Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Bayesian Model Choice and Search Strategies for Mapping Interacting Quantitative Trait Loci

Most complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.

Genetic dissection of hybrid incompatibilities between Drosophila simulans and D. mauritiana. II. Mapping hybrid male sterility loci on the third chromosome

Hybrid male sterility (HMS) is a rapidly evolving mechanism of reproductive isolation in Drosophila. Here we report a genetic analysis of HMS in third-chromosome segments of Drosophila mauritiana that were introgressed into a D. simulans background. Qualitative genetic mapping was used to localize 10 loci on 3R and a quantitative trait locus (QTL) procedure (multiple-interval mapping) was used to identify 19 loci on the entire chromosome. These genetic incompatibilities often show dominance and complex patterns of epistasis. Most of the HMS loci have relatively small effects and generally at least two or three of them are required to produce complete sterility. Only one small region of the third chromosome of D. mauritiana by itself causes a high level of infertility when introgressed into D. simulans. By comparison with previous studies of the X chromosome, we infer that HMS loci are only approximately 40% as dense on this autosome as they are on the X chromosome. These results are consistent with the gradual evolution of hybrid incompatibilities as a by-product of genetic divergence in allopatric populations.

Stochastic search variable selection for identifying multiple quantitative trait loci

In this article, we utilize stochastic search variable selection methodology to develop a Bayesian method for identifying multiple quantitative trait loci (QTL) for complex traits in experimental designs. The proposed procedure entails embedding multiple regression in a hierarchical normal mixture model, where latent indicators for all markers are used to identify the multiple markers. The markers with significant effects can be identified as those with higher posterior probability included in the model. A simple and easy-to-use Gibbs sampler is employed to generate samples from the joint posterior distribution of all unknowns including the latent indicators, genetic effects for all markers, and other model parameters. The proposed method was evaluated using simulated data and illustrated using a real data set. The results demonstrate that the proposed method works well under typical situations of most QTL studies in terms of number of markers and marker density.

Estimating polygenic effects using markers of the entire genome

Molecular markers have been used to map quantitative trait loci. However, they are rarely used to evaluate effects of chromosome segments of the entire genome. The original interval-mapping approach and various modified versions of it may have limited use in evaluating the genetic effects of the entire genome because they require evaluation of multiple models and model selection. Here we present a Bayesian regression method to simultaneously estimate genetic effects associated with markers of the entire genome. With the Bayesian method, we were able to handle situations in which the number of effects is even larger than the number of observations. The key to the success is that we allow each marker effect to have its own variance parameter, which in turn has its own prior distribution so that the variance can be estimated from the data. Under this hierarchical model, we were able to handle a large number of markers and most of the markers may have negligible effects. As a result, it is possible to evaluate the distribution of the marker effects. Using data from the North American Barley Genome Mapping Project in double-haploid barley, we found that the distribution of gene effects follows closely an L-shaped Gamma distribution, which is in contrast to the bell-shaped Gamma distribution when the gene effects were estimated from interval mapping. In addition, we show that the Bayesian method serves as an alternative or even better QTL mapping method because it produces clearer signals for QTL. Similar results were found from simulated data sets of F(2) and backcross (BC) families.

Mapping unexplored genomes: a genetic linkage map of the Hawaiian cricket Laupala

As with many organisms of evolutionary interest, the Hawaiian cricket Laupala genome is not well characterized genetically. Mapping such an unexplored genome therefore presents challenges not often faced in model genetic organisms and not well covered in the literature. We discuss the evolutionary merits of Laupala as a model for speciation studies involving prezygotic change, our choice of marker system for detecting genetic variation, and the initial genetic expectations pertaining to the construction of any unknown genomic map in general and to the Laupala linkage map construction in particular. We used the technique of amplified fragment length polymorphism (AFLP) to develop a linkage map of Laupala. We utilized both EcoRI/MseI- and EcoRI/PstI-digested genomic DNA to generate AFLP bands and identified 309 markers that segregated among F(2) interspecific hybrid individuals. The map is composed of 231 markers distributed over 11 and 7 species-specific autosomal groups together with a number of putative X chromosome linkage groups. The integration of codominant markers enabled the identification of five homologous linkage groups corresponding to five of the seven autosomal chromosomal pairs found in Laupala.

Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species

With the advent of new molecular marker technologies, it is now feasible to initiate genome projects for outcrossing plant species, which have not received much attention in genetic research, despite their great agricultural and environmental value. Because outcrossing species typically have heterogeneous genomes, data structure for molecular markers representing an entire genome is complex: some markers may have more alleles than others, some markers are codominant whereas others are dominant, and some markers are heterozygous in one parent but fixed in the other parent whereas the opposite can be true for other markers. A major difficulty in analyzing these different types of marker at the same time arises from uncertainty about parental linkage phases over markers. In this paper, we present a general maximum-likelihood-based algorithm for simultaneously estimating linkage and linkage phases for a mixed set of different marker types containing fully informative markers (segregating 1:1:1:1) and partially informative markers (or missing markers, segregating 1:2:1, 3:1, and 1:1) in a full-sib family derived from two outbred parent plants. The characterization of linkage phases is based on the posterior probability distribution of the assignment of alternative alleles at given markers to two homologous chromosomes of each parent, conditional on the observed phenotypes of the markers. Two- and multi-point analyses are performed to estimate the recombination fraction and determine the most likely linkage phase between different types of markers. A numerical example is presented to demonstrate the statistical properties of the model for characterizing the linkage phase between markers.

