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PubMed1999

Bayesian mapping of multiple quantitative trait loci from incomplete outbred offspring data.

A general fine-scale Bayesian quantitative trait locus (QTL) mapping method for outcrossing species is presented. It is suitable for an analysis of complete and incomplete data from experimental designs of F2 families or backcrosses. The amount of genotyping of parents and grandparents is optional, as well as the assumption that the QTL alleles in the crossed lines are fixed. Grandparental origin indicators are used, but without forgetting the original genotype or allelic origin information. The method treats the number of QTL in the analyzed chromosome as a random variable and allows some QTL effects from other chromosomes to be taken into account in a composite interval mapping manner. A block-update of ordered genotypes (haplotypes) of the whole family is sampled once in each marker locus during every round of the Markov Chain Monte Carlo algorithm used in the numerical estimation. As a byproduct, the method gives the posterior distributions for linkage phases in the family and therefore it can also be used as a haplotyping algorithm. The Bayesian method is tested and compared with two frequentist methods using simulated data sets, considering two different parental crosses and three different levels of available parental information. The method is implemented as a software package and is freely available under the name Multimapper/outbred at URL http://www.rni.helsinki.fi/mjs/.

Algorithms↗
PubMed1996

Mapping quantitative-trait loci in humans by use of extreme concordant sib pairs: selected sampling by parental phenotypes.

In two previous articles, we have considered sample sizes required to detect linkage for mapping quantitative-trait loci in humans, using extreme discordant sib pairs. Here, we examine further the use of extreme concordant sib pairs but consider the effect of parents' phenotypes. Sample sizes necessary to obtain a power of 80% with concordant sib pairs at a significance level of .0001 are given, stratified by parental phenotypes. When there is no residual correlation between sibs, the parental phenotypes have little impact on the sample sizes. When residual correlations between sibs exist, we show, however, that power can be considerably reduced by including extreme sib pairs when the parents also have similarly extreme values. Thus, we recommend the exclusion of such pairs from linkage studies. This recommendation reduces the required sample sizes by 3- to 28-fold. The degree of saving in the required sample sizes varies among different models and allele frequencies. The reduction is most dramatic (a 28-fold reduction) for a rare recessive gene.

Chromosome Mapping↗
PubMed2001

Bayesian association mapping for quantitative traits in a mixture of two populations.

We introduce a novel Bayesian approach to estimate and account for population structure simultaneously with association mapping of multiple quantitative trait loci. The method is designed for an analysis of unrelated individuals from a mixture of two populations (no admixture), where the individual population memberships are unknown. In our approach, the population structure is estimated and accounted for by using data on additional "grouping" markers which are assumed to be in Hardy-Weinberg equilibrium within the populations but have different allele frequencies between the populations. We use Bayesian hierarchical modeling and Markov chain Monte Carlo estimation, where we allow both population stratification and genetic heterogeneity. In our model the number of quantitative trait loci and their positions are treated as random variables, and we obtain their posterior distributions. Here we select the candidate and the grouping markers based on results from a preliminary SOLAR analysis.

Bayes Theorem↗
PubMed1996

Quantitative trait locus gene mapping: a new method for locating alcohol response genes.

Alcoholism is a multigenic trait with important non-genetic determinants. Studies with genetic animal models of susceptibility to several of alcohol's effects suggest that several genes contributing modest effects on susceptibility (Quantitative Trait Loci, or QTLs) are important. A new technique of QTL gene mapping has allowed the identification of the location in mouse genome of several such QTLs. The method is described, and the locations of QTLs affecting the acute alcohol withdrawal reaction are described as an example of the method. Verification of these QTLs in ancillary studies is described and the strengths, limitations, and future directions to be pursued are discussed. QTL mapping is a promising method for identifying genes in rodents with the hope of directly extrapolating the results to the human genome. This review is based on a paper presented at the First International Congress of the Latin American Society for Biomedical Research on Alcoholism, Santiago, Chile, November 1994.

