A general framework for analyzing the genetic architecture of developmental characteristics

Modeling soybean growth: A mixed model approach

The evaluation of plant and animal growth, separately for genetic and environmental effects, is necessary for genetic understanding and genetic improvement of environmental responses of plants and animals. We propose to extend an existing approach that combines nonlinear mixed-effects model (NLMEM) and the stochastic approximation of the Expectation-Maximization algorithm (SAEM) to analyze genetic and environmental effects on plant growth. These tools are widely used in many fields but very rarely in plant biology. During model formulation, a nonlinear function describes the shape of growth, and random effects describe genetic and environmental effects and their variability. Genetic relationships among the varieties were also integrated into the model using a genetic relationship matrix. The SAEM algorithm was chosen as an efficient alternative to MCMC methods, which are more commonly used in the domain. It was implemented to infer the expected growth patterns in the analyzed population and the expected curves for each variety through a maximum-likelihood and a maximum-a-posteriori approaches, respectively. The obtained estimates can be used to predict the growth curves for each variety. We illustrate the strengths of the proposed approach using simulated data and soybean plant growth data obtained from a soybean cultivation experiment conducted at the Arid Land Research Center, Tottori University. In this experiment, plant height was measured daily using drones, and the growth was monitored for approximately 200 soybean cultivars for which whole-genome sequence data were available. The NLMEM approach improved our understanding of the determinants of soybean growth and can be successfully used for the genomic prediction of growth pattern characteristics.

Time-sequential detection of quantitative trait loci and candidate genes underlying the dynamic growth of Salix suchowensis

Elucidating the genetic factors underlying long-term biological processes remains challenging since the relevant genes and their effects may vary across different developmental stages. In this study, we carried out a large-scale field trial of the progeny of an F1 full-sib pedigree of Salix suchowensis and measured plant height and ground diameter periodically over a time course of 240 days. With the obtained data, we characterized plant growth rhythms and performed time-sequential analyses of quantitative trait loci underlying the dynamic growth of the plants. The dynamic mapping of quantitative trait loci revealed that stem height and ground diameter were under the control of four quantitative trait loci, and the effects of these quantitative trait loci varied greatly throughout the growth process, in which two quantitative trait loci were found to exert a pleiotropic effect determining the correlation between stem height and ground diameter. The analysis of candidate genes in the target genetic intervals showed that the pleiotropic effect of the two quantitative trait loci arises from the colocalization of genes with independent effects on stem height and ground diameter. Further examination of the expression patterns of the candidate genes indicated that height and circumference growth involve different activities of leaf and cambium tissues. This study provides unprecedented information to help us understand the dynamic growth of plants and presents an applicable strategy for elucidating the genetic mechanism underlying a long-term biological process by using plant growth as an example.

Genomic Prediction of Green Fraction Dynamics in Soybean Using Unmanned Aerial Vehicles Observations

With the widespread use of high-throughput phenotyping systems, growth process data are expected to become more easily available. By applying genomic prediction to growth data, it will be possible to predict the growth of untested genotypes. Predicting the growth process will be useful for crop breeding, as variability in the growth process has a significant impact on the management of plant cultivation. However, the integration of growth modeling and genomic prediction has yet to be studied in depth. In this study, we implemented new prediction models to propose a novel growth prediction scheme. Phenotype data of 198 soybean germplasm genotypes were acquired for 3 years in experimental fields in Tottori, Japan. The longitudinal changes in the green fractions were measured using UAV remote sensing. Then, a dynamic model was fitted to the green fraction to extract the dynamic characteristics of the green fraction as five parameters. Using the estimated growth parameters, we developed models for genomic prediction of the growth process and tested whether the inclusion of the dynamic model contributed to better prediction of growth. Our proposed models consist of two steps: first, predicting the parameters of the dynamics model with genomic prediction, and then substituting the predicted values for the parameters of the dynamics model. By evaluating the heritability of the growth parameters, the dynamic model was able to effectively extract genetic diversity in the growth characteristics of the green fraction. In addition, the proposed prediction model showed higher prediction accuracy than conventional genomic prediction models, especially when the future growth of the test population is a prediction target given the observed values in the first half of growth as training data. This indicates that our model was able to successfully combine information from the early growth period with phenotypic data from the training population for prediction. This prediction method could be applied to selection at an early growth stage in crop breeding, and could reduce the cost and time of field trials.

Inferring multilayer interactome networks shaping phenotypic plasticity and evolution

Phenotypic plasticity represents a capacity by which the organism changes its phenotypes in response to environmental stimuli. Despite its pivotal role in adaptive evolution, how phenotypic plasticity is genetically controlled remains elusive. Here, we develop a unified framework for coalescing all single nucleotide polymorphisms (SNPs) from a genome-wide association study (GWAS) into a quantitative graph. This framework integrates functional genetic mapping, evolutionary game theory, and predator-prey theory to decompose the net genetic effect of each SNP into its independent and dependent components. The independent effect arises from the intrinsic capacity of a SNP, only expressed when it is in isolation, whereas the dependent effect results from the extrinsic influence of other SNPs. The dependent effect is conceptually beyond the traditional definition of epistasis by not only characterizing the strength of epistasis but also capturing the bi-causality of epistasis and the sign of the causality. We implement functional clustering and variable selection to infer multilayer, sparse, and multiplex interactome networks from any dimension of genetic data. We design and conduct two GWAS experiments using Staphylococcus aureus, aimed to test the genetic mechanisms underlying the phenotypic plasticity of this species to vancomycin exposure and Escherichia coli coexistence. We reconstruct the two most comprehensive genetic networks for abiotic and biotic phenotypic plasticity. Pathway analysis shows that SNP-SNP epistasis for phenotypic plasticity can be annotated to protein-protein interactions through coding genes. Our model can unveil the regulatory mechanisms of significant loci and excavate missing heritability from some insignificant loci. Our multilayer genetic networks provide a systems tool for dissecting environment-induced evolution.

Modeling genome-wide by environment interactions through omnigenic interactome networks

How genes interact with the environment to shape phenotypic variation and evolution is a fundamental question intriguing to biologists from various fields. Existing linear models built on single genes are inadequate to reveal the complexity of genotype-environment (G-E) interactions. Here, we develop a conceptual model for mechanistically dissecting G-E interplay by integrating previously disconnected theories and methods. Under this integration, evolutionary game theory, developmental modularity theory, and a variable selection method allow us to reconstruct environment-induced, maximally informative, sparse, and casual multilayer genetic networks. We design and conduct two mapping experiments by using a desert-adapted tree species to validate the biological application of the model proposed. The model identifies previously uncharacterized molecular mechanisms that mediate trees' response to saline stress. Our model provides a tool to comprehend the genetic architecture of trait variation and evolution and trace the information flow of each gene toward phenotypes within omnigenic networks.

