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.     

Detection of quantitative trait loci influencing growth trajectories of adventitious roots in Populus using functional mapping

The capacity to root from cuttings is a key factor for the mass deployment of superior genotypes in clonal forestry. We studied the genetic basis of rooting capacity by mapping quantitative trait loci (QTLs) that control growth rate and form of root traits in a full-sib family of 93 hybrids derived from an interspecific cross between two Populus species, P. deltoides and P. euramericana. The hybrid family was typed for different marker systems (including SSRs, AFLPs, RAPDs, ISSRs, and SNPs), leading to the construction of two linkage maps based on the female P. deltoides (D map) and male P. euramericana (E map) with a pseudotestcross mapping strategy. The two maps were scanned by functional mapping to detect QTLs that control early growth trajectories of two rooting traits, maximal single-root length and the total number of roots per cutting, measured at five time points in water culture. Of the six QTLs detected for these two growth traits, only one is segregating in P. deltoides with poor rooting capacity, while the other five are segregating in P. euramericana showing good rooting capacity. Tests with functional mapping suggest different developmental patterns of the genetic effects of these root QTLs in time course. Five QTLs were detected to change their effects on root growth trajectories with time, whereas one detected to affect root growth consistently in time course. Knowledge about the genetic and developmental control mechanisms of root QTLs will have important implications for the genetic improvement of vegetative propagation traits in Populus.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behaviour of a system, differential equations have proved to be powerful for modelling and unravelling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge–Kutta fourth-order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behavior of a system, differential equations have proven to be powerful for modeling and unraveling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge-Kutta fourth order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

Functional mapping - how to map and study the genetic architecture of dynamic complex traits

The development of any organism is a complex dynamic process that is controlled by a network of genes as well as by environmental factors. Traditional mapping approaches for analysing phenotypic data measured at a single time point are too simple to reveal the genetic control of developmental processes. A general statistical mapping framework, called functional mapping, has been proposed to characterize, in a single step, the quantitative trait loci (QTLs) or nucleotides (QTNs) that underlie a complex dynamic trait. Functional mapping estimates mathematical parameters that describe the developmental mechanisms of trait formation and expression for each QTL or QTN. The approach provides a useful quantitative and testable framework for assessing the interplay between gene actions or interactions and developmental changes.     

Functional mapping imprinted quantitative trait loci underlying developmental characteristics

Background

Genomic imprinting, a phenomenon referring to nonequivalent expression of alleles depending on their parental origins, has been widely observed in nature. It has been shown recently that the epigenetic modification of an imprinted gene can be detected through a genetic mapping approach. Such an approach is developed based on traditional quantitative trait loci (QTL) mapping focusing on single trait analysis. Recent studies have shown that most imprinted genes in mammals play an important role in controlling embryonic growth and post-natal development. For a developmental character such as growth, current approach is less efficient in dissecting the dynamic genetic effect of imprinted genes during individual ontology.

Results

Functional mapping has been emerging as a powerful framework for mapping quantitative trait loci underlying complex traits showing developmental characteristics. To understand the genetic architecture of dynamic imprinted traits, we propose a mapping strategy by integrating the functional mapping approach with genomic imprinting. We demonstrate the approach through mapping imprinted QTL controlling growth trajectories in an inbred F₂ population. The statistical behavior of the approach is shown through simulation studies, in which the parameters can be estimated with reasonable precision under different simulation scenarios. The utility of the approach is illustrated through real data analysis in an F₂ family derived from LG/J and SM/J mouse stains. Three maternally imprinted QTLs are identified as regulating the growth trajectory of mouse body weight.

Conclusion

The functional iQTL mapping approach developed here provides a quantitative and testable framework for assessing the interplay between imprinted genes and a developmental process, and will have important implications for elucidating the genetic architecture of imprinted traits.     

