Model selection for quantitative trait loci mapping in a full-sib family

Statistical methods for mapping quantitative trait loci (QTLs) in full-sib forest trees, in which the number of alleles and linkage phase can vary from locus to locus, are still not well established. Previous studies assumed that the QTL segregation pattern was fixed throughout the genome in a full-sib family, despite the fact that this pattern can vary among regions of the genome. In this paper, we propose a method for selecting the appropriate model for QTL mapping based on the segregation of different types of markers and QTLs in a full-sib family. The QTL segregation patterns were classified into three types: test cross (1:1 segregation), F₂ cross (1:2:1 segregation) and full cross (1:1:1:1 segregation). Akaike’s information criterion (AIC), the Bayesian information criterion (BIC) and the Laplace-empirical criterion (LEC) were used to select the most likely QTL segregation pattern. Simulations were used to evaluate the power of these criteria and the precision of parameter estimates. A Windows-based software was developed to run the selected QTL mapping method. A real example is presented to illustrate QTL mapping in forest trees based on an integrated linkage map with various segregation markers. The implications of this method for accurate QTL mapping in outbred species are discussed.     

A model for quantitative trait loci mapping,linkage phase,and segregation pattern estimation for a full-sib progeny

Quantitative trait loci (QTL) mapping is an important approach for the study of the genetic architecture of quantitative traits. For perennial species, inbred lines cannot be obtained due to inbreed depression and a long juvenile period. Instead, linkage mapping can be performed by using a full-sib progeny. This creates a complex scenario because both markers and QTL alleles can have different segregation patterns as well as different linkage phases between them. We present a two-step method for QTL mapping using full-sib progeny based on composite interval mapping (i.e., interval mapping with cofactors), considering an integrated genetic map with markers with different segregation patterns and conditional probabilities obtained by a multipoint approach. The model is based on three orthogonal contrasts to estimate the additive effect (one in each parent) and dominance effect. These estimatives are obtained using the EM algorithm. In the first step, the genome is scanned to detect QTL. After, segregation pattern and linkage phases between QTL and markers are estimated. A simulated example is presented to validate the methodology. In general, the new model is more effective than existing approaches, because it can reveal QTL present in a full-sib progeny that segregates in any pattern present and can also identify dominance effects. Also, the inclusion of cofactors provided more statistical power for QTL mapping.     

FunMap: functional mapping of complex traits

SUMMARY: FunMap is a Web-based user interface designed to map quantitative trait loci (QTL) affecting function-valued traits or infinite-dimensional traits in well-structured pedigrees or natural populations. User input includes three files: longitudinal trait data, marker genotypes and/or a linkage map. This software allows for a systematic genome-wide scan and significance test of QTL throughout the map. The dynamic change of QTL effects during the time course of growth is automatically drawn, from which specific biological hypotheses regarding the genetic control mechanisms of growth and development can be tested. AVAILABILITY: http://web.biostat.ufl.edu/~cma/genetics/software.html     

Selection bias in quantitative trait loci mapping

A simulation study was performed to see whether selection affected quantitative trait loci (QTL) mapping. Populations under random selection, under selection among full-sib families, and under selection within a full-sib family were simulated each with heritability of 0.3, 0.5, and 0.7. They were analyzed with the marker spacing of 10 cM and 20 cM. The accuracy for QTL detection decreased for the populations under selection within full-sib family. Estimates of QTL effects and positions differed (P < .05) from their input values. The problems could be ignored when mapping a QTL for the populations under selection among full-sib families. A large heritability helped reduction of such problems. When the animals were selected within a full-sib family, the QTL was detected for the populations with heritability of 0.5 or larger using the marker spacing of 10 cM, and with heritability of 0.7 using the marker spacing of 20 cM. This study implied that when selection was introduced, the accuracy for QTL detection decreased and the estimates of QTL effects were biased. A caution was warranted on the decision of data (including selected animals to be genotyped) for QTL mapping.     

Distribution of genomic regions differentiating oak species assessed by QTL detection

Pedunculate oak and sessile oak are two sympatric interfertile species that exhibit leaf morphological differences. We aimed to detect quantitative trait loci (QTLs) of these traits in order to locate genomic regions involved in species differentiation. A total of 15 leaf morphological traits were assessed in a mixed forest stand composed of Quercus petraea and Q. robur and in a full-sib pedigree of Q. robur. The progeny of the full-sib family were vegetatively propagated in two successive experiments comprising 174 and 216 sibs, and assessments were made on two leaves collected on each of the 1080 and 1530 cuttings corresponding to the two experiments. Traits that exhibited strong species differences in the mixed stand tended also to have higher repeatability values in the mapping population, thus indicating higher genetic control. A genetic map was constructed for QTL detection. Composite interval mapping with the one QTL model was used for QTL detection. From one to three QTLs were detected for 13 traits. In-depth analysis of the QTLs, controlling the five morphological traits that exhibited the highest interspecific differences in the mixed stand, indicated that they were distributed on six linkage groups, with two clusters comprising QTLs of at least two discriminant traits. These results were reinforced when error 1 for QTL detection was set at 5% at the chromosome level, as up to nine clusters could be identified. In conclusion, traits involved in interspecific differentiation of oaks are under polygenic control and widespread in clusters across the genome.     

