Testing quantitative trait locus effects in genetic backcross studies with double recombination occurring

Testing the existence of quantitative trait locus (QTL) effects is an important task in QTL mapping studies. In this paper, we assume the phenotype distributions from a location-scale distribution family, and consider to test the QTL effects in both location and scale in the backcross studies with double recombination occurring. Without equal scale assumption, the log-likelihood function is unbounded, which leads to the traditional likelihood ratio test being invalid. To deal with this problem, we propose a penalized likelihood ratio test (PLRT) for testing the QTL effects. The null limiting distribution of the PLRT is shown to be a supremum of a chi-square process. As a complement, we also investigate the null limiting distribution of the likelihood ratio test for the case with equal scale assumption. The limiting distributions of the two tests under local alternatives are also studied. Simulation studies are performed to evaluate the asymptotic results and a real-data example is given for illustration.

Molecular Breeding to Overcome Biotic Stresses in Soybean: Update

Soybean (Glycine max (L.) Merr.) is an important leguminous crop and biotic stresses are a global concern for soybean growers. In recent decades, significant development has been carried outtowards identification of the diseases caused by pathogens, sources of resistance and determination of loci conferring resistance to different diseases on linkage maps of soybean. Host-plant resistance is generally accepted as the bestsolution because of its role in the management of environmental and economic conditions of farmers owing to low input in terms of chemicals. The main objectives of soybean crop improvement are based on the identification of sources of resistance or tolerance against various biotic as well as abiotic stresses and utilization of these sources for further hybridization and transgenic processes for development of new cultivars for stress management. The focus of the present review is to summarize genetic aspects of various diseases caused by pathogens in soybean and molecular breeding research work conducted to date.

Discovery of a major QTL for root-knot nematode (Meloidogyne incognita) resistance in cultivated sweetpotato (Ipomoea batatas)

Utilizing a high-density integrated genetic linkage map of hexaploid sweetpotato, we discovered a major dominant QTL for root-knot nematode (RKN) resistance and modeled its effects. This discovery is useful for development of a modern sweetpotato breeding program that utilizes marker-assisted selection and genomic selection approaches for faster genetic gain of RKN resistance. The root-knot nematode [Meloidogyne incognita (Kofoid & White) Chitwood] (RKN) causes significant storage root quality reduction and yields losses in cultivated sweetpotato [Ipomoea batatas (L.) Lam.]. In this study, resistance to RKN was examined in a mapping population consisting of 244 progenies derived from a cross (TB) between 'Tanzania,' a predominant African landrace cultivar with resistance to RKN, and 'Beauregard,' an RKN susceptible major cultivar in the USA. We performed quantitative trait loci (QTL) analysis using a random-effect QTL mapping model on the TB genetic map. An RKN bioassay incorporating potted cuttings of each genotype was conducted in the greenhouse and replicated five times over a period of 10 weeks. For each replication, each genotype was inoculated with ca. 20,000 RKN eggs, and root-knot galls were counted ~62 days after inoculation. Resistance to RKN in the progeny was highly skewed toward the resistant parent, exhibiting medium to high levels of resistance. We identified one major QTL on linkage group 7, dominant in nature, which explained 58.3% of the phenotypic variation in RKN counts. This work represents a significant step forward in our understanding of the genetic architecture of RKN resistance and sets the stage for future utilization of genomics-assisted breeding in sweetpotato breeding programs.

Identification of quantitative trait loci for milk protein percentage in Murrah buffaloes

Milk protein is an important constituent of milk in buffaloes and is moderately heritable. The milk protein percentage varies significantly between breeds/herds/species. Buffaloes can be selected for higher milk protein percentage and this paper provides QTLs for marker assisted selection in buffaloes. The milk protein percentage records on 2,028 daughters belonging to 12 half sib families were analyzed for the identification of QTLs on 8 chromosomes in buffaloes using chromosome scans. The single marker analysis revealed 74 markers to be associated with milk protein percentage in 12 sire families. When common markers were removed from the analysis, 51 markers remained. The Interval mapping using R/qtl identified 69 QTLs in 12 half sib families on 8 chromosomes of buffalo. The meta QTL analysis defined 25 consensus QTL regions in buffaloes for milk protein percentage. Most of the QTLs identified have been reported for cattle however few new chromosomal locations were also identified to be associated with milk protein percentage in buffaloes. Comparative genomics revealed 1117 genes underlying the QTL regions associated with milk protein percentage. Among these, 109 genes were directly associated with protein metabolism. The protein-protein interaction among the genes and gene ontology analysis and pathways have been identified. These 109 genes have potential to be candidate genes for milk protein percentage in buffaloes.

