Simulation plays an essential role in the development of new computational and statistical methods for the genetic analysis of complex traits. Most simulations start with a statistical model using methods such as linear or logistic regression that specify the relationship between genotype and phenotype. This is appealing due to its simplicity and because these statistical methods are commonly used in genetic analysis. It is our working hypothesis that simulations need to move beyond simple statistical models to more realistically represent the biological complexity of genetic architecture. The goal of the present study was to develop a prototype genotype–phenotype simulation method and software that are capable of simulating complex genetic effects within the context of a hierarchical biology-based framework. Specifically, our goal is to simulate multilocus epistasis or gene–gene interaction where the genetic variants are organized within the framework of one or more genes, their regulatory regions and other regulatory loci. We introduce here the Heuristic Identification of Biological Architectures for simulating Complex Hierarchical Interactions (HIBACHI) method and prototype software for simulating data in this manner. This approach combines a biological hierarchy, a flexible mathematical framework, a liability threshold model for defining disease endpoints, and a heuristic search strategy for identifying high-order epistatic models of disease susceptibility. We provide several simulation examples using genetic models exhibiting independent main effects and three-way epistatic effects. Sorting out the genetic architecture of common human diseases will require a combination of computational, mathematical, and statistical methods that are capable of detecting, characterizing and interpreting a wide range of different genetic effects including gene–gene interactions, gene–environment interactions and locus heterogeneity Cordell, . A key cThere are two general components to the simulation of genetic epidemiology data. The first is the simulation of realistic patterns of genetic variation that mirror the distribution of allele frequencies and linkage disequilibrium that occur in human populations. The second is the simulation of complex traits from particular genetic variants. Numerous methods have been developed for the first component including forward-time simulators such as simuPOP [Peng and Amos, The goal of the present study was to develop a prototype genotype–phenotype simulation method and software that are capable of simulating complex genetic effects within the context of a hierarchical biology-based framework. Specifically, our goal is to simulate multilocus epistasis or gene–gene interaction where the genetic variants are organized within the framework of one or more genes, their regulatory regions and other regulatory loci (e.g. microRNA). Simulating data in this manner is important because the genomic context of genetic risk factors is becoming increasingly apparent as we analyze and interpret polymorphisms identified through genome-wide association studies [ENCODE Project Consortium et al., There are five components to our Heuristic Identification of Biological Architectures for simulating Complex Hierarchical Interactions (HIBACHI) simulation method. The first is the biological framework. The second is the mathematical framework. The third is the liability threshold model. The fourth is the heuristic methods for the discovery of high-order epistasis models. The final component is the prototype software package for simulating multiple data sets. We describe each of these in turn.The goal of this component is to provide a framework or scaffold for organizing the genetic variants and their phenotypic relationships. Although not complete, our approach is a step in the direction of using known biological relationship to focus a simulation. Our initial framework see Fig. starts wThe goal of this component is to provide a flexible mathematical framework for combining genotypic and nongenotypic values to produce phenotypic values. Each biology-based locus feeds into a mathematical function whose result is carried forward to the next function see Fig.. For exa6 function combinations using the biological framework described above.At each combination of loci the user can specify one of 25 different mathematic functions organized into groups labeled Basic, Logical, Bitwise, Unary, Large, and Miscellaneous. Basic functions include addition (ADD or +), subtraction (SUB or −), multiplication (MULT or ×), division (DIV or ÷), modulus (MOD), and modulus-2 (MOD2). Logical functions include greater than (GT or >), less than (LT or <), AND (&&), OR (∥), and XOR (^^). Bitwise functions include bitwise AND (BITA or &), bitwise OR (BITO or |), and bitwise XOR (BITX or ⊕). Unary functions include absolute value (ABS), NOT (∼), factorial (FAC or !), left and right. Large functions include power (POW), log, permute (PER or P), and choose (CHS or C). Miscellaneous functions include minimum (MIN) and maximum (MAX). These provide a comprehensive array of possible mathematical functions with 256 choices for the mathematical functions. Given a choice of functions, the liability distribution from which the output of HIBACHI effectively samples can, in theory, always be computed mathematically, though the amount of computation required may be prohibitive. For instance, if all the functions are addition the output is obtained by sampling, once for each population member, from the distribution equal to the sixfold convolution product of the probability distributions iA of the six genetic factors. Specifically, if ijx are all the values of factor iA, the value of this distribution at x isWe have used a liability threshold model to simulate disease from the distribution of phenotypic values generated from the genotypic values and mathematical functions as described above  is easily computed:Thus the sum in (1) is taken over all attribute values Hence the product of probabilities in (1).x, the sum is taken over all values which combine as prescribed by the functions to give x.For choices of functions other than all addition, the distribution can be computed as in (1) with one change: Rather than summing over all values which sum to As an example we show how HIBACHI can model epistatic interactions. Let us assume each genetic variant has genotypes coded 0, 1, 2 that occur with probabilities 0.25, 0.5, and 0.25, respectively. Thus if the first function is MOD2 and the value of just the first genetic variant is known, then a little computation shows that the result of the first function is either 0 or 1, each occurring with equal probability. Similarly if the value of the second genetic variant is known, but not the first, the output of the first function is again 0 or 1 with equal probability. However, if the values of the first and second genetic variant are both known, then the output of the first function is completely determined. Thus the choice of XOR, a known epistasis function, for the first function generates a synergistic interaction between the first two genetic variants. Choosing from the other functions either left or right, as appropriate, from the Unary menu of HIBACHI passes the result of the first function and this epistatic behavior to HIBACHI's final output. With these choices, data sets generated by HIBACHI have the property that each of the first two genetic variant alone convey no more information about the output than guessing, whereas their values together completely determine the output.6 possible combinations of mathematic functions are too many to explore exhaustively by trial and error. We have therefore provided two initial stochastic search algorithms to facilitate this process. The first is a simple random search that will explore n randomly generated models where n is specified by the user. The second is a genetic algorithm that evolves a population of bitstrings specifying combinations of six mathematical functions. We have previously used an approach like this to evolve penetrance functions specifying two-way to five-way epistatic effects [Moore et al., m is randomly initialized and evaluated using a fitness function (described below). The best bitstrings are mutated and recombined to generate new bitstrings that generate a new population. This process of evolving combinations of mathematical functions using natural selection is carried out for l generations allowing the algorithm to explore a maximum of n = m × l possible models. Other stochastic search algorithms such as simulated annealing will be added at a later time giving the user several different options for the heuristic search. These will be important as the complexity of the simulation grows in future versions that allow additional genetic variants influencing additional genes and regulatory elements.The 25The key to the genetic algorithm search is the fitness function that specifies the value or quality of a particular set of mathematic functions represented as a bitstring. Here, we used an entropy-based method that measures the pure three-way epistatic interaction after subtracting out the one-way and two-way genetic effects [Hu et al., The goal of the software development was to produce a prototype that could be used to evaluate the method and to generate ideas for the design of a formal software package for public release. The HIBACHI prototype was programed in Java and Javascript with a graphic user interface (GUI) that allows the user to specify the mathematical functions for each point in the biological hierarchy see Fig. in additThe goal of evaluation was twofold. First, we wanted to confirm that HIBACHI is capable of producing genetic models with simple independent main effects and more complex epistatic interactions. To simplify the evaluation we varied and restricted analysis of the genetic models to only the three variants in from the two transcription factor genes and the enhancer. The other genetic and nongenetic factors were fixed as additive effects but subsequently ignored as if they had not been measured in a genetic study. As a baseline we generated genetic models using only the addition (+) functions (Model 1), one addition and one multiplication (X) function (Model 2), and two multiplication functions (Model 3). We then generated a similar model using only the XOR (^^) logic function (Model 4) that is known to generate statistical epistasis effects [Moore et al., 6 possible combinations of mathematic functions. We ran the genetic algorithm with a population size of 100 for 100 generations. This run represents a search of a maximum of 104 of the 256 possible models. The four best models were recorded and compared with Models 1–4 for strength of three-way interaction. It is important to note that we altered the mathematical functions for the remaining genetic loci and the environmental factor to match Models 1–4. The new models discovered represent Models 5–8.The second goal was to use the heuristic genetic algorithm to discover new models exhibiting three-way epistasis for the genetic variants defined above from among the 25We then simulated data for 1,000 cases and 1,000 controls from a total population size of 100,000 subjects with a common disease prevalence set to 0.10. Here, we assumed each locus had two alleles of equal frequency with genotype frequencies consistent with those expected under Hardy-Weinberg equilibrium. Example data sets from Models 1–8 were first analyzed using the MDR machine learning method and software package that was designed specifically for detecting and characterizing high-order gene–gene interactions. The three-locus MDR models were returned along with the accuracy of classification. In addition, we performed two different permutation tests to validate the significance of the model. First, we performed a standard permutation test of the null hypothesis of no association by randomizing the case-control labels 1,000 times. Second, we performed an explicit test of epistasis [Greene et al., Finally, we ran several popular machine learning algorithms to illustrate the utility of the HIBACHI simulations for comparing different methods. We selected only the functional variants from the example data sets described above for Models 1–8. Machine learning methods included naïve Bayes (NB), classification trees (CT), k-nearest neighbors (kNN), neural networks (NN), and support vector machines (SVM). The NB approach used a relative frequency prior with a LOESS window of 0.5 and 100 sample points. This method reflects the main effects in the data. The CT approach required at least five data points in each leaf of the tree and for each split. Leaves with the same majority class were recursively merged with an