees to reach sexual maturity. Early selection of progeny will dramatically increase the efficiency in developing new cultivars. Due to the fact that walnut growers are compensated based on human grader’s perception of color, an improvement to the CVS algorithm would include human input factors such as discrimination for veining, speckling or size can be considered.For further investigation, the creation and evaluation of genomic prediction models will enable the integration of all the small QTL effects to predict progeny with lighter pellicles, as the industry demands. To solidify results pertaining to the putative candidate genes for flavonoid production, an experiment setup to clone each gene and express them in bacteria would verify gene function and identify the origin of the chemical reactions occurring in response to developmental stages, environmental stress or autophagy.