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 differential equation model for functional mapping of a virus-cell dynamic system

The dynamic pattern of viral load in a patient’s body critically depends on the host’s genes. For this reason, the identification of those genes responsible for virus dynamics, although difficult, is of fundamental importance to design an optimal drug therapy based on patients’ genetic makeup. Here, we present a differential equation (DE) model for characterizing specific genes or quantitative trait loci (QTLs) that affect viral load trajectories within the framework of a dynamic system. The model is formulated with the principle of functional mapping, originally derived to map dynamic QTLs, and implemented with a Markov chain process. The DE-integrated model enhances the mathematical robustness of functional mapping, its quantitative prediction about the temporal pattern of genetic expression, and therefore its practical utilization and effectiveness for gene discovery in clinical settings. The model was used to analyze simulated data for viral dynamics, aimed to investigate its statistical properties and validate its usefulness. With an increasing availability of genetic polymorphic data, the model will have great implications for probing the molecular genetic mechanism of virus dynamics and disease progression.     

Functional mapping of growth and development

Understanding how an organism develops into a fully functioning adult from a mass of undifferentiated cells may reveal different strategies that allow the organism to survive under limiting conditions. Here, we review an analytical model for characterizing quantitative trait loci (QTLs) that underlie variation in growth trajectories and developmental timing. This model, called functional mapping, incorporates fundamental principles behind biological processes or networks that are bridged with mathematical functions into a statistical mapping framework. Functional mapping estimates parameters that determine the shape and function of a particular biological process, thus providing a flexible platform to test biologically meaningful hypotheses regarding the complex relationships between gene action and development.     

Mapping quantitative trait loci for murine growth: a closer look at genetic architecture

Over 20 years ago, D. S. Falconer and others launched an important avenue of research into the quantitative of body size growth in mice. This study continues in that tradition by locating quantitative trait loci (QTLs) responsible for murine growth, such as age-specific weights and growth periods, and examining the genetic architecture for body weight. We identified a large number of potential QTLs in an earlier F2 intercross (Intercross I) of the SM/J and LG/J inbred mouse strains. Many of these QTLs are replicated in a second F2 intercross (Intercross II) between the same two strains. These replicated regions provide candidate regions for future fine-mapping studies. We also examined body size and growth QTLs using the combined data set from these two intercrosses, resulting in 96 microsatellite markers being scored for 1045 individuals. An examination of the genetic architecture for age-specific weight and growth periods resulted in locating 20 separate QTLs, which were mainly additive in nature, although dominance was found to affect early growth and body size. QTLs affecting early and late growth were generally distinct, mapping to separate chromosome locations. This QTL pattern indicates largely separate genetic and physiological systems for early and later murine growth, as Falconer suggested. We also found sex-specific QTLs for body size with implications for the evolution of sexual dimorphism.     

Nonparametric functional mapping of quantitative trait loci underlying programmed cell death

The development of an organism represents a complex dynamic process, which is controlled by a network of genes and multiple environmental factors. Programmed cell death (PCD), a physiological cell suicide process, occurs during the development of most organisms and is, typically, a complex dynamic trait. Understanding how genes control this complex developmental process has been a long-standing topic in PCD studies. In this article, we propose a nonparametric model, based on orthogonal Legendre polynomials, to map genes or quantitative trait loci (QTLs) that govern the dynamic features of the PCD process. The model is built under the maximum likelihood-based functional mapping framework and is implemented with the EM algorithm. A general information criterion is proposed for selecting the optimal Legendre order that best fits the dynamic pattern of the PCD process. The consistency of the order selection criterion is established. A nonstationary structured antedependence model (SAD) is applied to model the covariance structure among the phenotypes measured at different time points. The developed model generates a number of hypothesis tests regarding the genetic control mechanism of the PCD process. Extensive simulation studies are conducted to investigate the statistical behavior of the model. Finally, we apply the model to a rice tiller number data set in which several QTLs are identified. The developed model provides a quantitative and testable framework for assessing the interplay between genes and the developmental PCD process, and will have great implications for elucidating the genetic architecture of the PCD process.     

Quantitative Trait Loci for Murine Growth

Body size is an archetypal quantitative trait with variation due to the segregation of many gene loci, each of relatively minor effect, and the environment. We examine the effects of quantitative trait loci (QTLs) on age-specific body weights and growth in the F(2) intercross of the LG/J and SM/J strains of inbred mice. Weekly weights (1-10 wk) and 75 microsatellite genotypes were obtained for 535 mice. Interval mapping was used to locate and measure the genotypic effects of QTLs on body weight and growth. QTL effects were detected on 16 of the 19 autosomes with several chromosomes carrying more than one QTL. The number of QTLs for age-specific weights varied from seven at 1 week to 17 at 10 wk. The QTLs were each of relatively minor, subequal effect. QTLs affecting early and late growth were generally distinct, mapping to different chromosomal locations indicating separate genetic and physiological systems for early and later murine growth.     