m-value of two. The kNN approach used 10 nearest neighbors. The NN approach included a single hidden layer with 10 nodes, a regularization factor of one and 1,000 maximum iterations. The SVM approach used a radial basis function as a kernel. The accuracy of each classifier was returned. All machine learning analyses were implemented using the open-access Orange data mining software package that includes a variety of tools for manipulating data, performing machine learning analyses, and evaluating results [Demšar et al., The biology-based framework and example liability distributions for Models 1–8 are shown as screenshots from the HIBACHI software in FiguresP-value of the MDR model from a standard permutation test, and the MDR P-value derived from a permutation test that explicitly tests for interaction holding all main effects constant. All eight models have MDR accuracies significantly above 0.5 ranging from 0.621 (moderate effect size) to 0.822 (large effect size). The models differ greatly with respect to their main effects and three-way interaction effects. As expected the Models 1–3 with only addition and/or multiplication functions score high on the information gain for main effects but very low for three-way interactions. The significant or near-significant P-values for the explicit permutation test are primarily due to some small to moderate two-way interactions (data not shown). Model 4–7 on the other hand have very low main effects and moderate three-way interactions with highly significant explicit tests of interaction. Model 8 was a bit different in that it contained a moderate main effect for one genetic variant in addition to a stronger three-way interaction. These eight models highlight the ability of HIBACHI to simulate a variety of different types of genetic effects including high-order epistatic interactions.TableTableWe have presented a prototype of a new biology-based method and software for simulating genotype–phenotype relationships in population-based data. This approach is different from other simulation methods in that it uses a hierarchical mathematical framework for mapping genotypic values from multiple loci to phenotypic values using gene structure and function as a scaffold. This will facilitate that simulation of genetic data that is more closely aligned with our understanding of how genetic variation impacts phenotypic variation through a hierarchy of biochemical mechanisms such as transcription and translation. This is important as it is becoming clear that the detection and interpretation of genetic associations in the context of genome-wide association studies (GWAS) and whole-genome sequencing (WGS) will depend on our understanding of genome biology including, for example, regulatory regions [Cowper-Sal lari et al., The approach presented here is a prototype that needs much more development. There are several important ways in which we envision modifying and extending the method and the software. First, we limited the initial simulation to six genetic variants from a single gene and some of its regulatory factors. This could be expanded significantly to include additional regulatory components and many more genetic variants within and across all the elements. For example, the mRNA gene could be broken down into introns and exons with multiple coding variants and noncoding variants that control mRNA splicing. The regulatory region could be expanded to include multiple variants in the promoter and enhancer with many transcription factor binding sites. Epigenetic variation could also be introduced. Enhancing the simulation is this way will expand the realism and complexity of a single locus. We also envision the protein product connecting with other protein products at a higher level through additional mathematical functions. The ability to include protein–protein interactions will allow for epistasis across protein-coding genes that extends beyond the regulatory networks described above. There is no reason why the simulation couldn't be expanded conceptually to cell–cell interactions and even tissue–tissue interactions that would introduce a systems-level component. Environmental and noise components would need to be incorporated into all levels of the hierarchy. These additional layers of complexity are needed to more closely mimic how real biological systems work.An important limitation of the current study is that we did not consider effect size for each genetic variant. Our models included moderate to large genetic effects that are not realistic for common diseases. This can be addressed directly by changing the encoding on the genotypes. For example, we used 0, 1, and 2 to encode the different genotypes. This produces genotypes that contribute zero, one or two units of risk to the liability distribution depending of course on the mathematical function. These numbers could be divided by 10, for example, to reduce the risk contribution relative to the other genotypes. This would naturally reduce the effect size. Alternatively, we could introduce coefficients at the mathematical function layer. There is no reason why the result of any mathematical function could not be combined with a constant using a second function thus modifying its contribution to the liability. Either one or both of these mechanisms would allow the user to alter effect size. The challenge of course is that it might not be apparent how the effect size will change given the hierarchical complexity of the rest of the model. This could be greatly facilitated by perhaps specifying relative effect sizes for each genetic variant that could be used as a fitness objective in a heuristic search of the model space. We address new directions for the heuristic search next.n-dimensional space according to their values for n different criteria. The set of models for which there are no better according to all the criteria are selected. These models are referred to as nondominated and are said to exist on the Pareto front. The goal is to generate variability in the models through a method such as a genetic algorithm to move the Pareto front forward. This approach is advantageous because a model can be good for one criteria but perhaps not for others and still be retained. This allows the stochastic search algorithm to explore different criteria without penalty thus preserving the diversity of a search that might otherwise stall if only one criterion is used. This approach has worked well in the context of evolutionary search algorithms [Moore et al., As the model complexity grows the heuristic search component will become more and more important as it becomes infeasible to develop models by hand due to the extreme number of parameters. We introduced here a simple random search and heuristic genetic algorithm that conducts a parallel stochastic search using the principles of natural selection. Other search algorithms such as simulated annealing will also be included in future versions thus allowing users to choose the search algorithm they think will be most effective. An element we think will be particularly effective for many different stochastic search algorithms is Pareto optimization [Coello et al., Finally, it will be important to develop an open-source and user-friendly software package that allows users to manually explore different models through a simple point and click interface such as that provided in Orange [Demšar et al.,


DNA methylation plays a fundamental role in the regulation of the genome, but the optimal strategy for analysis of genome-wide DNA methylation data remains to be determined. We developed a comprehensive analysis pipeline for epigenome-wide association studies (EWAS) using the Illumina Infinium HumanMethylation450 BeadChip, based on 2,687 individuals, with 36 samples measured in duplicate. We propose new approaches to quality control, data normalisation and batch correction through control-probe adjustment and establish a null hypothesis for EWAS using permutation testing. Our analysis pipeline outperforms existing approaches, enabling accurate identification of methylation quantitative trait loci for hypothesis driven follow-up experiments.The online version of this article (doi:10.1186/s13059-015-0600-x) contains supplementary material, which is available to authorized users. DNA methylation is involved in the regulation of numerous biological processes, including gene expression , cell diWe propose a comprehensive approach to the analysis of 450 K methylation array data. Our method was developed using data from over 2,600 samples from the London Life Sciences Prospective Population (LOLIPOP) study, including 36 samples measured in duplicate and identifies differential methylation on a single-marker level. Our pipeline, termed CPACOR , performs superiorly to published methods, and provides a blueprint for the analysis of large-scale Epigenome-Wide Association Studies (EWAS).. To maximise the impact of technical factors in the replication dataset, the initial and repeat sample analyses were carried out in separate batches.We analysed two DNA methylation datasets: a population study of type 2 diabetes comprising 2,687 samples; and a technical replication dataset comprising 36 samples measured in duplicate . To maxiWe performed an initial top-level quality control following analysis recommendations given by Illumina. We excluded 22 samples . The distributions for methylation values differ between autosomal and gender chromosome markers  is not sufficient to prevent spurious results. When the detection P value threshold is lowered to P <10−16 the proportion of Y-chromosome markers with non-zero call rate in females is reduced from 55% to 10%. The majority of these remaining markers represent previously unidentified cross-hybridising probes  reduces the proportion of outlying values, especially at markers with lower call rates, consistent with improved calling  at each marker in the population study as a metric for quality of marker calling . Adoptioshold P <0−16 reduP = 2.91 × 10−11) between duplicate pairs when a detection P value threshold of P <10−16 is applied compared to a threshold P <0.05  in the case samples. We then determined the proportion of the spiked markers that were ranked in the top 100 methylation markers by univariate regression analysis. Confirming our initial finding, quantile normalisation of intensity values performs best, followed by quantile normalisation of beta values and subset quantile normalisation. Whereas most methods lead to improved performance, some over-normalise resulting in a reduction of true signal compared to no normalisation  between 1,000 randomly chosen markers  ,28, whicWe used simulated case–control datasets to assess the performance of the CPACOR analysis pipeline  non non1) noAdjustment for technical and biological factors also reduces correlation between markers on the sex chromosomes, although to a lesser extent than autosomal markers, resulting in broader prediction intervals   and downQuantile normalisation of intensity valuesIntensity values are separated into six different probe-type categories defined by colour channel, probe-type and M/U subtype . Within each category intensity values are quantile normalised using limma . NormaliControl Probe AdjustmentWe use intensity values from the Infinium 450 K control probes  beta values adjusted for technical and biological factors and study-specific confounders such as gender and age .6.Logistic regression analysis to identify differential methylationTo detect differential methylation we perform a final (logistic) regression analysis for each methylation marker predicting disease status Y as a function of the beta value adjusted for technical and biological factors and PCs .We then perform a PCA on the resulting regression residuals (excluding markers with missing data) and include PC 1 to 5 as linear predictors in the final regression model (step 6).maximise the impact of technical factors in the replication dataset, the initial and repeat sample measurements were carried out in separate batches. Methylation was quantified following standard protocol (Infinium_HD_Methylation_Assay_Guide_15019519_B) with 1 ug of DNA as starting material and an elution volume of 14 uL after bisulphite conversion . Microarrays were imaged using an Illumina HiScan scanner.Two DNA methylation datasets were generated in this study:  a populaP value threshold of P <0.05 was chosen based on Illumina recommendations; beta values with detection P ≥0.05 were set to missing data. We determined the proportion of missing data points per sample and per marker, enabling calculation of sample and marker call rates, respectively. For the population study we excluded 17 samples with sample call rate <98%. We also removed five samples