Journal Article↗
PubMed1995

Multipoint interval mapping of quantitative trait loci, using sib pairs.

The sib-pair interval-mapping procedure of Fulker and Cardon is extended to take account of all available marker information on a chromosome simultaneously. The method provides a computationally fast multipoint analysis of sib-pair data, using a modified Haseman-Elston approach. It gives results very similar to those of the earlier interval-mapping procedure when marker information is relatively uniform and a coarse map is used. However, there is a substantial improvement over the original method when markers differ in information content and/or when a dense map is employed. The method is illustrated by using simulated sib-pair data.

Alleles↗
PubMed2004

A statistical model for high-resolution mapping of quantitative trait loci determining HIV dynamics.

Are there specific genes that control the pathogenesis of HIV infection? This question, which is of fundamental importance in designing personalized strategies of gene therapy to control HIV infection, can be examined by genetic mapping approaches. In this article, we present a new statistical model for unravelling the genetic mechanisms for the dynamic change of HIV that causes AIDS by marker-based linkage disequilibrium (LD) analyses. This new model is the extension of our functional mapping theory to integrate viral load trajectories within a genetic mapping framework. Earlier studies of HIV dynamics have led to various mathematical functions for modelling the kinetic curves of plasma virions and CD4 lymphocytes in HIV patients. Through incorporating these functions into the LD-based mapping procedure, we can identify and map individual quantitative trait loci (or QTL) responsible for viral pathogenesis. We derive a closed-form solution for estimating QTL allele frequency and marker-QTL linkage disequilibrium in the context of EM algorithm and implement the simplex algorithm to estimate the mathematical parameters describing the curve shapes of HIV pathogenesis. We performed different simulation scenarios based on currently used clinical designs in AIDS/HIV research to illustrate the utility and power of our model for genetic mapping of HIV dynamics. The implications of our model for genetic and genomic research into AIDS pathogenesis are discussed.

Acquired Immunodeficiency Syndrome↗
PubMed2003

Multitrait fine mapping of quantitative trait loci using combined linkage disequilibria and linkage analysis.

A novel multitrait fine-mapping method is presented. The method is implemented by a model that treats QTL effects as random variables. The covariance matrix of allelic effects is proportional to the IBD matrix, where each element is the probability that a pair of alleles is identical by descent, given marker information and QTL position. These probabilities are calculated on the basis of similarities of marker haplotypes of individuals of the first generation of genotyped individuals, using "gene dropping" (linkage disequilibrium) and transmission of markers from genotyped parents to genotyped offspring (linkage). A small simulation study based on a granddaughter design was carried out to illustrate that the method provides accurate estimates of QTL position. Results from the simulation also indicate that it is possible to distinguish between a model postulating one pleiotropic QTL affecting two traits vs. one postulating two closely linked loci, each affecting one of the traits.

Chromosome Mapping↗
PubMed2003

Fine mapping of quantitative trait loci for improved fruit characteristics from Lycopersicon chmielewskii chromosome 1.

The near-isogenic line (NIL) TA1150 contains a 56-cM introgression from Lycopersicon chmielewskii chromosome 1 and has several interesting phenotypic characteristics including fruit with orange color, high levels of soluble solids, thick pericarp, small stem scars, and good firmness. A set of overlapping recombinant lines (subNILs) was developed and field tested to fine map the quantitative trait loci (QTL) controlling these traits. The results indicated that the solids, pericarp thickness, and firmness QTL are distinct from the color locus. Several of the QTL mapped in this study, including the soluble-solids QTL, probably correspond to QTL mapped in other wild species of tomato. However, analysis of a set of TA523 subNILs containing complementary introgressions from Lycopesicon hirsutum chromosome 1 suggests that this wild species may contain a different locus for improved soluble solids. Thus, it might be possible to combine the L. chmielewskii and L. hirsutum alleles for these loci in a single line with the potential for extremely highly soluble solids. The TA1150 subNIL TA1688 contains the smallest introgression of the solids locus (approximately 19 cM), as well as the pericarp thickness and firmness QTL, with a yield that was equivalent to two of the three control lines. Isolation of recombinant subNILs from TA1688 should break the linkage between orange color and high solids and provide a small introgressed segment for marker-assisted breeding and genetic improvement of processing tomato.

