Non‐genetic information  that results in different phenotypes in animals can be transmitted from one generation to the next and thus is potentially involved in the inheritance of traits. However, in livestock species, animals are selected based on genetic inheritance only. The objective of the present study was to determine whether non‐genetic inherited effects play a role in the inheritance of residual feed intake (RFI) in two species: pigs and rabbits. If so, the path coefficients of the information transmitted from sire and dam to offspring would differ from the expected transmission factor of 0.5 that occurs if inherited information is of genetic origin only. Two pigs  and two rabbits  datasets were used in this study . The test of the path coefficients to 0.5 was performed for each dataset using likelihood ratio tests . The path coefficients differed significantly from 0.5 for one of the pig datasets (pig2). Although not significant, we observed, as a general trend, that sire path coefficients of transmission were lower than dam path coefficients in three of the datasets . These results suggest that phenomena other than genetic sources of inheritance explain the phenotypic resemblance between relatives for RFI, with a higher transmission from the dam's side than from the sire's side. Other factors are also transmitted across generations (i.e. are inherited) and are involved in determining the animal's phenotype, thus playing a role in the trait inheritance Mameli, . The thrBecause of the relatively high importance of feed‐related costs in animal production systems  and the beginning (BWstart) of the test period divided by the number of days elapsed, and the average metabolic body weight (AMBW) was computed as BWend1.6‐BWstart1.6(1.6×(BWend‐BWstart))  and were considered as repeated measurements of the same trait .The two rabbit lines were the paternal lines AGP39 and AGP59 of Hypharm, a French breeding company. These two rabbit lines are selected for body weight at 63 or 70 days, CY and resistance to digestive disorders. For both lines, at weaning, four kits of the first litter of each dam were placed in individual pens. They had free access to commercial pelleted feed until 63 days of age for AGP39 and 70 days of age for AGP59. Feed intake was recorded every week as the difference between the weight of feed delivered and refusals, for 5,213 rabbits over a 5‐week period for AGP39 and for 4,584 rabbits over a 6‐week period for AGP59. Rabbits were weighed after weaning and at the end of each week, and weekly ADG (WADG) was calculated as the difference between body weight at the end and at the beginning of each week divided by the number of days elapsed. Weekly feed intake (WFI) was recorded every week as the difference between the weight of feed delivered and refusals. Weekly metabolic body weight (WMBW) was computed as WBW2.2y is the ADFI over the growing period for pig1, the standardized zero‐centred ADFI over the test period for pig2, and the standardized WFI for AGP39 and AGP59, β is the vector of fixed effects; t is the vector of transmissible values; p is the vector of permanent environmental effects (included in the models for data with repeated measurements); m is the vector of maternal genetic effects; l is the vector of litter effects (week by litter combination for rabbit data); e is the vector of residuals; X,Z,W,S, and R are the corresponding known incidence matrices. For pig1 and rabbit data, all random effects were distributed as centred normal distributions with variance–covariance matrices equal to Aσm2 for the maternal genetic effects, Ipσp2 for the permanent environmental effects, Ilσl2 for the litter effect, Ieσe2 for the residual effects, where I are identity matrices of appropriate size. For pig2 data, to account for potential variance heterogeneity between candidates for selection and non‐candidates , random effects were distributed as centred normal distributions with variance–covariance matrices equal to A⊗Gm for the maternal genetic effects, Gm=σmCS2σmCS‐NCσmCS‐NCσmNC2 where σmCS2, and σmNC2 are the maternal genetic variances for the candidates and non‐candidates for selection, respectively, and σmCS‐NC is their covariance effects, IlCSσlCS200IlNCσlNC2 for the litter effect, IeCSσlCS200IeNCσlNC2 for the residual effects. The transmissible value t was normally distributed with matrix Mσt2 (M⊗Gt for the pig2 dataset), where M is the unknown transmission relationship matrix. Considering that for an animal i born from sire s and dam d: ti=ωsts+ωdtd+εt,i, εt,i∼Nσt2), the M matrix is a symmetric matrix with 1s on the diagonal and ijr as off‐diagonal elements. In the case of two animals i,j with n common ancestors (l) rij=∑l=1nrij,l, with rij,l=ωskij,lωdqij,l, kij,l=kil+kjl, qij,l=qil+qjl, where kil, qil are the number of sire and dam transmissions between ancestor l and animal i, respectively; ωs and ωd are the unknown sire and dam path coefficients of transmission, respectively, subject to the following constraints: 0≤ωs≤1, 0≤ωd≤1, 0≤ωs+ωd≤1  they can be both lower than 0.5 in agreement with the vertical transmission of epigenetic marks , which runs much faster than the unconstrained transmissibility model. Selection was performed by comparing step‐by‐step nested models using LRT (REML estimation). In addition, variance heterogeneity between groups for the different random effects and correlations (different from 1) was also tested using LRT for the pig2 dataset using the animal model. All LRT tests for parameters on the boundary of their parameter spaces  were performed by accounting for the change in the asymptotic distribution of the likelihood ratio statistic under H0   and the batch effect (36 levels), and ADG, AMW, LMP, CY were fitted as covariates. A litter random effect was not included in the models because its variance did not differ significantly from 0. For the pig2 dataset, fixed effects were the sex (three levels), pen within group (32 levels), batch (99 levels), group*herd (four levels), group*pen_size (10 levels), group*ADG (ADG as a covariate), group*BF (BF as a covariate) and AMBW as a covariate for the non‐candidates for selection. Selected random effect was the litter effect. The variances of the transmissible values were not different between groups. Transmissible and maternal genetic correlations between groups did not differ significantly from 1. Consequently, a unique vector of transmissible values was considered for the two groups and the maternal genetic correlation was fixed to 1 in the analysis. For all the other random effects, the variances differed significantly between the candidate and non‐candidate groups. For the two rabbit datasets, fixed effects were combined effects of week*batch (210 levels for AGP39 and 240 levels for AGP59), week*sex (10 levels for AGP39 and 12 levels for AGP59), week*litter size (35 levels for AGP39 and 42 levels for AGP59), week*WADG (WADG as a covariate) and week*WMBW (WMBW as a covariate). Selected random effects were the week*litter combination and permanent environmental effects.ωdσt2σt2+σmt2+σlt2+σpt2+σet2 and sire transmissibility: ωsσt2σt2+σmt2+σlt2+σpt2+σet2, which correspond to half the heritability in the animal model. To test the hypothesis of non‐genetic inheritance: H0 “sire and dam coefficients of transmission are equal to 0.5” was tested against the H1 hypothesis “at least one of the coefficients of transmission (sire or dam) differs from 0.5.” The transmissibility and animal models were compared by performing a LRT of size 5% (mixture 12χ12+12χ22). Indeed, the animal model is a special case of the transmissibility model for which sire and dam coefficients of transmission are fixed to 0.5; it is nested in the transmissibility model and LRT can be applied. If the null hypothesis H0 is rejected, it can be concluded that the underlying model is not purely additive genetic and values of the sire and dam path coefficients of transmission give information about the other sources of inheritance . To compare the predictions of the two models, the correlation between the sire and dam transmissible values obtained with the transmissibility model  and the animal model (0.5 t^ for sires and dams) was then computed. In addition, the percentage of animals in common in the 10% best animals based on their transmissible was computed.The parameters of the transmissibility model  can be estimated with the restricted maximum‐likelihood method (REML) using ASReml and the OWN Fortran program developed by David . Paramet3SE) than the dam coefficient (0.39 vs 0.44). Even if not significant, we observed the same trend for the pig1 and AGP39 datasets: a lower value of the sire