High-Resolution Genetic Map and QTL Analysis of Growth-Related Traits of Hevea brasiliensis Cultivated Under Suboptimal Temperature and Humidity Conditions

Rubber tree (Hevea brasiliensis) cultivation is the main source of natural rubber worldwide and has been extended to areas with suboptimal climates and lengthy drought periods; this transition affects growth and latex production. High-density genetic maps with reliable markers support precise mapping of quantitative trait loci (QTL), which can help reveal the complex genome of the species, provide tools to enhance molecular breeding, and shorten the breeding cycle. In this study, QTL mapping of the stem diameter, tree height, and number of whorls was performed for a full-sibling population derived from a GT1 and RRIM701 cross. A total of 225 simple sequence repeats (SSRs) and 186 single-nucleotide polymorphism (SNP) markers were used to construct a base map with 18 linkage groups and to anchor 671 SNPs from genotyping by sequencing (GBS) to produce a very dense linkage map with small intervals between loci. The final map was composed of 1,079 markers, spanned 3,779.7 cM with an average marker density of 3.5 cM, and showed collinearity between markers from previous studies. Significant variation in phenotypic characteristics was found over a 59-month evaluation period with a total of 38 QTLs being identified through a composite interval mapping method. Linkage group 4 showed the greatest number of QTLs (7), with phenotypic explained values varying from 7.67 to 14.07%. Additionally, we estimated segregation patterns, dominance, and additive effects for each QTL. A total of 53 significant effects for stem diameter were observed, and these effects were mostly related to additivity in the GT1 clone. Associating accurate genome assemblies and genetic maps represents a promising strategy for identifying the genetic basis of phenotypic traits in rubber trees. Then, further research can benefit from the QTLs identified herein, providing a better understanding of the key determinant genes associated with growth of Hevea brasiliensis under limiting water conditions.

Identification of quantitative trait loci for fat percentage in buffaloes

The milk fat percentage records of 2174 daughters belonging to 12 half sib families were analyzed for the identification of QTLs on 8 chromosomes in buffaloes using chromosome scans. The single marker analysis revealed 49 markers to be associated with milk fat percentage in 10 sire families. The interval mapping using R/qtl identified 43 QTLs on 8 chromosomes of buffalo. The meta-QTL analysis was carried out to define consensus QTLs in buffaloes and total 28 meta-QTL regions could be identified for milk fat percentage. Most of the QTLs identified in the experiments have been reported for cattle; however, few new chromosomal locations were also identified to be associated with fat percentage in buffaloes. The additional QTLs identified in buffalo may be due to high level of heterozygosity in buffalo compared to Holstein Friesian and other exotic milk breeds for which QTLs have beenreported. Assuming buffalo-cattle synteny, a total of 1118 genes were identified underlying the QTL regions, out of these 45 genes were identified to be associated with lipid metabolism. The interaction among the genes and gene ontology analysis confirmed their association with lipid metabolism. These 45 genes have potential to be candidate genes for milk fat percentage in buffaloes and underlie the QTL regions identified in buffaloes in the present study.

Composite Interval Mapping Based on Lattice Design for Error Control May Increase Power of Quantitative Trait Locus Detection

Experimental error control is very important in quantitative trait locus (QTL) mapping. Although numerous statistical methods have been developed for QTL mapping, a QTL detection model based on an appropriate experimental design that emphasizes error control has not been developed. Lattice design is very suitable for experiments with large sample sizes, which is usually required for accurate mapping of quantitative traits. However, the lack of a QTL mapping method based on lattice design dictates that the arithmetic mean or adjusted mean of each line of observations in the lattice design had to be used as a response variable, resulting in low QTL detection power. As an improvement, we developed a QTL mapping method termed composite interval mapping based on lattice design (CIMLD). In the lattice design, experimental errors are decomposed into random errors and block-within-replication errors. Four levels of block-within-replication errors were simulated to show the power of QTL detection under different error controls. The simulation results showed that the arithmetic mean method, which is equivalent to a method under random complete block design (RCBD), was very sensitive to the size of the block variance and with the increase of block variance, the power of QTL detection decreased from 51.3% to 9.4%. In contrast to the RCBD method, the power of CIMLD and the adjusted mean method did not change for different block variances. The CIMLD method showed 1.2- to 7.6-fold higher power of QTL detection than the arithmetic or adjusted mean methods. Our proposed method was applied to real soybean (Glycine max) data as an example and 10 QTLs for biomass were identified that explained 65.87% of the phenotypic variation, while only three and two QTLs were identified by arithmetic and adjusted mean methods, respectively.