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.

A genetic map in the Mimulus guttatus species complex reveals transmission ratio distortion due to heterospecific interactions

As part of a study of the genetics of floral adaptation and speciation in the Mimulus guttatus species complex, we constructed a genetic linkage map of an interspecific cross between M. guttatus and M. nasutus. We genotyped an F(2) mapping population (N = 526) at 255 AFLP, microsatellite, and gene-based markers and derived a framework map through repeated rounds of ordering and marker elimination. The final framework map consists of 174 marker loci on 14 linkage groups with a total map length of 1780 cM Kosambi. Genome length estimates (2011-2096 cM) indicate that this map provides thorough coverage of the hybrid genome, an important consideration for QTL mapping. Nearly half of the markers in the full data set (49%) and on the framework map (48%) exhibited significant transmission ratio distortion (alpha = 0.05). We localized a minimum of 11 transmission ratio distorting loci (TRDLs) throughout the genome, 9 of which generate an excess of M. guttatus alleles and a deficit of M. nasutus alleles. This pattern indicates that the transmission ratio distortion results from particular interactions between the heterospecific genomes and suggests that substantial genetic divergence has occurred between these Mimulus species. We discuss possible causes of the unequal representation of parental genomes in the F(2) generation.

Detection of closely linked multiple quantitative trait loci using a genetic algorithm

The existence of a quantitative trait locus (QTL) is usually tested using the likelihood of the quantitative trait on the basis of phenotypic character data plus the recombination fraction between QTL and flanking markers. When doing this, the likelihood is calculated for all possible locations on the linkage map. When multiple QTL are suspected close by, it is impractical to calculate the likelihood for all possible combinations of numbers and locations of QTL. Here, we propose a genetic algorithm (GA) for the heuristic solution of this problem. GA can globally search the optimum by improving the "genotype" with alterations called "recombination" and "mutation." The "genotype" of our GA is the number and location of QTL. The "fitness" is a function based on the likelihood plus Akaike's information criterion (AIC), which helps avoid false-positive QTL. A simulation study comparing the new method with existing QTL mapping packages shows the advantage of the new GA. The GA reliably distinguishes multiple QTL located in a single marker interval.

Construction of a genetic linkage map in tetraploid species using molecular markers

This article presents methodology for the construction of a linkage map in an autotetraploid species, using either codominant or dominant molecular markers scored on two parents and their full-sib progeny. The steps of the analysis are as follows: identification of parental genotypes from the parental and offspring phenotypes; testing for independent segregation of markers; partition of markers into linkage groups using cluster analysis; maximum-likelihood estimation of the phase, recombination frequency, and LOD score for all pairs of markers in the same linkage group using the EM algorithm; ordering the markers and estimating distances between them; and reconstructing their linkage phases. The information from different marker configurations about the recombination frequency is examined and found to vary considerably, depending on the number of different alleles, the number of alleles shared by the parents, and the phase of the markers. The methods are applied to a simulated data set and to a small set of SSR and AFLP markers scored in a full-sib population of tetraploid potato.

Evaluation of major genetic loci contributing to inbreeding depression for survival and early growth in a selfed family of Pinus taeda

The magnitude of fitness effects at genetic loci causing inbreeding depression at various life stages has been an important question in plant evolution. We used genetic mapping in a selfed family of loblolly pine (Pinus taeda L.) to gain insights on inbreeding depression for early growth and viability. Two quantitative trait loci (QTLs) were identified that explain much of the phenotypic variation in height growth through age 3 and may account for more than 13% inbreeding depression in this family. One of these QTLs maps to the location of cad-nl, a lignin biosynthesis mutation. Both QTLs show evidence of overdominance, although evidence for true versus pseudo-overdominance is inconclusive. Evidence of directional dominance for height growth was noted throughout the genome, suggesting that additional loci may contribute to inbreeding depression. A chlorophyll-deficiency mutation, spf did not appear to be associated with growth effects, but had significant effects on survival through age 3. Previously identified embryonic viability loci had little or no overall effect on germination, survival, or growth. Our results challenge, at least in part, the prevailing hypothesis that inbreeding depression for growth is due to alleles of small effect. However, our data support predictions that loci affecting inbreeding depression are largely stage specific.

Multipoint mapping of viability and segregation distorting loci using molecular markers

In line-crossing experiments, deviations from Mendelian segregation ratios are usually observed for some markers. We hypothesize that these deviations are caused by one or more segregation-distorting loci (SDL) linked to the markers. We develop both a maximum-likelihood (ML) method and a Bayesian method to map SDL using molecular markers. The ML mapping is implemented via an EM algorithm and the Bayesian method is performed via the Markov chain Monte Carlo (MCMC). The Bayesian mapping is computationally more intensive than the ML mapping but can handle more complicated models such as multiple SDL and variable number of SDL. Both methods are applied to a set of simulated data and real data from a cross of two Scots pine trees.

Multiple interval mapping for quantitative trait loci

A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from approximately 1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed approximately 10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0. 3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/chkao/).