3FunMap: full-sib family functional mapping of dynamic traits

MOTIVATION: Functional mapping that embeds the developmental mechanisms of complex traits shows great power to study the dynamic pattern of genetic effects triggered by individual quantitative trait loci (QTLs). A full-sib family, produced by crossing two heterozygous parents, is characteristic of uncertainties about cross-type at a locus and linkage phase between different loci. Integrating functional mapping into a full-sib family requires a model selection procedure capable of addressing these uncertainties. 3FunMap, written in VC++ 6.0, provides a flexible and extensible platform to perform full-sib functional mapping of dynamic traits. Functions in the package encompass linkage phase determination, marker map construction and the pattern identification of QTL segregation, dynamic tests of QTL effects, permutation tests and numerical simulation. We demonstrate the features of 3FunMap through real data analysis and computer simulation. AVAILABILITY: http://statgen.psu.edu/software.     

Construction of Three High-Density Genetic Linkage Maps and Dynamic QTL Mapping of Growth Traits in Yellow River Carp (Cyprinus carpio haematopterus)

To provide the theoretical basis for researching growth, development, and molecular marker-assisted breeding of the economically important Yellow River carp (Cyprinus carpio haematopterus) using dynamic quantitative trait locus (QTL) mapping, we constructed three genetic linkage maps from 207 progeny using a new modified genotyping-by-sequencing method. The three maps contained 16,886, 16,548, and 7482 single nucleotide polymorphism markers, respectively, with an average interval of 0.36 cM, 0.45 cM, and 1.00 cM. We identified 148 QTLs related to four growth traits that were located on 25 chromosomes from three growth stages of Yellow River carp. A total of 32, 36, 43, and 37 QTLs were associated with body length, height, width, and weight, respectively. Among them, 47 QTLs were detected for only one growth trait in one stage, but all of the other QTLs were co-localized. Of the 14 main QTLs, 13 were located on chromosome 12, which suggests the presence of growth-related genes on this chromosome. We then detected 17 candidate genes within 50 K upstream and downstream of the 14 main QTLs. This is the first report of the dynamic QTL mapping of growth traits of Yellow River carp, and the results can be used in future studies of growth, development, and molecular-assisted breeding of this species.     

Genetic dissection of height in maritime pine seedlings raised under accelerated growth conditions

Random Amplified Polymorphic DNAs (RAPDs) were used to investigate quantitative trait loci (QTL) for traits related to height growth on 126 F₂ seedlings of maritime pine (Pinuspinaster Ait). The haploid megagametophyte was used to determine the maternal genotype of each F₂ individual. The seedlings were raised for 2 years in a greenhouse under accelerated growth conditions consisting of intense fertilization combined with continuous light treatments. Total height was measured at different developmental stages, and height growth components were measured after the second growth period. QTLs were identified for each trait. For total height, QTLs of different developmental stages were located on distinct linkage groups. However, rather than a complete temporal change in QTL expression, our results showed that maturation may induce a progressive shift of the genetic control of height growth. This may provide an explanation for a low juvenile-mature phenotypic correlation previously reported for height. Height growth components related to the initiation (controlled by the apical meristem) and elongation of shoot cycles (controlled by the subapical meristem) were mapped to different chromosomes, suggesting that the activity of these meristems is controlled by separate genetic mechanisms.     

Quantitative trait loci for growth trajectories in Populus

Growth trajectories are a biological process important to plant and animal breeding, and to evolutionary genetic studies. In this article, we report the detection of quantitative trait loci (QTLs) responsible for growth trajectories in poplars that are used as a model system for the study of forest biology. These QTLs were localized on a genetic linkage map of polymorphic markers using a statistical mapping method incorporating growth-curve models. The effects of the QTLs on growth are described as a function of age, so that age-specific changes in QTL effects can be readily projected throughout the entire growth process. The QTLs identified display increased effects on growth when trees age, yet the timing of QTL activation is earlier for stem height than diameter, which is consistent with the ecological viewpoint of canopy competition. The implications of the results for breeding and silviculture are discussed.     

