Hypernetwork modeling and topology of high-order interactions for complex systems.

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks. Such hypernetworks can distinguish between how pairwise interactions modulate a third agent (active HOI) and how the altered state of each agent in turn governs interactions between other agents (passive HOI). The simultaneous occurrence of active and passive HOI can drive complex systems to evolve at multiple time and space scales. We apply the model to reconstruct a hypernetwork of hexa-species microbial communities, and by dissecting the topological architecture of the hypernetwork using GLMY homology theory, we find distinct roles of pairwise interactions and HOI in shaping community behavior and dynamics. The statistical relevance of the hypernetwork model is validated using a series of in vitro mono-, co-, and tricultural experiments based on three bacterial species.

The metabolomic physics of complex diseases.

Human diseases involve metabolic alterations. Metabolomic profiles have served as a vital biomarker for the early identification of high-risk individuals and disease prevention. However, current approaches can only characterize individual key metabolites, without taking into account the reality that complex diseases are multifactorial, dynamic, heterogeneous, and interdependent. Here, we leverage a statistical physics model to combine all metabolites into bidirectional, signed, and weighted interaction networks and trace how the flow of information from one metabolite to the next causes changes in health state. Viewing a disease outcome as the consequence of complex interactions among its interconnected components (metabolites), we integrate concepts from ecosystem theory and evolutionary game theory to model how the health state-dependent alteration of a metabolite is shaped by its intrinsic properties and through extrinsic influences from its conspecifics. We code intrinsic contributions as nodes and extrinsic contributions as edges into quantitative networks and implement GLMY homology theory to analyze and interpret the topological change of health state from symbiosis to dysbiosis and vice versa. The application of this model to real data allows us to identify several hub metabolites and their interaction webs, which play a part in the formation of inflammatory bowel diseases. The findings by our model could provide important information on drug design to treat these diseases and beyond.

Association of SNP-SNP interactions of surfactant protein genes with severity of respiratory syncytial virus infection in children.

The severity of respiratory syncytial virus (RSV) may be linked to host genetic susceptibility. Surfactant protein (SP) genetic variants have been associated with RSV severity, but the impact of single-nucleotide polymorphism (SNP)-SNP interactions remains unexplored. Therefore, we used a novel statistical model to investigate the association of SNP-SNP interactions of SFTP genes with RSV severity in two- and three-interaction models. We analyzed available genotype and clinical data from prospectively enrolled 405 children diagnosed with RSV, categorizing them into moderate or severe RSV groups. Using Wang's statistical model, we studied significant associations of SNP-SNP interactions with RSV severity in a case-control design. We observed, first, association of three interactions with increased risk of severe RSV in a two-SNP model. One intragenic interaction was between SNPs of SFTPA2, and the other two were intergenic, involving SNPs of hydrophilic and hydrophobic SPs alone. We also observed, second, association of 22 interactions with RSV severity in a three-SNP model. Among these, 20 were unique, with 12 and 10 interactions associated with increased or decreased risk of RSV severity, respectively, and included at least one SNP of either SFTPA1 or SFTPA2. All interactions were intergenic except one, among SNPs of SFTPA1. The remaining interactions were either among SNPs of hydrophilic SPs alone (n = 8) or among SNPs of both hydrophilic or hydrophobic SPs (n = 11). Our findings indicate that SNPs of all SFTPs may contribute to genetic susceptibility to RSV severity. However, the predominant involvement of SFTPA1 and/or SFTPA2 SNPs in these interactions underscores their significance in RSV severity.NEW & NOTEWORTHY Although surfactant protein (SP) genetic variants are associated with respiratory syncytial virus (RSV) severity, the impact of single-nucleotide polymorphism (SNP)-SNP interactions of SP genes remained unexplored. Using advanced statistical models, we uncovered 22 SNP-SNP interactions associated with RSV severity, with notable involvement of SFTPA1 and SFTPA2 SNPs. This highlights the comprehensive role of all SPs in genetic susceptibility to RSV severity, shedding light on potential avenues for targeted interventions.

Mapping the Influence of Light Intensity on the Transgenerational Genetic Architecture of Arabidopsis thaliana.