Identification of QTLs for Resistance to Sclerotinia sclerotiorum in Carioca Common Bean by the Moving Away Method

The aim of this study was to use multiple DNA markers for detection of QTLs related to resistance to white mold in an F₂ population of common bean evaluated by the straw test method. The DNA from 186 F₂ plants and from the parents was extracted for genotypic evaluation using SSR, AFLP, and SRAP markers. For phenotypic analysis, 186 F_2:4 progenies and ten lines were evaluated, in a 14 × 14 triple lattice experimental design. The adjusted mean values of the F_2:4 progenies were used for identification of QTLs by Bayesian shrinkage analysis. Significant differences were observed among the progenies for reaction to white mold. In identification of QTLs, 17 markers identified QTLs for resistance—13 SSRs and 4 AFLPs. The moving away method under the Bayesian approach proved to be efficient in the identification of QTLs when a genetic map is not used due to the low density of markers. The ME1 and BM211 markers are near the QTLs, with the effect of increasing resistance to white mold, and they have high heritability. They are thus promising for marker-assisted selection.

Fine-mapping of qRfg2, a QTL for resistance to Gibberella stalk rot in maize

Stalk rot is one of the most devastating diseases in maize worldwide. In our previous study, two QTLs, a major qRfg1 and a minor qRfg2, were identified in the resistant inbred line '1145' to confer resistance to Gibberella stalk rot. In the present study, we report on fine-mapping of the minor qRfg2 that is located on chromosome 1 and account for ~8.9% of the total phenotypic variation. A total of 22 markers were developed in the qRfg2 region to resolve recombinants. The progeny-test mapping strategy was developed to accurately determine the phenotypes of all recombinants for fine-mapping of the qRfg2 locus. This fine-mapping process was performed from BC(4)F(1) to BC(8)F(1) generations to narrow down the qRfg2 locus into ~300 kb, flanked by the markers SSRZ319 and CAPSZ459. A predicted gene in the mapped region, coding for an auxin-regulated protein, is believed to be a candidate for qRfg2. The qRfg2 locus could steadily increase the resistance percentage by ~12% across different backcross generations, suggesting its usefulness in enhancing maize resistance against Gibberella stalk rot.

Gaussian process based bayesian semiparametric quantitative trait Loci interval mapping

In linkage analysis, it is often necessary to include covariates such as age or weight to increase power or avoid spurious false positive findings. However, if a covariate term in the model is specified incorrectly (e.g., a quadratic term misspecified as a linear term), then the inclusion of the covariate may adversely affect power and accuracy of the identification of quantitative trait loci (QTL). Furthermore, some covariates may interact with each other in a complicated fashion. We implement semiparametric models for single and multiple QTL mapping. Both mapping methods include an unspecified function of any covariate found or suspected to have a more complex than linear but unknown relationship with the response variable. They also allow for interactions among different covariates. This analysis is performed in a Bayesian inference framework using Markov chain Monte Carlo. The advantages of our methods are demonstrated via extensive simulations and real data analysis.

Variable selection for large p small n regression models with incomplete data: mapping QTL with epistases

BACKGROUND

Identifying quantitative trait loci (QTL) for both additive and epistatic effects raises the statistical issue of selecting variables from a large number of candidates using a small number of observations. Missing trait and/or marker values prevent one from directly applying the classical model selection criteria such as Akaike's information criterion (AIC) and Bayesian information criterion (BIC).

RESULTS

We propose a two-step Bayesian variable selection method which deals with the sparse parameter space and the small sample size issues. The regression coefficient priors are flexible enough to incorporate the characteristic of "large p small n" data. Specifically, sparseness and possible asymmetry of the significant coefficients are dealt with by developing a Gibbs sampling algorithm to stochastically search through low-dimensional subspaces for significant variables. The superior performance of the approach is demonstrated via simulation study. We also applied it to real QTL mapping datasets.

CONCLUSION

The two-step procedure coupled with Bayesian classification offers flexibility in modeling "large p small n" data, especially for the sparse and asymmetric parameter space. This approach can be extended to other settings characterized by high dimension and low sample size.