with swapped gender labels identified by high call rates for Y-chromosome markers. After re-evaluation of the detection P value threshold, beta values with detection P ≥10−16 were set to missing data. We re-calculated sample call rates and excluded one further individual with sample call rate <98% from the study.Illumina Infinium 450 K data were retrieved as described and an initial top-level Quality Control was performed following the analysis recommendations given by the array manufacturer. In brief, we applied Illumina Background Correction to all intensity values and calculate the percentage methylation at each CpG site assayed . An initial detection For each methylation marker we define outliers based on the interquartile range (IQR), such that beta values are considered as outliers if they fall below Quartile 1–1.5 × IQR or above Quartile 3 + 1.5 × IQR. Outlier rates are calculated as the number of outlying beta values divided by the number of non-missing beta values.normalize.illumina.control’; not to be confused with CPA); ;  subset wth CPA);  peak-basAfter each normalisation we determined the Pearson correlation coefficients between replicates for the 36 samples measured in duplicate. Pearson correlation coefficients are calculated  at the mP values for each permuted datasets and ranked the 100 spiked markers by their association P values. For each magnitude the 10 permuted dataset provide a total of 1,000 ranks for 1,000 spiked markers.To assess the degree of true signal detectable after each normalisation method, we performed spike-in simulations. Based on the population study, disease labels were randomised to generate 10 permutated datasets. From each permuted dataset 100 markers were randomly selected and spiked. For each ‘spike-marker’ raw beta values of samples with a case label are increased by a defined proportion of the standard deviation of the respective marker. Based on these spiked beta values we calculate intensity values for the methylated and the unmethylated probe, such that for half of the spiked probes the methylated intensity is changed and for the other half the unmethylated intensity is changed. Negative intensity values resulting from this process are set to zero. Intensity values were spiked over a range of magnitudes  resulting in 10 sets per magnitude (10 permutations per magnitude). Using univariate logistic regression we calculated To assess the degree of technical biases and batch effects, we analysed a technical replication dataset comprising 36 samples measured in duplicate. To maximise the impact of technical factors the initial and repeat sample analyses were carried out in separate batches. We performed regression analyses to identify differentially methylated positions between replicates. Using paired linear regression we predict replicate status as a function of the beta value with and without adjustments for control probe PCs.champ.runCombat) [We performed batch correction for technical technical replication dataset based on quantile normalised beta values using ComBat  to companCombat) , performperm) as outcome  for -log and beta-coefficients with respect to results from model .To make permutation-analysis of the large-scale population study computationally tractable for 1,000 permutations we performed a linear regression of model  and retr outcome . This ap outcome : we calc outcome -values fest) explain a higher proportion of variance in the methylation data than measured white blood cell subpopulations, which may reflect the wider range of lymphocyte sub-classes in estimated sub-populations. Adjustment for white blood cells is therefore based on estimated white blood cell sub-populations and (measured) total white blood cell counts (WBCtot).For the population study estimated white blood cell subpopulations  were Bonferroni-corrected and plotted on the -log10 scale  and CPA . PCs were Figure .7\documeLocal correlation was determined for all possible pairs of autosomal markers up to 5,000 bp apart. Distance between markers was based on the annotated position of the CpG sites on the forward strand. Pearson correlation coefficient between marker pairs were calculated based on beta values (raw) and residuals derived from models . A largeSpike-in simulations were carried out as described. Each permuted dataset was then analysed using different stages of the CPACOR pipeline and other published 450 k analysis pipelines -17 . Default parameters were chosen as specified and results of each analysis step  were retrieved.et al. (d = 133) and default parameters were chosen as specified. To derive P values we performed 50 bootstraps, which required 50 hours of compute time and 130 GB RAM.Adjusted and unadjusted beta coefficients were calculated using RefFreeEWAS. Dimensionality was estimated as described by Houseman Non-CpG markers. Autosomal probes that measure methylation at CpA and CpT rather than CpG sites  based on the Illumina annotation.et al. [Cross-mapping probes. Methylation probe sequences reported to map to >1 genomic location  identified by Price et al. .Probes with SNPs. Methylation markers with one or more SNPs located within the probe sequence (including the G-base of the CpG site) that have minor allele frequency >1% in the samples studied. .We assessed the following probe types for their impact on association test results:Analysis of methylation markers on the sex chromosomes was performed as described for autosomal markers, but separately in males (chromosome X and Y) and females (chromosome X). In addition to samples with autosomal call rates <98% we excluded samples with chromosome X and Y call rates <98%. This results in 1,780 samples for chromosome Y (25 samples excluded), 1,802 for chromosome X in males (3 samples excluded) and 859 samples for chromosome X in females. Separately for each dataset we performed quantile normalisation and adjusted for control probe PCs, age, white blood cells and PC 1 to 5.http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE55763.Methylation array data can be accessed through the Gene Expression Omnibus at


Priors can be based on biological knowledge or predicted variant function, or even be used to integrate gene expression or other omics data. Based on Genetic Analysis Workshop (GAW) 19 data, this article discusses diversity and usefulness of functional variant scores provided, for example, by PolyPhen2, SIFT, or RegulomeDB annotations. Incorporating functional scores into variant filters or weights and adjusting the significance level for correlations between variants yielded significant associations with blood pressure traits in a large family study of Mexican Americans (GAW19 data set). Marker rs218966 in gene PHF14 and rs9836027 in MAP4 significantly associated with hypertension; additionally, rare variants in SNUPN significantly associated with systolic blood pressure. Variant weights strongly influenced the power of kernel methods and burden tests. Apart from variant weights in test statistics, prior weights may also be used when combining test statistics or to informatively weight p values while controlling false discovery rate (FDR). Indeed, power improved when gene expression data for FDR-controlled informative weighting of association test p values of genes was used. Finally, approaches exploiting variant correlations included identity-by-descent mapping and the optimal strategy for joint testing rare and common variants, which was observed to depend on linkage disequilibrium structure.High-density genetic marker data, especially sequence data, imply an immense multiple testing burden. This can be ameliorated by filtering genetic variants, exploiting or accounting for correlations between variants, jointly testing variants, and by incorporating informative  With the availability of very dense genetic marker data sets, such as sequence data, even large association studies can become underpowered. This raises the need to filter, or prioritize, or jointly test genetic variants.priors on genes may be derived from methylation or expression data if available in the same individuals. Alternatively, one may use external information. Recently, multiple annotation tools have become available using several databases and algorithms that predict functional effects of genetic variants. Commonly used are, for example, ANNOVAR (Annotate Variation) [priors, are discussed separately by Kent [Filters or riation) , Variantriation) , PolyPheriation) , SIFT (Sriation) , ENCODE riation) , Regulomriation) , CADD (Criation) , or Gerpriation) . Tools lriation)  human geriation) , Vega [1riation) , GENCODEriation) , and manriation) , Biocartriation) , or Pathriation) . This ar by Kent .p values while controlling the false discovery rate (FDR) [p values may be weighted based on functional annotations. For aggregation tests on genes, p value weights can be utilized to integrate gene expression or other omics data [Many researchers filter genetic variants. The simplest forms of filters are minor allele frequency (MAF), candidate genes or variants, or considering the exome. Filters and statistical models are chosen to increase the power under a hypothetical disease model. The advent of sequencing renewed interest in disease mechanisms less frequent but more penetrant than common single nucleotide polymorphisms (SNPs) of genome-wide association studies (GWAS). This led, for example, to screening for recessive variants by examining runs of homozygosity , 18. Whete (FDR) , 32. Forics data .priors  19 group on filtering variants and placing informative s Tables . These iAnalyzed data were provided by GAW 19 and included a family sample (n = 959) with extended pedigrees of Mexican Americans from the San Antonio Family Heart Study (SAFHS) and the San Antonio Family Diabetes/Gallbladder Study (SAFDS/ SAFGS) . The famAll approaches described herein are nonlongitudinal analyses of BP traits  in relation to minor allele dosages of sequence SNVs or genome-wide SNPs.priors are mostly based on regression models [Statistical methods employed by this group  where ne is the effective number of independent tests [Almeida et al  adjustednt tests ; yieldinσS2, σD2), which were combined into an overall slope estimate IBD mapping aims to detect loci sharing ancestral segments in unrelated individuals. In particular, unrelated subject-pairs with smaller trait differences are expected to share significantly more rare causative variants than pairs with larger trait differences. Liu et al  estimate of zero . The sigpriors can be incorporated by variant weights in aggregation tests such as burden tests or SKAT [xik of a set of i = 1, …, m variants into a burden score sk = ∑i = 1mωixik per individual k using a priori specified variant weights ωi. One tests trait association with genetic burden sk. Although burden tests are powerful when causal SNVs have the same effect direction, SKAT is more powerful when effect directions differ or if many noncausal SNVs are included in testing [prior on genetic model space [Genetic  or SKAT . Burden  testing , 49. SKA testing . Specifiel space . SNV weiel space ).beta-weights such as ωj = b(MAFi) [b is the probability density function of a beta random variable. Malzahn et al [Typically, rarer SNVs get assigned more weight to counterbalance their reduced power compared to more frequent SNVs. Used are, for example, weights Fj1−MAFj , inverse b(MAFi) , where bhn et al  comparedhn et al  or protehn et al .f(s) = S2 where s equaled the reverse order of categories, namely s = 6, 5, 4, 3, 2, 1 for category 1 (“most likely affecting binding and expression”) to category 6 . Kim and Wei [ωj = b(MAFj)), and burden test T5 (ωj = f(sj) versus p values with good small sample size behavior.Kim and Wei  categori and Wei  tested rP values were obtained by permutation procedure. SNV weights ωi accounted for putative effect direction and distinguished between functional SNVs in binding-sites (|ωi| = 10), not in binding-sites (|ωi| = 5), and nonfunctional SNVs (|ωi| = 1). The informatively weighted LRT was compared with C-α and CMC burden tests.Zhang et al  used a lrare and Qcommon, separately on rare SNVs and common SNVs, in the same region of interest, for the same trait, based on the same genetic null model. As SKAT is a variance-component test, combining Qrare and Qcommon [When not filtering for rare or common SNVs, optimal joint testing of both becomes an issue. Suppose, one computed 2 SKAT statistics, Q Qcommon 1\documenλ) relative to the common SNV variance-component . The weighted sum test (1) is another way of structuring a prior in SKAT. Note that Qrare and Qcommon may use different kernel functions or different SNV weights. Malzahn et al [all SNVs with appropriate weights into a single kernel. Exact p values for SKAT and weighted sum test (1) were obtained by Davies method [p values resulting from the separate rare SNV and common SNV SKAT statistics. Fisher pooling accounted for correlations by Satterthwaite approximation and Brown’s method ..