Functional QTL mapping and genomic prediction of canopy height in wheat measured using a robotic field phenotyping platform

Genetic studies increasingly rely on high-throughput phenotyping, but the resulting longitudinal data pose analytical challenges. We used canopy height data from an automated field phenotyping platform to compare several approaches to scanning for quantitative trait loci (QTLs) and performing genomic prediction in a wheat recombinant inbred line mapping population based on up to 26 sampled time points (TPs). We detected four persistent QTLs (i.e. expressed for most of the growing season), with both empirical and simulation analyses demonstrating superior statistical power of detecting such QTLs through functional mapping approaches compared with conventional individual TP analyses. In contrast, even very simple individual TP approaches (e.g. interval mapping) had superior detection power for transient QTLs (i.e. expressed during very short periods). Using spline-smoothed phenotypic data resulted in improved genomic predictive abilities (5-8% higher than individual TP prediction), while the effect of including significant QTLs in prediction models was relatively minor (<1-4% improvement). Finally, although QTL detection power and predictive ability generally increased with the number of TPs analysed, gains beyond five or 10 TPs chosen based on phenological information had little practical significance. These results will inform the development of an integrated, semi-automated analytical pipeline, which will be more broadly applicable to similar data sets in wheat and other crops.

Functional QTL mapping and genomic prediction of canopy height in wheat measured using a robotic field phenotyping platform

Genetic studies increasingly rely on high-throughput phenotyping, but the resulting longitudinal data pose analytical challenges. We used canopy height data from an automated field phenotyping platform to compare several approaches to scanning for quantitative trait loci (QTLs) and performing genomic prediction in a wheat recombinant inbred line mapping population based on up to 26 sampled time points (TPs). We detected four persistent QTLs (i.e. expressed for most of the growing season), with both empirical and simulation analyses demonstrating superior statistical power of detecting such QTLs through functional mapping approaches compared with conventional individual TP analyses. In contrast, even very simple individual TP approaches (e.g. interval mapping) had superior detection power for transient QTLs (i.e. expressed during very short periods). Using spline-smoothed phenotypic data resulted in improved genomic predictive abilities (5-8% higher than individual TP prediction), while the effect of including significant QTLs in prediction models was relatively minor (<1-4% improvement). Finally, although QTL detection power and predictive ability generally increased with the number of TPs analysed, gains beyond five or 10 TPs chosen based on phenological information had little practical significance. These results will inform the development of an integrated, semi-automated analytical pipeline, which will be more broadly applicable to similar data sets in wheat and other crops.

Genome-wide association study identified novel candidate loci affecting wood formation in Norway spruce

Norway spruce is a boreal forest tree species of significant ecological and economic importance. Hence there is a strong imperative to dissect the genetics underlying important wood quality traits in the species. We performed a functional genome-wide association study (GWAS) of 17 wood traits in Norway spruce using 178 101 single nucleotide polymorphisms (SNPs) generated from exome genotyping of 517 mother trees. The wood traits were defined using functional modelling of wood properties across annual growth rings. We applied a Least Absolute Shrinkage and Selection Operator (LASSO-based) association mapping method using a functional multilocus mapping approach that utilizes latent traits, with a stability selection probability method as the hypothesis testing approach to determine a significant quantitative trait locus. The analysis provided 52 significant SNPs from 39 candidate genes, including genes previously implicated in wood formation and tree growth in spruce and other species. Our study represents a multilocus GWAS for complex wood traits in Norway spruce. The results advance our understanding of the genetics influencing wood traits and identifies candidate genes for future functional studies.

Mapping and Predicting Non-Linear Brassica rapa Growth Phenotypes Based on Bayesian and Frequentist Complex Trait Estimation

Predicting phenotypes based on genotypes and understanding the effects of complex multi-locus traits on plant performance requires a description of the underlying developmental processes, growth trajectories, and their genomic architecture. Using data from Brassica rapa genotypes grown in multiple density settings and seasons, we applied a hierarchical Bayesian Function-Valued Trait (FVT) approach to fit logistic growth curves to leaf phenotypic data (length and width) and characterize leaf development. We found evidence of genetic variation in phenotypic plasticity of rate and duration of leaf growth to growing season. In contrast, the magnitude of the plastic response for maximum leaf size was relatively small, suggesting that growth dynamics vs. final leaf sizes have distinct patterns of environmental sensitivity. Consistent with patterns of phenotypic plasticity, several QTL-by-year interactions were significant for parameters describing leaf growth rates and durations but not leaf size. In comparison to frequentist approaches for estimating leaf FVT, Bayesian trait estimation resulted in more mapped QTL that tended to have greater average LOD scores and to explain a greater proportion of trait variance. We then constructed QTL-based predictive models for leaf growth rate and final size using data from one treatment (uncrowded plants in one growing season). Models successfully predicted non-linear developmental phenotypes for genotypes not used in model construction and, due to a lack of QTL-by-treatment interactions, predicted phenotypes across sites differing in plant density.

Evo-Devo-EpiR: a genome-wide search platform for epistatic control on the evolution of development

Evo-devo is a theory proposed to study how phenotypes evolve by comparing the developmental processes of different organisms or the same organism experiencing changing environments. It has been recognized that nonallelic interactions at different genes or quantitative trait loci, known as epistasis, may play a pivotal role in the evolution of development, but it has proven difficult to quantify and elucidate this role into a coherent picture. We implement a high-dimensional genome-wide association study model into the evo-devo paradigm and pack it into the R-based Evo-Devo-EpiR, aimed at facilitating the genome-wide landscaping of epistasis for the diversification of phenotypic development. By analyzing a high-throughput assay of DNA markers and their pairs simultaneously, Evo-Devo-EpiR is equipped with a capacity to systematically characterize various epistatic interactions that impact on the pattern and timing of development and its evolution. Enabling a global search for all possible genetic interactions for developmental processes throughout the whole genome, Evo-Devo-EpiR provides a computational tool to illustrate a precise genotype-phenotype map at interface between epistasis, development and evolution.

