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Despite its importance to agriculture, the genetic basis of heterosis is still not well understood. The main competing hypotheses include dominance, overdominance, and epistasis. NC design III is an experimental design that has been used for estimating the average degree of dominance of quantitative trait loci (QTL) and also for studying heterosis. In this study, we first develop a multiple-interval mapping (MIM) model for design III that provides a platform to estimate the number, genomic positions, augmented additive and dominance effects, and epistatic interactions of QTL. The model can be used for parents with any generation of selfing. We apply the method to two data sets, one for maize and one for rice. Our results show that heterosis in maize is mainly due to dominant gene action, although overdominance of individual QTL could not completely be ruled out due to the mapping resolution and limitations of NC design III. For rice, the estimated QTL dominant effects could not explain the observed heterosis. There is evidence that additive x additive epistatic effects of QTL could be the main cause for the heterosis in rice. The difference in the genetic basis of heterosis seems to be related to open or self pollination of the two species. The MIM model for NC design III is implemented in Windows QTL Cartographer, a freely distributed software.

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

Many statistical methods have been developed to map multiple quantitative trait loci (QTL) in experimental cross populations. Among these methods, multiple-interval mapping (MIM) can map QTL with epistasis simultaneously. However, the previous implementation of MIM is for continuously distributed traits. In this study we extend MIM to ordinal traits on the basis of a threshold model. The method inherits the properties and advantages of MIM and can fit a model of multiple QTL effects and epistasis on the underlying liability score. We study a number of statistical issues associated with the method, such as the efficiency and stability of maximization and model selection. We also use computer simulation to study the performance of the method and compare it to other alternative approaches. The method has been implemented in QTL Cartographer to facilitate its general usage for QTL mapping data analysis on binary and ordinal traits.

Species diversity may have evolved by differential regulation of a similar set of genes. To analyze and compare the genetic architecture of transcript regulation in different genetic backgrounds of Eucalyptus, microarrays were used to examine variation in mRNA abundance in the differentiating xylem of a E. grandis pseudo-backcross population [E. grandis x [F.sub.1] hybrid (E. grandis x E. globulus)]. Least-squares mean estimates of transcript levels were generated for 2608 genes in 91 interspecific backcross progeny. The quantitative measurements of variation in transcript abundance for specific genes were mapped as expression QTL (eQTL) in two single-tree genetic linkage maps ([F.sub.1] hybrid paternal and E. grandis maternal). EQTL were identified for 1067 genes in the two maps, of which 811 were located in the [F.sub.1] hybrid paternal map, and 451 in the E. grandis maternal map. EQTL for 195 genes mapped to both parental maps, the majority of which localized to nonhomologous linkage groups, suggesting trans-regulation by different loci in the two genetic backgrounds. For 821 genes, a single eQTL that explained up to 70% of the transcript-level variation was identified. Hotspots with colocalized eQTL were identified in both maps and typically contained genes associated with specific metabolic and regulatory pathways, suggesting coordinated genetic regulation.

A quantitative genetic model relates the genotypic value of an individual to the alleles at the loci that contribute to the variation in a population in terms of additive, dominance, and epistatic effects. This partition of genetic effects is related to the partition of genetic variance. A number of models have been proposed to describe this relationship: some are based on the orthogonal partition of genetic variance in an equilibrium population. We compare a few representative models and discuss their utility and potential problems for analyzing quantitative trait loci (QTL) in a segregating population. An orthogonal model implies that estimates of the genetic effects are consistent in a full or reduced model in an equilibrium population and are directly related to the partition of the genetic variance in the population. Linkage disequilibrium does not affect the estimation of genetic effects in a full model, but would in a reduced model. Certainly linkage disequilibrium would complicate the detection of QTL and epistasis. Using different models does not influence the detection of QTL and epistasis. However, it does influence the estimation and interpretation of genetic effects.

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 chromsome, we infer that HMS loci are only ~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.

We use the orthogonal contrast scales proposed by Cockerham to construct a genetic model, called Cockerham's model, for studying epistasis between genes. The properties of Cockerham's model in modeling and mapping epistatic genes under linkage equilibrium and disequilibrium are investigated and discussed. Because of its orthogonal property, Cockerham's model has several advantages in partitioning genetic variance into components, interpreting and estimating gene effects, and application to quantitative trait loci (QTL) mapping when compared to other models, and thus it can facilitate the study of epistasis between genes and be readily used in QTL mapping. The issues of QTL mapping with epistasis are also addressed. Real and simulated examples are used to illustrate Cockerham's model, compare different models, and map for epistatic QTL. Finally, we extend Cockerham's model to multiple loci and discuss its applications to QTL mapping.