path coefficient of transmission compared with the dam path coefficient of transmission . On the contrary, the sire and dam path coefficients estimated in the AGP59 line were both equal to 0.5 indicating that for that rabbit line the transmissibility model was equivalent to the animal model, resulting in similar estimates for the different variance components of the models. For the three other datasets, the variances of the transmissible value tended to be higher than the variances of the direct genetic effects obtained with the animal model, especially for the pig2 dataset for which it was nearly two times higher. The sire and dam transmissibility estimates for these three datasets tended to be higher than those obtained with the animal model, indicating a stronger parent–offspring regression than that considered with the animal model.Parameter estimates obtained with the animal and transmissibility models are provided in Table When the breeding values were compared with the sire and dam transmissible values Table , we foun4We chose the transmissibility model to detect non‐genetic inheritance for RFI in two different species. Non‐genetic inheritance is assumed when at least one of the two path coefficients of transmission (sire or dam) estimated by the transmissibility model differs from 0.5. It has been shown that, conversely to a model that aims at dissociating genetic from non‐genetic inherited effects, the parameters of the transmissibility model are practically identifiable in most situations, which is its main advantage , sire and dam path coefficients of transmission were equal to 0.5, whereas in the three other datasets, the sire path coefficient of transmission tended to be lower than the dam path coefficient, although significantly different from 0.5 in the pig2 dataset only. Close inspection of the data structure  of both AGP59 and AGP39 datasets did not provide any insights that might explain this difference. An explanation could be the length of the test period which was longer for the AGP59 line compared with the AGP39 line. The impact of environment experienced by the animal on non‐genetic heritable effects may therefore have been more pronounced in the AGP59 line, resulting in a modification of the non‐genetic inherited effects that consequently differed more from those of the parents.® Xeon® E5‐2698v3 processor). To overcome this difficulty, we shall consider revising our program for estimating the parameters of the transmissibility model, which is currently based on ASReml, and to create a stand‐alone software dedicated to the transmissibility model. Research is underway on this subject. Finally, it should be noticed that standard errors of estimates were generally slightly higher in the transmissibility than in the animal model, which is certainly a consequence of the additional parameters to estimate.The power to detect non‐genetic inheritance with the transmissibility model increases with the size of the population, the deepness of the population structure , the relative importance of non‐genetic inherited variance, the difference between sire and dam path coefficients of transmission and the magnitude of their difference from 0.5 , we observed, as a general trend between the animal and transmissibility model, a decrease of the residual variance, maternal genetic variance and a higher transmissibility variance compared with the genetic variance. This confirms the confusion that exists between maternal genetic and non‐genetic inherited effects. The lower genetic variance compared with the transmissibility variance is explained by the use in the animal model of a set value for the path coefficients of transmission (0.5), that is generally too high. Consequently, to find the best fit for the covariances between the different types of relatives in the population, the genetic variance estimate is smaller than the transmissibility variance. However, it should be noted that for the pig1 dataset, the dam path coefficient estimated in the transmissibility model was higher than 0.50 (0.53), but the transmissibility variance was still slightly higher than the genetic variance due to the sire path coefficient of transmission being lower than 0.5 (0.46). Finally, our results suggest that phenomena other than genetic sources of inheritance explain the phenotypic resemblance for RFI observed between relatives, with a higher transmission from the dam's side than from the sire's side. It is likely that one of these non‐genetic inherited effects is the gut microbiota. Indeed, it has been reported in pigs and rabbits that the gut microbiota affects RFI. Microbiota might be crucial in improving FE in herbivores, because gut microbes hydrolyse the plant fibres that mammalian digestive enzymes cannot degrade  or higher than the transmissibility obtained with the animal model, the expected response to selection on direct effects  would be higher  with the transmissibility model. However, it is important to note that selection on transmissible values implies selection on a combination of genetic, epigenetic, microbiota and cultural inherited values. If selection is relaxed, part of the benefit on the transmissible value achieved by previous selection will theoretically gradually disappear and only genetic progress will be maintained (Tal et al., To conclude, this study aimed at detecting non‐genetic inheritance for FE in different species. The results obtained were not entirely consistent across species, but mainly support the existence of non‐genetic inheritance for this trait, with a higher path coefficient of transmission for the dam's side than for the sire's side.The authors declare that there is no conflict of interest regarding the publication of this article.


Walnut shell suture strength directly impacts the ability to maintain shell integrity during harvest and processing, susceptibility to insect damage and other contamination, and the proportion of kernel halves recovered during cracking. Suture strength is therefore an important breeding objective. Here, two methods of phenotyping this trait were investigated: 1) traditional, qualitative and rather subjective scoring on an interval scale by human observers, and; 2) quantitative and continuous measurements captured by a texturometer. The aim of this work was to increase the accuracy of suture strength phenotyping and to then apply two mapping approaches, quantitative trait loci (QTL) mapping and genome wide association (GWAS) models, in order to dissect the genetic basis of the walnut suture trait. Using data collected on trees within the UC Davis Walnut Improvement Program (n = 464), the genetic correlation between the texturometer method and qualitatively scored method was high (0.826). Narrow sense heritability calculated using quantitative measurements was 0.82. A major QTL for suture strength was detected on LG05, explaining 34% of the phenotypic variation; additionally, two minor QTLs were identified on LG01 and LG11. All three QTLs were confirmed with GWAS on corresponding chromosomes. The findings reported in this study are relevant for application towards a molecular breeding program in walnut. English walnuts grown in the United States are sold in-shell, primarily for export at 234,000 tons per year, and shelled for domestic market at 452,000 tons per year totaling 686,000 tons . The terShell suture strength is a key component of shell integrity, an important economic trait. Walnut shells need to remain intact during harvest and storage  to exclude dirt, insects, moisture, or other contaminates. Weak sutures are often the major entry points and can allow nuts to crack open during harvest or transport, resulting in crop loss. During walnut processing, nuts with weak sutures crack in the wrong direction, reducing or eliminating recovery of kernel halves , which hThe English walnut improvement program (WIP) at the University of California, Davis was initiated in 1949, has released over 20 cultivars, and is currently one of the most important walnut breeding programs worldwide. Shell suture strength, an important breeding objective, which has a strong genetic component, but also can vary with tree age. As a walnut tree matures, shells thicken and sutures often improve . ResearcTogether quantitative trait locus (QTL) mapping and genome-wide association studies (GWAS) can be successful in uncovering the genetic basis of complex traits . GWAS isThe objectives of this work were: 1) to develop a method for obtaining quantified measurements of suture strength on a continuous scale by using a texturometer machine, developed initially to characterize food texture , to streTable 1). The