Method for the mapping of a female partial-sterile locus on a molecular marker linkage map

The female gametophyte is an absolutely essential structure for angiosperm reproduction, and female sterility has been reported in a number of crops. In this paper, a maximum-likelihood method is presented for estimating the position and effect of a female partial-sterile locus in a backcross population using the observed data of dominant or codominant markers. The ML solutions are obtained via Bailey’s method. The process for the estimating of the recombination fractions and the viabilities of female gametes are described, and the variances of the estimates of the parameters are also presented. Application of the method is demonstrated using a set of simulated data. This method circumvents the problems of the traditional mapping methods for female sterile genes which were based on data from seed set or embryo-sac morphology and anatomy.     

Dissecting Genetic Architecture Underlying Seed Traits in Multiple Environments

The seeds of flowering plants develop from double fertilization and play a vital role in reproduction and supplying human and animal food. The genetic variation of seed traits is influenced by multiple genetic systems, e.g., maternal, embryo, and/or endosperm genomes. Understanding the genetic architecture of seed traits is a major challenge because of this complex mechanism of multiple genetic systems, especially the epistasis within or between different genomes and their interactions with the environment. In this study, a statistical model was proposed for mapping QTL with epistasis and QTL-by-environment (QE) interactions underlying endosperm and embryo traits. Our model integrates the maternal and the offspring genomes into one mapping framework and can accurately analyze maternal additive and dominant effects, endosperm/embryo additive and dominant effects, and epistatic effects of two loci in the same or two different genomes, as well as interaction effects of each genetic component of QTL with environment. Intensive simulations under different sampling strategies, heritabilities, and model parameters were performed to investigate the statistical properties of the model. A set of real cottonseed data was analyzed to demonstrate our methods. A software package, QTLNetwork-Seed-1.0.exe, was developed for QTL analysis of seed traits.     

Multi-QTL Mapping for Quantitative Traits Using Epistatic Distorted Markers

The interaction between segregation distortion loci (SDL) has been often observed in all kinds of mapping populations. However, little has been known about the effect of epistatic SDL on quantitative trait locus (QTL) mapping. Here we proposed a multi-QTL mapping approach using epistatic distorted markers. Using the corrected linkage groups, epistatic SDL was identified. Then, these SDL parameters were used to correct the conditional probabilities of QTL genotypes, and these corrections were further incorporated into the new QTL mapping approach. Finally, a set of simulated datasets and a real data in 304 mouse F₂ individuals were used to validate the new method. As compared with the old method, the new one corrects genetic distance between distorted markers, and considers epistasis between two linked SDL. As a result, the power in the detection of QTL is higher for the new method than for the old one, and significant differences for estimates of QTL parameters between the two methods were observed, except for QTL position. Among two QTL for mouse weight, one significant difference for QTL additive effect between the above two methods was observed, because epistatic SDL between markers C66 and T93 exists (P = 2.94e-4).     

Statistical evaluation of multiple-locus linkage data in experimental species and its relevance to human studies: application to nonobese diabetic (NOD) mouse and human insulin-dependent diabetes mellitus (IDDM).

Common, familial human disorders generally do not follow Mendelian inheritance patterns, presumably because multiple loci are involved in disease susceptibility. One approach to mapping genes for such traits in humans is to first study an analogous form in an animal model, such as mouse, by using inbred strains and backcross experiments. Here we describe methodology for analyzing multiple-locus linkage data from such experimental backcrosses, particularly in light of multilocus genetic models, including the effects of epistasis. We illustrate these methods by using data from backcrosses involving nonobese diabetic mouse, which serves as an animal model for human insulin-dependent diabetes mellitus. We show that it is likely that a minimum of nine loci contribute to susceptibility, with strong epistasis effects among these loci. Three of the loci actually confer a protective effect in the homozygote, compared with the heterozygote. Further, we discuss the relevance of these studies for analogous studies of the human form of the trait. Specifically, we show that the magnitude of the gene effect in the experimental backcross is likely to correlate only weakly, at best, with the expected magnitude of effect for a human form, because in humans the gene effect will depend more heavily on disease allele frequencies than on the observed penetrance ratios; such allele frequencies are unpredictable. Hence, the major benefit from animal studies may be a better understanding of the disease process itself, rather than identification of cells through comparison mapping in humans by using regions of homology.     