Polyploidy has been recognized as an important step in the evolutionary diversification of flowering plants and may have a significant impact on plant breeding. Statistical analyses for linkage mapping in polyploid species can be difficult due to considerable complexities in polysomic inheritance. In this article, we develop a novel statistical method for linkage analysis of polymorphic markers in a full-sib family of autotetraploids. This method is established on multivalent pairings of homologous chromosomes at meiosis and can provide a simultaneous maximum-likelihood estimation of the double reduction frequencies of and recombination fraction between two markers. The EM algorithm is implemented to provide a tractable way for estimating relative proportions of different modes of gamete formation that generate identical gamete genotypes due to multivalent pairings. Extensive simulation studies were performed to demonstrate the statistical properties of this method. The implications of the new method for understanding the genome structure and organization of polyploid species are discussed.

Genetic effects on an index of wing shape on chromosome 2 of Drosophila melanogaster were mapped using isogenic recombinants with transposable element markers. At least 10 genes with small additive effects are dispersed evenly along the chromosome. Many interactions exist, with only small net effects in homozygous recombinants and little effect on phenotypic variance. Heterozygous chromosome segments show almost no dominance. Pleiotropic effects on leg shape are only minor. At first view, wing shape genes form a rather homogeneous class, but certain complexities remain unresolved.

Polyploidy has played an important role in higher plant evolution and applied plant breeding. Polyploids are commonly categorized as allopolyploids resulting from the increase of chromosome number through hybridization and subsequent chromosome doubling or autopolyploids due to chromosome doubling of the same genome. Allopolyploids undergo bivalent pairing at meiosis because only homologous chromosomes pair. For autopolyploids, however, all homologous chromosomes can pair at the same time so that multivalents and, therefore, double reductions are formed. In this article, we use a maximum-likelihood method to develop a general polyploid model for estimating gene segregation patterns from molecular markers in a full-sib family derived from an arbitrary polyploid combining meiotic behaviors of both bivalent and multivalent pairings. Two meiotic parameters, one describing the preference of homologous chromosome pairing (expressed as the preferential pairing factor) typical of allopolyploids and the other specifying the degree of double reduction of autopolyploids, are estimated. The type of molecular markers used can be fully informative vs. partially informative or dominant vs. codominant. Simulation studies show that our polyploid model is well suited to estimate the preferential pairing factor and the frequency of double reduction at meiosis, which should help to characterize gene segregation in the progeny of autopolyploids. The implications of this model for linkage mapping, population genetic studies, and polyploid classification are discussed.

Design III is an experimental design originally proposed by R. E. COMSTOCK and H. F. ROBINSON for estimating genetic variances and the average degree of dominance for quantitative trait loci (QTL) and has recently been extended for mapping QTL. In this paper, we first extend COMSTOCK and ROBINSON'S analysis of variance to include linkage, two-locus epistasis and the use of [F.sub.3] parents. Then we develop the theory and statistical analysis of orthogonal contrasts and contrast x environment interaction for a single marker locus to characterize the effects of QTL. The methods are applied to the maize data of C. W. STUBER. The analyses strongly suggest that there are multiple linked QTL in many chromosomes for several traits examined. QTL effects are largely environment-independent for grain yield, ear height, plant height and ear leaf area and largely environment dependent for days to tassel, grain moisture and ear number. There is significant QTL epistasis. The results are generally in favor of the hypothesis of dominance of favorable genes to explain the observed heterosis in grain yield and other traits, although epistasis could also play an important role and overdominance at individual QTL level can not be ruled out.

Two closely related species of Drosophila, D. simulans and D. mauritiana, differ markedly in morphology of the posterior lobe of the male genital arch. Both size and shape aspects of lobe variation can be quantified by a morphometric descriptor based on elliptical Fourier and principal components analyses. The genetic architecture of this quantitative trait (PC1) was investigated by hybridizing inbred lines to produce two backcross populations of [approximately]200 individuals each, which were analyzed jointly by a composite interval mapping procedure with the aid of 18 marker loci. The parental lines show a large difference in PC1 (30.4 environmental standard deviations), and the markers account for >80% of the phenotypic variation in backcross populations. Eight of 15 intervals analyzed show convincing evidence of quantitative trait loci (QTL), and the range of estimated QTL effects is 5.7-15.9% of the parental difference (1.7-4.8 environmental standard deviations). These estimates may represent the joint effects of multiple QTL within a single interval (which averaged 23 cM in length). Although there is some evidence of partial dominance of mauritiana alleles and for epistasis, the pattern of inheritance is largely additive.

Multiple trait analysis on mapping quantitative trait loci (QTL) can be performed on the basis of the composite interval mapping method. This joint analysis generally has three advantages: the statistical power of detecting QTL is increased by this joint analysis; the precision of parameter estimation can be improved by this joint analysis; and, most important, the joint analysis provides appropriate procedures to test a number of biologically interesting hypotheses involving multiple traits.