Power of QTL mapping experiments in commercial Atlantic salmon populations, exploiting linkage and linkage disequilibrium and effect of limited recombination in males

Whereas detection and positioning of genes that affect quantitative traits (quantitative trait loci (QTL)) using linkage mapping uses only information from recombinants in the genotyped generations, linkage disequilibrium (LD) mapping uses historical recombinants. Thus, whereas linkage mapping requires large family sizes to detect and accurately position QTL, LD mapping is more dependent on the number of families sampled from the population. In commercial Atlantic salmon breeding programmes, only a small number of individuals per family are routinely phenotyped for traits such as disease resistance and meat colour. In this paper, we assess the power and accuracy of combined linkage disequilibrium linkage analysis (LDLA) to detect QTL in the commercial population using simulation. When 15 half-sib sire families (each sire mated to 30 dams, each dam with 10 progeny) were sampled from the population for genotyping, we were able to detect a QTL explaining 10% of the phenotypic variance in 85% of replicates and position this QTL within 3 cM of the true position in 70% of replicates. When recombination was absent in males, a feature of the salmon genome, power to detect QTL increased; however, the accuracy of positioning the QTL was decreased. By increasing the number of sire families sampled from the population to be genotyped to 30, we were able to increase both the proportion of QTL detected and correctly positioned (even with no recombination in males). QTL with much smaller effect could also be detected. The results suggest that even with the existing recording structure in commercial salmon breeding programmes, there is considerable power to detect and accurately position QTL using LDLA.     

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.     

Semiparametric functional mapping of quantitative trait loci governing long-term HIV dynamics

MOTIVATION: Functional mapping has proven to be powerful for characterizing quantitative trait loci (QTL) that control complex dynamic traits. More recently, functional mapping has been extended to identify the host QTL responsible for HIV dynamics by incorporating a parametric bi-exponential function for earlier stages of viral load trajectories. However, existing functional mapping cannot be used to map long-term HIV dynamics because no mathematical functions are available for later stages of HIV dynamic changes. RESULTS: We derived a statistical model for functional mapping of dynamic QTL through characterizing HIV load trajectories during a long-term period semiparametrically. The new model was constructed within the maximum likelihood framework and implemented with the EM-simplex algorithm. It allows for the test of differences in the genetic control of short- and long-term HIV dynamics and the characterization of the effects of viral-host genome interaction. Extensive simulation studies have been performed to test the statistical behavior of this model. The new model will provide an important tool for genetic and genomic studies of human complex diseases like HIV/AIDS and their pathological progression. AVAILABILITY: Available on request from the corresponding author.     

A semiparametric approach for composite functional mapping of dynamic quantitative traits

Functional mapping has emerged as a powerful tool for mapping quantitative trait loci (QTL) that control developmental patterns of complex dynamic traits. Original functional mapping has been constructed within the context of simple interval mapping, without consideration of separate multiple linked QTL for a dynamic trait. In this article, we present a statistical framework for mapping QTL that affect dynamic traits by capitalizing on the strengths of functional mapping and composite interval mapping. Within this so-called composite functional-mapping framework, functional mapping models the time-dependent genetic effects of a QTL tested within a marker interval using a biologically meaningful parametric function, whereas composite interval mapping models the time-dependent genetic effects of the markers outside the test interval to control the genome background using a flexible nonparametric approach based on Legendre polynomials. Such a semiparametric framework was formulated by a maximum-likelihood model and implemented with the EM algorithm, allowing for the estimation and the test of the mathematical parameters that define the QTL effects and the regression coefficients of the Legendre polynomials that describe the marker effects. Simulation studies were performed to investigate the statistical behavior of composite functional mapping and compare its advantage in separating multiple linked QTL as compared to functional mapping. We used the new mapping approach to analyze a genetic mapping example in rice, leading to the identification of multiple QTL, some of which are linked on the same chromosome, that control the developmental trajectory of leaf age.     