parental crosses were made between 2006 and 2013. Most male parents were used only once, a few males were used two to four times, and one male, ‘Ivanhoe’ was used 13 times; two males were also used reciprocally as females and vice versa. The largest family (n = 180) was a cross between ‘Chandler’, characterized by strong suture lines, and ‘Idaho’, which has weak suture lines, and it was utilized for the QTL mapping approach. All other families, 25 founder trees, and two cultivars ‘Robert Livermore’ and ‘Vina’, representing diverse germplasm from Afghanistan, China, Japan, and France, were included in the GWAS analysis. The range of ages for trees was 4–14 years, with an average of 7.21 years. Founder trees were grafted on RX1, or VX211 rootstock, clonal Paradox, or Paradox seedling. ‘Chandler’ × ‘Idaho’ F1 trees consisted of a mixture of grafted and seedlings on their own rootstock. The parental trees and seedlings utilized in this experiment were grown in 12 blocks at the UC Davis orchards. The founder trees were spaced 30 feet apart, the ‘Chandler’ × ‘Idaho’ trees were spaced 10 feet apart, while the seedling in all remaining blocks were spaced six feet apart. All blocks were watered with micro-sprinklers.A total of 736 walnut trees derived from 40 F1 families of the UC Davis WIP, with an average of 15 trees per family, were evaluated  were collected and phenotyped in 2015 and 2016. Walnuts were considered ‘mature’ when the hull easily separated from the shell. Harvested walnuts were placed in labeled mesh polypropylene bags, and air dried at 21°C for two weeks. The walnuts harvested in 2015 were stored in-shell in bins at -5°C and 81.65% relative humidity for a period of five months before evaluation. During the four months of evaluation, walnuts were stored in-shell in bins at 0°C and 87.90% relative humidity. The 2016 and 2017 harvested walnuts were placed directly in storage at 0°C and 87.90% relative humidity for a period of two months before evaluation and retained there for five months during evaluation.Fig 1). For an individual tree, walnut shells that were sizably smaller than the others were discarded; in addition, dried, desiccated kernels were discarded from the dataset . The application of force and the time required to deform the walnut shell were continuously recorded over a span of seconds. From these data points, using a custom macro, the integral of the force , the initial rupture, or first crack in the shell, and the maximum force (i.e. the maximum amount of pressure the shell could withstand without collapsing completely) were measured . Additionally, the texturometer was set as follows: pre-test speed 1.0 mm/sec, test speed 2.00 mm/sec, post-test speed 10.0 mm/sec, trigger force 0.005kg, return to start distance 4.0 mm, calibrated with 2.0 kg weight (S1 Table). Basic statistics , analysis of variance, and a simple linear regression were performed in R using packages ‘car’, ‘lme4’, ‘agricolae’, ‘ggplot2’, ‘lsmeans’ and ‘lmertest’ to compare the texturometer method with current manual evaluation-method. The Shapiro-Wilks normality test was performed to test normality of phenotypic data.From each individual tree, 15 walnuts were measured with a texturometer. From the 524 trees not in the ‘Chandler’ × ‘Idaho’ family, ten nuts per tree were cracked by hand with a hammer and scored for ease of separating the shell along the suture line using an interval scale from 1 to 9, where 1 = open suture, 3 = very weak suture, 5 = moderately strong, and 9 = suture much stronger than surrounding shell . With thy was the record of the individual tree, μ was the overall mean, a was the additive genetic value, and e was the error term. Year was fit as the only significant fixed effect, while the additive genetic values were fit as the only random effect. When considering only the texturometer methods, male parent, block, and year were added as fixed effects, and the additive genetic value was set as random. A conditional Wald F-test was used to test the significance of fixed effects in the model, and log-likelihood ratio test was used to choose the best model. A bivariate model was used to estimate the covariance of texturometer trait measurements to both manual evaluation and to Julian harvest date. A repeatability model was applied to assess the repeated observations that were acquired in the two-year dataset with all the same factors (year as fixed) as in the univariate and bivariate model. Narrow-sense heritability was calculated as defined: h2 = Va/Vp, the additive genetic variance divided by the phenotypic variance.The ASReml-R 3  softwareFor each individual tree, the mean of the texturometer data points was calculated on the 15 walnut measurements/tree. In order to obtain one value per individual for both years of data collection, the adjusted means were determined using the R package ‘lsmeans’, with block and year as fixed factors in the model. Phenotypic data was analyzed for each year separately and the adjusted means were calculated for both years.J. regia 700K SNP Array [Using the custom Axiom NP Array , 339K poGenetic maps were constructed in R package ASMap  utilizinJ. regia ‘Chandler’ reference genome v.2.0 (available at https://www.hardwoodgenomics.org/Genome-assembly/2539069).Linkage groups were oriented and numbered according to the SNP physical locations onto the new chromosome-level assembly of the scanone) with both maximum likelihood and “Haley Knott” regression algorithms [scantwo) in order to assess interactions and possible linkage of multiple QTLs. Interval mapping results were then compared with multiple QTL (MQM) [fitqtl. To adjust QTL locations in a multiple QTL model, the function refineqtl was utilized.QTL mapping was performed using the R package ‘R/qtl’ . Simple gorithms . Bayes 0TL (MQM)  mapping TL (MQM) . To estiQuality control of SNPs was performed prior to GWAS. Using PLINK 1.9 , only SNJ. regia 700K SNP Array [In order to evaluate the structure of the mapping population, principal component analysis (PCA) was utilized. Different filtering parameters were applied from those described above: Poly High Resolution SNPs generated with the Axiom NP Array  were disNP Array . A screeThe estimated breeding values that were generated from variance components calculations in R-ASReml 3  were useMapchart v2.32 was used for visualization of QTL maps . R packaJ. regia database mapped onto the new chromosome-level assembly of the J. regia ‘Chandler’ reference genome v2.0.Blocks of linkage disequilibrium around the most significant trait-associated loci were defined with Haploview 4.2 using the default algorithm of , where LS1 Fig). Age and block were not significant factors in the linear model when estimating ANOVA, while year of harvest was a significant factor.For the two-year dataset (2015–2016) on the 526 individuals, the proportion of within family variance for integral measurements was determined to be 22%, while the proportion of among family variance was 77%. With inclusion of the ‘Chandler’ × ‘Idaho’ dataset, the proportion of within family variance decreased to 19.21%, and the proportion of among family variance increased to 80.64%. Suture strength phenotypic data collected in 2015, 2016 and 2017 were found to be significantly different from each other . The data was not normally distributed, according to the Shapiro-Wilks normality test (ρ < 0.05), and outliers were removed from further analysis. For the 24 families that contained more than 10 individuals, family 11–011 (95-026-16 × 03-001-3382) had the highest Least Square Mean (LSM) score , while family 11–029 (03-001-665 × 01-007-2) had the lowest LSM score . The ‘Chandler’ × ‘Idaho’ family walnut shells displayed a great amount of diversity in size and shape (Table 2). For texturometer-based methods, the additive genetic component for initial rupture, integral and maximum force was much higher than environmental variance, and therefore high heritability was observed for all traits . When considering block as a random effect, the proportion of block variance was estimated to be 9.75%, and when estimating family or male parent effects, the proportion of family variance was found to be 1.96% while the proportion of male parent variance was 13.11%. For the manual evaluation, the proportion of block variance was not significant (ρ > 0.05), and therefore it was not considered in the model. The estimated breeding value coefficient of variation for texturometer was found to be about ten times higher than that of the manual evaluation method (Table 2). When considering only ‘Chandler’ × ‘Idaho’ mapping population (n = 180) the environmental variance increased to 