QTL ANALYSIS OF FLORAL TRAITS IN LOUISIANA IRIS HYBRIDS

The formation of hybrid zones between nascent species is a widespread phenomenon. The evolutionary consequences of hybridization are influenced by numerous factors, including the action of natural selection on quantitative trait variation. Here we examine how the genetic basis of floral traits of two species of Louisiana Irises affects the extent of quantitative trait variation in their hybrids. Quantitative trait locus (QTL) mapping was used to assess the size (magnitude) of phenotypic effects of individual QTL, the degree to which QTL for different floral traits are colocalized, and the occurrence of mixed QTL effects. These aspects of quantitative genetic variation would be expected to influence (1) the number of genetic steps (in terms of QTL substitutions) separating the parental species phenotypes; (2) trait correlations; and (3) the potential for transgressive segregation in hybrid populations. Results indicate that some Louisiana Iris floral trait QTL have large effects and QTL for different traits tend to colocalize. Transgressive variation was observed for six of nine traits, despite the fact that mixed QTL effects influence few traits. Overall, our QTL results imply that the genetic basis of floral morphology and color traits might facilitate the maintenance of phenotypic divergence between Iris fulva and Iris brevicaulis, although a great deal of phenotypic variation was observed among hybrids.

Shared quantitative trait loci underlying the genetic correlation between continuous traits

We review genetic correlations among quantitative traits in light of their underlying quantitative trait loci (QTL). We derive an expectation of genetic correlation from the effects of underlying loci and test whether published genetic correlations can be explained by the QTL underlying the traits. While genetically correlated traits shared more QTL (33%) on average than uncorrelated traits (11%), the actual number of shared QTL shared was small. QTL usually predicted the sign of the correlation with good accuracy, but the quantitative prediction was poor. Approximately 25% of trait pairs in the data set had at least one QTL with antagonistic effects. Yet a significant minority (20%) of such trait pairs have net positive genetic correlations due to such antagonistic QTL 'hidden' within positive genetic correlations. We review the evidence on whether shared QTL represent single pleiotropic loci or closely linked monotropic genes, and argue that strict pleiotropy can be viewed as one end of a continuum of recombination rates where r=0. QTL studies of genetic correlation will likely be insufficient to predict evolutionary trajectories over long time spans in large panmictic populations, but will provide important insights into the trade-offs involved in population and species divergence.

Experimental Methods for Measuring Gene Interactions

The role of epistasis in evolution has long been contentious. Resolving the issue requires empirical measurements that are statistically adequate and evolutionarily relevant. We review experimental methods for measuring epistasis, some that are commonly used but weak and others that are less frequently used but stronger. We review statistical genetic methods based on analyses of variances and means as well as molecular genetic methods for detecting gene interactions. We also highlight relevant empirical studies that illustrate the implementation of particular methods. In spite of the inherent weaknesses of most methods, epistasis is surprisingly common. We conclude with a discussion of how technologies for investigating genome-wide epistasis are bridging the gap between physiological and statistical epistasis for model organisms.

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.

Associating phenotypes with molecular events: recent statistical advances and challenges underpinning microarray experiments

Progress in mapping the genome and developments in array technologies have provided large amounts of information for delineating the roles of genes involved in complex diseases and quantitative traits. Since complex phenotypes are determined by a network of interrelated biological traits typically involving multiple inter-correlated genetic and environmental factors that interact in a hierarchical fashion, microarrays hold tremendous latent information. The analysis of microarray data is, however, still a bottleneck. In this paper, we review the recent advances in statistical analyses for associating phenotypes with molecular events underpinning microarray experiments. Classical statistical procedures to analyze phenotypes in genetics are reviewed first, followed by descriptions of the statistical procedures for linking molecular events to measured gene expression phenotypes (microarray-based gene expression) and observed phenotypes such as diseases status. These statistical procedures include (1) prior analysis, such as data quality controls, and normalization analyses for minimizing the effects of experimental artifacts and random noise; (2) gene selections and differentiation procedures based on inferential statistics for the class comparisons; (3) dynamic temporal patterns analysis through exploratory statistics such as unsupervised clustering and supervised classification and predictions; (4) assessing the reliability of microarray studies using real-time PCR and the reproducibility issues from many studies and multiple platforms. In addition, the post analysis to associate the discovered patterns of gene expression to pathway and functional analysis for selected genes are also considered in order to increase our understanding of interconnected gene processes.

