Interval mapping of quantitative trait loci for time-to-event data with the proportional hazards mixture cure model

Interval mapping using normal mixture models has been an important tool for analyzing quantitative traits in experimental organisms. When the primary phenotype is time-to-event, it is natural to use survival models such as Cox's proportional hazards model instead of normal mixtures to model the phenotype distribution. An extra challenge for modeling time-to-event data is that the underlying population may consist of susceptible and nonsusceptible subjects. In this article, we propose a semiparametric proportional hazards mixture cure model which allows missing covariates. We discuss applications to quantitative trait loci (QTL) mapping when the primary trait is time-to-event from a population of mixed susceptibility. This model can be used to characterize QTL effects on both susceptibility and time-to-event distribution, and to estimate QTL location. The model can naturally incorporate covariate effects of other risk factors. Maximum likelihood estimates for the parameters in the model as well as their corresponding variance estimates can be obtained numerically using an EM-type algorithm. The proposed methods are assessed by simulations under practical settings and illustrated using a real data set containing survival times of mice after infection with Listeria monocytogenes. An extension to multiple intervals is also discussed.     

Semiparametric methods for mapping quantitative trait loci with censored data

Statistical methods for the detection of genes influencing quantitative traits with the aid of genetic markers are well developed for normally distributed, fully observed phenotypes. Many experiments are concerned with failure-time phenotypes, which have skewed distributions and which are usually subject to censoring because of random loss to follow-up, failures from competing causes, or limited duration of the experiment. In this article, we develop semiparametric statistical methods for mapping quantitative trait loci (QTLs) based on censored failure-time phenotypes. We formulate the effects of the QTL genotype on the failure time through the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model and derive efficient likelihood-based inference procedures. In addition, we show how to assess statistical significance when searching several regions or the entire genome for QTLs. Extensive simulation studies demonstrate that the proposed methods perform well in practical situations. Applications to two animal studies are provided.     

Identification of X-linked quantitative trait loci affecting cold tolerance in Drosophila melanogaster and fine mapping by selective sweep analysis

Drosophila melanogaster is a cosmopolitan species that colonizes a great variety of environments. One trait that shows abundant evidence for naturally segregating genetic variance in different populations of D. melanogaster is cold tolerance. Previous work has found quantitative trait loci (QTL) exclusively on the second and the third chromosomes. To gain insight into the genetic architecture of cold tolerance on the X chromosome and to compare the results with our analyses of selective sweeps, a mapping population was derived from a cross between substitution lines that solely differed in the origin of their X chromosome: one originates from a European inbred line and the other one from an African inbred line. We found a total of six QTL for cold tolerance factors on the X chromosome of D. melanogaster. Although the composite interval mapping revealed slightly different QTL profiles between sexes, a coherent model suggests that most QTL overlapped between sexes, and each explained around 5–14% of the genetic variance (which may be slightly overestimated). The allelic effects were largely additive, but we also detected two significant interactions. Taken together, this provides evidence for multiple QTL that are spread along the entire X chromosome and whose effects range from low to intermediate. One detected transgressive QTL influences cold tolerance in different ways for the two sexes. While females benefit from the European allele increasing their cold tolerance, males tend to do better with the African allele. Finally, using selective sweep mapping, the candidate gene CG16700 for cold tolerance colocalizing with a QTL was identified.     

Verification of selective DNA pooling methodology through identification and estimation of the DGAT1 effect

The discovery of markers linked to genes that are responsible for traits of interest to the dairy industry might prove useful because they could aid in selection and breeding decisions. We have developed a selective DNA pooling methodology to allow us to efficiently screen the bovine genome in order to find genes responsible for production traits. Using markers on chromosome 14 as a test case, we identified a gene (DGAT1) previously known to affect three traits (fat yield, protein yield and total milk yield). Furthermore, we predicted similar effects to those previously shown for DGAT1 in a New Zealand Holstein-Friesian herd. Additionally, we showed a low error rate (1.6%) for the pooling procedure. Hence we are confident that we can apply this procedure to an entire genome scan in the search for quantitative trait loci (QTL).     