33–40% for texturometer phenotypes and therefore narrow-sense heritability estimates were lower than the individuals in the breeding program (S2 Table). For the ‘Chandler’ × ‘Idaho’ dataset, year and age of tree were significant factors in the model. When performing the analysis on all individuals including the Chandler’ × ‘Idaho’, narrow-sense heritability for texturometer phenotypes (0.79–0.81) was higher than when only considering the mapping population (S3 Table).With the manual evaluation method, additive genetic variance was found to be lower than environmental variance, which corresponded to its low narrow-sense heritability of 0.16 (S4 Table); cultivars Chandler, Vina, Hartley, Tulare, and S. Franquette had lower breeding values for the integral trait than for the seedlings in the UC Davis WIP. Individuals from the families 11–011 (95-026-16 × 03-001-3382), 10–016 (00-005-44 × 03-001-2357), 09–028 (95-027-38 × 95-007-13) and 11–030 (04-003-107 × Ivanhoe) were found (S4 Table) among the top 20 individuals for suture strength. Estimated breeding values based upon manual evaluation resulted in categorical data that was restricted to scores between 4.3 and 5.3 , while for the texturometer phenotypes, the EBVs were continuous and normally distributed on scale between 10–45 kg of force applied .Estimated breeding values (EBVs) of top 20 individuals with highest integral values  are displayed in (2G > 0.60) between integral and manual evaluation initial rupture and maximum force, while harvest date and integral were poorly correlated .There was high correlation . The ‘Idaho’ genetic map consisted of 1,753 markers for a total length of 1,693.88 cM and an average distance between markers of 0.70 cM .The ‘Chandler’ genetic map was arranged on 16 linkage groups with a total of 1,165 markers, a total length of 998.31 cM, and an average distance between markers of 0.9 cM (Table 3). Five QTLs were also detected on LG1, LG09 and LG11 of ‘Idaho’, explaining 3.86–17.12% of the phenotypic variation (Table 3). In addition, the CIM algorithm detected the same QTLs in which the SIM and MQM algorithm detected  regression algorithm and MQM mapping, five QTLs in total were detected for the three texturometer-based measures on LG05 and LG11 of ‘Chandler’, explaining 1.9–25.8% of the phenotypic variation .The total amount of SNPs utilized for PCA after filtering was 45,441. By looking at the entire dataset of 730 individuals of the UC Davis WIP, PC1 accounted for 12.46% of the genetic variation and PC2 for 9.10% of the variation. The ‘Chandler’ × ‘Idaho’ population is quite distinct from the other individuals of the breeding program, and the founders are on the opposite side of each other along the PC1. Parents of the other families are dispersed across the PCA plot (Table 4). Two significant associations were determined on Chr05 for the manual evaluation phenotype, which were in moderate LD and 300 kb away from each other ; the MLMM detected association was in high LD with the locus associated with the integral phenotype 1.86 Mbp away, .Sixteen significant genotype-to-phenotype associations were detected in total . The significant associations detected with FarmCPU algorithm were consistent with associations detected with MLMM, with the addition of significant loci at or near the threshold for the texturometer methods on Chrs 01, 02, 07, 08, 09, 11, 13.Utilizing the texturometer phenotypes, five significantly associated SNPs were identified on Chr05 using the MLMM algorithm, and were consistent for all phenotypes and no other associations were determined . Both maximum force and initial rupture significant loci were in LD with the two SNPs associated with integral phenotype , 179 Kb and 269 Kb away (same LD block of 436 Kb) and even at distances 1.39 Mbp away  . The SNP on Chr05 associated to the manual evaluation trait was found to be in a distant LD block 1.45 Mbp apart from the texturometer LD block . Most significant SNPs for both manual evaluation and texturometer phenotypes had negative effects, for the alternative allele . Physical positions of the most significant SNPs in GWAS are in overlapping chromosomal regions for QTLs on LG05 and LG11 in ‘Chandler’ .Candidate genes were identified for texturometer phenotypes on Chr05. FAR1 was identified for maximum force and integral. It plays a role in growth and development with light perception capture via phytochrome signaling . PeptideSuture strength in nuts is poorly understood because there has not been a universal method of measurement. We describe a quantitative phenotyping method for measuring the strength of walnut shell suture and demonstrate its usefulness in improving the ability to discriminate between strong and weak sutured individuals by decreasing the variability inherent in subjective phenotyping.In line with our texturometer findings, other studies have measured the suture strength of walnut ,8 and ma2, while the texturometer method gave a moderately high heritability, and thus more accurately predicts suture strength. In comparing variance components, the texturometer method gave a lower residual error than manual evaluation, indicating reduced phenotyping error. Progress in suture strength over time in the UCD WIP is indicated by breeding values of seedling trees higher than that of the founders.Narrow-sense heritability is a measure of how strongly the phenotype is correlated with genotype . In our Our phenotyping method based on a texturometer indicated that the integral measurement can most accurately account for total energy required to rupture the walnut shell suture because it considers the total stress and strain placed upon the suture, rather than force alone. A computerized penetrometer was used similarly in an apple breeding program to accurately select top performing individuals , and a dWe observed some degree of the Beavis effect  between Marker-trait associations enabled us to discover, for the first time, the relatively simple control for the suture strength trait in walnut. We performed a combined approach of QTL mapping and GWAS analysis in order to identify specific loci contributing to trait variation. While we observed that the manual evaluation method was able to detect significant loci in GWAS analysis, the significance was just at the threshold line and the SNP was further away from the candidate gene detected with the texturometer methods. The texturometer methods yielded a higher heritability and genetic positions that were in high LD with each other, contributed to greater amount of variance, and were much more highly significant than the manual evaluation.These statistical associations are important for the development of molecular markers to be tested and applied in breeding programs, use of which will aid in quick and accurate parental and seedling selection of individuals with appropriate and moderate shell suture strength. The use of machines for phenotyping to replace human measurements can increase the accuracy of breeding in phenotypically based breeding programs. Here we have also shown that quantitative phenotyping was necessary to detect precise marker trait associations. We utilized the power of both QTL mapping and GWAS to determine causative loci for the suture strength trait, which can now enable genomic predictions, and can contribute to marker-assisted development.S1 FigA. = 3 suture-lined, B. = protrusion, C. = small, D. = dessicated, E. = “normal”.(TIF)Click here for additional data file.S2 FigA. ‘Chandler’ genetic map with 1165 markers. B. ‘Idaho’ genetic map with 1753 markers.(TIF)Click here for additional data file.S3 FigA. ‘Chandler’ Chr05. B. ‘Chandler’ Chr11. C. ‘Idaho’ Chr01. D. ‘Idaho’ Chr11.Positions highlighted red are significant marker-trait associations. (TIF)Click here for additional data file.S4 FigA1. Initial rupture genome-wide scan, A2. Initial rupture chromosomes 5 and 11, B1. Integral genome-wide scan, B2. Integral chromosomes 5 and 11, C1. Maximum force genome-wide scan, C2. Maximum force chromosome 5 and 11.Simple interval mapping displayed in blue, composite interval mapping displayed in red, covariate displayed in green. (TIF)Click here for additional data file.S5 FigA1. Initial rupture genome-wide scan, A2. Initial rupture chromosomes 1, 9, and 11, B1. Integral genome-wide scan, B2. Integral chromosomes 1, 9, and 11, C1. Maximum force genome-wide scan, C2. Maximum force chromosome 1, 9, and 11.Simple interval mapping displayed in blue, composite interval mapping displayed in red, covariate displayed in green. (TIF)Click here for additional data file.S1 TablePre-test speed is the speed of probe prior to test start, Test-speed is the speed at which the probe moves for the duration of the test, Post-test is the speed at which the probe returns to the start position, Trigger force is the resistance at which the probe is sensitive to as it presses the walnut, Return to start distance is the amount of compression of the probe to the walnut shell, Calibration was performed prior to each set of tests with a 2 kg weight.