λ) relatQ = (1 − ρ)QSKAT + ρQburden where 0 ≤ ρ ≤ 1 [Note that analogously to equation , SKAT-O  ≤ ρ ≤ 1 .p values, , for association of average BP T with rare SNV burden Ho et al  obtainedωi = 0, 1, − 1. Earlier, Genovese et al [p values ωi = 1, for simplicity) also associated with gene expression Restricting the number of rare SNVs avoids collapsing too many null variants. Ho et al  used these et al  and Roedse et al  had provHo et al  determinTand further if gene expression T and test (4) for rare minor allele burden P value weights Association tests (2) to (4) were made conditionally independent by adjusting test (3) for trait value mentclass2pt{minimThe results for this GAW19 working group varied widely as a result of the different objectives of each contributor. Table H0, extreme p values follow a beta distribution [ne for n single-locus tests. For whole genome sequence, PHF14 associated with SBP and rs9836027 in MAP4 associated with DBP.Under ribution . Almeidaribution  reportedZPLD1 by using CADD functional scores and sequence for the most promising region at 3q12.3.Liu et al  scanned simulated BP, SIFT and RegulomeDB annotations yield mismatched filters or priors whenever they deviate from the PolyPhen2 score used to simulate SNV effects. For example, SIFT annotated some SNVs with large effects in gene TNN as benign mutations  were only found when including RegulomeDB scores as variant weights for rare SNV analysis [SNUPN [In the GAW19 trait simulation model, SNV effect sizes were based on PolyPhen2 functional prediction scores Fig. . Differeons Fig.  and onlyons Fig. . Neverthanalysis . One of s [SNUPN  which iss [SNUPN . Kim ands [SNUPN  and Zhans [SNUPN  both recs [SNUPN  observeds [SNUPN  found ths [SNUPN . LD strus [SNUPN .Fig. 2SNp values for association of rare SNV burden with BP [p ≤0.05). P value weights were determined such that evidence for phenotype associated gene expression lowered burden test p values. As no gene reached multiple-testing adjusted significance, Ho et al [When using gene expression data to informatively weight gene-wise  with BP , 153 genHo et al  used genAll analyses presented herein used a cross-sectional design by analyzing trait data of the first examination, the first available examination, or longitudinally averaged traits. This mainly contributed to differences in sample size and trait variability. Furthermore, analyzing trait values at different time points may affect the marginal effect of genes that interact with age.Prior weights can be included at different stages of the testing procedure. They can be incorporated into the test statistic of SKAT or burden tests, used when combining test statistics, or applied to association test p values. Selecting variant-sets also should take genetic structures into consideration, such as LD or IBD sharing. Moreover, the effective number of independent tests can be determined relatively easily by extreme value theory. This enables appropriate adjustment of the significance level for multiple testing to avoid an overly conservative approach. Ideally, variant grouping and selection, inclusion of biological information, and significance level adjustment can be applied simultaneously. Strategies like these are useful in increasing power in analyses of highly dense genetic data sets.Including biological knowledge increased the power of association studies performed in our GAW group; especially filtering variants based on putative functional relevance. prior. This is feasible as functional annotations yield strong filters that greatly reduce the SNV space.Filtering variants clearly boosted power in the discussed studies. However, filtering might also lose information. Functional scores such as PolyPhen2, SIFT, CADD, or RegulomeDB differ as they focus on different information about SNVs. Moreover, appropriateness of functional scores for a considered trait is a priori unknown. Hence, one is well advised to use and combine multiple functional annotations into a single filter or


Prunus persica) fruit consumption in many countries, foremost due to unsatisfactory quality. The sugar content is one of the most important quality traits perceived by consumers, and the development of novel peach cultivars with sugar-enhanced content is a primary objective of breeding programs to revert the market inertia. Nevertheless, the progress reachable through classical phenotypic selection is limited by the narrow genetic bases of peach breeding material and by the complex quantitative nature of the trait, which is deeply affected by environmental conditions and agronomical management. The development of molecular markers applicable in MAS or MAB has become an essential strategy to boost the selection efficiency. Despite the enormous advances in ‘omics’ sciences, providing powerful tools for plant genotyping, the identification of the genetic bases of sugar-related traits is hindered by the lack of adequate phenotyping methods that are able to address strong within-plant variability. This review provides an overview of the current knowledge of the metabolic pathways and physiological mechanisms regulating sugar accumulation in peach fruit, the main advances in phenotyping approaches and genetic background, and finally addressing new research priorities and prospective for breeders.The last decade has been characterized by a decrease in peach ( Prunus persica L.) have traditionally focused on the selection of traits associated with fruit appearance and textural attributes.1 Fruit size, color, and firmness represent crucial components for retailers, making peaches attractive for consumers, resistant to postharvest handling, and allowing an extended shelf-life.2 Despite the significant improvements by breeding of such characters and the large number of newly released cultivars, in recent decades, a general decrease of peach consumption in the USA and European countries is observed.3 Poor or inconsistent flavor quality has been often recognized as the major limiting factor for acceptance by the consumers, shifting preferences toward other more flavorful fruit types. The peach cultivars present on the marketplace are often judged flavorless and appear to lack the strong ‘peach flavor’ expected by consumers, even when harvested at optimum maturity stage.5 The improvement of peach quality represents a crucial aspect for promoting consumption, prompting breeders toward the selection of novel and more flavorful cultivars6 that can develop flavors before the onset of the softening process. Many cultivars released in the last twenty years show important progress in flavor, attested by the introduction of the ‘low-acid’ (LA) trait, which characterizes cultivars, such as Big Top, which has a markedly sweet taste, due to both the low level of acidity and a medium to high sugar content.7 Although LA cultivars have been mainly developed for Asian market preferences, a general trend to increase peach sweetness has also been noted in important USA and European breeding programs.9 For example, among more than 300 cultivars released in the USA during the last decade, approximately 20% feature high soluble solids (more than 15° Brix), of which only 16% are early ripening, almost exclusively nectarines.10 Important international research projects are focusing on the development of new molecular tools to elucidate the genetic bases of important fruit quality traits, such as the projects RosBREED and FruitBreedomics.12Breeding programs of peach and nectarine . Although the sugar content is significantly correlated with SSC, the 17 Sugars represent a fundamental component of fruit edible quality, predominantly conferring sweetness, one of the main attributes influencing the degree of consumer satisfaction for peaches.19 The sweetness intensity depends on the overall sugar amount as well as on the specific sugar profile  because fructose, glucose and sorbitol have approximately 1.7, 0.8 and 0.6-fold the sweetener power of sucrose.20 The early findings of Robertson and Meredith21 suggest that low-quality peaches contain lower fructose and higher sorbitol and glucose compared with high-quality peaches. However, the level of acidity strongly affects the sweetness perception. As demonstrated by the comparison of the chemical analysis and sensory profiles, sweetness is mainly correlated with the ratio between sugars and acids, the overall organic acids concentration, the amount of citrate and shikimate and fruit juiciness.22–26 Sugars also affect mouth-feel attributes and aroma perception; in particular, sucrose and sorbitol are highly correlated with the overall taste and aroma.24Flavor is a combination of taste, aroma and mouth-feel attributes, defining a specific sensory profile that ultimately affects consumer judgment regarding the overall quality of fruits. In peach, taste largely depends on the water-soluble compounds, such as sugars and organic acids, conferring a sweetness and/or sourness sensation, and phenolic compounds, conferring astringency or bitterness.27 The degree of liking for peaches widely depends on the ripe soluble solid concentration (RSSC), which is the SSC of ready-to-eat peaches.29 The EU has established a minimum of 8° Brix for the peach market (Commission Regulation No. 1861/2004), despite many authors suggesting the introduction of higher SSC values, depending on the acidity levels.30–32 However, the establishment of a universal and reliable SSC value, assuring a minimal level of consumer satisfaction, is a difficult task. In general, consumer acceptance tends to increase along with RSSC levels, particularly when this parameter is low.33 In normal acidic cultivars, consumer acceptance increases rapidly with RSSC until a threshold value, specific for each cultivar, is exceeded; then, a further increase does not produce significant changes. In LA cultivars, the relationship between consumer acceptance and RSSC is more linear, progressively increasing until approximately 100% satisfaction at maximum RSSC values.29 In addition, the optimal sugar contents for peaches vary depending on the consumer group involved.34 Many researchers highlighted the importance of cultivar grading based on their dominant organoleptic characteristic, then developing a reliable minimum quality index within each group, thus helping to match fruit characteristics to consumers’ specific requirements.35A series of early studies associated SSC levels with increased consumer acceptance or lack of flavor.37 Mature peach fruit also contains detectable amounts of other sugars, such as maltose, isomaltose, raffinose, xylose, trehalose, 1-O-methyl-glucoside and fucose, and the polyols galactinol, glycerol, myo-inositol and maltitol.38 Starch is accumulated at the early stages of fruit development and is then rapidly metabolized, becoming almost undetectable at harvest.39 The total sugar content increases continuously during peach development up to full maturity, remaining constant or slightly decreasing during postharvest storage.40 Hexoses are the most abundant sugars in immature peach fruit until the beginning of rapid growth by cell elongation (S-III), when Suc becomes the predominant type.42 An interesting exception has been reported for the cultivar ‘Allgold’, in which Suc is the main sugar, even at the early stages of fruit growth,37 an aspect not further investigated in peaches. The accumulation pattern of Glc and Fru is generally characterized by reduced variations along fruit development, although their content is slightly higher at the early stages and progressively declines until maturity.44 The Glc:Fru ratio varies depending on genotype, usually from 0.8 to 1 for most commercial cultivars and is approximately constant across fruit development stages.46 The Suc content slowly increases in young developing fruit, remaining low until the S-III stage, when the accumulation rate increases, reaching maximum content prior to the onset of ripening, during the stage of fruit growth slowdown (S-IV).38 Sor levels remain low throughout fruit development, although peak accumulation has been detected during the S-II to S-III transition, followed by a sharp decline during the ripening process.39 A similar peak at pit hardening was observed for other sugars, such as xylose, raffinose, maltose and galactinol in cv. ‘Dixiland’.38 In particular, raffinose and galactinol are key antioxidant molecules related to stress protection, and their content is highly variable among peach varieties.47 During postharvest storage, Suc remains constant or slightly decreases, whereas hexoses increase or decrease,40 