Methods for multiple-marker mapping of quantitative trait loci in half-sib populations

In this paper we consider the detection of individual loci controlling quantitative traits of interest (quantitative trait loci or QTLs) in the large half-sib family structure found in some species. Two simple approaches using multiple markers are proposed, one using least squares and the other maximum likelihood. These methods are intended to provide a relatively fast screening of the entire genome to pinpoint regions of interest for further investigation. They are compared with a more traditional single-marker least-squares approach. The use of multiple markers is shown to increase power and has the advantage of providing an estimate for the location of the QTL. The maximum-likelihood and the least-squares approaches using multiple markers give similar power and estimates for the QTL location, although the likelihood approach also provides estimates of the QTL effect and sire heterozygote frequency. A number of assumptions have been made in order to make the likelihood calculations feasible, however, and computationally it is still more demanding than the least-squares approach. The least-squares approach using multiple markers provides a fast method that can easily be extended to include additional effects.     

肉牛的数量性状基因座定位研究进展

遗传图谱的发展为寻找和定位影响重要数量性状变异的基因提供了便利。迄今为止,育种学家已经在肉牛的1、2、5、6、14、15、17、18、19、21、23、27、和29号常染色体上发现了QTL的踪迹。候选基因的研分显示肌肉生长抑制素基因等可能就是生长和屠宰重性状的QTL,基困组统计定位则揭示最有可能的QTL区域在2、5、6、15、19、27、29号染色体上。进一步的定位仍需遗传学家、分子生物学家及育种学家的共同努力。     

Multipoint genetic mapping of quantitative trait loci with dominant markers in outbred populations

We present a multipoint algorithm for mapping quantitative trait loci (QTLs) using dominant markers. The algorithm is designed for outbred populations and is particularly suited for large families. The algorithm works with either codominant or dominant markers, either of which may be interspersed within the same linkage map. Concurrently, the algorithm also partitions dominance variance at the QTL. Computer simulations show that with large families, QTL mapping with dominant markers can be almost as powerful as with bi-allelic, codominant markers. Yet despite this, other situations show a large standard deviation in the estimate of the QTL position, thus making QTL mapping with dominant markers in outbred populations a useful detection tool, albeit limited in its resolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Power analysis of QTL detection in half-sib families using selective DNA pooling

Individual loci of economic importance (QTL) can be detected by comparing the inheritance of a trait and the inheritance of loci with alleles readily identifiable by laboratory methods (genetic markers). Data on allele segregation at the individual level are costly and alternatives have been proposed that make use of allele frequencies among progeny, rather than individual genotypes. Among the factors that may affect the power of the set up, the most important are those intrinsic to the QTL: the additive effect of the QTL, and its dominance, and distance between markers and QTL. Other factors are relative to the choice of animals and markers, such as the frequency of the QTL and marker alleles among dams and sires. Data collection may affect the detection power through the size of half-sib families, selection rate within families, and the technical error incurred when estimating genetic frequencies. We present results for a sensitivity analysis for QTL detection using pools of DNA from selected half-sibs. Simulations showed that conclusive detection may be achieved with families of at least 500 half-sibs if sires are chosen on the criteria that most of their marker alleles are either both missing, or one is fixed, among dams.     

Assessment of DNA pooling strategies for mapping of QTLs

The synthesis of DNA pools from segregating populations is an efficient strategy for identifying DNA markers closely linked to genes or genomic regions of interest. To-date, DNA pooling based solely upon phenotypic information, or bulked segregant analysis, has been employed only in the analysis of simply-inherited traits. We have assessed the utility of phenotype-based DNA pools for tagging (e.g., identifying DNA markers closely-linked to) quantitative trait loci (QTLs), segregating in the presence of other such loci, and expressing phenotypes which are influenced by the environment. Theoretical estimates suggest that QTL alleles with phenotypic effects of 0.75–1.0 standard deviations (SD), or larger, should be detectable in back-cross (BC), F₂ and recombinant inbred (RI) or doubled haploid (DH) populations of manageable size (100–200 plants/lines). However, post hoc analysis of three data sets, used in QTL mapping of tomato and rice, indicate that the majority of QTLs identified had allele effects of less than 0.75 SD, and thus could not be easily tagged in DNA pools. Segregation distortion can have a large effect on the allelic composition of DNA pools, necessitating the use of more individuals in the pools to minimize false positive and false negative results. In general, we suggest that use of phenotype-based DNA pools might be successful in tagging QTLs of very large effect, but is unlikely to permit comprehensive identification of the majority of QTLs affecting a complex trait. DNA pools constructed from a priori information should, however, be useful in identifying new DNA markers for regions of the genome known to contain QTLs.     