Wright's method of approximating the number of genes governing quantitative traits takes into consideration the means and variances of the measured characteristics in two parental strains and their offsprings. However, this method does not account for unequal allelic contribution as well as linkage. A modification in the method taking these two parameters into consideration was designed in order to correct the bias of Wright's method.

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.

The nature of genetic variation for Drosophila longevity in a population of recombinant inbred lines was investigated by estimating quantitative genetic parameters and mapping quantitative trait loci (QTL) for adult life span in five environments: standard culture conditions, high and low temperature, and heatshock and starvation stress. There was highly significant genetic variation for life span within each sex and environment. In the analysis of variance of life span pooled over sexes and environments, however, the significant genetic variation appeared in the genotype x sex and genotype x environment interaction terms. The genetic correlation of longevity across the sexes and environments was not significantly different from zero in these lines. We estimated map positions and effects of QTL affecting life span by linkage to highly polymorphic roo transposable element markers, using a multiple-trait composite interval mapping procedure. A minimum of 17 QTL were detected; all were sex and/or environment-specific. Ten of the QTL had sexually antagonistic or antagonistic pleiotropic effects in different environments. These data provide support for the pleiotropy theory of senescence and the hypothesis that variation for longevity might be maintained by opposing selection pressures in males and females and variable environments. Further work is necessary to assess the generality of these results, using different strains, to determine heterozygous effects and to map the life span QTL to the level of genetic loci.

The size and shape of the posterior lobe of the male genital arch differs dramatically between Drosophila simulans and D. mauritiana. This difference can be quantified with a morphometric descriptor (PC1) based on elliptical Fourier and principal components analyses. The genetic basis of the interspecific difference in PC1 was investigated by the application of quantitative trait locus (QTL) mapping procedures to segregating backcross populations. The parental difference (35 environmental standard deviations) and the heritability of PC1 in backcross populations ([is greater than]90%) are both very large. The use of multiple interval mapping gives evidence for 19 different QTL. The greatest additive effect estimate accounts for 11.4% of the parental difference but could represent multiple closely linked QTL. Dominance parameter estimates vary among loci from essentially no dominance to complete dominance, and mauritiana alleles tend to be dominant over simulans alleles. Epistasis appears to be relatively unimportant as a source of variation. All but one of the additive effect estimates have the same sign, which means that one species has nearly all plus alleles and the other nearly all minus alleles. This result is unexpected under many evolutionary scenarios and suggests a history of strong directional selection acting on the posterior lobe.

Loci on the third chromosome of Drosophila melanogaster that affect an index of wing shape were mapped, using recombinant isogenic lines, with transposable elements as markers. Many genes with small subequal effects are dispersed along the whole chromosome. Their alleles act nearly additively in heterozygotes. They have small correlated effects on leg shape, but no detectable effects on halteres. Small negative net interactions occur over most of the chromosome. The data set of 519 recombinant isogenic lines can be explained reasonably well by two models. One model posits an indefinitely large number of loci with no interactions. The other model posits 11 loci with additive effects whose sum equals the total phenotypic range and with large positive and negative interactions that nearly cancel each other.

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/).

Presents models and methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. Correlated structure of multiple traits; Testing procedures for mapping, pleiotropy and QTL.

Presents a method of quantitative trait loci (QTL) mapping using combined interval mapping and multiple regression. Interval test as the basis of the QTL mapping method; Advantages over the conventional methods; Simulation study of QTL mapping illustrating the utility, properties, and advantages of the method.

Despite its importance to agriculture, the genetic basis of heterosis is still not well understood. The main competing hypotheses include dominance, overdominance, and epistasis. NC design III is an experimental design that has been used for estimating the average degree of dominance of quantitative trait loci (QTL) and also for studying heterosis. In this study, we first develop a multiple-interval mapping (MIM) model for design III that provides a platform to estimate the number, genomic positions, augmented additive and dominance effects, and epistatic interactions of QTL. The model can be used for parents with any generation of selfing. We apply the method to two data sets, one for maize and one for rice. Our results show that heterosis in maize is mainly due to dominant gene action, although overdominance of individual QTL could not completely be ruled out due to the mapping resolution and limitations of NC design III. For rice, the estimated QTL dominant effects could not explain the observed heterosis. There is evidence that additive × additive epistatic effects of QTL could be the main cause for the heterosis in rice. The difference in the genetic basis of heterosis seems to be related to open or self pollination of the two species. The MIM model for NC design III is implemented in Windows QTL Cartographer, a freely distributed software. [ABSTRACT FROM AUTHOR]