The role of epistasis in the manifestation of heterosis: a systems-oriented approach.

Heterosis is widely used in breeding, but the genetic basis of this biological phenomenon has not been elucidated. We postulate that additive and dominance genetic effects as well as two-locus interactions estimated in classical QTL analyses are not sufficient for quantifying the contributions of QTL to heterosis. A general theoretical framework for determining the contributions of different types of genetic effects to heterosis was developed. Additive x additive epistatic interactions of individual loci with the entire genetic background were identified as a major component of midparent heterosis. On the basis of these findings we defined a new type of heterotic effect denoted as augmented dominance effect di* that comprises the dominance effect at each QTL minus half the sum of additive x additive interactions with all other QTL. We demonstrate that genotypic expectations of QTL effects obtained from analyses with the design III using testcrosses of recombinant inbred lines and composite-interval mapping precisely equal genotypic expectations of midparent heterosis, thus identifying genomic regions relevant for expression of heterosis. The theory for QTL mapping of multiple traits is extended to the simultaneous mapping of newly defined genetic effects to improve the power of QTL detection and distinguish between dominance and overdominance.

Mixture model equations for marker-assisted genetic evaluation.

Marker-assisted genetic evaluation needs to infer genotypes at quantitative trait loci (QTL) based on the information of linked markers. As the inference usually provides the probability distribution of QTL genotypes rather than a specific genotype, marker-assisted genetic evaluation is characterized by the mixture model because of the uncertainty of QTL genotypes. It is, therefore, necessary to develop a statistical procedure useful for mixture model analyses. In this study, a set of mixture model equations was derived based on the normal mixture model and the EM algorithm for evaluating linear models with uncertain independent variables. The derived equations can be seen as an extension of Henderson's mixed model equations to mixture models and provide a general framework to deal with the issues of uncertain incidence matrices in linear models. The mixture model equations were applied to marker-assisted genetic evaluation with different parameterizations of QTL effects. A sire-QTL-effect model and a founder-QTL-effect model were used to illustrate the application of the mixture model equations. The potential advantages of the mixture model equations for marker-assisted genetic evaluation were discussed. The mixed-effect mixture model equations are flexible in modelling QTL effects and show desirable properties in estimating QTL effects, compared with Henderson's mixed model equations.

An analysis of polygenes affecting wing shape on chromosome 2 in Drosophila melanogaster.

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.

A multivalent pairing model of linkage analysis in autotetraploids.

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.

A general polyploid model for analyzing gene segregation in outcrossing tetraploid species.

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.

Preliminary interspecific genetic maps of the populus genome constructed from RAPD markers.

We have constructed RAPD-based linkage maps for an interspecific cross between two species of the genus Populus (P. adenopoda and P. alba), based on a double pseudo-test-cross strategy. Of a total of 360 polymorphic fragments scored, 290 showed a test-cross configuration, corresponding to DNA polymorphisms heterozygous in one parent and null in the other. In the female parent, P. adenopoda, 82 markers were grouped in 19 different linkage groups (553 cM), whereas in the male parent P. alba, 197 markers established a much more complete framework map with an observed genome length of 2300 cM covering 87% of the total P. alba genome. The larger number of test-cross markers detected for the P. alba parent than for the P. adenopoda parent might be due to a higher level of heterozygosity in the former than in the latter. In this study, we detected only a small percentage (2%) of the intercross dominant markers heterozygous in both parents and segregating 3:1 in the progeny. The further focus in this mapping study should be on the identification of more intercross markers, to align the two parent-specific maps into a consensus map for mapping important genes causing species differentiation during long evolutionary divergences.

Joint linkage and linkage disequilibrium mapping in natural populations.

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.

Inferring linkage disequilibrium between a polymorphic marker locus and a trait locus in natural populations.

Three approaches are proposed in this study for detecting or estimating linkage disequilibrium between a polymorphic marker locus and a locus affecting quantitative genetic variation using the sample from random mating populations. It is shown that the disequilibrium over a wide range of circumstances may be detected with a power of 80% by using phenotypic records and marker genotypes of a few hundred individuals. Comparison of ANOVA and regression methods in this article to the transmission disequilibrium test (TDT) shows that, given the genetic variance explained by the trait locus, the power of TDT depends on the trait allele frequency, whereas the power of ANOVA and regression analyses is relatively independent from the allelic frequency. The TDT method is more powerful when the trait allele frequency is low, but much less powerful when it is high. The likelihood analysis provides reliable estimation of the model parameters when the QTL variance is at least 10% of the phenotypic variance and the sample size of a few hundred is used. Potential use of these estimates in mapping the trait locus is also discussed.