A Bayesian Nonparametric Approach for Mapping Dynamic Quantitative Traits

In biology, many quantitative traits are dynamic in nature. They can often be described by some smooth functions or curves. A joint analysis of all the repeated measurements of the dynamic traits by functional quantitative trait loci (QTL) mapping methods has the benefits to (1) understand the genetic control of the whole dynamic process of the quantitative traits and (2) improve the statistical power to detect QTL. One crucial issue in functional QTL mapping is how to correctly describe the smoothness of trajectories of functional valued traits. We develop an efficient Bayesian nonparametric multiple-loci procedure for mapping dynamic traits. The method uses the Bayesian P-splines with (nonparametric) B-spline bases to specify the functional form of a QTL trajectory and a random walk prior to automatically determine its degree of smoothness. An efficient deterministic variational Bayes algorithm is used to implement both (1) the search of an optimal subset of QTL among large marker panels and (2) estimation of the genetic effects of the selected QTL changing over time. Our method can be fast even on some large-scale data sets. The advantages of our method are illustrated on both simulated and real data sets.     

Relationship between microsatellite marker alleles on chromosomes 1-5 originating from the Rhode Island Red and Green-legged Partrigenous breeds and egg production and quality traits in F(2) mapping population

The objective of this study was to determine the relationship between the origin of marker alleles from the Rhode Island Red (RIR) and Green-legged Partrigenous (GlP) breeds and chosen egg production and quality traits in F(2) generation consisting of 10 full-sib families. Polymorphism analysis of 23 microsatellite markers within the mapping population (519 F(2)) was made. In parental generation 17 alleles were identified as specific for the GlP and 23 for the RIR. The least squares method was used to evaluate the significance of effects of genotype (GlP/GlP, RIR/RIR, GlP/RIR) on the analysed quantitative traits. Thirty traits of egg production and quality were measured during the laying period. It was shown that the effects of the genotype (GlP/GlP, RIR/RIR, GlP/RIR) at the loci on analysed traits of F(2) animals were diversified. Significant effects were found for 16 traits. These results confirm that the analysed microsatellite loci may be linked to the genes affecting egg production and quality traits. The loci examined and the experimental population constitutes a valuable material for QTL mapping (linkage analysis).     

Genetic Linkage Mapping and Analysis of Muscle Fiber-Related QTLs in Common Carp (Cyprinus carpio L.)

A genetic linkage map of common carp (Cyprinus carpio L.) was constructed using Type I and Type II microsatellite markers and a pseudo-testcross mapping strategy. The microsatellite markers were isolated from microsatellite-enriched genomic libraries and tested for their segregation in a full-sib mapping panel containing 92 individuals. A total of 161 microsatellite loci were mapped into 54 linkage groups. The total lengths of the female, male and consensus maps were 2,000, 946, and 1,852?cM, with an average marker spacing of approximately 13, 7, and 11?cM, respectively. Muscle fiber-related traits, including muscle fiber cross-section area and muscle fiber density, were mapped to the genetic map. Three QTLs for muscle fiber cross-section area and two QTLs for muscle fiber density were identified when considering both significant and suggestive QTL effects. The QTLs with largest effects for muscle fiber cross-section area and muscle fiber density were 21.9% and 18.9%, and they were located in LG3, respectively.     

An algorithm for molecular dissection of tumor progression

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.     

A multiparental cross population for mapping QTL for agronomic traits in durum wheat (Triticum turgidum ssp. durum)

Multiparental cross designs for mapping quantitative trait loci (QTL) provide an efficient alternative to biparental populations because of their broader genetic basis and potentially higher mapping resolution. We describe the development and deployment of a recombinant inbred line (RIL) population in durum wheat (Triticum turgidum ssp. durum) obtained by crossing four elite cultivars. A linkage map spanning 2664 cM and including 7594 single nucleotide polymorphisms (SNPs) was produced by genotyping 338 RILs. QTL analysis was carried out by both interval mapping on founder haplotype probabilities and SNP bi‐allelic tests for heading date and maturity date, plant height and grain yield from four field experiments. Sixteen QTL were identified across environments and detection methods, including two yield QTL on chromosomes 2BL and 7AS, with the former mapped independently from the photoperiod response gene Ppd‐B1, while the latter overlapped with the vernalization locus VRN‐A3. Additionally, 21 QTL with environment‐specific effects were found. Our results indicated a prevalence of environment‐specific QTL with relatively small effect on the control of grain yield. For all traits, functionally different QTL alleles in terms of direction and size of genetic effect were distributed among parents. We showed that QTL results based on founder haplotypes closely matched functional alleles at known heading date loci. Despite the four founders, only 2.1 different functional haplotypes were estimated per QTL, on average. This durum wheat population provides a mapping resource for detailed genetic dissection of agronomic traits in an elite background typical of breeding programmes.     

Bayesian mapping of quantitative trait loci for complex binary traits

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.     