depending on the cultivar and the storage conditions.Peach fruit accumulates different types of soluble sugars and sugar alcohols, mainly sucrose (Suc), glucose (Glc), fructose (Fru) and sorbitol (Sor). Suc is the predominant sugar in the peach mesocarp at maturity, accounting for approximately 40 to 85% of the total sugars content, followed by Glc and Fru (in variable ratios), together representing approximately 10–25%, and Sor, accounting for less than 10%.in vitro regeneration.48 Most of the knowledge at the functional level originates from other Rosaceae species or model plants, which provide useful information regarding the general aspects of carbohydrate metabolism, but do not allow for framing of the possible specific behavior in peaches.A considerable amount of research has been conducted on carbohydrate biosynthesis, transport and accumulation in peaches. However, functional validation of candidate genes is particularly complex due to the recalcitrance of peach to 49 In mature peach leaves, Sor accounts for approximately 70% of the transported carbohydrates , whereas Glc and Fru are present in lower amounts.50 The sugar unloading pathways in peach fruit tissues have not been fully elucidated nor has the primary carbohydrate source supplying the rapid fruit growth and Suc accumulation during the S-III stage. Evidence has been provided for an apoplastic Suc transfer at the S-I and S-III stages,42 which is also observed in apple and pear,52 and a preferential utilization of Suc in growing fruits.53 However, both apoplastic and symplastic routes have been proposed for sugar uptake54 because in other species, the unloading route varies according to the fruit developmental stage and growth conditions.56 Membrane sugar transporters regulate carbohydrate movement between compartments and may exert strict control on their fluxes. At the molecular level, peach genome availability has allowed for the identification of major sugar-transporter gene family members. The involvement of SOTs transporters in active Sor unloading pathways has been elucidated in sour cherry,57 and 10 SOT genes have been identified in peach, three of which are expressed in mesocarp tissues.58 Moreover, three membrane-localized Suc/H+ symporter proteins (SUTs) involved in apoplastic loading/unloading have also been characterized: PpSUT1, barely detectable in fruit tissues, PpSUT2, mainly expressed in phloematic cells and PpSUT4, the most abundant transcript, expressed in both parenchyma and phloem tissues.42PpSUT2 is predominantly located on the plasma membrane, suggesting a role in Suc retrieval from the symplastic continuum into the phloem. In the S-I stage, PpSUT4 is localized in the tonoplast and has a role in the regulation of Suc release to sustain cell metabolism, whereas at the S-III stage, the expression of PpSUT4 decreases, allowing for the start of Suc accumulation into the vacuole. In addition to sorbitol and sucrose transporters, 29 members of the hexose transporter gene families  are also present in the peach genome, with at least 13 isoforms expressed in the mesocarp tissues.58–60 Recently, a novel family of conserved Suc transporters was discovered in Arabidopsis, the SWEET uniporter proteins, localized at the plasma-membrane or tonoplast.62 In peach, 15 putative SWEET coding sequences were found, two of which are expressed in the fruit, suggesting a possible conserved role in Suc distribution.42 Molecular and functional evidence are still missing, as for the rest of the hexose transporters families.Carbohydrate partitioning in peach fruit is regulated by a complex network of metabolic activities and physiological processes, including carbohydrate biosynthesis in source tissues, long-distance translocation by phloematic flux, metabolism and accumulation in fruit sink tissues. Sor and Suc are the main translocated assimilates in the phloem sap of the Rosaceae family.63 Upon translocation, Suc is cleaved to Glc and Fru by sucrose synthase (SUS) and invertase (INV) enzymes.64 Both enzymes act on the Suc substrate, but SUS yields Fru and UDP-glucose (UDPG), enabling reversible Suc synthesis, whereas INV converts Suc irreversibly into Glc and Fru. A total of six PpSUS genes are present in the genome, all expressed in mesocarp tissues. PpSUS1, the only studied isoform, is prevalently expressed in fruit compared to leaves and is upregulated during fruit ripening and postharvest storage.65 However, the enzyme activity of SUS remains constant or only slightly increases throughout fruit ripening.66 Regarding the invertase gene family, six cell-wall (CWINV), two vacuolar (VINV) and eight neutral/alkaline (NINV) genes were identified, with at least three, two and seven isoforms expressed in the fruit mesocarp, respectively.58 CWINVs and VINVs are acid invertases (AI), localized to either the cell-wall or vacuole, whereas NINVs are neutral invertases (NI) with cytosolic localization.66 In model plants that import and metabolize sucrose alone, extracellular invertase plays a pivotal role in sugar partitioning by facilitating apoplastic phloem unloading.68–70 For example, a lack of acid invertase activity characterizes the sucrose-accumulating species S. chmielewski, and the silencing of the vacuolar invertase gene TIV1 in tomato increases sucrose, thereby reducing the hexoses content.72 In peach, the physiological relevance of invertase activity has not be fully addressed. Both AI and NI activities strongly increase during the S-I to S-II transition, remaining stable until ripening and after harvest.38 In contrast, the capacities of NI and AI are stable throughout fruit development in a BC2 inter-specific [SD × Summergrand] × Zephyr population (S × Z).44 Expression studies of four neutral invertase isoforms (PpNI1-4) suggest a major role for PpNI2, whose transcript strongly increases at the S-III stage concomitantly with the rise in Suc accumulation, whereas PpNI1 is mainly expressed during the early stages of peach development.73 Molecular evidence regarding acid invertases is limited to the PpCWINV1 isoform, mainly expressed in leaves.66 As suggested in apple,74 and therefore also conceivable for sorbitol-transporting species, such as peach, Suc hydrolysis by invertase may play only a minor role in fruit sugar assimilation.The sugar distribution within the cell compartments of the fruit mesocarp varies depending on the developmental stage, shifting from a predominant cytoplasmic localization in young fruit to the vacuole at maturity.39 Despite SO activity being detected in peach fruit,75 it plays only a minor role in Sor metabolism.76 SDH is encoded by seven genes in peach, with at least four detected in fruit.58 The expression pattern of one PpSDH gene during peach development showed two peaks, at the end of the S-I stage and during fruit ripening, which is in agreement with the rates of SDH activity.77 Comparing the commercial and native peach accessions showing high and low Fru content, respectively, Kanayama et al.78 suggested that the metabolic capacity of SDH might be responsible for the different Fru levels in fruits. However, this hypothesis was not confirmed because no significant difference in SDH activity was observed in progeny segregating for Fru content.44In fruit, Sor can be rapidly oxidized into Fru by NAD-dependent sorbitol dehydrogenase (SDH) or sorbitol oxidase (SO).79 G1P enters the starch biosynthesis pathway, whereas F6P can enter the glycolytic pathway or can be combined with UDPG to synthesize Suc by sucrose phosphate synthase (SPS) and sucrose-phosphate phosphatase (SPP) through an essentially irreversible reaction.81 The enzymes PGM and UGP, which are linked to hexose phosphates metabolism, displayed the highest capacities,44 although the low G1P and starch contents in peach fruit suggest that UGPase activity may be directed toward UDPG biosynthesis. HK and FRK capacities are higher during the final stage of peach fruit development in genotypes with high Glc:Fru ratios.44 Among the four putative SPS genes identified in peach, only PpSPS1 and2 have been studied in detail. PpSPS1 did not significantly change during peach fruit development, whereas PpSPS2 was upregulated during the S-III to S-IV transition, with a further increase detected postharvest.66 In contrast, SPS activity increased only during the early stages of fruit development.44The pool of Glc and Fru resulting from sucrose and sorbitol metabolism can be stored in the vacuoles or phosphorylated to glucose-6-phosphate (G6P) and fructose-6-phosphate (F6P) by hexokinase (HK) and fructokinase (FRK), whereas the interconversion between F6P, G6P, UDPG and glucose-1-phosphate (G1P) is catalyzed by phosphoglucoisomerase (PGI), phosphoglucomutase (PGM) and UDP-glucose pyrophosphorylase (UGP) by readily reversible reactions.44 temporal variations in enzymatic activities are too small compared to the broad changes in metabolite concentrations, revealing a remarkable stability across years and genotypes with variable sugar compositions. Genome-wide data on the transcriptional profiling of both sugar transporters and structural genes along peach fruit development are not available; thus, the role of different isoforms belonging to multigenic families is unclear.Collectively, the wide number of studies analyzing the gene expression and activities of key structural enzymes does not provide a clear framework that explains sugar accumulation patterns in peach fruit. As demonstrated by extensive analysis of sugar-related enzymes,P. persica, characterized by a narrow genetic base and low intraspecific diversity.83 The comparison of fruit composition among peach cultivars, P. davidiana (the wild-related species more distant to peach) and hybrids, suggests that peach domestication and hybridization have resulted in a large increase of sugar content.84 In P. davidiana, the fruit sugar content is significantly lower than peach (<100 mg/g of dry weight), Suc is predominant and Fru is higher than Glc. Information regarding the variability of the sugar composition in F1 peach × P. davidiana hybrids is limited to a few Summergrand × P1908 selections (SD) showing a total sugar content similar to peach and higher Glc and Fru content with respect to peach parentals.84 In BC2 interspecific [SD × Summergrand] × Zephyr (S × Z) progenies, the Glc:Fru ratio is approximately 1:1 in most seedlings, despite approximately 10–15% of the individuals showing transgressive segregation for high Glc content compared to peach parentals.86 In other wild species, P. davidiana var. potaninii, P. mira, P. kansuensis and P. ferganensis, the fruit sugar composition remains largely uncharacterized, as with the rest of the Eastern Asia germplasm. Recently, comparative population genomic studies have begun to explore the genetic variability associated with landraces, ornamental and wild species belonging to the Chinese peach germplasm, providing rough information regarding the fruit SSC, ranging from 7.7° to 17.5° in P. persica and 10° to 16° Brix in wild accessions .90In many crops, wild accessions have been proven to be a useful source for the introgression of important traits associated with fruit quality and/or for the mapping of the genomic regions undergoing strong selective pressure during domestication. This aspect could be of particular importance for cessions .87–89 Thet al.36 Suc was the predominant sugar in native and ornamental peaches, with similar amounts compared to commercial peaches. Moreover, Japanese and Western cultivars were characterized by nearly equal percentages of Fru and Glc, contrary to native and ornamental peaches, which are characterized by a high Glc:Fru ratio and Sor amounts  and total sugar content (89.1–184.5 gL−1). Font i Forcada et al.91 comparing 94 traditional Spanish (mostly non-melting flesh types) and worldwide accessions, reported extensive variability of both the overall sugar content and composition. The total sugar content varied from 63 to 136 g/kg FW , whereas SSC ranged from 12° to 18° Brix. However, in a survey of 120 Eastern and Western cultivars released during the last century , reduced variability in fruit SSC was reported, ranging from 9.1° to 13.9° Brix, with significant but very low differences between Eastern and Western cultivars .92The sugar composition of many commercial, native and ornamental peach cultivars of Japanese germplasm was investigated by Moriguchi  amounts . The maj amounts .13,21,2293–95 The analysis of traits of interest in segregating populations allows estimation of the crucial parameters for the establishment of an effective breeding strategy, such as environmental effects, phenotypic frequencies and heritability. Overall, seedlings from different cross populations exhibited wide phenotypic variability for the total sugar content  