Computational identification of genes modulating stem height-diameter allometry

The developmental variation in stem height with respect to stem diameter is related to a broad range of ecological and evolutionary phenomena in trees, but the underlying genetic basis of this variation remains elusive. We implement a dynamic statistical model, functional mapping, to formulate a general procedure for the computational identification of quantitative trait loci (QTLs) that control stem height-diameter allometry during development. Functional mapping integrates the biological principles underlying trait formation and development into the association analysis of DNA genotype and endpoint phenotype, thus providing an incentive for understanding the mechanistic interplay between genes and development. Built on the basic tenet of functional mapping, we explore two core ecological scenarios of how stem height and stem diameter covary in response to environmental stimuli: (i) trees pioneer sunlit space by allocating more growth to stem height than diameter and (ii) trees maintain their competitive advantage through an inverse pattern. The model is equipped to characterize 'pioneering' QTLs (piQTLs) and 'maintaining' QTLs (miQTLs) which modulate these two ecological scenarios, respectively. In a practical application to a mapping population of full-sib hybrids derived from two Populus species, the model has well proven its versatility by identifying several piQTLs that promote height growth at a cost of diameter growth and several miQTLs that benefit radial growth at a cost of height growth. Judicious application of functional mapping may lead to improved strategies for studying the genetic control of the formation mechanisms underlying trade-offs among quantities of assimilates allocated to different growth parts.

Goldfish morphology as a model for evolutionary developmental biology

Morphological variation of the goldfish is known to have been established by artificial selection for ornamental purposes during the domestication process. Chinese texts that date to the Song dynasty contain descriptions of goldfish breeding for ornamental purposes, indicating that the practice originated over one thousand years ago. Such a well-documented goldfish breeding process, combined with the phylogenetic and embryological proximities of this species with zebrafish, would appear to make the morphologically diverse goldfish strains suitable models for evolutionary developmental (evodevo) studies. However, few modern evodevo studies of goldfish have been conducted. In this review, we provide an overview of the historical background of goldfish breeding, and the differences between this teleost and zebrafish from an evolutionary perspective. We also summarize recent progress in the field of molecular developmental genetics, with a particular focus on the twin-tail goldfish morphology. Furthermore, we discuss unanswered questions relating to the evolution of the genome, developmental robustness, and morphologies in the goldfish lineage, with the goal of blazing a path toward an evodevo study paradigm using this teleost species as a new model species. For further resources related to this article, please visit the WIREs website.

E-Index for Differentiating Complex Dynamic Traits

While it is a daunting challenge in current biology to understand how the underlying network of genes regulates complex dynamic traits, functional mapping, a tool for mapping quantitative trait loci (QTLs) and single nucleotide polymorphisms (SNPs), has been applied in a variety of cases to tackle this challenge. Though useful and powerful, functional mapping performs well only when one or more model parameters are clearly responsible for the developmental trajectory, typically being a logistic curve. Moreover, it does not work when the curves are more complex than that, especially when they are not monotonic. To overcome this inadaptability, we therefore propose a mathematical-biological concept and measurement, E-index (earliness-index), which cumulatively measures the earliness degree to which a variable (or a dynamic trait) increases or decreases its value. Theoretical proofs and simulation studies show that E-index is more general than functional mapping and can be applied to any complex dynamic traits, including those with logistic curves and those with nonmonotonic curves. Meanwhile, E-index vector is proposed as well to capture more subtle differences of developmental patterns.

Plasticity in Vegetative Growth over Contrasted Growing Sites of an F1 Olive Tree Progeny during Its Juvenile Phase

Climatic changes impact fruit tree growth and severely limit their production. Investigating the tree ability to cope with environmental variations is thus necessary to adapt breeding and management strategies in order to ensure sustainable production. In this study, we assessed the genetic parameters and genotype by environment interaction (GxE) during the early tree growth. One hundred and twenty olive seedlings derived from the cross ‘Olivière’ x ‘Arbequina’ were examined across two sites with contrasted environments, accounting for ontogenetic trends over three years. Models including the year of growth, branching order, environment, genotype effects, and their interactions were built with variance function and covariance structure of residuals when necessary. After selection of a model, broad sense heritabilities were estimated. Despite strong environmental effect on most traits, no GxE was found. Moreover, the internal structure of traits co-variation was similar in both sites. Ontogenetic growth variation, related to (i) the overall tree form and (ii) the growth and branching habit at growth unit scale, was not altered by the environment. Finally, a moderate to strong genetic control was identified for traits at the whole tree scale and at internode scale. Among all studied traits, the maximal internode length exhibited the highest heritability (H² = 0.74). Considering the determinant role of this trait in tree architecture and its stability across environments, this study consolidates its relevance for breeding.

Mapping complex traits as a dynamic system

Despite increasing emphasis on the genetic study of quantitative traits, we are still far from being able to chart a clear picture of their genetic architecture, given an inherent complexity involved in trait formation. A competing theory for studying such complex traits has emerged by viewing their phenotypic formation as a "system" in which a high-dimensional group of interconnected components act and interact across different levels of biological organization from molecules through cells to whole organisms. This system is initiated by a machinery of DNA sequences that regulate a cascade of biochemical pathways to synthesize endophenotypes and further assemble these endophenotypes toward the end-point phenotype in virtue of various developmental changes. This review focuses on a conceptual framework for genetic mapping of complex traits by which to delineate the underlying components, interactions and mechanisms that govern the system according to biological principles and understand how these components function synergistically under the control of quantitative trait loci (QTLs) to comprise a unified whole. This framework is built by a system of differential equations that quantifies how alterations of different components lead to the global change of trait development and function, and provides a quantitative and testable platform for assessing the multiscale interplay between QTLs and development. The method will enable geneticists to shed light on the genetic complexity of any biological system and predict, alter or engineer its physiological and pathological states.

An allometric model for mapping seed development in plants

Despite a tremendous effort to map quantitative trait loci (QTLs) responsible for agriculturally and biologically important traits in plants, our understanding of how a QTL governs the developmental process of plant seeds remains elusive. In this article, we address this issue by describing a model for functional mapping of seed development through the incorporation of the relationship between vegetative and reproductive growth. The time difference of reproductive from vegetative growth is described by Reeve and Huxley’s allometric equation. Thus, the implementation of this equation into the framework of functional mapping allows dynamic QTLs for seed development to be identified more precisely. By estimating and testing mathematical parameters that define Reeve and Huxley’s allometric equations of seed growth, the dynamic pattern of the genetic effects of the QTLs identified can be analyzed. We used the model to analyze a soybean data, leading to the detection of QTLs that control the growth of seed dry weight. Three dynamic QTLs, located in two different linkage groups, were detected to affect growth curves of seed dry weight. The QTLs detected may be used to improve seed yield with marker-assisted selection by altering the pattern of seed development in a hope to achieve a maximum size of seeds at a harvest time.