Biased estimators of quantitative trait locus heritability and location in interval mapping

In many empirical studies, it has been observed that genome scans yield biased estimates of heritability, as well as genetic effects. It is widely accepted that quantitative trait locus (QTL) mapping is a model selection procedure, and that the overestimation of genetic effects is the result of using the same data for model selection as estimation of parameters. There are two key steps in QTL modeling, each of which biases the estimation of genetic effects. First, test procedures are employed to select the regions of the genome for which there is significant evidence for the presence of QTL. Second, and most important for this demonstration, estimates of the genetic effects are reported only at the locations for which the evidence is maximal. We demonstrate that even when we know there is just one QTL present (ignoring the testing bias), and we use interval mapping to estimate its location and effect, the estimator of the effect will be biased. As evidence, we present results of simulations investigating the relative importance of the two sources of bias and the dependence of bias of heritability estimators on the true QTL heritability, sample size, and the length of the investigated part of the genome. Moreover, we present results of simulations demonstrating the skewness of the distribution of estimators of QTL locations and the resulting bias in estimation of location. We use computer simulations to investigate the dependence of this bias on the true QTL location, heritability, and the sample size.

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.

Pleiotropy, Epistasis and New QTL: The Genetic Architecture of Honey Bee Foraging Behavior

The regulation of division of labor in social insects, particularly in the honey bee (Apis mellifera L.), has received considerable attention from a number of biological subdisciplines, including quantitative and behavioral genetics, because of the high complexity of the behavioral traits involved. The foraging choices of honey bee workers can be accurately quantified, and previous studies have made the foraging behavior of honey bees one of the best studied naturally occurring behavioral phenotypes. Three quantitative trait loci (QTL) have been identified that influence a set of foraging variables, including the concentration of nectar collected and the amount of pollen and nectar brought back to the hive. This study extends previous genetic investigations and represents the most comprehensive investigation of the genetic architecture of these foraging variables. We examined the effects of markers for the three established QTL and for one further candidate gene (Amfor), in two reciprocal backcross populations. These populations were also used to carry out two new QTL mapping studies, with over 400 Amplified Fragment Length Polymorphism (AFLP) markers in each. We detected a variety of effects of the genetic markers for the established QTL and the candidate gene, which were mostly epistatic in nature. A few new QTL could be detected with a variety of mapping techniques. Our results add complexity to the genetic architecture of the foraging behavior of the honey bee. Specifically, we support the hypotheses that pln1, pln2, pln3, and Amfor are involved in the regulation of foraging behavior in the honey bee and add some new factors that deserve further study in the future.

Quantitative trait locus analyses and the study of evolutionary process

The past decade has seen a proliferation of studies that employ quantitative trait locus (QTL) approaches to diagnose the genetic basis of trait evolution. Advances in molecular techniques and analytical methods have suggested that an exact genetic description of the number and distribution of genes affecting a trait can be obtained. Although this possibility has met with some success in model systems such as Drosophila and Arabidopsis, the pursuit of an exact description of QTL effects, i.e. individual gene effect, in most cases has proven problematic. We discuss why QTL methods will have difficulty in identifying individual genes contributing to trait variation, and distinguish between the identification of QTL (or marker intervals) and the identification of individual genes or nucleotide differences within genes (QTN). This review focuses on what ecologists and evolutionary biologists working with natural populations can realistically expect to learn from QTL studies. We highlight representative issues in ecology and evolutionary biology and discuss the range of questions that can be addressed satisfactorily using QTL approaches. We specifically address developing approaches to QTL analysis in outbred populations, and discuss practical considerations of experimental (cross) design and application of different marker types. Throughout this review we attempt to provide a balanced description of the benefits of QTL methodology to studies in ecology and evolution as well as the inherent assumptions and limitations that may constrain its application.

Mapping major quantitative trait loci for postnatal growth in an intersubspecific backcross between C57BL/6J and Philippine wild mice by using principal component analysis

A number of quantitative trait loci (QTLs) for postnatal growth have previously been reported in mice. As effects of the QTLs are usually small and similar to one another in magnitude, it is generally difficult to know which loci are major contributors to postnatal growth. We applied principal component analysis to a genome-wide search for QTLs affecting postnatal growth in body weight weekly recorded from 3 to 10 weeks of age in an intersubspecific backcross population of C57BL/6J inbred mice (Mus musculus domesticus) and wild mice (M. m. castaneus) captured in the Philippines, in order to discover new QTLs from a gene pool of the wild mice and uncover major loci underlying variation in postnatal growth. Principal component analysis classified phenotypic variation in body weights at different ages into two independent principal components: the first principal component (PC1) extracted information on the entire growth process and the second principal component (PC2) contrasted middle (3-6 weeks of age) with late (6-10 weeks) growth phases. Simple interval mapping and composite interval mapping revealed 10 significant QTLs with main effects on PC1 or PC2 on eight chromosomes. Of these, the six main-effect QTLs interacted epistatically with one another or three new additional QTLs on different chromosomal regions without main effects. Several of the identified QTLs with main effects and/or epistatic interaction effects appeared to be sex specific. These results suggest that the identified 13 QTLs, most of which affected the entire growth process, are very important contributors to complex genetic networks of postnatal growth.