and for individual sugars and a broad range of SSC (from below 9 to over 17° Brix), suggesting that there is genetic potential to improve the sugar content and composition in commercial peaches. All traits displayed continuous variation, following a normal or bimodal distribution among progenies, which is typical of quantitative or polygenic inheritance. Depending on the season, phenotypes can significantly deviate from these distributions. Suc was the predominant sugar in almost all progenies, whereas Glc and Fru ranged within 0.4–2.5. Sor was also variable within progenies, although the range of variability rarely exceeded the Glc or Fru amount. Although the mean values of each sugar were variable in the progenies within the parental range, a remarkable percentage of transgressive individuals with higher content with respect to either parental has been reported in almost all populations. Such transgressive segregation indicates that it could be possible to select for high sugar content in most seedling populations. Some works provided a rough estimate of sugar heritability.96 A moderate to high broad sense heritability has been calculated for SSC (0.33 to 0.72), based on 13 genotypes and approximately 2000 observations, and low heritability for both total and individual sugar .96 In contrast, high heritability of Suc, Glc, Fru, Sor and total sugars, ranging between 0.65 and 0.90, was estimated in a reciprocal cross ‘Zaoxing’ (an LA flat peach) × ‘Zaolupan’ (a non-LA round peach), despite the size of the progenies being insufficient to provide a reliable evaluation.46 Interestingly, Wu et al.46 demonstrated that maternal inheritance did not affect the sugar composition.The variability of the sugar contents and their profile has been evaluated in many intraspecific and interspecific progenies .1,14,37,97 As described before, the sugar content varies depending on the fruit developmental stage and is mainly regulated by carbohydrate supply, metabolic transformation and dilution effect due to variation in fruit volume.98 These physiological and metabolic processes are influenced by field practices, such as irrigation,100 fertilization,102 rootstock:scion interactions,103–105 training system,106 pruning and canopy management.108 Additionally, environmental variables, such as temperature, solar radiation, photoperiod, precipitation and soil patterns, influence the tree-growing environment and have been widely proven to result in wide variations in sugar accumulation.16 The variability of the sugar contents between trees is smaller compared to the within-tree variability, which reaches differences up to 10° Brix.109 Sources of within-tree variability have been mainly ascribed to fruit position in the tree, microclimatic gradients inside the canopy, leaf to fruit ratio and the vigor of fruit-bearing shoots. These factors mainly affect the availability of carbohydrates supporting fruit growth.110 Nevertheless, even under condition of unlimited carbohydrate availability, as in thinned trees, differences in fruit sink activity result in substantial variations in fruit sugars.112 Not negligible, the SSC variability within a single fruit can be as high as 4° Brix, with differences commonly found between the blossom/stem-end and between cheeks/suture.114 For these reasons, the accuracy of the SSC and sugar content estimation could be improved by evaluating a larger number of fruits within a single tree rather than by increasing the number of trees per genotype.85A large proportion of phenotypic variability for the peach sugar content depends on environmental factors and genotype-by-environment interactions. Fruit sugar variations in different growing seasons and locations, within trees of the same orchards, within the same tree and also within the fruit itself, are not negligible in comparison with the variation between genotypes.115 The relationship between yield and SSC is generally negative, although the degree of correlation varies depending on genotypes.14 High crop load has been negatively associated with carbohydrate accumulation in fruits because it alters the source–sink balance, causing an increase of sink competition among fruits.116 Several authors have reported contradictory results regarding the seasonal variability of the sugar composition.86Climate and crop load are considered the most important sources of year-to-year variability.The effects of environmental conditions and field practices on sugar accumulation in peaches have been deeply investigated, helping to explain the major causes of within tree variability in fruit composition. Collectively, the authors agree that the SSC, total and individual sugar contents are strongly affected by seasonal variability, in contrast to the sugar profile, which is relatively constant across environments and genotypes. However, how the environment affects the metabolic fluxes at both the enzymatic and gene expression levels remains to be elucidated.117–119 Ecophysiological modeling relies on the analysis of parameters involved in the development of traits, instead on their direct measurement.120 The identification of key genetic parameters allows for simulation of the performance of genotypes in many environments because they are independent of the environment. Such parameters can be considered as genotypic traits and are more suitable for association studies compared to the direct measure of complex traits affected by the environment. In peach, the SUGAR model has been developed to simulate the variations of the sugar composition during the S-III stage of fruit development based on carbohydrate supply, changes in fruit metabolism and assimilates dilution.98 Simplified forms of the model have also been applied to simulate the refractometric index,121 to analyze genotypic variation of the total sugars content in a segregating population,122 or to account for different Glc:Fru ratios in some genotypes.46 The SUGAR model was implemented in a more general ‘virtual peach fruit model’, integrating submodels for carbon assimilation, allocation and water fluxes to predict the evolution of important fruit quality traits.123 Among the several genotypic parameters that compose the model, 10 were able to explain 52% of variability in the fruit sweetness index.124 In particular, hydraulic conductance of the fruit surface (aL) and the coefficient of the transfer function between sugars and other compounds (ksugar) are the main parameters linked to sugar content and also highly correlated with other associated with fruit growth demand and duration.122 Some QTLs associated with ecophysiological parameters and influencing fruit sugar metabolism, although showing a low stability across years, were identified.125 For example, rsu  co-located on linkage group (LG) 1 with QTLs for fresh mass and early fruit growth. QTLs for sugar content on LG2, 4, and 7, co-located with QTLs for parameters involved in fruit water fluxes, such as aL and ρ (permeation coefficient of the fruit surface to water vapor). QTLs for growth duration (ddmax) were co-located with those for aL, ksugar and rsu. This preliminary study demonstrated the potential usefulness of ecophysiological models. However, to increase their applicability, the models should also include additional genetic information via genotype-dependent parameters by easily measurable physiological traits and known QTLs or, even better, genes.126Sugar accumulation in fruit is a complex quantitative trait, affected by environmental conditions and dependent on many interconnected physiological and metabolic processes, and controlled by multiple genes that interact with the environment and crop management. Quantitative trait loci (QTL) underlying the traits of quantitative nature often explain low phenotypic variability, with reduced stability across years and strong genotype-by-environment or genotype-by-management interactions. The virtual profiling of phenotypes through ecophysiological process-based simulation models (PBSM) represents a promising approach to overcome such difficulties due to their ability to mimic complex systems and to integrate multiscale levels of control.96 although current USA breeding programs suggest the possibility to develop early-ripening peaches with moderately high SSC.10 In contrast, the improvement of traits related to individual sugar contents, characterized by low heritability, is more complex to achieve by conventional selection. The identification of genetic determinants controlling these traits and the development of markers closely linked to relevant QTLs might allow for a marker-assisted selection (MAS) approach by pyramiding combinations of genes and assembling target traits more precisely.The improvement of peach quality traits has been achieved through traditional phenotypic selection within the seedling populations. However, this procedure is expensive and time-consuming, requires the screening of a large number of individuals, and above all, is mostly effective in fixing highly heritable traits. The selection for increased SSC, reportedly having moderate heritability, has allowed for a certain improvement of the sugar content in medium to late ripening cultivars, despite the variations caused by environmental and field practices. The development of peach cultivars with short fruit development periods (FDP) with high SSC is difficult due to the negatively correlated selection response between FDP and SSC,127 apple,128 sweet cherry129 and apricot,130 indicating some levels of synteny among Rosaceae species. Despite the huge amount of available data, the genetic determinants underlining these QTLs have not been identified, except in a few cases for tomato, a model species for unveiling the molecular mechanisms regulating sugar accumulation in fruit. Among the identified loci in tomato, the most important are linked to altered sugar transport, starch biosynthesis or Suc invertase activities, such as the fine-mapped Brix 9-2-5 locus, which located an apoplastic invertase.132 A quantitative trait nucleotides (QTN) caused by an amino acidic substitution in the LIN5 gene is responsible for the altered activity between the cultivated and wild species allozymes.133QTLs for sugar-related traits have been mapped in a large number of species, including strawberry,134 QTL mapping experiments for the sugar content in peach have been conducted using biparental crosses for a limited number of genetic markers. The most significant QTLs associated with sugar-related traits currently identified in peach are shown in Prunus reference map; therefore, information on QTLs locations cannot be used for a comparative mapping.135 A major QTL for the total soluble solid content was stably mapped on the central part of LG4, near the MD locus, in ‘Ferjalou Jalousia’ × ‘Fantasia’ (J × F),136 ‘Contender’ × ‘Ambra’(C × A),137 and S × Z progenies.86 Other QTLs were also detected on LG5 and 6, although in different map intervals.136 In sour cherry, a QTL for SSC was mapped on LG6, suggesting that this linkage group might be conserved between the two Prunus species.129 Additional loci for SSC were identified in a BC1 population derived from a cross between a peach selection ‘IF7310828’ and P. ferganensis ‘P72’ (IF × P72) at the top of LG6 and on the distal part of LG2,138 as also observed in a ‘Bolero’ × ‘Oro A’ population.137 Recently, an association study involving a large number of accessions belonging to the USA reference set for the peach germplasm have identified two genomic regions linked to SSC, on the central part of LG6 and at the bottom of LG7, although unstable across the two years of phenotypic observation.139 Many of the QTLs for SSC have been confirmed by a large association study involving over 1000 accessions within the FruitBreedomics project, albeit apart from QTLs located near the MD locus, the others have intensities close to the threshold probability .In peach, genetic determinants for some important fruit quality traits have been identified, excluding sugar-related traits, for which knowledge is still limited.136 However, only a few loci were confirmed across the two populations. A QTL with a main effect on the Suc content was mapped on LG5, in the region of the D locus in J × F progenies, and on the distal part of LG7 in S × Z progenies.136 QTLs linked to Glc, Fru and Sor content all seem gathered in clusters on LG4, 5 and 6. However, in the S × Z population, a major QTL for Fru content was also found on LG1 (at the FRU locus) in addition to minor QTLs affecting both Glc and Fru co-located on the distal part of LG2 and 7.86 Non-significant QTLs were identified for the total sugar content, except two minor QTLs located on LG5, at the D and G loci.136 Unexpectedly, Quilot et al.86 reported the presence of several favorable