Dynamic quantitative trait locus analysis of seed vigor at three maturity stages in rice

Seed vigor is an important characteristic of seed quality. In this study, one rice population of recombinant inbred lines (RILs) was used to determine the genetic characteristics of seed vigor, including the germination potential, germination rate, germination index and time for 50% of germination, at 4 (early), 5 (middle) and 6 weeks (late) after heading in two years. A total of 24 additive and 9 epistatic quantitative trait loci (QTL) for seed vigor were identified using QTL Cartographer and QTLNetwork program respectively in 2012; while 32 simple sequence repeat (SSR) markers associated with seed vigor were detected using bulked segregant analysis (BSA) in 2013. The additive, epistatic and QTL × development interaction effects regulated the dry maturity developmental process to improve seed vigor in rice. The phenotypic variation explained by each additive, epistatic QTL and QTL × development interaction ranged from 5.86 to 40.67%, 4.64 to 11.28% and 0.01 to 1.17%, respectively. The QTLs were rarely co-localized among the different maturity stages; more QTLs were expressed at the early maturity stage followed by the late and middle stages. Twenty additive QTLs were stably expressed in two years which might play important roles in establishment of seed vigor in different environments. By comparing chromosomal positions of these stably expressed additive QTLs with those previously identified, the regions of QTL for seed vigor are likely to coincide with QTL for grain size, low temperature germinability and seed dormancy; while 5 additive QTL might represent novel genes. Using four selected RILs, three cross combinations of seed vigor for the development of RIL populations were predicted; 19 elite alleles could be pyramided by each combination.

Genetic linkage map construction and QTL identification of juvenile growth traits in Torreya grandis

Torreya grandis Fort. ex Lindl, a conifer species widely distributed in Southeastern China, is of high economic value by producing edible, nutrient seeds. However, knowledge about the genome structure and organization of this species is poorly understood, thereby limiting the effective use of its gene resources. Here, we report on a first genetic linkage map for Torreya grandis using 96 progeny randomly chosen from a half-sib family of a commercially cultivated variety of this species, Torreya grandis Fort. ex Lindl cv. Merrillii. The map contains 262 molecular markers, i.e., 75 random amplified polymorphic DNAs (RAPD), 119 inter-simple sequence repeats (ISSR) and 62 amplified fragments length polymorphisms (AFLP), and spans a total of 7,139.9 cM, separated by 10 linkage groups. The linkage map was used to map quantitative trait loci (QTLs) associated with juvenile growth traits by functional mapping. We identified four basal diameter-related QTLs on linkage groups 1, 5 and 9; four height-related QTLs on linkage groups 1, 2, 5 and 8. It was observed that the genetic effects of QTLs on growth traits vary with age, suggesting the dynamic behavior of growth QTLs. Part of the QTLs was found to display a pleiotropic effect on basal diameter growth and height growth.

A model-free approach for detecting interactions in genetic association studies

Over the past few decades, genome-wide association studies analyzed by efficient statistical procedures have successfully identified single-nucleotide polymorphisms (SNPs) that are associated with complex traits or human diseases. However, due to the overwhelming number of SNPs, most approaches have focused on additive genetic model without genome-wide SNP-SNP interactions. In this study, we propose an efficient statistical procedure in a genetic model-free framework for detecting SNPs exhibiting main genetic effects as well as epistatic interactions. Specifically, the association between phenotype and genotype is characterized by an unknown function to be estimated using nonparametric techniques, and a two-stage non-parametric independence screening procedure is proposed to sequentially identify potentially important main genetic effects and interactions. Finally, the subset of genetic predictors implied by two-stage non-parametric independence screening is analyzed by penalized regressions such as LASSO, and a final model is identified. In this framework, specific genetic model is not assumed and interactions are not only among marginally important SNPs. Therefore, SNPs that are involved in genetic regulatory networks but missed by previous studies are expected to be recognized. In simulation studies, we show that the procedure is computationally efficient and has an outstanding finite sample performance in selecting potential SNPs as well as SNP-SNP interactions. A real data analysis further indicates the importance of epistatic interactions in explaining body mass index.

From flower to seed: identifying phenological markers and reliable growth functions to model reproductive development in the common bean (Phaseolus vulgaris L.)

The lack of dependable morphological indicators for the onset and end of seed growth has hindered modeling work in the common bean (Phaseolus vulgaris L.). We have addressed this problem through the use of mathematical growth functions to analyse and identify critical developmental stages, which can be linked to existing developmental indices. We performed this study under greenhouse conditions with an Andean and a Mesoamerican genotype of contrasting pod and seed phenotypes, and three selected recombinant inbred lines. Pods from tagged flowers were harvested at regular time intervals for various measurements. Differences in flower production and seed and pod growth trajectories among genotypes were detected via comparisons of parameters of fitted growth functions. Regardless of the genotype, the end of pod elongation marked the beginning of seed growth, which lasted until pods displayed a sharp decline in color, or pod hue angle. These results suggest that the end of pod elongation and the onset of color change are reliable indicators of important developmental transitions in the seed, even for widely differing pod phenotypes. We also provide a set of equations that can be used to model different aspects of reproductive growth and development in the common bean.

Genetic mapping and genomic selection using recombination breakpoint data

The correct models for quantitative trait locus mapping are the ones that simultaneously include all significant genetic effects. Such models are difficult to handle for high marker density. Improving statistical methods for high-dimensional data appears to have reached a plateau. Alternative approaches must be explored to break the bottleneck of genomic data analysis. The fact that all markers are located in a few chromosomes of the genome leads to linkage disequilibrium among markers. This suggests that dimension reduction can also be achieved through data manipulation. High-density markers are used to infer recombination breakpoints, which then facilitate construction of bins. The bins are treated as new synthetic markers. The number of bins is always a manageable number, on the order of a few thousand. Using the bin data of a recombinant inbred line population of rice, we demonstrated genetic mapping, using all bins in a simultaneous manner. To facilitate genomic selection, we developed a method to create user-defined (artificial) bins, in which breakpoints are allowed within bins. Using eight traits of rice, we showed that artificial bin data analysis often improves the predictability compared with natural bin data analysis. Of the eight traits, three showed high predictability, two had intermediate predictability, and two had low predictability. A binary trait with a known gene had predictability near perfect. Genetic mapping using bin data points to a new direction of genomic data analysis.