Light is a crucial environmental factor that influences the phenotypic development of plants. Despite extensive studies on the physiological, biochemical, and molecular mechanisms of the impact of light on phenotypes, genetic investigations regarding light-induced transgenerational plasticity in Arabidopsis thaliana remain incomplete. In this study, we used thaliana as the material, then gathered phenotypic data regarding leaf number and plant height under high- and low-light conditions from two generations. In addition to the developed genotype data, a functional mapping model was used to locate a series of significant single-nucleotide polymorphisms (SNPs). Under low-light conditions, a noticeable adaptive change in the phenotype of leaf number in the second generation suggests the presence of transgenerational genetic effects in thaliana under environmental stress. Under different lighting treatments, 33 and 13 significant genes associated with transgenerational inheritance were identified, respectively. These genes are largely involved in signal transduction, technical hormone pathways, light responses, and the regulation of organ development. Notably, genes identified under high-light conditions more significantly influence plant development, whereas those identified under low-light conditions focus more on responding to external environmental stimuli.

Recursive Test of Hardy-Weinberg Equilibrium in Tetraploids.

Testing for deviations from Hardy-Weinberg equilibrium (HWE) can provide fundamental information about genetic variation and evolutionary processes in natural populations. In contrast to diploids, where genotype frequencies remain constant after a single episode of random mating, polyploids, characterized by polysomic inheritance, approach HWE gradually. Here, we mathematically show the asymptotic trajectory of tetraploid equilibrium from any initial genotype frequencies. We formulate a statistical framework to test and estimate the degree of deviation from HWE at individual loci in allotetraploids and autotetraploids. Knowledge about HWE test fills an important gap in population genetic studies of tetraploids related to their evolution and ecology.

Unlocking allelic variation in circadian clock genes to develop environmentally robust and productive crops.

MAIN CONCLUSION: Molecular mechanisms of biological rhythms provide opportunities to harness functional allelic diversity in core (and trait- or stress-responsive) oscillator networks to develop more climate-resilient and productive germplasm. The circadian clock senses light and temperature in day-night cycles to drive biological rhythms. The clock integrates endogenous signals and exogenous stimuli to coordinate diverse physiological processes. Advances in high-throughput non-invasive assays, use of forward- and inverse-genetic approaches, and powerful algorithms are allowing quantitation of variation and detection of genes associated with circadian dynamics. Circadian rhythms and phytohormone pathways in response to endogenous and exogenous cues have been well documented the model plant Arabidopsis. Novel allelic variation associated with circadian rhythms facilitates adaptation and range expansion, and may provide additional opportunity to tailor climate-resilient crops. The circadian phase and period can determine adaptation to environments, while the robustness in the circadian amplitude can enhance resilience to environmental changes. Circadian rhythms in plants are tightly controlled by multiple and interlocked transcriptional-translational feedback loops involving morning (CCA1, LHY), mid-day (PRR9, PRR7, PRR5), and evening (TOC1, ELF3, ELF4, LUX) genes that maintain the plant circadian clock ticking. Significant progress has been made to unravel the functions of circadian rhythms and clock genes that regulate traits, via interaction with phytohormones and trait-responsive genes, in diverse crops. Altered circadian rhythms and clock genes may contribute to hybrid vigor as shown in Arabidopsis, maize, and rice. Modifying circadian rhythms via transgenesis or genome-editing may provide additional opportunities to develop crops with better buffering capacity to environmental stresses. Models that involve clock gene‒phytohormone‒trait interactions can provide novel insights to orchestrate circadian rhythms and modulate clock genes to facilitate breeding of all season crops.

A statistical framework for recovering pseudo-dynamic networks from static data.

MOTIVATION: The collection of temporal or perturbed data is often a prerequisite for reconstructing dynamic networks in most cases. However, these types of data are seldom available for genomic studies in medicine, thus significantly limiting the use of dynamic networks to characterize the biological principles underlying human health and diseases. RESULTS: We proposed a statistical framework to recover disease risk-associated pseudo-dynamic networks (DRDNet) from steady-state data. We incorporated a varying coefficient model with multiple ordinary differential equations to learn a series of networks. We analyzed the publicly available Genotype-Tissue Expression data to construct networks associated with hypertension risk, and biological findings showed that key genes constituting these networks had pivotal and biologically relevant roles associated with the vascular system. We also provided the selection consistency of the proposed learning procedure and evaluated its utility through extensive simulations. AVAILABILITY AND IMPLEMENTATION: DRDNet is implemented in the R language, and the source codes are available at https://github.com/chencxxy28/DRDnet/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

LD block disorder-specific pleiotropic roles of novel CRHR1 in type 2 diabetes and depression disorder comorbidity.