alleles for sugar content provided by P. davidiana parental, despite the low-sugar phenotype of its fruit. This aspect should be confirmed in the future, considering that the introgression of such valuable alleles in peach would require several rounds of backcrosses to eliminate the many unfavorable traits conferred by P. Davidiana, such as size, flavor and external appearance.Main QTL mapping experiments for the content of individual sugars have been performed on J × F and S × Z populations, identifying several genomic regions.140 such intervals are too large to enable QTLs map-based cloning. The likelihood of hundreds of genes being present within these regions makes it difficult to identify the linked gene(s).Overall, the mapping experiments suggest that both the total and individual sugar contents in peach fruit are governed by several QTLs with minor effects, often gathered in clusters. In many cases, such QTLs are unstable, due to strong environmental effects and are characterized by low LOD scores and small percentages of explained phenotypic variability. The number of loci governing sugar content is only roughly estimated, as well their genomic position, spanning regions on the order of 5–10 cM. Despite the availability of genome sequences and the attempts to identify candidate genes for the control of sugar-related traits,The evaluation of possible correlations between the sugar composition and physicochemical parameters is of particular importance for breeders, either to improve related traits simultaneously or to reduce undesirable side effects when selecting for one of the correlated traits. The relationships of sugar with fruit size, shape, flesh color, flesh adhesion to pit, pubescence and maturity date have been investigated.96 A significant and positive correlation between FDP and the SSC, Glc and Fru contents has been observed in a J × F progeny94 and in a germplasm collection showing extensive difference for maturity date.91 In contrast, these correlations were not evident in other progenies, although a general tendency towards higher SSC was noted in the latest ripening accessions. The correlation between ripening date and sugar content is supported by QTL co-localization on LG2136 and by the co-localization of a QTL for SSC at the MD locus, supporting the hypothesis of a pleiotropic effect.137 An NAC gene, a candidate for the control of ripening time in peaches, has been recently fine-mapped at the MD locus;141 however, it is unknown how it may affect sugar accumulation at the functional level.The duration of the fruit development period (FDP) and maturity date (MD) affect the sugar contents, as broadly indicated by the reduced SSC of early-ripening fruits in comparison with mid-to-late ripening ones. A good correlation was reported between SSC and FDP (>0.60), and there was no relationship with blooming date.142 For example, fruit fresh mass at harvest explained only a small amount of the total sugars variability in 14 different peach progenies.14 A significant relationship between the mesocarp DW, SSC and sugars was found in an S × Z population,86 and a negative correlation has been reported between the Glc content and both FW and DW.85 Although a correlation between fruit DW and sugar content is expected because carbohydrates compose approximately 60% of the DW, significant variability for sugar content has been found among fruits of similar weight because, as observed in tomato introgression lines, the proportion of DW consisting of sugars may vary depending on the metabolic utilization of the assimilates for growth or for storage.143 Differences in sink efficiency of individual fruits play a critical role in both DW and soluble sugar accumulation in peach.144 It has been hypothesized that assimilate partitioning within individual fruits depends on differences in the mesocarp cell number and size because their variability explains 77% of the variation in the Suc content between fruits within a single tree.145 A strong correlation between the sugar concentration and the rate of cell expansion has also been observed in peach,146 and in melon fruit, a preferential accumulation of Suc in larger cells has been demonstrated.147 Moreover, fruit cell expansion is also regulated by the water balance at the whole plant level and fruit transpiration, ultimately affecting sugar concentration via dilution.149 Crop load can significantly alter the relationship between fruit mass and SSC, particularly in high-load conditions.150 The correlation between fruit size and sugar content is evident when comparing peach and nectarine fruit. For example, the comparison of two peaches, ‘Tropic Beauty’ and ‘Fla.M3-1’, and their respective nectarine mutants ‘TBN’ and ‘M3-1N’, suggested that the increased sugar concentration in nectarines depends on a decrease of the fruit size compared to the original peach. Therefore, the mutation affects the fruit growth and not its ability to accumulate sugars.151 A higher SSC content was also observed in sibling peach and nectarine seedlings from three hybrid families,152 as well in the nectarine mutant ‘Yuval’ compared to its original peach ‘Oded’.153 The G locus, controlling the peach/nectarine trait, has been recently characterized by a variant discovery approach, identifying an LTR retro-element insertion in exon 3 of the candidate gene PpMYB25 as the cause of the recessive glabrous phenotype.154 The fruit weight reduction in nectarines suggests a pleiotropic effect of this mutation on the sugar content. Alternatively, the reduced size depends on a tightly linked QTL. Nevertheless, contrasting results have been reported by mapping experiments with a QTL for fruit size and sugar content co-localized near the G locus in S × Z but not in J × F populations.93 In addition, QTLs for high Fru and Glc concentrations co-located with QTLs, showing a negative effect on fruit size on LG4, 5 and 7.86 The co-localization of QTLs with opposite allelic effects for sugar content and fruit weight has also been observed in tomato, suggesting that some genes may have pleiotropic effects.155The relationship between fruit weight (or size) and sugar content has obvious implications for fruit quality, although the relationship is complex and often not trivial. Some studies have documented a weak or not significant correlation between sugars and both fruit dry (DW) and fresh (FW) weight.156 In progenies segregating for peach/nectarines and flat/round traits, SSC tends to decrease in round peach fruit compared to flat-peach and flat-nectarines, respectively.157 As described above for locus G, the increase of SSC may be due to the pleiotropic effects of size reduction because locus S, controlling the flat-shape trait, is associated with a QTL for fruit weight on LG6 in a J × F progeny.93A general tendency for a greater sugar content in flat-peach has been observed by exploring germplasm resources.159 The co-localization on LG1 of the FRU locus, controlling the Fru content and sweetness,86 with the Y locus, controlling the yellow/white color of the flesh,160 might explain the association of both traits.A significant association between the sugar composition and flesh color has not been highlighted, although sugars tend to be higher in white-flesh cultivars.F locus), slightly but significantly higher SSC, total and individual sugar contents were found in freestone fruits.14 However, other authors reported no significant association,85 or, in contrast, higher total sugars in clingstone cultivars.91 Although a QTL for sugar content has been reported on LG4, where the F locus is located,86 the difference does not depend on the linkage of the two traits but rather on the genetic background of the analyzed genotypes.In the case of the freestone/clingstone trait , which are generally prized by consumers. However, as demonstrated by several studies, the increase of the sugars content is not always accompanied by a parallel increase in the liking degree. Therefore, the selection of new cultivars should be defined as a more specific target to be achieved, based on detailed information regarding consumer preferences and perceptions.An improvement of the sugar content has been observed in recently released cultivars from different conventional breeding programs. Nevertheless, further and substantial improvements by classical breeding methods are limited by the scarce knowledge of the gene network expressing the phenotype. Although the strong influence of environmental factors and genotypic × environment interactions could mask the effects of minor QTLs, the genetic determinants regulating sugar accumulation could be identified, allowing for the identification of molecular markers to be used in marker-assisted selection (MAS) or breeding (MAB). Even when several minor QTLs are made available, marker-assisted approaches could represent the best strategy for an efficient screening procedure, through QTLs pyramiding. Unfortunately, none of the putative identified QTLs governing sugar-related traits in peach have been fine-mapped. The lack of detailed information on their effects and genome location, as well as their validation in different genetic backgrounds, prevents the development of suitable molecular markers for breeding purposes.Prunus genomes, together with a wide array of new technologies, offers unheard-of opportunities to breeders. NGS technologies have been implemented in linkage mapping experiments to develop novel and promising approaches, such as RAD-Seq,161 GBS,162 GS,163 and QTL-Seq.164 These powerful approaches could allow for the creation of high-resolution maps with a high number of molecular markers. However, these tools could suffer the same limitations as classic linkage mapping strategies because the increment of markers density is often not sufficient for unambiguous QTLs identification. Map resolution can be limited by the few recombinant events occurring in early generations and more often by the small size of the segregating progenies. The increase of progeny size is often difficult to achieve due to the time and the costs of field management. Alternative strategies of QTL mapping based on advanced backcross, NILs, RILs or double haploids, are not easy to perform in a tree crop. Furthermore, genome-wide association studies (GWAS) are ineffective in peaches, at least when applied to the European and USA germplasm, which are characterized by narrow genetic bases and high levels of linkage disequilibrium (LD).165The availability and the high level of synteny among several 166 the availability of accurate and high-throughput phenotyping tools is of paramount importance. Although data collection of sugar contents is not difficult from a technical standpoint, the phenotyping is hindered by the strong environmental effects and the high within-tree variability, in turn representing another reason for the lack of accuracy of the QTLs mapping experiments. A full understanding of the processes underlying the interconnections among yield, fruit growth, dry and fresh mass accumulation and sugars partitioning is essential in the environmental variability and its interaction with genotype. Ecophysiological modeling represents a viable approach to improve the phenotyping of complex traits; however, such models are currently in progress and are rarely applied by breeders because they depend on parameters that are not easily measurable.To exploit the full potential of the above described technologies and to increase the genetic gains through so-called precision breeding,in vitro transformation for the functional validation of candidate genes; defining more specific targets to be achieved for sugar levels based on fruit type, consumer preferences and perceptions.In conclusion, the following priorities should be followed for the improvement of sugar content in peach fruit by a genetic approach: deepening the knowledge of the physiological and metabolic processes regulating sugar accumulation with the aid of new ‘omics’ tools; developing innovative phenotyping methods to address the strong environmental and genotype × environment effects, even enhancing the accuracy and simplifying the application of ecophysiological models; exploration of the phenotypic variability associated with sugar-related traits, for example, within the Far-East germplasm, to increase the genetic variability and the resolution power of association studies; improvement of the efficiency of This work was supported by MASPES  and FRUITBREEDOMICS .MC: searched and critically reviewed the available literature, wrote the paper.DB: conceived the paper, contributed to the writing of the manuscript and critically revised it.AC: searched the available literature, drafted and revised the manuscript.All authors: read and approved the final manuscript.