QTL mapping of growth-related traits in a full-sib family of rubber tree (Hevea brasiliensis) evaluated in a sub-tropical climate

The rubber tree (Hevea spp.), cultivated in equatorial and tropical countries, is the primary plant used in natural rubber production. Due to genetic and physiological constraints, inbred lines of this species are not available. Therefore, alternative approaches are required for the characterization of this species, such as the genetic mapping of full-sib crosses derived from outbred parents. In the present study, an integrated genetic map was obtained for a full-sib cross family with simple sequence repeats (SSRs) and expressed sequence tag (EST-SSR) markers, which can display different segregation patterns. To study the genetic architecture of the traits related to growth in two different conditions (winter and summer), quantitative trait loci (QTL) mapping was also performed using the integrated map. Traits evaluated were height and girth growth, and the statistical model was based in an extension of composite interval mapping. The obtained molecular genetic map has 284 markers distributed among 23 linkage groups with a total length of 2688.8 cM. A total of 18 QTLs for growth traits during the summer and winter seasons were detected. A comparison between the different seasons was also conducted. For height, QTLs detected during the summer season were different from the ones detected during winter season. This type of difference was also observed for girth. Integrated maps are important for genetics studies in outbred species because they represent more accurately the polymorphisms observed in the genitors. QTL mapping revealed several interesting findings, such as a dominance effect and unique segregation patterns that each QTL could exhibit, which were independent of the flanking markers. The QTLs identified in this study, especially those related to phenotypic variation associated with winter could help studies of marker-assisted selection that are particularly important when the objective of a breeding program is to obtain phenotypes that are adapted to sub-optimal regions.

Comparative analysis of quantitative trait loci for body weight, growth rate and growth curve parameters from 3 to 72 weeks of age in female chickens of a broiler-layer cross

Background

Comparisons of quantitative trait loci (QTL) for growth and parameters of growth curves assist in understanding the genetics and ultimately the physiology of growth. Records of body weight at 3, 6, 12, 24, 48 and 72 weeks of age and growth rate between successive age intervals of about 500 F₂ female chickens of the Roslin broiler-layer cross were available for analysis. These data were analysed to detect and compare QTL for body weight, growth rate and parameters of the Gompertz growth function.

Results

Over 50 QTL were identified for body weight at specific ages and most were also detected in the nearest preceding and/or subsequent growth stage. The sum of the significant and suggestive additive effects for bodyweight at specific ages accounted for 23-43% of the phenotypic variation. A single QTL for body weight on chromosome 4 at 48 weeks of age had the largest additive effect (550.4 ± 68.0 g, 11.5% of the phenotypic variation) and a QTL at a similar position accounted 14.5% of the phenotypic variation at 12 weeks of age. Age specific QTL for growth rate were detected suggesting that there are specific genes that affect developmental processes during the different stages of growth. Relatively few QTL influencing Gompertz growth curve parameters were detected and overlapped with loci affecting growth rate. Dominance effects were generally not significant but from 12 weeks of age they exceeded the additive effect in a few cases. No evidence for epistatic QTL pairs was found.

Conclusions

The results confirm the location for body weight and body weight gain during growth that were identified in previous studies and were consistent with QTL for the parameters of the Gompertz growth function. Chromosome 4 explained a relatively large proportion of the observed growth variation across the different ages, and also harboured most of the detected QTL for Gompertz parameters, confirming its importance in controlling growth. Very few QTL were detected for body weight or gain at 48 and 72 weeks of age, probably reflecting the effect of differences in reproduction and random environmental effects.

A statistical procedure to map high-order epistasis for complex traits

Genetic interactions or epistasis have been thought to play a pivotal role in shaping the formation, development and evolution of life. Previous work focused on lower-order interactions between a pair of genes, but it is obviously inadequate to explain a complex network of genetic interactions and pathways. We review and assess a statistical model for characterizing high-order epistasis among more than two genes or quantitative trait loci (QTLs) that control a complex trait. The model includes a series of start-of-the-art standard procedures for estimating and testing the nature and magnitude of QTL interactions. Results from simulation studies and real data analysis warrant the statistical properties of the model and its usefulness in practice. High-order epistatic mapping will provide a routine procedure for charting a detailed picture of the genetic regulation mechanisms underlying the phenotypic variation of complex traits.

Dynamic modeling of genes controlling cancer stem cell proliferation

The growing evidence that cancer originates from stem cells (SC) holds a great promise to eliminate this disease by designing specific drug therapies for removing cancer SC. Translation of this knowledge into predictive tests for the clinic is hampered due to the lack of methods to discriminate cancer SC from non-cancer SC. Here, we address this issue by describing a conceptual strategy for identifying the genetic origins of cancer SC. The strategy incorporates a high-dimensional group of differential equations that characterizes the proliferation, differentiation, and reprogramming of cancer SC in a dynamic cellular and molecular system. The deployment of robust mathematical models will help uncover and explain many still unknown aspects of cell behavior, tissue function, and network organization related to the formation and division of cancer SC. The statistical method developed allows biologically meaningful hypotheses about the genetic control mechanisms of carcinogenesis and metastasis to be tested in a quantitative manner.

Varying coefficient models for mapping quantitative trait loci using recombinant inbred intercrosses

There has been a great deal of interest in the development of methodologies to map quantitative trait loci (QTL) using experimental crosses in the last 2 decades. Experimental crosses in animal and plant sciences provide important data sources for mapping QTL through linkage analysis. The Collaborative Cross (CC) is a renewable mouse resource that is generated from eight genetically diverse founder strains to mimic the genetic diversity in humans. The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines share similar genetic structures of F(2) individuals but with up to eight alleles segregating at any one locus. In contrast to F(2) mice, genotypes of RIX can be inferred from the genotypes of their RI parents and can be produced repeatedly. Also, RIX mice typically do not share the same degree of relatedness. This unbalanced genetic relatedness requires careful statistical modeling to avoid false-positive findings. Many quantitative traits are inherently complex with genetic effects varying with other covariates, such as age. For such complex traits, if phenotype data can be collected over a wide range of ages across study subjects, their dynamic genetic patterns can be investigated. Parametric functions, such as sigmoidal or logistic functions, have been used for such purpose. In this article, we propose a flexible nonparametric time-varying coefficient QTL mapping method for RIX data. Our method allows the QTL effects to evolve with time and naturally extends classical parametric QTL mapping methods. We model the varying genetic effects nonparametrically with the B-spline bases. Our model investigates gene-by-time interactions for RIX data in a very flexible nonparametric fashion. Simulation results indicate that the varying coefficient QTL mapping has higher power and mapping precision compared to parametric models when the assumption of constant genetic effects fails. We also apply a modified permutation procedure to control overall significance level.