Alleles↗
PubMed2006

The sex-specific genetic architecture of quantitative traits in humans.

Mapping genetically complex traits remains one of the greatest challenges in human genetics today. In particular, gene-environment and gene-gene interactions, genetic heterogeneity and incomplete penetrance make thorough genetic dissection of complex traits difficult, if not impossible. Sex could be considered an environmental factor that can modify both penetrance and expressivity of a wide variety of traits. Sex is easily determined and has measurable effects on recognizable morphology; neurobiological circuits; susceptibility to autoimmune disease, diabetes, asthma, cardiovascular and psychiatric disease; and quantitative traits like blood pressure, obesity and lipid levels, among others. In this study, we evaluated sex-specific heritability and genome-wide linkages for 17 quantitative traits in the Hutterites. The results of this study could have important implications for mapping complex trait genes.

Genetic Linkage↗
PubMed2001

Interval mapping of quantitative trait loci in autotetraploid species.

This article presents a method for QTL interval mapping in autotetraploid species for a full-sib family derived by crossing two parents. For each offspring, the marker information on each chromosome is used to identify possible configurations of chromosomes inherited from the two parents and the locations of crossovers on these chromosomes. A branch and bound algorithm is used to identify configurations with the minimum number of crossovers. From these configurations, the conditional probability of each possible QTL genotype for a series of positions along the chromosome can be estimated. An iterative weighted regression is then used to relate the trait values to the QTL genotype probabilities. A simulation study is performed to assess this approach and to investigate the effects of the proportion of codominant to dominant markers, the heritability, and the population size. We conclude that the method successfully locates QTL and estimates their parameters accurately, and we discuss different modes of action of the QTL that may be modeled.

Algorithms↗
PubMed2005

The role of pedigree information in combined linkage disequilibrium and linkage mapping of quantitative trait loci in a general complex pedigree.

Combined linkage disequilibrium and linkage (LDL) mapping can exploit historical as well as recent and observed recombinations in a recorded pedigree. We investigated the role of pedigree information in LDL mapping and the performance of LDL mapping in general complex pedigrees. We compared using complete and incomplete genotypic data, spanning 5 or 10 generations of known pedigree, and we used bi- or multiallelic markers that were positioned at 1- or 5-cM intervals. Analyses carried out with or without pedigree information were compared. Results were compared with linkage mapping in some of the data sets. Linkage mapping or LDL mapping with sparse marker spacing ( approximately 5 cM) gave a poorer mapping resolution without considering pedigree information compared to that with considering pedigree information. The difference was bigger in a pedigree of more generations. However, LDL mapping with closely linked markers ( approximately 1 cM) gave a much higher mapping resolution regardless of using pedigree information. This study shows that when marker spacing is dense and there is considerable linkage disequilibrium generated from historical recombinations between flanking markers and QTL, the loss of power due to ignoring pedigree information is negligible and mapping resolution is very high.

Alleles↗
PubMed2003

Exponential mapping of quantitative trait loci governing allometric relationships in organisms.

Allometric scaling relationships or quarter-power rules, as a universal biological law, can be viewed as having some genetic component, and the particular genes (or quantitative trait loci, QTL) underlying these allometric relationships can be mapped using molecular markers. We develop a mathematical and statistical model for mapping allometric QTL on the basis of nonlinear power functions using Taylor's approximation theory. Simulation studies indicate that the QTL position and effect can be estimated using our model, but the estimation precision can be improved from the higher- over lower-order approximation when the sample size used and gene effects are small. The application of our approach in a real example from forest trees leads to successful detection of a QTL governing the allometric relationship between 3rd-year stem height and 3rd-year stem biomass. It is expected that our model will have broad implications for genetic, evolutionary, biomedical and breeding research.