Genetic studies often collect data on multiple traits. Most genetic association analyses, however, consider traits separately and ignore potential correlation among traits, partially because of difficulties in statistical modeling of multivariate outcomes. When multiple traits are measured in a pedigree longitudinally, additional challenges arise because in addition to correlation between traits, a trait is often correlated with its own measures over time and with measurements of other family members. We developed a Bayesian model for analysis of bivariate quantitative traits measured longitudinally in family genetic studies. For a given trait, family-specific and subject-specific random effects account for correlation among family members and repeated measures, respectively. Correlation between traits is introduced by incorporating multivariate random effects and allowing time-specific trait residuals to correlate as in seemingly unrelated regressions. The proposed model can examine multiple single-nucleotide variations simultaneously, as well as incorporate familyspecific, subject-specific, or time-varying covariates. Bayesian multiplicity technique is used to effectively control false positives. Genetic Analysis Workshop 18 simulated data illustrate the proposed approach's applicability in modeling longitudinal multivariate outcomes in family genetic association studies. High-throughput genotyping advances have generated large amounts of genetic data. At the same time, numerous related phenotypes are often collected in genetic studies of complex traits. To understand how genetic variants influence multiple traits, it is necessary to consider correlation among variants and multiple traits jointly ,2. HowevWe propose a Bayesian joint modeling of longitudinally measured multiple traits in family genetic studies. Explicitly considering the correlation structure between multiple traits using multivariate random effects  and seemj of pedigree i at time t. Here I families in the study; i; and j of pedigree i. Here, the number of measurement We consider SNV association models with a longitudinal bivariate quantitative outcome in family studies. Let X is a vector of subject-specific time-invariant covariates and Z is a vector of time-varying covariates. j of pedigree i, coded as 0, 1, or 2 indicating the number of minor alleles and G is the number of SNVs in the model. Here, This Bayesian bivariate model uses bivariate normal random family and subject effects, and a bivariate normal distribution for the residual errors, as in seemingly unrelated regressions, to jointly model the 2 traits and allow them to be correlated.q, while q follows a Beta distribution, that is, p values, a higher posterior inclusion probability indicates greater confidence of a true result. For each SNV, we estimate posterior inclusion probability asBayesian multiplicity adjustment is a Bayesian solution to multiplicity problems . Throughon is 1/G. This BeS is the model space being visited by the Markov chain Monte Carlo (MCMC); Here, Two outcomes, diastolic (DBP) and systolic blood pressure (SBP), were evaluated. Covariates included sex, age, and smoking status. To adjust for antihypertensive medications use, we calculated the mean difference of blood pressure (BP) between observations with medication use (med = 1) and those without medication (med = 0) among observations with hypertension (htn = 1);that is, analysis .MAP4 on chromosome 3. There are 894 SNVs in the gene; 14 influence both DBP and SBP, and 1 influences SBP. Among the 15 causal SNVs, three are common ; all others are rare. All analyses were based on replication set 1. To investigate effectiveness of Bayesian multiplicity adjustment, a random set of noise variants of size 1, 15, 30, 60, and 90 were added from MAP4. Selection of noise variants was truly random and did not account for LD with causal SNVs. After burn-in and thinning every 10th iteration, 50,000 samples were drawn for MCMC simulations.Included were 849 individuals from 20 pedigrees . Each individual has 3 observations. Our focus is on SNVs in We compared our method with two other methods. One method is a Bayesian univariate model where the off diagonal of the variance and covariance matrices in equations (1), (2), and (3) are zero, thus the 2 traits are modeled independently. The univariate model can handle longitudinal data and multi-variants, and uses Bayesian multiplicity techniques to adjust for multiple comparisons. The other is the family-based measured genotype approach (MGA), which is a standard approach to analyze family genetic studies and compares polygenic models with or without each SNV as a covariate . MGA modUsing a threshold of 0.5 for the posterior inclusion probability, the Bayesian bivariate model detected 5 of the 15 SNVs between SBP and DBP with 1 noise variant . However, MGA identified 8 and 6 false positives for DBP and SBP, respectively. The Bayesian univariate model identified 2 causal SNVs and 1 false positive for both DBP and SBP.As the 90 noise variants were randomly selected, examining the LD structure is also important. Among the true positives, two pairs (SNVs 5 and 8 and SNVs 7 and 10) have a high LD Overall the Bayesian bivariate model resulted in posterior estimates of beta values very similar to the reported effect size from Genetic Analysis Workshop (GAW) data generators Figure . HoweverWe developed a novel Bayesian model for analysis of multiple longitudinal traits and multi-variant models in family genetic studies. This is a significant advance because previous studies have looked at bivariate models, longitudinal data, or multi-SNV models separately. For the first time, we have developed an analytic approach that can incorporate all of these issues jointly. The model considers bivariate random family and random subject effects to account for correlation between outcomes, family members, and repeated measures of the same individual. The seemingly unrelated regression technique is used to correlate the residuals of the 2 outcomes measured at the same time for the same individual. Inherent in this method is Bayesian multiplicity for the control of false positives. Using the GAW18 simulated data set, we demonstrated the feasibility of the proposed model.Compared to the Bayesian univariate model in which the 2 outcomes are modeled separately, our method had similar power, but fewer false positives. Compared to MGA, our Bayesian bivariate approach had fewer false positives regardless of LD between causal and noise SNVs. While the noise variants in LD with our causal variants did not result in increased false positives using the Bayesian approach, given the multi-variant nature of the analysis it is possible that the LD in these noise parameters may have reduced power to detect causal effects. Although different from our proposed method in many aspects, MGA represents a standard practice for analysis of family-based genetic studies. This comparison of different approaches is important because it demonstrates that given the low false positives, the Bayesian model is potentially better than current standard practice.Several other studies have shown improved power of joint modeling of multiple traits over univariate analyses -13. Howeate sets . FurtherIt is important to note that the model inference is based on computationally expensive MCMC simulation. Although we didn't use any special algorithms to efficiently sample the model space and the number of iterations was relatively small given the extremely large model space, the posterior inclusion probabilities became stable very early in the MCMC chain. This suggests that posterior inclusion probabilities can provide valid model inference. Sensitivity analyses with more optimistic priors on inclusion probabilities gave more power while controlling false positives. However, prior knowledge or evidence must support the use of this type of prior.In summary, we introduced a Bayesian model for analysis of bivariate quantitative traits measured longitudinally in family genetic studies. This method extends the previous joint modeling methods and permits simultaneous analysis of multiple traits with longitudinal data. Furthermore, this method incorporates multi-variant effects while effectively controlling the false-positive rate.The authors declare that they have no competing interests.LD conceived and performed the statistical analysis and drafted the manuscript. LJM contributed to the design of the statistical analysis.HH helped with statistical analysis. BGK, ESA, TBM, DWF, HH, XZ, VP, LK, and LJM helped with the writing of the manuscript. All authors read and approved the final manuscript.