(XLSX)Click here for additional data file.S2 TableEBV μ mean, EBV σ standard deviation, EBV CV coefficient of variation, VAadditive genetic variance, VRresidual genetic variance, h2narrow-sense heritability, r repeatability.Harvested data collected in 2016, 2017 for 181 individuals. (XLSX)Click here for additional data file.S3 TableEBV μ mean, EBV σ standard deviation, EBV CV coefficient of variation, VAadditive genetic variance, VRresidual genetic variance, h2narrow-sense heritability, r repeatability.Harvested data collected in 2015, 2016, 2017 for 736 individuals. (XLSX)Click here for additional data file.S4 TableThe first 5 entrees are standard cultivars displayed for comparison.(XLSX)Click here for additional data file.S5 TableA for each trait were calculated and rescaled to give genetic correlations between traits r2G .Covariance components, COV(XLSX)Click here for additional data file.S6 TableFCPU is FarmCPU model. Trait abbreviations I = integral, ME = manual evaluation, IR = initial rupture, MF = maximum force, ID = ‘Idaho’, CR = ‘Chandler’, 16 = 2016, 17 = 2017.(XLSX)Click here for additional data file.S1 File‘Chandler’ × ‘Idaho’ phenotypic dataset utilized for QTL mapping.(XLSX)Click here for additional data file.S2 FileGWAS panel of individuals within the UC Davis WIP.(XLSX)Click here for additional data file.


The traditional approach to biomarker discovery for any pathology has been through hypothesis-based research one candidate at a time. The objective of this study was to develop an agnostic approach for the simultaneous screening of plasma for consistent molecular differences between a group of individuals exhibiting a pathology and a group of healthy individuals. To achieve this, we focused on developing a predictive tool based on plasma for the amount of brain amyloid-β deposition as observed in PET scans. The accumulation of brain amyloid-β (Aβ) plaques is a key risk factor for the development of Alzheimer’s disease. A contrast was established between cognitively normal individuals above the age of 70 that differed for the amount of brain amyloid-β observed in PET scans (INSIGHT study group). Positive selection was performed against a pool of plasma from individuals with high brain amyloid and negative selection against a pool of plasma from individuals with low brain amyloid This enriched, selected library was then applied to plasma samples from 11 individuals with high levels of brain amyloid and 11 individuals with low levels of brain Aβ accumulation. Each of these individually selected libraries was then characterized by next generation sequencing, and the relative frequency of 10,000 aptamer sequences that were observed in each selection was screened for ability to explain variation in brain amyloid using sparse partial least squares discriminant analysis. From this analysis a subset of 44 aptamers was defined, and the individual aptamers were synthesized. This subset was applied to plasma samples from 70 cognitively normal individuals all above the age of 70 that differed for brain amyloid deposition. 54 individuals were used as a training set, and 15 as a test set. Three of the 15 individuals in the test set were mis-classified resulting in an overall accuracy of 80% with 86% sensitivity and 75% specificity. The aptamers included in the subset serve directly as biomarkers, thus we have named them Aptamarkers. There are two potential applications of these results: extending the predictive capacity of these aptamers across a broader range of individuals, and/or using the individual aptamers to identify targets through covariance analysis and reverse omics approaches. We are currently expanding applications of the Aptamarker platform to other diseases and target matrices. Improvement in disease diagnostics is key to developing effective treatments for a variety of pathologies. Identification of biological markers specific to a stage and/or type of pathology is crucial to developing effective treatments. Diseases such as Crohn’s disease, pancreatic cancer, lupus, nonalcoholic steatohepatitis (NASH), and Alzheimer’s disease are all in need of greater understanding of disease pathology and biomarker identification.In Alzheimer’s disease, the over-accumulation of brain amyloid-β (Aβ) is one of the earliest pathomechanistic alterations characterizing the complexity of AD , 2. In sRecent successful achievements with the analysis of Aβ peptide ratios in blood are encouraging as less expensive and minimally invasive means of detecting AD-related pathophysiological dynamics in the preclinical stages of the disease –7.With this in mind, we set out to develop a biomarker-based diagnostic method to screen for molecular differences between cognitively normal individuals above the age of 70 with varying levels of amyloid-β brain deposition based on phenotypic contrasts. Using deep data work to agnostically enable the identification of blood-based biomarkers specific to AD pathology, we apply aptamer library selection, Next Generation Sequencing (NGS), and an analysis of aptamer frequency across individuals to develop an Aptamarker  approachIt would seem that nature chose proteins as the means of enabling antigen detection through antibodies rather than oligonucleotides because the diversity of side chains within twenty amino acids provides higher levels of information potential than the diversity of nucleotides within four nucleotides. With traditional aptamer selection this constraint is overcome through the use of a naïve library of 1E15 random sequences, which is larger than the predicted naïve library of antibodies present in humans (1E6 to 1E7) . The immin vivo without a need to immobilize these targets first.A primary challenge with aptamer selection is parsing aptamer sequences that bind to a target molecule from those that do not. In traditional SELEX approaches, this is achieved by immobilizing the target and washing away aptamer sequences that do not bind. However, target immobilization compromises the capacity of selection, as the act of complexing a target molecule to a support structure can result in a shape or complex that would not exist outside of the immobilization system. We invented FRELEX  to enable the partitioning of bound aptamers from unbound aptamers in a way that does not rely on target immobilization, allowing us to select aptamers against all of the complexes found among the molecular constituents of plasma in their native state. In this study, we are able to screen for aptamers that optimally bind to biomarkers in plasma that are enriched in amyloid-β brain deposition biomarkers as they would naturally appear Using these approaches we have developed the concept of the Aptamaker, wherein aptamer binding within a system–in this case, pooled serum from individuals with brain amyloid-β deposition–can act directly as biomarkers themselves. The relative frequency of the Aptamarker is a surrogate for the relative frequency of the biomarker it binds to.This study represents the first application of the Aptamarker platform to the examination of human blood samples and development of a potentially effective screening and diagnostic tool for AD that can replace the expensive and invasive PET scan/CSF analysis.5’ AACTACATGGTATGTGGTGAACT (N40) GACGTACAATGTACCCTATAGTG 3’ . Primers used for amplification were purchased from Integrated DNA Technologies.The ssDNA library for selection was composed of a 40-mer random region flanked by two constant regions for primer hybridization INveStIGation of AlzHeimer’s PredicTors in Subjective Memory Complainers” (INSIGHT-preAD) study, a French academic university-based cohort which is part of the Alzheimer Precision Medicine Initiative (APMI) and its Cohort Program (APMI-CP) . The last subset was characterized on a BioRad CFC instrument in an identical manner except that reactions were performed for 35 cycles instead of 30.Cq values were calculated on the basis of the derivative of each amplification cycle exceeding six standard deviations of the average derivative from PCR cycles 3 to 10. PCR efficiency was calculated by determining the slope of the increase in fluorescence from the Cq value to the Cq value characterized as nearest to the maximum derivative across cycles. Cq values from the BioRad