Genetic analysis and molecular mapping of a new fertility restorer gene Rf8 for Triticum timopheevi cytoplasm in wheat (Triticum aestivum L.) using SSR markers

A study on mode of inheritance and mapping of fertility restorer (Rf) gene(s) using simple sequence repeat (SSR) markers was conducted in a cross of male sterile line 2041A having Triticum timopheevi cytoplasm and a restorer line PWR4099 of common wheat (Triticum aestivum L.). The F₁ hybrid was completely fertile indicating that fertility restoration is a dominant trait. Based on the pollen fertility and seed set of bagged spikes in F₂ generation, the individual plants were classified into fertile and sterile groups. Out of 120 F₂ plants, 97 were fertile and 23 sterile (based on pollen fertility) while 98 plants set ≥5 seeds/spike and 22 produced ≤4 or no seed. The observed frequency fits well into Mendelian ratio of 3 fertile: 1 sterile with χ² value of 2.84 for pollen fertility and 2.17 for seed setting indicating that the fertility restoration is governed by a single dominant gene in PWR4099. The three linked SSR markers, Xwmc503, Xgwm296 and Xwmc112 located on the chromosome 2DS were placed at a distance of 3.3, 5.8 and 6.7 cM, respectively, from the Rf gene. Since, no known Rf gene is located on the chromosome arm 2DS, the Rf gene in PWR4099 is a new gene and proposed as Rf8. The closest SSR marker, Xwmc503, linked to the Rf8 was validated in a set of Rf, maintainer and cytoplasmic male sterile lines. The closely linked SSR marker Xwmc503 may be used in marker-assisted backcross breeding facilitating the transfer of fertility restoration gene Rf8 into elite backgrounds with ease.     

Sequential elimination of major-effect contributors identifies additional quantitative trait loci conditioning high-temperature growth in yeast

Several quantitative trait loci (QTL) mapping strategies can successfully identify major-effect loci, but often have poor success detecting loci with minor effects, potentially due to the confounding effects of major loci, epistasis, and limited sample sizes. To overcome such difficulties, we used a targeted backcross mapping strategy that genetically eliminated the effect of a previously identified major QTL underlying high-temperature growth (Htg) in yeast. This strategy facilitated the mapping of three novel QTL contributing to Htg of a clinically derived yeast strain. One QTL, which is linked to the previously identified major-effect QTL, was dissected, and NCS2 was identified as the causative gene. The interaction of the NCS2 QTL with the first major-effect QTL was background dependent, revealing a complex QTL architecture spanning these two linked loci. Such complex architecture suggests that more genes than can be predicted are likely to contribute to quantitative traits. The targeted backcrossing approach overcomes the difficulties posed by sample size, genetic linkage, and epistatic effects and facilitates identification of additional alleles with smaller contributions to complex traits.     

How to perform meaningful estimates of genetic effects

Although the genotype-phenotype map plays a central role both in Quantitative and Evolutionary Genetics, the formalization of a completely general and satisfactory model of genetic effects, particularly accounting for epistasis, remains a theoretical challenge. Here, we use a two-locus genetic system in simulated populations with epistasis to show the convenience of using a recently developed model, NOIA, to perform estimates of genetic effects and the decomposition of the genetic variance that are orthogonal even under deviations from the Hardy-Weinberg proportions. We develop the theory for how to use this model in interval mapping of quantitative trait loci using Halley-Knott regressions, and we analyze a real data set to illustrate the advantage of using this approach in practice. In this example, we show that departures from the Hardy-Weinberg proportions that are expected by sampling alone substantially alter the orthogonal estimates of genetic effects when other statistical models, like F₂ or G2A, are used instead of NOIA. Finally, for the first time from real data, we provide estimates of functional genetic effects as sets of effects of natural allele substitutions in a particular genotype, which enriches the debate on the interpretation of genetic effects as implemented both in functional and in statistical models. We also discuss further implementations leading to a completely general genotype-phenotype map.     

Sexual Selection, Epistasis and Species Boundaries in Sympatric Hawaiian Picture-winged Drosophila

The Hawaiian picture-winged flies in the genus Drosophila are a spectacular example of rapid evolutionary diversification in which sexual selection is considered an important mechanism for reproductive isolation and speciation. We investigated the behavioral reproductive isolation of two closely related and sympatric Hawaiian picture-winged Drosophila species, D. silvestris and D. heteroneura, which are known to hybridize in nature and produce viable and fertile hybrids. We compared the mating success of parental, F1 and backcross males in pairings with D. heteroneura females. The F1 males were produced by mating D. heteroneura males with D. silvestris females, and the backcross males were produced by mating F1 females with D. heteroneura males. The mating success of backcross males paired with D. heteroneura females were significantly reduced relative to that of parental and F1 males. This reduced mating success occurred primarily at a late stage of courtship where female choice of mate may be important. Two- and three-gene models demonstrate that epistasis involving a few genes could account for the observed variation in male mating success. These results are consistent with negative epistasis in the backcross generation and support the importance of sexual selection and negative epistasis in the evolution and maintenance of these species.     