Major depressive disorder (MDD) and type 2 diabetes (T2D) are complex disorders whose comorbidity can be due to hypercortisolism and may be explained by dysfunction of the corticotropin-releasing hormone receptor 1 (CRHR1) and cortisol feedback within the hypothalamic-pituitary-adrenal axis (HPA axis). To investigate the role of the CRHR1 gene in familial T2D, MDD, and MDD-T2D comorbidity, we tested 152 CRHR1 single-nucleotide-polymorphisms (SNPs), via 2-point parametric linkage and linkage disequilibrium (LD; i.e., association) analyses using 4 models, in 212 peninsular families with T2D and MDD. We detected linkage/LD/association to/with MDD and T2D with 122 (116 novel) SNPs. MDD and T2D had 4 and 3 disorder-specific novel risk LD blocks, respectively, whose risk variants reciprocally confirm one another. Comorbidity was conferred by 3 novel independent SNPs. In silico analyses reported novel functional changes, including the binding site of glucocorticoid receptor-alpha [GR-α] on CRHR1 for transcription regulation. This is the first report of CRHR1 pleiotropic linkage/LD/association with peninsular familial MDD and T2D. CRHR1 contribution to MDD is stronger than to T2D and may antecede T2D onset. Our findings suggest a new molecular-based clinical entity of MDD-T2D and should be replicated in other ethnic groups.

Novel Risk Variants in the Oxytocin Receptor Gene (OXTR) Possibly Linked to and Associated with Familial Type 2 Diabetes.

The oxytocin system is well-known for its role in social bonding and reproduction. Recently, the oxytocin system was found to play other metabolic roles such as regulation of food intake, peripheral glucose uptake, and insulin sensitivity. Variants in OXTR gene have been associated with overeating, increased cardiovascular risk, and type 2 diabetes (T2D). We tested 20 microarray-derived single nucleotide polymorphisms in the OXTR gene in 212 Italian families with rich family history for T2D and found four novel and one previously reported variant suggestively significant for linkage and association with the risk of T2D. Our study has shed some light into the genetics of susceptibility to T2D at least in Italian families.

Computational characterization of double reduction in autotetraploid natural populations.

Population genetic theory has been well developed for diploid species, but its extension to study genetic diversity, variation and evolution in autopolyploids, a class of polyploids derived from the genome doubling of a single ancestral species, requires the incorporation of multisomic inheritance. Double reduction, which is characteristic of autopolyploidy, has long been believed to shape the evolutionary consequence of organisms in changing environments. Here, we develop a computational model for testing and estimating double reduction and its genomic distribution in autotetraploids. The model is implemented with the expectation-maximization (EM) algorithm to dissect unobservable allelic recombinations among multiple chromosomes, enabling the simultaneous estimation of allele frequencies and double reduction in natural populations. The framework fills an important gap in the population genetic theory of autopolyploids.

Long-read genome assembly and genetic architecture of fruit shape in the bottle gourd.

The bottle gourd (Lagenaria siceraria, Cucurbitaceae) is an important horticultural crop exhibiting tremendous diversity in fruit shape. The genetic architecture of fruit shape variation in this species remains unknown. We assembled a long-read-based, high-quality reference genome (ZAAS_Lsic_2.0) with a contig N50 value over 390-fold greater than the existing reference genomes. We then focused on dissection of fruit shape using a one-step geometric morphometrics-based functional mapping approach. We identified 11 quantitative trait loci (QTLs) responsible for fruit shape (fsQTLs), reconstructed their visible effects and revealed syntenic relationships of bottle gourd fsQTLs with 12 fsQTLs previously reported in cucumber, melon or watermelon. Homologs of several well-known and newly identified fruit shape genes, including SUN, OFP, AP2 and auxin transporters, were comapped with bottle gourd QTLs.

Implication of Melanocortin Receptor Genes in the Familial Comorbidity of Type 2 Diabetes and Depression.