Algorithms↗
PubMed1995

Polygenic disease: methods for mapping complex disease traits.

Improved genotyping technology has made it feasible to use a genetic approach to map genes involved in the etiology of common human diseases. We discuss here recent developments in several different statistical approaches to linkage analysis of these traits, including affected-sib-pair methods, the affected-pedigree-member method, regressive models and linkage-disequilibrium-based approaches. We discuss advantages and disadvantages of the various approaches, as well as factors influencing study design and the ability to detect loci. Statistical methodology in this area is advancing rapidly and will help enable the mapping and cloning of loci involved in susceptibility to common multifactorial diseases.

Autistic Disorder↗
PubMed1996

A generalization of the mixture model in the mapping of quantitative trait loci for progeny from a biparental cross of inbred lines.

The recent advent of molecular markers has created a great potential for the understanding of quantitative inheritance. In parallel to rapid developments and improvements in molecular marker technologies, biometrical models have been constructed, refined and generalized for the mapping of quantitative trait loci (QTL). However, current models present restrictions in terms of breeding designs to which they apply. In this paper, we develop an approach for the generalization of the mixture model for progeny from a single bi-parental cross of inbred lines. Detailed derivations are given for genetic designs involving populations developed by selfing, i.e., where marker genotypes are obtained from Fx (x > or = 2) individuals and where phenotypes are measured on Fy (y > or = x) individuals or families. Extensions to designs involving doubled-haploids, backcross-derived individuals and random matings are outlined. The derivations presented here can easily be combined with current QTL mapping approaches.

Crosses, Genetic↗
PubMed2006

An updated 'Essex' by 'Forrest' linkage map and first composite interval map of QTL underlying six soybean traits.

DNA marker maps based on single populations are the basis for gene, loci and genomic analyses. Individual maps can be integrated to produce composite maps with higher marker densities if shared marker orders are consistent. However, estimates of marker order in composite maps must include sets of markers that were not polymorphic in multiple populations. Often some of the pooled markers were not codominant, or were not correctly scored. The soybean composite map was composed of data from five separate populations based on northern US germplasm but does not yet include 'Essex' by 'Forrest' recombinant inbred line (RIL) population (E x F) or any southern US soybean cultivars. The objectives were, to update the E x F map with codominant markers, to compare marker orders among this map, the Forrest physical map and the composite soybean map and to compare QTL identified by composite interval maps to the earlier interval maps. Two hundred and thirty seven markers were used to construct the core of the E x F map. The majority of marker orders were consistent between the maps. However, 19 putative marker inversions were detected on 12 of 20 linkage groups (LG). Eleven marker distance compressions were also found. The number of inverted markers ranged from 1 to 2 per LG. Thus, marker order inversions may be common in southern compared to northern US germplasm. A total of 61 QTL among 37 measures of six traits were detected by composite interval maps, interval maps and single point analysis. Seventeen of the QTL found in composite intervals had previously been detected among the 29 QTL found in simple interval maps. The genomic locations of the known QTL were more closely delimited. A genome sequencing project to compare Southern and Northern US soybean cultivars would catalog and delimit inverted regions and the associated QTL. Gene introgression in cultivar development programs would be accelerated.

Chromosome Mapping↗
PubMed2003

[QTLs mapping of leaf traits and root vitality in a recombinant inbred line population of rice].