Modeling haplotype-haplotype interactions in case-control genetic association studies

Haplotype analysis has been increasingly used to study the genetic basis of human diseases, but models for characterizing genetic interactions between haplotypes from different chromosomal regions have not been well developed in the current literature. In this article, we describe a statistical model for testing haplotype-haplotype interactions for human diseases with a case-control genetic association design. The model is formulated on a contingency table in which cases and controls are typed for the same set of molecular markers. By integrating well-established quantitative genetic principles, the model is equipped with a capacity to characterize physiologically meaningful epistasis arising from interactions between haplotypes from different chromosomal regions. The model allows the partition of epistasis into different components due to additive × additive, additive × dominance, dominance × additive, and dominance × dominance interactions. We derive the EM algorithm to estimate and test the effects of each of these components on differences in the pattern of genetic variation between cases and controls and, therefore, examine their role in the pathogenesis of human diseases. The method was further extended to investigate gene-environment interactions expressed at the haplotype level. The statistical properties of the models were investigated through simulation studies and its usefulness and utilization validated by analyzing the genetic association of sarcoidosis from a human genetics project.

Functional mapping of dynamic traits with robust t-distribution

Functional mapping has been a powerful tool in mapping quantitative trait loci (QTL) underlying dynamic traits of agricultural or biomedical interest. In functional mapping, multivariate normality is often assumed for the underlying data distribution, partially due to the ease of parameter estimation. The normality assumption however could be easily violated in real applications due to various reasons such as heavy tails or extreme observations. Departure from normality has negative effect on testing power and inference for QTL identification. In this work, we relax the normality assumption and propose a robust multivariate -distribution mapping framework for QTL identification in functional mapping. Simulation studies show increased mapping power and precision with the distribution than that of a normal distribution. The utility of the method is demonstrated through a real data analysis.

A mathematical framework for functional mapping of complex phenotypes using delay differential equations

All biological phenomena occurring at different levels of organization from cells to organisms can be modeled as a dynamic system, in which the underlying components interact dynamically to comprehend its biological function. Such a systems modeling approach facilitates the use of biochemically and biophysically detailed mathematical models to describe and quantify "living cells," leading to an in-depth and precise understanding of the behavior, development and function of a biological system. Here, we illustrate how this approach can be used to map genes or quantitative trait loci (QTLs) that control a complex trait using the example of the circadian rhythm system which has been at the forefront of analytical mathematical modeling for many years. We integrate a system of biologically meaningful delay differential equations (DDEs) into functional mapping, a statistical model designed to map dynamic QTLs involved in biological processes. The DDEs model the ability of circadian rhythm to generate autonomously sustained oscillations with a period close to 24h, in terms of time-varying mRNA and protein abundances. By incorporating the Runge-Kutta fourth order algorithm within the likelihood-based context of functional mapping, we estimated the genetic parameters that define the periodic pattern of QTL effects on time-varying mRNA and protein abundances and their dynamic association as well as the linkage disequilibrium of the QTL and a marker. We prove theorems about how to choose appropriate parameters to guarantee periodic oscillations. We further used simulation studies to investigate how a QTL influences the period and the amplitude of circadian oscillations through changing model parameters. The model provides a quantitative framework for assessing the interplay between genetic effects of QTLs and rhythmic responses.

Bayesian functional mapping of dynamic quantitative traits

Without consideration of other linked QTLs responsible for dynamic trait, original functional mapping based on a single QTL model is not optimal for analyzing multiple dynamic trait loci. Despite that composite functional mapping incorporates the effects of genetic background outside the tested QTL in mapping model, the arbitrary choice of background markers also impact on the power of QTL detection. In this study, we proposed Bayesian functional mapping strategy that can simultaneously identify multiple QTL controlling developmental patterns of dynamic traits over the genome. Our proposed method fits the change of each QTL effect with the time by Legendre polynomial and takes the residual covariance structure into account using the first autoregressive equation. Also, Bayesian shrinkage estimation was employed to estimate the model parameters. Especially, we specify the gamma distribution as the prior for the first-order auto-regressive coefficient, which will guarantee the convergence of Bayesian sampling. Simulations showed that the proposed method could accurately estimate the QTL parameters and had a greater statistical power of QTL detection than the composite functional mapping. A real data analysis of leaf age growth in rice is used for the demonstration of our method. It shows that our Bayesian functional mapping can detect more QTLs as compared to composite functional mapping.

A flexible estimating equations approach for mapping function-valued traits

In genetic studies, many interesting traits, including growth curves and skeletal shape, have temporal or spatial structure. They are better treated as curves or function-valued traits. Identification of genetic loci contributing to such traits is facilitated by specialized methods that explicitly address the function-valued nature of the data. Current methods for mapping function-valued traits are mostly likelihood-based, requiring specification of the distribution and error structure. However, such specification is difficult or impractical in many scenarios. We propose a general functional regression approach based on estimating equations that is robust to misspecification of the covariance structure. Estimation is based on a two-step least-squares algorithm, which is fast and applicable even when the number of time points exceeds the number of samples. It is also flexible due to a general linear functional model; changing the number of covariates does not necessitate a new set of formulas and programs. In addition, many meaningful extensions are straightforward. For example, we can accommodate incomplete genotype data, and the algorithm can be trivially parallelized. The framework is an attractive alternative to likelihood-based methods when the covariance structure of the data is not known. It provides a good compromise between model simplicity, statistical efficiency, and computational speed. We illustrate our method and its advantages using circadian mouse behavioral data.

Simultaneous estimation of multiple quantitative trait loci and growth curve parameters through hierarchical Bayesian modeling

A novel hierarchical quantitative trait locus (QTL) mapping method using a polynomial growth function and a multiple-QTL model (with no dependence in time) in a multitrait framework is presented. The method considers a population-based sample where individuals have been phenotyped (over time) with respect to some dynamic trait and genotyped at a given set of loci. A specific feature of the proposed approach is that, instead of an average functional curve, each individual has its own functional curve. Moreover, each QTL can modify the dynamic characteristics of the trait value of an individual through its influence on one or more growth curve parameters. Apparent advantages of the approach include: (1) assumption of time-independent QTL and environmental effects, (2) alleviating the necessity for an autoregressive covariance structure for residuals and (3) the flexibility to use variable selection methods. As a by-product of the method, heritabilities and genetic correlations can also be estimated for individual growth curve parameters, which are considered as latent traits. For selecting trait-associated loci in the model, we use a modified version of the well-known Bayesian adaptive shrinkage technique. We illustrate our approach by analysing a sub sample of 500 individuals from the simulated QTLMAS 2009 data set, as well as simulation replicates and a real Scots pine (Pinus sylvestris) data set, using temporal measurements of height as dynamic trait of interest.