instrument were calculated by the internal BioRad software.22. The use of sPLS-DA is motivated by its dimension reduction effectiveness through the construction of a small set of orthogonal components (latent variables) summarizing the manifest Cq values. All of the Aptamarker values and the ratios between them are considered variables. We only computed the ratios in one direction. This still means however that the number of variables far exceeds the number of samples analyzed and as such increases the risk of spurious relationships between variables and variance for Aβ brain deposition. The sparse component of this package enables us to reduce the number of variables and dimensions in which variance is considered to mitigate this problem.All statistical analyses were performed using the R software program (version 3.4.4) . To asseA predictive model was built based on a random sample of 54 individuals from the 70 individuals analyzed. One individual sample was excluded from the analysis as an outlier. This left an additional 15 individual samples as a test set. For data analysis, ratios of all Cq values from the 54 samples were determined and added to the Cq values alone as a combined dataset. This data set was normalized to zero mean and standard deviation of unity for each Cq value or Cq value ratio. This normalized matrix was then used as explanatory variables in sPLS-DA to account for the Aβ brain lesion status, categorized as negative “neg” or positive “pos” based on a SUVr threshold of 0.79.In addition, a cross-validation analysis was performed with sPLS-DA with a manual k-folds analysis. Alternative sets of 54 training samples and 15 test samples were chosen 5 times. An sPLS-DA model was created with each of the iterations of the training set and applied to the test set. We allowed the sPLS-DA to normalize the training set to mean = 0 and standard deviation = - 1. We used the mean and the standard deviation from these training sets to apply the same normalization to the test sets. The predicted values for the test set were evaluated for whether they predicted low or high amyloid by subtracting the mean of the negative samples in the training set from the observed value, and dividing by the standard deviation of the negative samples in the training set, and likewise for the positive samples in the training set. The value that was the closest to zero arising from this evaluation was used to establish the low or high amyloid prediction.The overall number of samples was too small for us to evaluate the effect of genotype or sex on the model. A difficulty with sPLS-DA model fitting is that when the model is unbalanced in the sense that one class of individuals outweighs the other class considerably, the model tends to favour the more dominant class at the expense of predicting the less dominant class appropriately. With partitions for either sex or ApoE genotype the model failed because of unbalanced training sets. Both sex and genotype will be considered fully in our current work with a larger data set.The sPLS-DA analysis of the 54 training samples resulted in the retention of 961 variables, all explaining variance in one principle component. The loading values of these 961 variables were distributed as shown in We applied this mathematical model to the Aptamarker results obtained with 15 samples that were not part of the initial training set with the following confusion matrix result.                   Aptamarker negative    Aptamarker positivePet scan negative                   6                    2Pet scan positive                   1                    6This results in a sensitivity of 85%, a specificity of 75% and an overall accuracy of 80%. The distribution of the individual 15 test samples based on their predicted values is provided in We determined that by including only those variables that exhibited loading values greater than 0.04 or less than -0.04 this confusion matrix was maintained. This reduces the number of variables necessary within the prediction to 245. The inclusion of an individual Aptamarker in a ratio value varied from a minimum of three ratios to a maximum of 37.The average result from the cross-validation analysis was 70% for sensitivity, 59% for specificity and 65% for accuracy. These values demonstrate that the model as it stands is not sufficiently robust for commercial development. There is a need to improve this model through analysis of more samples.By training our enriched aptamer library against a random sample of 54 individuals from the original INSIGHT-preAD group pool, and applying it to the remaining relevant 15 individuals, we observed a predictive accuracy of 80%, with 86% sensitivity, and 75% specificity for brain amyloid deposition. The cross-validation exercise resulted in lower predictive accuracy (65%), lower sensitivity (70%) and lower specificity (59%). These values demonstrate that the interpretation of the Aptamarker patterns across the individuals can be used to explain a portion of the variation for brain amyloid deposition on the basis of aptamer binding to biomarkers in plasma. We have designated the overall process as the Aptamarkers platform.1–42 concentrations and elevated CSF total tau (t-tau) or hyperphosphorylated tau (p-tau) concentrations or positivity to Aβ-PET . This will demonstrate whether the variance in the trait that we are explaining using the Aptamarkers platform is identical or whether this strategy represents an added value to the variance obtained by the established core biomarkers.To further these results, we are looking to integrate this approach with the results obtained using traditional core pathophysiological biomarkers for AD diagnosis across the same samples: low CSF AβThe concept of using aptamer frequency following a single round of selection as a characterization of the concentration of the targets that aptamers bind to and the subsequent use of aptamers directly as biomarkers is an entirely new concept. The investigation reported herein resulted in a predictive capacity that is similar to that achieved in plasma with Aβ peptide ratios. This is sufficiently encouraging for us to expand this research with increased sample quantities.Additionally, we are developing mathematical models to assess the efficacy of the aptamer library selection and to further refine the way aptamers are chosen for the third step in the Aptamarker platform.The evaluation of the second step of the platform–characterization of candidate aptamers through a single round of selection and NGS analysis–is prone to an over-fitting error, given that the number of variables (sequence frequency of aptamers) far outnumbers the number of samples. Different aptamers are chosen as meaningful arising from this step depending on the iteration of the model building software (different random seeds). We are also working on the development of a rigorous process that will enable the identification of meaningful sequences from this data set that recur most frequently. We are building a statistical model to support this aspect of the analysis.In terms of developing a comprehensive diagnostic tool for AD, as well as other diseases, on an individual level, the Aptamarkers platform approach hold promise. The Aptamarkers platform allows the unbiased assessment of differences in plasma samples independent from the type of the biological molecule . As suchThe Aptamarkers platform can be represented as a trade for increased depth of analysis  in exchange for a loss of information regarding the biological nature of the biomarkers. From a diagnostic viewpoint, the nature of the specific biomarker and/or its potential role in the pathophysiology of the disease is not necessary. It is only required to demonstrate that the biomarker provides a statistically relevant diagnosis of the disease. It is entirely feasible to use the Aptamarkers platform as a tool to discover the molecular entities that they bind to by immobilizing each known Aptamarker sequence in an affinity column and passing plasma through it. Given the broad spectrum of potential targets, including proteins, peptides, oligonucleotides, metabolites, and combinations of these molecules, this use of aptamers to discover the identity of the actual biomarkers is not trivial.A key concern regarding the application of this platform the subject of measurement is unknown in that we do not know what the aptamers are binding to. This concern can be addressed in several ways:The existing relationship between a biomarker and a disease state does not need to be known in order to be useful. The advent of genomic analysis has led to the correlation of genetic variation in