Identification of an ovulation rate QTL in cattle on BTA14 using selective DNA pooling and interval mapping

Increased twinning incidence in beef cattle has the potential to improve production efficiency. However, phenotypic selection for twinning rate is difficult because of the trait's low heritability and the long time interval necessary to collect phenotypic records. Therefore, this trait and the correlated trait of ovulation rate are ideal candidates for marker-assisted selection. The objective of this study was to complete a genome-wide search for ovulation rate quantitative trait loci (QTL) in two related sire families. The families (paternal halfsib sires 839802 and 839803) were from a population of cattle selected for ovulation rate at the USDA Meat Animal Research Center, Clay Center, Nebraska. Putative ovulation rate QTL have previously been identified in the 839802 family on chromosomes 7 and 19; however, marker coverage in the original scan was not complete. This study fills the gaps in marker coverage of the earlier study by adding approximately 60 informative microsatellites to each sire family. Each family was genotyped using selective DNA pooling. Sons and daughters were included in either the high or low pool based on their estimated breeding value deviations from the mid-parent average (EBVMD) for ovulation rate. Approximately 40% (839802) and 26% (839803) of available progeny comprised the high and low pools combined. Pooled typing revealed possible associations (nominal P < 0.05) between ovulation rate and marker genotype for 11 and 15 microsatellites in the 839802 and 839803 families, respectively. Subsequent interval mapping strengthened support for the presence of an ovulation rate QTL on BTA14 (chromosome-wise P < 0.02).     

An optimal DNA pooling strategy for progressive fine mapping

We present a cost-effective DNA pooling strategy for fine mapping of a single Mendelian gene in controlled crosses. The theoretical argument suggests that it is potentially possible for a single-stage pooling approach to reduce the overall experimental expense considerably by balancing costs for genotyping and sample collection. Further, the genotyping burden can be reduced through multi-stage pooling. Numerical results are provided for practical guidelines. For example, the genotyping effort can be reduced to only a small fraction of that needed for individual genotyping at a small loss of estimation accuracy or at a cost of increasing sample sizes slightly when recombination rates are 0.5% or less. An optimal two-stage pooling scheme can reduce the amount of genotyping to 19.5%, 14.5% and 6.4% of individual genotyping efforts for identifying a gene within 1, 0.5, and 0.1 cM, respectively. Finally, we use a genetic data set for mapping the rice xl(t) gene to demonstrate the feasibility and efficiency of the DNA pooling strategy. Taken together, the results demonstrate that this DNA pooling strategy can greatly reduce the genotyping burden and the overall cost in fine mapping experiments.     

Empirical evaluation of selective DNA pooling to map QTL in dairy cattle using a half-sib design by comparison to individual genotyping and interval mapping

This study represents the first attempt at an empirical evaluation of the DNA pooling methodology by comparing it to individual genotyping and interval mapping to detect QTL in a dairy half-sib design. The findings indicated that the use of peak heights from the pool electropherograms without correction for stutter (shadow) product and preferential amplification performed as well as corrected estimates of frequencies. However, errors were found to decrease the power of the experiment at every stage of the pooling and analysis. The main sources of errors include technical errors from DNA quantification, pool construction, inconsistent differential amplification, and from the prevalence of sire alleles in the dams. Additionally, interval mapping using individual genotyping gains information from phenotypic differences between individuals in the same pool and from neighbouring markers, which is lost in a DNA pooling design. These errors cause some differences between the markers detected as significant by pooling and those found significant by interval mapping based on individual selective genotyping. Therefore, it is recommended that pooled genotyping only be used as part of an initial screen with significant results to be confirmed by individual genotyping. Strategies for improving the efficiency of the DNA pooling design are also presented.     

Interval mapping of quantitative trait loci for reproductive,morphological, and seed traits of soybean (Glycine max L.)

Quantitative trait loci (QTL) were mapped in segregating progeny from a cross between two soybean (Glycine max (L.) Merr.) cultivars: Minsoy (PI 27.890) and Noir 1 (PI 290.136). The 15 traits analyzed included reproductive, morphological, and seed traits, seed yield and carbon isotope discrimination ratios (¹³C/¹²C). Genetic variation was detected for all of the traits, and transgressive segregation was a common phenomenon. One hundred and thirty-two linked genetic markers and 24 additional unlinked markers were used to locate QTL by interval mapping and one-way analysis of variance, respectively. Quantitative trait loci controlling 11 of the 15 traits studied were localized to intervals in 6 linkage groups. Quantitative trait loci for developmental and morphological traits (R1, R5, R8, plant height, canopy height, leaf area, etc.) tended to be clustered in three intervals, two of which were also associated with seed yield. Quantitative trait loci for seed oil were separated from all the other QTL. Major QTL for maturity and plant height were linked to RFLP markers R79 (31% variation) and G173 (53% variation). Quantitative trait loci associated with unlinked markers included possible loci for seed protein and weight. Linkage between QTL is discussed in relation to the heritability and genetic correlation of the traits.     