QTL analysis of leaf morphological characters in a Quercus robur full-sib family (Q. robur × Q. robur ssp. slavonica)

The distinction between white oak species (section Quercus sensu stricto ) is largely based on leaf morphological characters. There is, however, considerable within-species variation and no single species-diagnostic character, possibly due to phenotypic plasticity and/or underlying genetic variation. The aim of the present study was to identify quantitative trait loci (QTL) underlying the high within-species variation for leaf morphological characters in an F₁ full-sib family derived from a cross between Q. robur and Q. robur ssp. slavonica . In accordance with an earlier QTL mapping study in an intraspecific Q. robur full-sib family, polygenic inheritance was detected for leaf morphological characters that are used to discriminate between the species Quercus robur and Q. petraea . QTLs were distributed over ten linkage groups, showed a moderate effect in terms of phenotypic variance explained (PVE) in the mapping pedigree (3.6–9.6%), but accounted for a considerable amount of the parental differences. Co-localisation of QTLs on the same linkage group in different genetic backgrounds was found for the number and percentage of intercalary veins (NV, PV) on linkage group 3 and for NV on linkage group 5, revealing a high congruence in the relative QTL positions. The generally low correspondence of the other QTLs in the different mapping pedigrees may be an effect of the genetic background and of the environment. In conclusion, leaf morphological characters were found to be under polygenic control, and a comparison to earlier published results led to the identification of two QTLs that were stable across different genetic backgrounds.     

QTL analysis of leaf morphological characters in a Quercus robur full-sib family (Q. robur x Q. robur ssp. slavonica)

The distinction between white oak species (section Quercus sensu stricto) is largely based on leaf morphological characters. There is, however, considerable within-species variation and no single species-diagnostic character, possibly due to phenotypic plasticity and/or underlying genetic variation. The aim of the present study was to identify quantitative trait loci (QTL) underlying the high within-species variation for leaf morphological characters in an F(1) full-sib family derived from a cross between Q. robur and Q. robur ssp. slavonica. In accordance with an earlier QTL mapping study in an intraspecific Q. robur full-sib family, polygenic inheritance was detected for leaf morphological characters that are used to discriminate between the species Quercus robur and Q. petraea. QTLs were distributed over ten linkage groups, showed a moderate effect in terms of phenotypic variance explained (PVE) in the mapping pedigree (3.6-9.6%), but accounted for a considerable amount of the parental differences. Co-localisation of QTLs on the same linkage group in different genetic backgrounds was found for the number and percentage of intercalary veins (NV, PV) on linkage group 3 and for NV on linkage group 5, revealing a high congruence in the relative QTL positions. The generally low correspondence of the other QTLs in the different mapping pedigrees may be an effect of the genetic background and of the environment. In conclusion, leaf morphological characters were found to be under polygenic control, and a comparison to earlier published results led to the identification of two QTLs that were stable across different genetic backgrounds.     

Novel linkage mapping approach using DNA pooling in human and animal genetics. II. Detection of quantitative traits loci in dairy cattle

Selective DNA pooling is an advanced methodology for linkage mapping of quantitative trait loci (QTL) in farm animals. The principle is based on densitometric estimates of marker allele frequency in pooled DNA samples of phenotypically extreme individuals from half-sib, backcross and F(2) experimental designs in farm animals. This methodology provides a rapid and efficient analysis of a large number of individuals with short tandem repeat markers that are essential to detect QTL through the genome - wide searching approach. Several strategies involving whole genome scanning with a high statistical power have been developed for systematic search to detect the quantitative traits loci and linked loci of complex traits. In recent studies, greater success has been achieved in mapping several QTLs in Israel-Holstein cattle using selective DNA pooling. This paper outlines the currently emerged novel strategies of linkage mapping to identify QTL based on selective DNA pooling with more emphasis on its theoretical pre-requisite to detect linked QTLs, applications, a general theory for experimental half-sib designs, the power of statistics and its feasibility to identify genetic markers linked QTL in dairy cattle. The study reveals that the application of selective DNA pooling in dairy cattle can be best exploited in the genome-wide detection of linked loci with small and large QTL effects and applied to a moderately sized half-sib family of about 500 animals.     

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.     

多维功能作图在胡杨幼苗生长QTL的应用

功能作图框架能够表征复杂动态性状背后的数量性状位点(Quantitative trait locus, QTL)或核苷酸。此前,功能作图广泛应用于单个性状或两个性状的QTL定位当中,多个相关性状功能作图的研究相对匮乏。本研究通过对SAD(Structured antedependence)模型进一步推导,得到在多个性状时用于拟合时间相关协方差矩阵的结构化模型,并使用胡杨(Populus euphratica Oliv.)340个F₁代群体的4个生长相关性状以及模拟实验对多维功能作图模型进行测试。结果显示,共定位出173个显著位点,分布于除4、9、10、15、16以外的染色体。功能注释涉及参与叶绿体早期发育、生长素横向运输、提高植物非生物胁迫耐受性以及作为跨膜运输系统开关等生物学过程的32个基因。