Mapping of quantitative trait loci based on growth models

An approach called growth model-based mapping (GMM) of quantitative trait loci (QTLs) is proposed in this paper. The principle of the approach is to fit the growth curve of each individual or line with a theoretical or empirical growth model at first and then map QTLs based on the estimated growth parameters with the method of multiple-trait composite interval mapping. In comparison with previously proposed approaches of QTL mapping based on growth data, GMM has several advantages: (1) it can greatly reduce the amount of phenotypic data for QTL analysis and thus alleviate the burden of computation, particularly when permutation tests or simulation are performed to estimate significance thresholds; (2) it can efficiently analyze unbalanced phenotype data because both balanced and unbalanced data can be used for fitting growth models; and (3) it may potentially help us to better understand the genetic basis of quantitative trait development because the parameters in a theoretical growth model may often have clear biological meanings. A practical example of rice leaf-age development is presented to demonstrate the utility of GMM.     

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.     

Quantitative trait loci analysis for the developmental behavior of Soybean (Glycine max L. Merr.)

Quantitative trait loci (QTLs) identified so far in soybean were mainly derived in the final stage of plant development, which did not apply to the exploitation of genetic effects that were expressed during a specific developmental stage. Thus, the aim of this study was to identify conditional QTLs associated with yield traits at a specific developmental interval of soybean plant. The 143 recombinant inbred lines developed from the cross of soybean cultivars ‘Charleston’ and ‘Dongnong 594’ were used for the developmental QTLs analysis of pod number in the main stem and plant height by composite interval mapping method combined with mixed genetic model. The results indicated that the number and type of QTLs and their genetic effects for the two agronomic traits were different in a series of measuring stages. A total of 10 unconditional QTLs in 6 linkage groups and 5 conditional QTLs in 3 linkage groups were identified for the pod number of the main stem, while 13 unconditional QTLs in 7 linkage groups and 12 conditional QTLs in 6 linkage groups were identified for plant height. Many QTLs that were detected in the early stages were different from those detected at the later stages. Some QTLs existed only at one stage and others existed across two or three stages. Five marker intervals (satt509-satt251, sat_099-sat_113, sat_113-OPAW19_4, satt457-OPC10_85, sat_095-OPBA08_5) were proven to be associated both with the development of pod number in the main stem and the development of plant height. The present study suggested that the development of pods and plant height in soybean were governed by time-dependent gene expression.     

QTL Analysis of Head Splitting Resistance in Cabbage (Brassica oleracea L. var. capitata) Using SSR and InDel Makers Based on Whole-Genome Re-Sequencing

Head splitting resistance (HSR) in cabbage is an important trait closely related to both quality and yield of head. However, the genetic control of this trait remains unclear. In this study, a doubled haploid (DH) population derived from an intra-cross between head splitting-susceptible inbred cabbage line 79–156 and resistant line 96–100 was obtained and used to analyze inheritance and detect quantitative trait loci (QTLs) for HSR using a mixed major gene/polygene inheritance analysis and QTL mapping. HSR can be attributed to additive-epistatic effects of three major gene pairs combined with those of polygenes. Negative and significant correlations were also detected between head Hsr and head vertical diameter (Hvd), head transverse diameter (Htd) and head weight (Hw). Using the DH population, a genetic map was constructed with simple sequence repeat (SSR) and insertion–deletion (InDel) markers, with a total length of 1065.9 cM and average interval length of 4.4 cM between adjacent markers. Nine QTLs for HSR were located on chromosomes C3, C4, C7, and C9 based on 2 years of phenotypic data using both multiple-QTL mapping and inclusive composite interval mapping. The identified QTLs collectively explained 39.4 to 59.1% of phenotypic variation. Three major QTLs (Hsr 3.2, 4.2, 9.2) showing a relatively larger effect were robustly detected in different years or with different mapping methods. The HSR trait was shown to have complex genetic mechanisms. Results from QTL mapping and classical genetic analysis were consistent. The QTLs obtained in this study should be useful for molecular marker-assisted selection in cabbage breeding and provide a foundation for further research on HSR genetic regulation.