Asymptotic distribution for epistatic tests in case-control studies

We propose a statistical model for dissecting a multilocus genotypic value into its main (additive and dominant) effects and epistatic effects between different loci in a case-control association study. The model can discern four different kinds of epistasis, additive × additive, additive × dominant, dominant × additive, and dominant × dominant interactions. To test each kind of epistasis, a χ(2) test statistic was computed for a two by two contingency table derived from combined genotypes in both case and control groups. We derived an analytical approach for estimating the asymptotic distribution of the χ(2) test statistic for epistatic tests under the null hypothesis, with the result being consistent with that from Monte Carlo simulations. The new model was used to analyze a case-control data set for candidate gene studies of stroke, leading to the identification of several significant interactions between causal SNPs on this disease.

Functional mapping of reaction norms to multiple environmental signals through nonparametric covariance estimation

BACKGROUND

The identification of genes or quantitative trait loci that are expressed in response to different environmental factors such as temperature and light, through functional mapping, critically relies on precise modeling of the covariance structure. Previous work used separable parametric covariance structures, such as a Kronecker product of autoregressive one [AR(1)] matrices, that do not account for interaction effects of different environmental factors.

RESULTS

We implement a more robust nonparametric covariance estimator to model these interactions within the framework of functional mapping of reaction norms to two signals. Our results from Monte Carlo simulations show that this estimator can be useful in modeling interactions that exist between two environmental signals. The interactions are simulated using nonseparable covariance models with spatio-temporal structural forms that mimic interaction effects.

CONCLUSIONS

The nonparametric covariance estimator has an advantage over separable parametric covariance estimators in the detection of QTL location, thus extending the breadth of use of functional mapping in practical settings.

Modeling the genetic etiology of pharmacokinetic-pharmacodynamic links with the ARMA process

Substantial variability exists among different patients in response to drugs. The identification of genetic factors that contribute to the interpersonal differentiation has been an important task for pharmacogenetic research and drug discovery. In this article, we have derived a high-dimensional statistical model for unveiling the genetic machinery for drug response by integrating two different but biologically related processes--pharmacokinetics (PK) and pharmacodynamics (PD)--into a genetic mapping framework. Using an integrated model of PK and PD, we can identify specific DNA sequence variants and test how they relate to the differential effect of the body to the drug (PK) and the effect of the drug on the body (PD). To effectively model a two-stage hierarchic structure of the covariance matrix at the PD and PK level, we have for the first time introduced an autoregressive moving-average (ARMA) process to the mixture-based likelihood function for sequence mapping. Closed-form estimates of the determinant and inverse of the ARMA-based covariance matrix are incorporated into the estimation step, which significantly increases the computational efficiency. Simulation studies have been performed to test the statistical behavior of our model. Potential applications of this model to pharmacogenetic research are discussed.

Functional mapping of genotype-environment interactions for soybean growth by a semiparametric approach

BACKGROUND

Functional mapping is a powerful approach for mapping quantitative trait loci (QTLs) that control biological processes. Functional mapping incorporates mathematical aspects of growth and development into a general QTL mapping framework and has been recently integrated with composite interval mapping to build up a so-called composite functional mapping model, aimed to separate multiple linked QTLs on the same chromosomal region.

RESULTS

This article reports the principle of using composite functional mapping to estimate the effects of QTL-environment interactions on growth trajectories by parametrically modeling the tested QTL in a marker interval and nonparametrically modeling the markers outside the interval as co-factors. With this new model, we can characterize the dynamic patterns of the genetic effects of QTLs governing growth trajectories, estimate the global effects of the underlying QTLs during the course of growth and development, and test the differentiation in the shapes of QTL genotype-specific growth curves between different environments. By analyzing a real example from a soybean genome project, our model detects several QTLs that cause significant genotype-environment interactions for plant height growth processes.

CONCLUSIONS

The model provides a basis for deciphering the genetic architecture of trait expression adjusted to different biotic and abiotic environments for any organism.

Comparison of analyses of the QTLMAS XIII common dataset. II: QTL analysis

BACKGROUND

Five participants of the QTL-MAS 2009 workshop applied QTL analyses to the workshop common data set which contained a time-related trait: cumulative yield. Underlying the trait were 18 QTLs for three parameters of a logistic growth curve that was used for simulating the trait.

METHODS

Different statistical models and methods were employed to detect QTLs and estimate position and effect sizes of QTLs. Here we compare the results with respect to the numbers of QTLs detected, estimated positions and percentage explained variance. Furthermore, limiting factors in the QTL detection are evaluated.

RESULTS

All QTLs for the asymptote and the scaling factor of the logistic curve were detected by at least one of the participants. Only one out of six of the QTLs for the inflection point was detected. None of the QTLs were detected by all participants. Dominant, epistatic and imprinted QTLs were reported while only additive QTLs were simulated. The power to map QTLs for the inflection point increased when more time points were added.

CONCLUSIONS

For the detection of QTLs related to the asymptote and the scaling factor, there were no strong differences between the methods used here. Also, it did not matter much whether the time course data were analyzed per single time point or whether parameters of a growth curve were first estimated and then analyzed.In contrast, the power for detection of QTLs for the inflection point was very low and the frequency of time points appeared to be a limiting factor. This can be explained by a low accuracy in estimating the inflection point from a limited time range and a limited number of time points, and by the low correlation between the simulated values for this parameter and the phenotypic data available for the individual time points.

Bayesian analysis for genetic architecture of dynamic traits

The dissection of the genetic architecture of quantitative traits, including the number and locations of quantitative trait loci (QTL) and their main and epistatic effects, has been an important topic in current QTL mapping. We extend the Bayesian model selection framework for mapping multiple epistatic QTL affecting continuous traits to dynamic traits in experimental crosses. The extension inherits the efficiency of Bayesian model selection and the flexibility of the Legendre polynomial model fitting to the change in genetic and environmental effects with time. We illustrate the proposed method by simultaneously detecting the main and epistatic QTLs for the growth of leaf age in a doubled-haploid population of rice. The behavior and performance of the method are also shown by computer simulation experiments. The results show that our method can more quickly identify interacting QTLs for dynamic traits in the models with many numbers of genetic effects, enhancing our understanding of genetic architecture for dynamic traits. Our proposed method can be treated as a general form of mapping QTL for continuous quantitative traits, being easier to extend to multiple traits and to a single trait with repeat records.