proteins of unknown function with the propensity to develop a disease. These correlations are necessarily included in predictive models.The most important concern for a clinician is to correctly diagnose a disease state. Knowledge that a biomarker may be related to a pathophysiological basis for such a state may be of scientific comfort but in practical terms in terms of prescribing treatments is not as important as the statistical correlation between diagnosis, treatment choice and treatment outcome.There are biomarkers that are routinely used in healthcare where the association with the disease is either unknown or tentative at best. For example, with Alzheimer’s disease the using Apo E genetic status as a predictor for the potential to develop the disease. Pathophysiological hypotheses to support the strong statistical correlation are currently being built and tested, but this was driven by the statistical correlation, not the evident relationship with the pathology.It is possible to use the Aptamarkers that we discover to identify what they bind to. The primary difficulty in this approach is the technical constraints involved in identifying complexes between metabolites and mis-folded or non-trypsin-digested peptides, not the ability to use aptamers to pull out specifically bound molecules. We postulate that a more effective approach to identifying binding will be through covariance analysis in association with hypothesis.The identification of Aptamarkers is not trivial, however their application once identified is straightforward. The process only involves a single positive FRELEX selection on a gold chip, followed by characterization with the Aptamarkers platform through qPCR analysis. This is simple to perform, does not require expensive equipment, and the results are highly reliable (CV < 5%). The platform as it has been developed could be automated and scaled, making it a potentially valuable diagnostic resource.Considerable development work is required before commercialization of this approach can be considered. We consider the predictive capacity demonstrated herein for this test as encouraging for analysis of a larger number of samples, further refinement and improvement of the test. The significant correlation between Aβ deposition across the twelve samples predicted correctly was also encouraging given that all training of mathematical models was based on binary separation of low and high amyloid. The observation of such a significant relationship to actual Aβ deposition levels was unexpected and is encouraging in terms of the Aptamarkers describing aspects of the pathophysiology of the disease.The Aptamarker platform is intriguing because of the agnostic nature of the aptamer selection. This approach allows screening of all possible molecules in blood, proteins, metabolites, non-coding RNA and complexes formed among these molecules for possible relationship to the pathophysiology or pathophysiologies underlying not only an early risk factor for Alzheimer’s disease such Aβ brain deposition, but the pathophysiology of any disease. Efforts are currently underway within our laboratory to extend this application beyond Alzheimer’s disease into other types of diseases.


For complex diseases, genome-wide pathway association studies have become increasingly promising. Currently, however, pathway-based association analysis mainly focus on a single phenotype, which may insufficient to describe the complex diseases and physiological processes. This work proposes a combination model to evaluate the association between a pathway and multiple phenotypes and to reduce the run time based on asymptotic results. For a single phenotype, we propose a semi-supervised maximum kernel-based U-statistics (mSKU) method to assess the pathway-based association analysis. For multiple phenotypes, we propose the fisher combination function with dependent phenotypes (FC) to transform the p-values between the pathway and each marginal phenotype individually to achieve pathway-based multiple phenotypes analysis. With real data from the Alzheimer Disease Neuroimaging Initiative (ADNI) study and Human Liver Cohort (HLC) study, the FC-mSKU method allows us to specify which pathways are specific to a single phenotype or contribute to common genetic constructions of multiple phenotypes. If we only focus on single-phenotype tests, we may miss some findings for etiology studies. Through extensive simulation studies, the FC-mSKU method demonstrates its advantages compared with its counterparts. Recent years, genome-wide association studies (GWAS) have successfully identified common genetic variants underlying complex diseases. However, traditional GWAS focus on the relationships between single nucleotide polymorphisms (SNPs) and single phenotypes, which can only explain a small portion of heritability . FurtherHowever, most diseases and physiological processes are complex and comprehensive, and not just a single phenotype variable can be fully described. For example, body mass index (BMI) cannot fully represent the obesity characteristics associated with cardiovascular and cerebrovascular diseases. It only roughly measures the average body weight for a given surface area but cannot express the distribution of fat. Studies have shown that three phenotypes  can better reflect the risk of cardiovascular and cerebrovascular diseases . MultiplFor multiple phenotypes analysis, the multivariate analysis of variance (MANOVA) makes an regression of a single SNP on multiple phenotypes, which selects the SNP leading to the smallest p-value (in a gene or pathway) as the gene or pathway level p-value , 12. HowCurrently, for complex diseases, most pathway-based association studies focus on a single phenotype. It is a natural choice to extend genome-wide pathway-based single phenotype association tests to pathway-based multiple phenotypes analysis. Here, we propose a combination model. In the first part, we introduce a pathway-based method, the semi-supervised maximum kernel-based U-statistic (mSKU) to evaluate the effect  of a pathway on a single phenotype. It has also given strategy to further release the computation burden based on asymptotic results under the setting of high-dimensional. Specially, mSKU considered a semi-supervised testing procedure (a SNP screening step) , 18 at tKij = K to justify the similarity of the i-th and j-th samples. There are several widely used kernel functions: the linear kernel  = xiTxj+c), Gaussian kernel  = (αxiTxj+c)d) functions. If we assume the h (⋅) function denotes the real relationship between a pathway and a phenotype, then different kernel functions generate different “beliefs” about the “real” functions. If the optimal kernel is used, the corresponding KBT test will achieve the maximum power. However, in practice, the optimal h(⋅) function is usually unknown [K1,K2,……,KM) kernel functions.The method is built upon kernel-based test (KBT) . A kerne unknown . Here, wp−‖xi−xj‖σ2) and pS1 Appendix in K1,K2,……,KM) kernel functions, they selected the maximum statistic as the final test statistic. Selecting the mKU test statistic is equivalent to the minimum p-value method. However, the minimum p-value method has to bear computational burdens such as permutation to evaluate the statistical significance. Here, the mKU method focuses on the maximum test statistic and takes advantage of the derived asymptotic normality to decrease the calculation pressure under the high-dimensional assumption.Tao et al  proposedTn,m and m = 1,……,M. The p‐value is completely determined by Qm, so maximizing Qm means minimizing a nonlinear function of p-values. The formula for the maximum statistic can be described as follows:Let nρkl,n = cov as n→∞ for k,l = 1,……,M. Assuming that each candidate kernel Km satisfies condition (1), thenZ1,Z2,……,ZM)T obeys a multivariate normal distribution  normal distribution to higher dimensions.) with mean OM and covariance matrix Definite The maximum test strategy has several advantages. First, it achieves the best power among the candidate kernel functions. Second, by taking advantage of asymptotic normality proved in this study, the computational burden is greatly reduced and the results are protected from being overly conservative or inflated. Third, it is suitable for high-dimensional cases and performs well in the calculations. When the number of variants in a pathway is large enough, the proposed method is safe to apply.Some researchers considered that without a SNP screening step, using all SNPs to summarize information from a pathway can result in reduced test power for pathway analysis, because of the inclusion of SNPs unrelated