Joint mapping of quantitative trait loci using F2 populations

In this paper, the theory of joint mapping of quantitative trait loci is extended to F₂ populations. Two independent regression equations, related to the additive and dominance effects respectively, are derived. Therefore, there are three alternative strategies for mapping QTLs, called additive-based mapping (ABM), dominance-based mapping (DBM) and additive-dominance-based mapping (ADBM). Simulation results have shown that ADBM is the most appropriate in most situations.     

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.     

Marker-based mapping of quantitative trait loci using replicated progenies

Summary When heritability of the trait under investigation is low, replicated progenies can bring about a major reduction in the number of individuals that need to be scored for marker genotype in determining linkage between marker loci and quantitative trait loci (QTL). Savings are greatest when heritability of the trait is low, but are much reduced when heritability of the quantitative trait is moderate to high. Required numbers for recombinant inbred lines will be greater than those required for a simple F₂ population when heritabilities are moderate to high and the proportion of recombination between marker locus and quantitative trait locus is substantial.Contribution No. 2613-E of the Agricultural Research Organization, 1989 series     

Lineage-specific mapping of quantitative trait loci

We present an approach for quantitative trait locus (QTL) mapping, termed as ‘lineage-specific QTL mapping'', for inferring allelic changes of QTL evolution along with branches in a phylogeny. We describe and analyze the simplest case: by adding a third taxon into the normal procedure of QTL mapping between pairs of taxa, such inferences can be made along lineages to a presumed common ancestor. Although comparisons of QTL maps among species can identify homology of QTLs by apparent co-location, lineage-specific mapping of QTL can classify homology into (1) orthology (shared origin of QTL) versus (2) paralogy (independent origin of QTL within resolution of map distance). In this light, we present a graphical method that identifies six modes of QTL evolution in a three taxon comparison. We then apply our model to map lineage-specific QTLs for inbreeding among three taxa of yellow monkey-flower: Mimulus guttatus and two inbreeders M. platycalyx and M. micranthus, but critically assuming outcrossing was the ancestral state. The two most common modes of homology across traits were orthologous (shared ancestry of mutation for QTL alleles). The outbreeder M. guttatus had the fewest lineage-specific QTL, in accordance with the presumed ancestry of outbreeding. Extensions of lineage-specific QTL mapping to other types of data and crosses, and to inference of ancestral QTL state, are discussed.     

Efficient association mapping of quantitative trait loci with selective genotyping

Selective genotyping (i.e., genotyping only those individuals with extreme phenotypes) can greatly improve the power to detect and map quantitative trait loci in genetic association studies. Because selection depends on the phenotype, the resulting data cannot be properly analyzed by standard statistical methods. We provide appropriate likelihoods for assessing the effects of genotypes and haplotypes on quantitative traits under selective-genotyping designs. We demonstrate that the likelihood-based methods are highly effective in identifying causal variants and are substantially more powerful than existing methods.     

Fractioned DNA pooling: a new cost-effective strategy for fine mapping of quantitative trait loci

Selective DNA pooling (SDP) is a cost-effective means for an initial scan for linkage between marker and quantitative trait loci (QTL) in suitable populations. The method is based on scoring marker allele frequencies in DNA pools from the tails of the population trait distribution. Various analytical approaches have been proposed for QTL detection using data on multiple families with SDP analysis. This article presents a new experimental procedure, fractioned-pool design (FPD), aimed to increase the reliability of SDP mapping results, by "fractioning" the tails of the population distribution into independent subpools. FPD is a conceptual and structural modification of SDP that allows for the first time the use of permutation tests for QTL detection rather than relying on presumed asymptotic distributions of the test statistics. For situations of family and cross mapping design we propose a spectrum of new tools for QTL mapping in FPD that were previously possible only with individual genotyping. These include: joint analysis of multiple families and multiple markers across a chromosome, even when the marker loci are only partly shared among families; detection of families segregating (heterozygous) for the QTL; estimation of confidence intervals for the QTL position; and analysis of multiple-linked QTL. These new advantages are of special importance for pooling analysis with SNP chips. Combining SNP microarray analysis with DNA pooling can dramatically reduce the cost of screening large numbers of SNPs on large samples, making chip technology readily applicable for genomewide association mapping in humans and farm animals. This extension, however, will require additional, nontrivial, development of FPD analytical tools.