Power of a Labrador Retriever-Greyhound pedigree for linkage analysis of hip dysplasia and osteoarthritis

OBJECTIVE

To estimate the number of dogs required to find linkage to heritable traits of hip dysplasia in dogs from an experimental pedigree.

ANIMALS

147 Labrador Retrievers, Greyhounds, and their crossbreed offspring.

PROCEDURE

Labrador Retrievers with hip dysplasia were crossed with unaffected Greyhounds. Age at detection of femoral capital ossification, distraction index (DI), hip joint dorsolateral subluxation (DLS) score, and hip joint osteoarthritis (OA) were recorded. Power to find linkage of a single marker to a quantitative trait locus (QTL) controlling 100% of the variation in a dysplastic trait in the backcross dogs was determined.

RESULTS

For the DI at the observed effect size, recombination fraction of 0.05, and heterozygosity of 0.75, 35 dogs in the backcross of the F1 to the Greyhound generation would yield linkage at a power of 0.8. For the DLS score, 35 dogs in the backcross to the Labrador Retriever generation would be required for linkage at the same power. For OSS, 45 dogs in the backcross to the founding Labrador Retrievers would yield linkage at the same power. Fewer dogs were projected to be necessary to find linkage to hip OA. Testing for linkage to the DLS at 4 loci simultaneously, each controlling 25% of the phenotypic variation, yielded an overall power of 0.7 CONCLUSIONS AND CLINICAL SIGNIFICANCE: Based on this conservative single-marker estimate, this pedigree has the requisite power to find microsatellites linked to susceptibility loci for hip dysplasia and hip OA by breeding a reasonable number of backcross dogs.

Sex-specific quantitative trait loci govern susceptibility to Theiler's murine encephalomyelitis virus-induced demyelination

Susceptibility to Theiler's murine encephalomyelitis virus-induced demyelination (TMEVD), a mouse model for multiple sclerosis (MS), is genetically controlled. Through a mouse-human comparative mapping approach, identification of candidate susceptibility loci for MS based on the location of TMEVD susceptibility loci may be possible. Composite interval mapping (CIM) identified quantitative trait loci (QTL) controlling TMEVD severity in male and female backcross populations derived from susceptible DBA/2J and resistant BALBc/ByJ mice. We report QTL on chromosomes 1, 5, 15, and 16 affecting male mice. In addition, we identified two QTL in female mice located on chromosome 1. Our results support the existence of three linked sex-specific QTL on chromosome 1 with opposing effects on the severity of the clinical signs of TMEV-induced disease in male and female mice.

Interacting quantitative trait loci control loss of peripheral tolerance and susceptibility to autoimmune ovarian dysgenesis after day 3 thymectomy in mice

Day 3 thymectomy (D3Tx) results in a loss of peripheral tolerance mediated by CD4(+)CD25(+) T cells and the development of autoimmune ovarian dysgenesis (AOD) in A/J and (C57BL/6J x A/J)F(1) (B6AF(1)) hybrids but not in C57BL/6J mice. Quantitative trait loci (QTL) linkage analysis using a B6AF(1) x C57BL/6J backcross population verified Aod1 and Aod2 that were previously mapped as qualitative traits. Additionally, three new QTL intervals, Aod3, Aod4, and Aod5, on chromosomes 1, 2, and 7, respectively, influencing specific subphenotypes of AOD were identified. QTL linkage analysis using the A x B and B x A recombinant inbred lines verified Aod3 and confirmed linkage to H2. Aod5 colocalized with Mater, an ovarian-specific autoantigen recognized by anti-ovarian autoantibodies in the sera of D3Tx mice. Sequence analysis of Mater identified allelic, strain-specific splice variants between A/J and C57BL/6J mice making it an attractive candidate gene for Aod5. Interaction analysis revealed significant epistatic effects between Aod1-5 and Gasa2, a locus associated with susceptibility to D3Tx-induced autoimmune gastritis, as well as with H2. These results indicate that the QTL controlling D3Tx-induced autoimmune phenomenon are both organ specific and more generalized in their effects with respect to the genesis and activity of the immunoregulatory mechanisms maintaining peripheral tolerance.