A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines.

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.

Genotype-environment interaction for quantitative trait loci affecting life span in Drosophila melanogaster.

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 heat-shock 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.

Genetic architecture of a morphological shape difference between two Drosophila species.

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 (>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.

An analysis of polygenes affecting wing shape on chromosome 3 in Drosophila melanogaster.

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.

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/).

Estimating the genetic architecture of quantitative traits.

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated parameters. Multiple interval mapping, which was recently proposed for simultaneously mapping multiple quantitative trait loci (QTL), is well suited to the identification and estimation of the genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance. With multiple traits and multiple environments involved in a QTL mapping experiment, pleiotropic effects and QTL by environment interactions can also be estimated. We review the method and discuss issues associated with multiple interval mapping, such as likelihood analysis, model selection, stopping rules and parameter estimation. The potential power and advantages of the method for mapping multiple QTL and estimating the genetic architecture are discussed. We also point out potential problems and difficulties in resolving the details of the genetic architecture as well as other areas that require further investigation. One application of the analysis is to improve genome-wide marker-assisted selection, particularly when the information about epistasis is used for selection with mating.

Sex-specific quantitative trait loci affecting longevity in Drosophila melanogaster.

Senescence, the decline in survivorship and fertility with increasing age, is a near-universal property of organisms. Senescence and limited lifespan are thought to arise because weak natural selection late in life allows the accumulation of mutations with deleterious late-age effects that are either neutral (the mutation accumulation hypothesis) or beneficial (the antagonistic pleiotropy hypothesis) early in life. Analyses of Drosophila spontaneous mutations, patterns of segregating variation and covariation, and lines selected for late-age fertility have implicated both classes of mutation in the evolution of aging, but neither their relative contributions nor the properties of individual loci that cause aging in nature are known. To begin to dissect the multiple genetic causes of quantitative variation in lifespan, we have conducted a genome-wide screen for quantitative trait loci (QTLs) affecting lifespan that segregate among a panel of recombinant inbred lines using a dense molecular marker map. Five autosomal QTLs were mapped by composite interval mapping and by sequential multiple marker analysis. The QTLs had large sex-specific effects on lifespan and age-specific effects on survivorship and mortality and mapped to the same regions as candidate genes with fertility, cellular aging, stress resistance and male-specific effects. Late age-of-onset QTL effects are consistent with the mutation accumulation hypothesis for the evolution of senescence, and sex-specific QTL effects suggest a novel mechanism for maintaining genetic variation for lifespan.

General formulas for obtaining the MLEs and the asymptotic variance-covariance matrix in mapping quantitative trait loci when using the EM algorithm.

We present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance-covariance matrix of the positions and effects of quantitative trait loci (QTLs) in a finite normal mixture model when the EM algorithm is used for mapping QTLs. The general formulas are based on two matrices D and Q, where D is the genetic design matrix, characterizing the genetic effects of the QTLs, and Q is the conditional probability matrix of QTL genotypes given flanking marker genotypes, containing the information on QTL positions. With the general formulas, it is relatively easy to extend QTL mapping analysis to using multiple marker intervals simultaneously for mapping multiple QTLs, for analyzing QTL epistasis, and for estimating the heritability of quantitative traits. Simulations were performed to evaluate the performance of the estimates of the asymptotic variances of QTL positions and effects.

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

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study.

Design III with marker loci.

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 F3 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.

Genetic analysis of a morphological shape difference in the male genitalia of Drosophila simulans and D. mauritiana.

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 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.

Mapping of body weight loci on mouse chromosome X.

Inheritance of overweight in humans appears to be under polygenic control. Study on the mouse model may help to determine candidate regions in human genome for the search of overweight genes. Inbred mouse strains showed wide variation in body weight and can provide an experimental model for the study of inheritance of overweight. By genetic linkage analysis, we report the mapping of two loci, named Bw1 and Bw2 (body weight 1 and 2), on Chromosome (Chr) X that strongly affect adult body weight in two interspecific testcross male populations (HSB) and ASB) of mice. In addition, another locus, named Bw3, is also mapped on Chr X in ASB populations. These loci account for up to 24% of the phenotypic variation in both populations. Considering the conserved synteny between mouse and humans Chr X, these results provide candidate regions on Chr X that can be tested for linkage with overweight in humans.