By employing a recombinant inbred line (RIL) population of 247 lines derived from an inidca-indica cross Zhenshan 97B x Milyang 46, a linkage map consisting of 158 DNA markers was constructed and used for the determination of QTLs conditioning five leaf traits and root exudates. The leaf traits analyzed were leaf area, leaf length, leaf width, leaf perimeter and leaf length/width ratio measured on top first leaf, top second and top third leaves. The RIL population showed transgressive segregation on each trait, and highly significant or significant positive correlations were observed between all traits except between leaf length and width, and between leaf perimeter and length/width ratio. A total of 24 QTLs located in 9 intervals were detected to have significant additive effects for leaf traits analyzed, with LOD scores ranging 2.9-11.8 and 4.0%-32.5% phenotypic variation explained for a single QTL. Clustering of QTLs for leaf traits was evident. In interval RM197-RZ516 on chromosome 6, 2 QTLs for leaf length, 2 QTLs for leaf width and 3 QTLs for leaf length/width ratio of different leaves were detected, among which the alleles for increasing trait values were from Zhenshan 97B for leaf length and leaf length/width ratio, and from Milyang 46 for leaf width. In interval RM1-RG532 on chromosome 1,2 QTLs for leaf length and 2 QTLs for leaf perimeter were detected on top first leaf and top second leaf, respectively, and all the alleles for increasing trait values were from Milyang 46. In this interval, larger additive effects were observed for QTLs detected on top first leaf than at top second leaf. In interval RZ667-B10B on chromosome 6, a QTL for leaf perimeter of top second leaf was detected, accounting for 8.0% phenotypic variation. In intervals RZ66-RM264 and RG81-RM313 on chromosome 8 and 12, each QTL was detected for leaf length of top third leaf and explained for 9.0% and 15.3% phenotypic variation, respectively. Epistasis analysis detected 56 and 4 significant additive-by-additive interactions for leaf traits and root vitality, explaining 2.7% to 13.7% and 6.8% to 14.9% of the total phenotypic variation, respectively. On comparison with QTLs for yield traits detected in the same population previously, it was found that the majority of QTLs for leaf traits and root vitality and those for yield traits were located in similar intervals. Fine mapping of QTLs for both leaf and yield traits in these chromosomal regions would facilitate investigations of the source-sink relationship in rice.

Chromosome Mapping↗
PubMed1995

Interval mapping of quantitative trait loci using a sib-pair linkage method.

Fulker and Cardon's interval mapping extension of Haseman and Elston's sib-pair linkage method was used to map loci affecting the quantitative phenotypes presented as part of Problem 2, both adjusted and not adjusted for covariates: Q1 was adjusted for age and the environmental factor (EF); Q2 and Q3 for EF; and Q4 for age, sex, and EF. Adjusted Q2 and Q4 were also log-transformed. The effect of candidate locus C5 (D5G28) on Q1 was detected by a test of association--apparently, allele 1 of C5 is protective (leading to lower values of Q1), allele 2 has no effect, and allele 3 contributes to elevated levels of Q1. C5 accounted for 5.2% of the variation in Q1; it was included as an additional concomitant in the adjustment procedure. Analysis of the correlational structure among the variables revealed that Q4 was not associated with either affected status or Q1 after controlling for the effects of age, and we concluded that Q4 probably does not itself play a role in the etiology of the disease. Mapping studies using a significance level of 0.05 lead to the detection of all the genes, but also resulted in a high frequency of false positive results. On the other hand, using a 0.0005 significance level resulted in the detection of D2G10-11 for both Q1 and Q3, and D1G2 was detected for Q2. One false positive was detected using this significance level and the effects of D1G2 on Q1 and D5G22-23 on Q4 were missed. There was no systematic effect of adjustment for covariates on the detection of loci, although in general, analysis of adjusted phenotypes yielded substantially higher rates of false positives. Finally, this mapping approach correctly located D1G2 and D2G10-11 for Q1 using the nonadjusted phenotype, and D1G10-11 for Q3 using the adjusted phenotype. The maximum difference between the estimated map location from the true location was 1.5 cM. It would be important to estimate the error interval around these inferred locations in order to assess the utility of this method for fine mapping over small (e.g,. 2 cM) intervals.

Chromosome Mapping↗