Mapping and analysis of quantitative trait loci in experimental populations

Simple statistical methods for the study of quantitative trait loci (QTL), such as analysis of variance, have given way to methods that involve several markers and high-resolution genetic maps. As a result, the mapping community has been provided with statistical and computational tools that have much greater power than ever before for studying and locating multiple and interacting QTL. Apart from their immediate practical applications, the lessons learnt from this evolution of QTL methodology might also be generally relevant to other types of functional genomics approach that are aimed at the dissection of complex phenotypes, such as microarray assessment of gene expression.

Genetic control of susceptibility to experimental Lyme arthritis is polygenic and exhibits consistent linkage to multiple loci on chromosome 5 in four independent mouse crosses

C3H/He mice infected with Borrelia burgdorferi develop severe arthritis and are high antibody responders, while infected C57BL/6 and BALB/c mice develop mild arthritis and less robust humoral responses. Genetic analysis using composite interval mapping (CIM) on reciprocal backcross populations derived from C3H/HeN and C57BL/6N or C3H/HeJ and BALB/cAnN mice identified 12 new quantitative trait loci (QTL) linked to 10 murine Lyme disease phenotypes. These QTL reside on chromosomes 1, 2, 4, 6, 7, 9, 10, 12, 14, 15, 16, and 17. A reanalysis of an F(2) intercross between C57BL/6N and C3H/HeN mice using CIM identified two new QTL on chromosomes 4 and 15 and confirmed the location of seven previously identified loci. Two or more experimental crosses independently verified six QTL controlling phenotypes after B. burgdorferi infection. Additionally, Bb2 on chromosome 5 was reproduced in four experimental populations and was linked to the candidate locus Cora1. Evidence of four distinct QTL residing within the 30-cM region of chromosome 5 encompassing the previously mapped Bb2 and Bb3 loci was shown by CIM. Interestingly, some alleles contributing to susceptibility to Lyme arthritis were derived from C57BL/6N and BALB/cAnN mice, showing that disease-resistant strains harbor susceptibility alleles.

Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion

We describe an approximate method for the analysis of quantitative trait loci (QTL) based on model selection from multiple regression models with trait values regressed on marker genotypes, using a modification of the easily calculated Bayesian information criterion to estimate the posterior probability of models with various subsets of markers as variables. The BIC-delta criterion, with the parameter delta increasing the penalty for additional variables in a model, is further modified to incorporate prior information, and missing values are handled by multiple imputation. Marginal probabilities for model sizes are calculated, and the posterior probability of nonzero model size is interpreted as the posterior probability of existence of a QTL linked to one or more markers. The method is demonstrated on analysis of associations between wood density and markers on two linkage groups in Pinus radiata. Selection bias, which is the bias that results from using the same data to both select the variables in a model and estimate the coefficients, is shown to be a problem for commonly used non-Bayesian methods for QTL mapping, which do not average over alternative possible models that are consistent with the data.

Statistical issues in the analysis of quantitative traits in combined crosses

We consider some practical statistical issues in QTL analysis where several crosses originate in multiple inbred parents. Our results show that ignoring background polygenic variation in different crosses may lead to biased interval mapping estimates of QTL effects or loss of efficiency. Threshold and power approximations are derived by extending earlier results based on the Ornstein-Uhlenbeck diffusion process. The results are useful in the design and analysis of genome screen experiments. Several common designs are evaluated in terms of their power to detect QTL.

Mapping quantitative trait loci in plants: uses and caveats for evolutionary biology

Gregor Mendel was either clever or lucky enough to study traits of simple inheritance in his pea plants; however, many plant characters of interest to modern geneticists are decidedly complex. Understanding the genetic basis of such complex, or quantitative, traits requires a combination of modern molecular genetic techniques and powerful statistical methods. These approaches have begun to give us insight into understanding the evolution of complex traits both in crops and in wild plants.

Identification of X chromosomal restriction fragment length polymorphism markers and their use in a gene localization study in Drosophila virilis and D. littoralis

We have identified six restriction fragment length polymorphism (RFLP) markers based on unique gene sequences on the X chromosome of Drosophila virilis and D. littoralis. The markers were localized by in situ hybridization on larval polytene chromosomes, and the conjugation of the X chromosomes of the two species was studied in salivary glands of interspecific hybrid female larvae. The gene arrangement of D. virilis and D. littoralis appeared to be very different at the proximal end of the X chromosome preventing recombination between RFLP markers located in this area. Simple quantitative trait loci (QTL) analysis showed that five of our marker genes (including nonA and Dmca1A, previously found to affect male courtship song in D. melanogaster) are linked with a gene(s) having a major effect on species differences in the male courtship song between D. virilis and D. littoralis. This shows that the song gene(s) may be located inside a large X-chromosomal inversion in D. littoralis (as previously suggested), but that it may also be located on an area between this inversion and the centromere, close to nonA and Dmca1A. Localization of this gene or gene complex will be continued with the aid of our newly identified RFLP markers by making interspecific crosses between D. virilis group species with more similar X chromosomes.