The melanocortin receptors are G-protein-coupled receptors, which are essential components of the hypothalamic-pituitary-adrenal axis, and they mediate the actions of melanocortins (melanocyte-stimulating hormones: α-MSH, ß-MSH, and γ-MSH) as well as the adrenocorticotropin hormone (ACTH) in skin pigmentation, adrenal steroidogenesis, and stress response. Three melanocortin receptor genes (MC1R, MC2R, and MC5R) contribute to the risk of major depressive disorder (MDD), and one melanocortin receptor gene (MC4R) contributes to the risk of type 2 diabetes (T2D). MDD increases T2D risk in drug-naïve patients; thus, MDD and T2D commonly coexist. The five melanocortin receptor genes might confer risk for both disorders. However, they have never been investigated jointly to evaluate their potential contributing roles in the MDD-T2D comorbidity, specifically within families. In 212 Italian families with T2D and MDD, we tested 11 single nucleotide polymorphisms (SNPs) in the MC1R gene, 9 SNPs in MC2R, 3 SNPs in MC3R, 4 SNPs in MC4R, and 2 SNPs in MC5R. The testing used 2-point parametric linkage and linkage disequilibrium (LD) (i.e., association) analysis with four models (dominant with complete penetrance (D1), dominant with incomplete penetrance (D2), recessive with complete penetrance (R1), and recessive with incomplete penetrance (R2)). We detected significant (p ≤ 0.05) linkage and/or LD (i.e., association) to/with MDD for one SNP in MC2R (rs111734014) and one SNP in MC5R (rs2236700), and to/with T2D for three SNPs in MC1R (rs1805007 and rs201192930, and rs2228479), one SNP in MC2R (rs104894660), two SNPs in MC3R (rs3746619 and rs3827103), and one SNP in MC4R genes (Chr18-60372302). The linkage/LD/association was significant across different linkage patterns and different modes of inheritance. All reported variants are novel in MDD and T2D. This is the first study to report risk variants in MC1R, MC2R, and MC3R genes in T2D. MC2R and MC5R genes are replicated in MDD, with one novel variant each. Within our dataset, only the MC2R gene appears to confer risk for both MDD and T2D, albeit with different risk variants. To further clarity the role of the melanocortin receptor genes in MDD-T2D, these findings should be sought among other ethnicities as well.

Familial Linkage and Association of the NR3C1 Gene with Type 2 Diabetes and Depression Comorbidity.

Impairment in the hypothalamic-pituitary-adrenal (HPA) axis and cortisol pathway may be major contributing factors to the common pathogenesis of major depressive disorders (MDD) and type 2 diabetes (T2D). A significant player in the neuroendocrine HPA axis and cortisol response is the glucocorticoid receptor (GR), which is encoded by the nuclear receptor subfamily 3 group C member (NR3C1) gene. Variants in the NR3C1 gene have been reported in patients with MDD and obesity and found to confer reduced risk for quantitative metabolic traits and T2D in Cushing syndrome; variants have not been reported in T2D and MDD-T2D comorbid patients. We studied 212 original Italian families with a rich family history for T2D and tested 24 single nucleotide polymorphisms (SNPs) in the NR3C1 gene for linkage to and linkage disequilibrium (LD) with T2D and MDD across different inheritance models. We identified a total of 6 novel SNPs significantly linked/in LD to/with T2D (rs6196, rs10482633, rs13186836, rs13184611, rs10482681 and rs258751) and 1 SNP (rs10482668) significantly linked to/in LD with both T2D and MDD. These findings expand understanding of the role that NR3C1 variants play in modulating the risk of T2D-MDD comorbidity. Replication and functional studies are needed to confirm these findings.

Comorbidity of Novel CRHR2 Gene Variants in Type 2 Diabetes and Depression.