An optimal strategy for functional mapping of dynamic trait loci

As an emerging powerful approach for mapping quantitative trait loci (QTLs) responsible for dynamic traits, functional mapping models the time-dependent mean vector with biologically meaningful equations and are likely to generate biologically relevant and interpretable results. Given the autocorrelation nature of a dynamic trait, functional mapping needs the implementation of the models for the structure of the covariance matrix. In this article, we have provided a comprehensive set of approaches for modelling the covariance structure and incorporated each of these approaches into the framework of functional mapping. The Bayesian information criterion (BIC) values are used as a model selection criterion to choose the optimal combination of the submodels for the mean vector and covariance structure. In an example for leaf age growth from a rice molecular genetic project, the best submodel combination was found between the Gaussian model for the correlation structure, power equation of order 1 for the variance and the power curve for the mean vector. Under this combination, several significant QTLs for leaf age growth trajectories were detected on different chromosomes. Our model can be well used to study the genetic architecture of dynamic traits of agricultural values.

Nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci

Estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits. We present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points. Specifically, we adopt Huang et al.'s (2006, Biometrika 93, 85-98) approach of invoking the modified Cholesky decomposition and converting the problem into modeling a sequence of regressions of responses. A regularized covariance estimator is obtained using a normal penalized likelihood with an L(2) penalty. This approach, embedded within a mixture likelihood framework, leads to enhanced accuracy, precision, and flexibility of functional mapping while preserving its biological relevance. Simulation studies are performed to reveal the statistical properties and advantages of the proposed method. A real example from a mouse genome project is analyzed to illustrate the utilization of the methodology. The new method will provide a useful tool for genome-wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture, biology, and health sciences.

Functional mapping of human growth trajectories

Human height is an important trait from biological and social perspectives. Genes have been widely recognized to be involved in human body growth, but their detailed controlling mechanisms are poorly understood. Here, we present a computational model for functional mapping of quantitative trait loci (QTLs) that control trajectories of human height growth through an interactive network. The model integrates mathematical equations of human growth curves into the mixture model-based functional mapping framework, allowing the identification and mapping of individual QTLs responsible for the developmental pattern of human growth. The model was derived on a random sample of subjects from a natural population, for each of which molecular markers within candidate genes or throughout the entire genome are typed and height data from childhood to adulthood are collected. A series of testable hypotheses are formulated about the genetic control of developmental timing and duration at different stages. The model was used to characterize epistatic QTLs for height growth hidden in 548 Japanese girls which is a semi-real data set with simulated the marker genotypes. With an increasing availability of genetic polymorphic data, the model will have great implications for probing the genetic and developmental mechanisms of human body growth and its associated diseases.

Genetic dissection of complex endosperm traits

The endosperm of plants is a major source of food, feed and industrial raw materials. The genetic analysis of endosperm traits poses numerous challenges due to the endosperm's complex genetic composition and unique physical and developmental properties. Modern molecular techniques and statistical methods have greatly improved the mapping of quantitative trait loci underlying endosperm traits and have led to revolutionary insights regarding epistatic and epigenetic effects. This article describes the current state of the methodologies used in the genetic dissection of endosperm traits and highlights practical issues and statistical concepts and procedures.

Age-dependent quantitative trait loci affecting growth traits in Scottish Blackface sheep

To dissect age-dependent quantitative trait loci (QTL) associated with growth and to examine changes in QTL effects over time, the Gompertz growth model was fitted to longitudinal live weight data on 788 Scottish Blackface lambs from nine half-sib families. QTL were mapped for model parameters and weekly live weights and growth rates using microsatellite markers on chromosomes 1, 2, 3, 5, 14, 18, 20 and 21. QTL significance (using alpha = 0.05 chromosome-wide significance thresholds, unless otherwise stated) varied with age, and those for growth rate occurred earlier than equivalent QTL for live weight. A chromosome 20 QTL for growth rate was significant from 4 to 9 weeks (maximum significance at 6 weeks) and for maximum growth rate. For live weight, this QTL was significant from 8 to 16 weeks (maximum significance at 12 weeks). A nominally significant chromosome 14 QTL was detected for growth rates from birth to week 2 in the same families and location as an 8-week weight QTL. In addition, at the same position on chromosome 14, a QTL was significant for growth rate for 17-28 weeks (maximum significance at 24 weeks). A chromosome 3 QTL was significant for weights at early ages (birth to week 4) and a growth rate QTL on chromosome 18 was significant from 8 to 12 weeks. Fitting growth curves allowed the combination of information from multiple measurements into a few biologically meaningful variables, and the detection of growth QTL that were not observed from analyses of raw weight data. These QTL describe distinct parts of an animal's growth curve trajectory, possibly enabling manipulation of this trajectory.

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, "naturally occurring" zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F(2) intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.

A nonlinear mixed-effect mixture model for functional mapping of dynamic traits

Functional mapping has emerged as a next-generation statistical tool for mapping quantitative trait loci (QTL) that affect complex dynamic traits. In this article, we incorporated the idea of nonlinear mixed-effect (NLME) models into the mixture-based framework of functional mapping, aimed to generalize the spectrum of applications for functional mapping. NLME-based functional mapping, implemented with the linearization algorithm based on the first-order Taylor expansion, can provide reasonable estimates of QTL genotypic-specific curve parameters (fixed effect) and the between-individual variation of these parameters (random effect). Results from simulation studies suggest that the NLME-based model is more general than traditional functional mapping. The new model can be useful for the identification of the ontogenetic patterns of QTL genetic effects during time course.

A statistical model for the identification of genes governing the incidence of cancer with age

The cancer incidence increases with age. This epidemiological pattern of cancer incidence can be attributed to molecular and cellular processes of individual subjects. Also, the incidence of cancer with ages can be controlled by genes. Here we present a dynamic statistical model for explaining the epidemiological pattern of cancer incidence based on individual genes that regulate cancer formation and progression. We incorporate the mathematical equations of age-specific cancer incidence into a framework for functional mapping aimed at identifying quantitative trait loci (QTLs) for dynamic changes of a complex trait. The mathematical parameters that specify differences in the curve of cancer incidence among QTL genotypes are estimated within the context of maximum likelihood. The model provides testable quantitative hypotheses about the initiation and duration of genetic expression for QTLs involved in cancer progression. Computer simulation was used to examine the statistical behavior of the model. The model can be used as a tool for explaining the epidemiological pattern of cancer incidence.