A century of biometrical genetics

We briefly review the major contribution of biometrics to genetics over the last century (population genetic models, familial correlations, segregation analysis, and gene mapping) and current areas of active research and then speculate about what problems will be tackled in the next century.

Identification of genetic loci controlling the characteristics and severity of brain and spinal cord lesions in experimental allergic encephalomyelitis

Experimental allergic encephalomyelitis (EAE) is the principal genetically determined animal model for multiple sclerosis (MS), the major inflammatory disease of the central nervous system (CNS). Although genetics clearly play a role in susceptibility to MS, attempts to identify the underlying genes have been disappointing. Considerable variation exists between MS patients with regard to the severity of clinical signs, mechanism of demyelination, and location of CNS lesions, confounding the interpretation of genetic data. A mouse-human synteny mapping approach may allow the identification of candidate susceptibility loci for MS based on the location of EAE susceptibility loci. To date, 16 regions of the mouse genome have been identified that control susceptibility or clinical signs of EAE. In this work, we examined the genetic control of histopathological lesions of EAE in an F2 intercross population generated from the EAE susceptible SJL/J and EAE resistant B10.S/DvTe mouse strains. Composite interval mapping was used to identify 10 quantitative trait loci (QTL), including seven newly identified loci controlling the distribution and severity of CNS lesions associated with murine EAE. QTL on chromosome 10 control lesions in the brain, whereas QTL on chromosomes 3, 7, and 12 control lesions in the spinal cord. Furthermore, sexually dimorphic QTL on chromosomes 2, 9, and 11 control CNS lesions in females, whereas QTL on chromosomes 10, 11, 12, 16, and 19 control lesions in males. Our results suggest that the severity and location of CNS lesions in EAE are genetically controlled, and that the genetic component controlling the character and severity of the lesions can be influenced by sex.

Two Independent Loci Control Agamospermy (Apomixis) in the Triploid Flowering Plant Erigeron annuus

Asexual seed production (agamospermy) via gametophytic apomixis in flowering plants typically involves the formation of an unreduced megagametophyte (via apospory or diplospory) and the parthenogenetic development of the unreduced egg cell into an embryo. Agamospermy is almost exclusively restricted to polyploids. In this study, the genetic basis of agamospermy was investigated in a segregating population of 130 F1's from a cross between triploid (2n = 27) agamospermous Erigeron annuus and sexual diploid (2n = 18) E. strigosus. Correlations between markers and phenotypes and linkage analysis were performed on 387 segregating amplified fragment length polymorphisms (AFLPs). Results show that four closely linked markers with polysomic inheritance are significantly associated with parthenogenesis and that 11 cosegregating markers with univalent inheritance are completely associated with diplospory. This indicates that diplospory and parthenogenesis are unlinked and inherited independently. Further, the absence of agamospermy in diploid F1's appears to be best explained by a combination of recessive-lethal gametophytic selection against the parthenogenetic locus and univalent inheritance of the region bearing diplospory. These results may have major implications for attempts to manipulate agamospermy for agricultural purposes and for interpreting the evolution of the trait.

Accounting for variability in the use of permutation testing to detect quantitative trait loci

Locating quantitative trait loci (QTL), or genomic regions associated with known molecular markers, is of increasing interest in a wide variety of applications ranging from human genetics to agricultural genetics. The hope of locating QTL (or genes) affecting a quantitative trait is that it will lead to characterization and possible manipulations of these genes. However, the complexity of both statistical and genetic issues surrounding the location of these regions calls into question the asymptotic statistical results supplying the distribution of the test statistics employed. Coupled with the power of current-day computing, permutation theory was reintroduced for the purpose of estimating the distribution of any test statistic used to test for the location of QTL. Permutation techniques have offered an attractive alternative to significance measures based on asymptotic theory. The ideas of permutation testing are extended in this application to include confidence intervals for the thresholds and p-values estimated in permutation testing procedures. The confidence intervals developed account for the Monte Carlo error associated with practical applications of permutation testing and lead to an effective method of determining an efficient permutation sample size.