The corticotropin-releasing hormone receptor 2 (CRHR2) gene encodes CRHR2, contributing to the hypothalamic-pituitary-adrenal stress response and to hyperglycemia and insulin resistance. CRHR2-/- mice are hypersensitive to stress, and the CRHR2 locus has been linked to type 2 diabetes and depression. While CRHR2 variants confer risk for mood disorders, MDD, and type 2 diabetes, they have not been investigated in familial T2D and MDD. In 212 Italian families with type 2 diabetes and depression, we tested 17 CRHR2 single nucleotide polymorphisms (SNPs), using two-point parametric-linkage and linkage-disequilibrium (i.e., association) analysis (models: dominant-complete-penetrance-D1, dominant-incomplete-penetrance-D2, recessive-complete-penetrance-R1, recessive-incomplete-penetrance-R2). We detected novel linkage/linkage-disequilibrium/association to/with depression (3 SNPs/D1, 2 SNPs/D2, 3 SNPs/R1, 3 SNPs/R2) and type 2 diabetes (3 SNPs/D1, 2 SNPs/D2, 2 SNPs/R1, 1 SNP/R2). All detected risk variants are novel. Two depression-risk variants within one linkage-disequilibrium block replicate each other. Two independent novel SNPs were comorbid while the most significant conferred either depression- or type 2 diabetes-risk. Although the families were primarily ascertained for type 2 diabetes, depression-risk variants showed higher significance than type 2 diabetes-risk variants, implying CRHR2 has a stronger role in depression-risk than type 2 diabetes-risk. In silico analysis predicted variants' dysfunction. CRHR2 is for the first time linked to/in linkage-disequilibrium/association with depression-type 2 diabetes comorbidity and may underlie the shared genetic pathogenesis via pleiotropy.

HiGwas: how to compute longitudinal GWAS data in population designs.

SUMMARY: Genome-wide association studies (GWAS), particularly designed with thousands and thousands of single-nucleotide polymorphisms (SNPs) (big p) genotyped on tens of thousands of subjects (small n), are encountered by a major challenge of p ≪ n. Although the integration of longitudinal information can significantly enhance a GWAS's power to comprehend the genetic architecture of complex traits and diseases, an additional challenge is generated by an autocorrelative process. We have developed several statistical models for addressing these two challenges by implementing dimension reduction methods and longitudinal data analysis. To make these models computationally accessible to applied geneticists, we wrote an R package of computer software, HiGwas, designed to analyze longitudinal GWAS datasets. Functions in the package encompass single SNP analyses, significance-level adjustment, preconditioning and model selection for a high-dimensional set of SNPs. HiGwas provides the estimates of genetic parameters and the confidence intervals of these estimates. We demonstrate the features of HiGwas through real data analysis and vignette document in the package. AVAILABILITY AND IMPLEMENTATION: https://github.com/wzhy2000/higwas. CONTACT: rwu@phs.psu.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Prioritizing genetic variants in GWAS with lasso using permutation-assisted tuning.

MOTIVATION: Large scale genome-wide association studies (GWAS) have resulted in the identification of a wide range of genetic variants related to a host of complex traits and disorders. Despite their success, the individual single-nucleotide polymorphism (SNP) analysis approach adopted in most current GWAS can be limited in that it is usually biologically simple to elucidate a comprehensive genetic architecture of phenotypes and statistically underpowered due to heavy multiple-testing correction burden. On the other hand, multiple-SNP analyses (e.g. gene-based or region-based SNP-set analysis) are usually more powerful to examine the joint effects of a set of SNPs on the phenotype of interest. However, current multiple-SNP approaches can only draw an overall conclusion at the SNP-set level and does not directly inform which SNPs in the SNP-set are driving the overall genotype-phenotype association. RESULTS: In this article, we propose a new permutation-assisted tuning procedure in lasso (plasso) to identify phenotype-associated SNPs in a joint multiple-SNP regression model in GWAS. The tuning parameter of lasso determines the amount of shrinkage and is essential to the performance of variable selection. In the proposed plasso procedure, we first generate permutations as pseudo-SNPs that are not associated with the phenotype. Then, the lasso tuning parameter is delicately chosen to separate true signal SNPs and non-informative pseudo-SNPs. We illustrate plasso using simulations to demonstrate its superior performance over existing methods, and application of plasso to a real GWAS dataset gains new additional insights into the genetic control of complex traits. AVAILABILITY AND IMPLEMENTATION: R codes to implement the proposed methodology is available at https://github.com/xyz5074/plasso. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A multiple robust propensity score method for longitudinal analysis with intermittent missing data.