to disease , 18, 23.For each SNP, we fit a logistic regression model to compute an association measure with the genotype  as the predictor and the disease status as outcome variable.i-th SNP, let pi be the p-value of single SNP .For αm, let Δm = {SNPi∈G:pi<αm,i = 1,…,nSNP} be subset of SNPs below the threshold with association measures. In this paper, we set αm = 0.05.For a given threshold As performing a univariate association test is much easier than performing a multivariate association test, combining p-values of marginal tests to form joint statistics has become a popular tool to address genetic variants associated with multiple phenotypes . By compp1,p2,……,pk; Under the null hypothesis, Yang et al [ beta distribution. This distribution arises naturally, and the waiting time between the Poisson distributed events are relevant to each other.) with scale parameter 2α and shape parameter β/2. Therefore, if the parameters of α and β are estimated, the global p-value of T can be correspondingly obtained. If we define the mean of T as μ and the variance of T as σ2, then the corresponding α and β can be computed as α = σ2/2μ and β = 2μ2/σ2. The technical details of the derivation of μ and σ2 are shown in S2 Appendix in With the Fisher combination method, to test the association between a pathway and multiple phenotypes, we only need to test the association between the pathway and each marginal phenotype individually.function , which ing et al  showed tβ/2,2α) is the function of the gamma distribution with scale parameter 2α and shape parameter β/2. Thus, we have adjusted k marginal p-values  to a combined p-value, which is promising way for exploring the relationship between a pathway and the correlated multiple phenotypes.The global p-value of the T statistic can be calculated by a gamma distribution function:https://github.com/SAONLIB/RMMLR. Jaeyoon Chung et al. [We demonstrated the performance of our FC-mSKU method by extensive simulation studies and compared the proposed method with methods of multivariate multiple linear regression (RMMLR), MultiPhen-GATES and O’Brien-VEGAS. Through transforming the genotype and phenotype dataset, RMMLR proposed by Saonli Basu et al.  is an img et al.  combinedhttps://sourceforge.net/projects/episimsimulator/.In this study, we applied EpiSIM software  to simulϵki  are random errors of t-dim with a multivariate normal distribution; Yki  are t-dim multiple phenotypes; Zi1~N and Zi2~Ber(0.6) stand for independent covariates; Xi are p-dim SNPs in the pathways. Under each scenario, we simulated 1,000 replicates and set the significance level to 0.05. Under the null hypothesis  = 0), we recorded the proportion of results that did not correctly reject the null hypothesis to assess the type I error rates. To assess the power, we set up four scenarios for the h(∙) function and recorded the proportion of results that correctly rejected the null hypothesis. Under Scenario M, we supposed h(x) = 0.27(x5−x10)+cos(x10)exp(−x102/5), where the tenth SNP had nonlinear effects on the five response phenotypes, and the fifth and tenth SNPs had different directions of main effect. Under Scenario N, we presumed h(x) = 0.37x5+0.62x10−0.06x15, where these three SNPs were marginally linearly associated with the multiple phenotypes without inner interaction. Here, to further test the situations when large numbers of SNPs affected the multiple phenotypes, we set the following model:HP was predefined as a set of 60 SNPs with main effects and HQ was predefined as a set of 90 SNP pairs representing 90 simple interactions. Both {αm,m∈HP} and {βmm′,∈HQ} were independently obtained from a Unif  distribution, and the parameters were fixed once they were generated for all the simulation replicates. Under Scenario P, we defined the coefficient as  = , which means a combination of relatively strong interaction influence and a weak main effect. Under Scenario Q, we set up  =  to predefine a model with a pure main effect.We simulated related quantitative phenotypes with the following model:With ρ = 0.7, the testing power of the four methods is shown in http://www.loni.ucla.edu/ADNI).Study resources and data from the North American ADNI study are available through this website, including Alzheimer’s disease patients, mild cognitive impairment subjects, and elderly controls. Alzheimer Disease (AD), which is caused by brain tissue deterioration, is an irreversible neurodegenerative disease. AD affects over approximately 5.5 million Americans, especially among people over the age of 65, and there are no prevention methods, and no cures have been discovered. Aiming at the early detection of AD and tracking its development, the ADNI is a longitudinal multicenter study to develop clinical, imaging, biochemical biomarkers and genetic analysis of AD.One of the most ubiquitous phenomena in natural populations is the variability in numbers. One of the most challenges in population and ecology is to explain and understand the variety and to find the possible underlying variation that may be modified from case-to-case. In this study, we propose the FC-mSKU method to explore the variation of pathways associated with the multiple phenotypes. We applied it to the dataset from the Alzheimer Disease Neuroimaging Initiative (ADNI) study. Data used in preparing this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database  and the whole brain. In total, 490 samples were screened from the ADNI1 and ADNI2 studies, and we only selected the samples with both complete phenotypic information for the volumes of brain cortical regions and complete genetic information. We excluded the SNPs with low MAFs  <0.05 or failed to pass through the Hardy-Weinberg exact test. The total number of SNPs eventually included in the research was 620,901. And they were further mapped into 315 pathways through the KEGG (Kyoto Encyclopedia of Genes and Genomes) by the clusterProfiler R package. On the one hand, it is well known that the volume of the whole brain is significantly reduced in patients with AD [S1 Fig in For each cortical region, we performed a pathway-based genome-wide association analysis with the mSKU method. The Q-Q plots of p-values for the five individual phenotypes are shown in https://www.synapse.org/#!Synapse:syn4499). We chose the activity measurements of the P450 enzyme as the phenotypes of interest [S2 Fig in We applied the FC-mSKU method to an analysis of the Human Liver Cohort (HLC) study to explore the genetic architecture of the P450 enzyme in humans. The database can be downloaded from the Sage Bionetworks platform with the Synapse ID of syn4499  the FC-mSKU method is powerful in the association analysis of ultrahigh dimensional SNPs and multiple phenotypes, and it also maintains reasonable type I error. Furthermore, through the application of the asymptotic results of the model statistics, the proposed method has significantly decreased the computational burden. (2) The kernel-based mSKU method jointly evaluates a subset variants in pathways and captures the potentially complex interaction mechanism among the gene set. It obviously performs better than many models that are restricted to linear interactions. (3) For multiple phenotypes analyses, the improved Fisher combination function with dependent variables not only considers the correlation between multiple phenotypes but also improves the computational speed.With the ADNI study, we identified four pathways  associated with the multiple phenotypes of brain atrophy in AD patients. Hsa05010, whose pathway name is Alzheimer Disease, has been proven to be closely associated with AD in the literature ; HoweverFrom the analyses of the HLC study and ADNI study, the FC-mSKU method allows us to specify which pathways are specific to a particular phenotype or contribute to the common genetic construction. It is known that pathways usually do not work in isolation, and cellular pathways with complex molecular networks are often more directly involved in the diseases. Therefore, if we only focus on the single-phenotype test, we may miss some ideas for etiology research. However, the proposed method only analyzed continuous multiple phenotypes. In the literature, many outcomes of complex diseases are measured by both discrete and continuous scales. For example, dizziness (binary outcome) and blood pressure (continuous outcome) are both very important phenotypes in hypertension research. In future studies, we will focus on mixed multiple phenotypes analysis (binary and continuous) in genetic association studies, which may be the most common judging criteria of complex diseases.S1 File(DOCX)Click here for additional data file.