Longitudinal data are very popular in practice, but they are often missing in either outcomes or time-dependent risk factors, making them highly unbalanced and complex. Missing data may contain various missing patterns or mechanisms, and how to properly handle it for unbiased and valid inference still presents a significant challenge. Here, we propose a novel semiparametric framework for analyzing longitudinal data with both missing responses and covariates that are missing at random and intermittent, a general and widely encountered situation in observational studies. Within this framework, we consider multiple robust estimation procedures based on innovative calibrated propensity scores, which offers additional relaxation of the misspecification of missing data mechanisms and shows more satisfactory numerical performance. Also, the corresponding robust information criterion on consistent variable selection for our proposed model is developed based on empirical likelihood-based methods. These advocated methods are evaluated in both theory and extensive simulation studies in a variety of situations, showing competing properties and advantages compared to the existing approaches. We illustrate the utility of our approach by analyzing the data from the HIV Epidemiology Research Study.

np2 QTL: networking phenotypic plasticity quantitative trait loci across heterogeneous environments.

Despite its critical importance to our understanding of plant growth and adaptation, the question of how environment-induced plastic response is affected genetically remains elusive. Previous studies have shown that the reaction norm of an organism across environmental index obeys the allometrical scaling law of part-whole relationships. The implementation of this phenomenon into functional mapping can characterize how quantitative trait loci (QTLs) modulate the phenotypic plasticity of complex traits to heterogeneous environments. Here, we assemble functional mapping and allometry theory through Lokta-Volterra ordinary differential equations (LVODE) into an R-based computing platform, np2 QTL, aimed to map and visualize phenotypic plasticity QTLs. Based on LVODE parameters, np2 QTL constructs a bidirectional, signed and weighted network of QTL-QTL epistasis, whose emergent properties reflect the ecological mechanisms for genotype-environment interactions over any range of environmental change. The utility of np2 QTL was validated by comprehending the genetic architecture of phenotypic plasticity via the reanalysis of published plant height data involving 3502 recombinant inbred lines of maize planted in multiple discrete environments. np2 QTL also provides a tool for constructing a predictive model of phenotypic responses in extreme environments relative to the median environment.

A unified DNA sequence and non-DNA sequence mapping model of complex traits.

Increasing evidence shows that quantitative inheritance is based on both DNA sequence and non-DNA sequence variants. However, how to simultaneously detect these variants from a mapping study has been unexplored, hampering our effort to illustrate the detailed genetic architecture of complex traits. We address this issue by developing a unified model of quantitative trait locus (QTL) mapping based on an open-pollinated design composed of randomly sampling maternal plants from a natural population and their half-sib seeds. This design forms a two-level hierarchical platform for a joint linkage-linkage disequilibrium analysis of population structure. The EM algorithm was implemented to estimate and test DNA sequence-based effects and non-DNA sequence-based effects of QTLs. We applied this model to analyze genetic mapping data from the OP design of a gymnosperm coniferous species, Torreya grandis, identifying 25 significant DNA sequence and non-DNA sequence QTLs for seedling height and diameter growth in different years. Results from computer simulation show that the unified model has good statistical properties and is powerful for QTL detection. Our model enables the tests of how a complex trait is affected differently by DNA-based effects and non-DNA sequence-based transgenerational effects, thus allowing a more comprehensive picture of genetic architecture to be charted and quantified.

A dissection model for mapping complex traits.

Many quantitative traits are composites of other traits that contribute differentially to genetic variation. Quantitative trait locus (QTL) mapping of these composite traits can benefit by incorporating the mechanistic process of how their formation is mediated by the underlying components. We propose a dissection model by which to map these interconnected components traits under a joint likelihood setting. The model can test how a composite trait is determined by pleiotropic QTLs for its component traits or jointly by different sets of QTLs each responsible for a different component. The model can visualize the pattern of time-varying genetic effects for individual components and their impacts on composite traits. The dissection model was used to map two composite traits, stemwood volume growth decomposed into its stem height, stem diameter and stem form components for Euramerican poplar adult trees, and total lateral root length constituted by its average lateral root length and lateral root number components for Euphrates poplar seedlings. We found the pattern of how QTLs for different components contribute to phenotypic variation in composite traits. The detailed understanding of the genetic machineries of composite traits will not only help in the design of molecular breeding in plants and animals, but also shed light on the evolutionary processes of quantitative traits under natural selection.