Empirical Threshold Values for Quantitative Trait Mapping

The detection of genes that control quantitative characters is a problem of great interest to the genetic mapping community. Methods for locating these quantitative trait loci (QTL) relative to maps of genetic markers are now widely used. This paper addresses an issue common to all QTL mapping methods, that of determining an appropriate threshold value for declaring significant QTL effects. An empirical method is described, based on the concept of a permutation test, for estimating threshold values that are tailored to the experimental data at hand. The method is demonstrated using two real data sets derived from F(2) and recombinant inbred plant populations. An example using simulated data from a backcross design illustrates the effect of marker density on threshold values.     

EvoluZion: a computer simulator for teaching genetic and evolutionary concepts

EvoluZion is a forward-in-time genetic simulator developed in Java and designed to perform real time simulations on the evolutionary history of virtual organisms. These model organisms harbour a set of 13 genes that codify an equal number of phenotypic features. These genes change randomly during replication, and mutant genes can have null, positive or negative effects on the organisms’ fitness, allowing to model effects of both selection pressures and drift on gene evolution. There are two versions of this program: version 1.6.x_haploid; focused on macroevolutionary events and depicting prokaryote-like organisms, and version 2.3.x_diploid that simulate diploid, sexually reproducing organisms, and it is more adequate to teach micro-evolution as well as key genetic concepts such as Mendel’s laws, epistasis, genetic linkage, genetic mapping among others. Different data sets can be collected periodically during running in order to perform further analyses. In addition, the complete genealogy of extant as well as extinct organisms can be recorded. EvoluZion is well suited for teaching evolutionary biology concepts to students of all levels in a pedagogic way. This is mainly due to three main program features: (i) its intuitive and simple graphical interface (ii) a visualisation similar to videogames (iii) flexible integration of a wide range of biological phenomena into a single simulation.     

An entropy-based approach for testing genetic epistasis underlying complex diseases

The genetic basis of complex diseases is expected to be highly heterogeneous, with complex interactions among multiple disease loci and environment factors. Due to the multi-dimensional property of interactions among large number of genetic loci, efficient statistical approach has not been well developed to handle the high-order epistatic complexity. In this article, we introduce a new approach for testing genetic epistasis in multiple loci using an entropy-based statistic for a case-only design. The entropy-based statistic asymptotically follows a χ² distribution. Computer simulations show that the entropy-based approach has better control of type I error and higher power compared to the standard χ² test. Motivated by a schizophrenia data set, we propose a method for measuring and testing the relative entropy of a clinical phenotype, through which one can test the contribution or interaction of multiple disease loci to a clinical phenotype. A sequential forward selection procedure is proposed to construct a genetic interaction network which is illustrated through a tree-based diagram. The network information clearly shows the relative importance of a set of genetic loci on a clinical phenotype. To show the utility of the new entropy-based approach, it is applied to analyze two real data sets, a schizophrenia data set and a published malaria data set. Our approach provides a fast and testable framework for genetic epistasis study in a case-only design.     

Linkage group correction using epistatic distorted markers in F2 and backcross populations

Epistasis has been frequently observed in all types of mapping populations. However, relatively little is known about the effect of epistatic distorted markers on linkage group construction. In this study, a new approach was proposed to correct the recombination fraction between epistatic distorted markers in backcross and F₂ populations under the framework of fitness and liability models. The information for three or four markers flanking with an epistatic segregation distortion locus was used to estimate the recombination fraction by the maximum likelihood method, implemented via an expectation–maximisation algorithm. A set of Monte Carlo simulation experiments along with a real data analysis in rice was performed to validate the new method. The results showed that the estimates from the new method are unbiased. In addition, five statistical properties for the new method in a backcross were summarised and confirmed by theoretical, simulated and real data analyses.     

Molecular mapping of the fertility restorer gene for ms-CW-type cytoplasmic male sterility of rice

Cytoplasmic male sterility (CMS) of rice (Oryza sativa L.) was first reported using the cytoplasm of a Chinese wild rice, Oryza rufipogon Griff. strain W1. However, it was not possible to characterize this ms-CW-type CMS in more detail until a restorer line had been developed due to the lack of restorer genes among cultivars thus far tested. The breeding of a restorer line (W1-R) was eventually achieved by transferring the restorer gene(s) of W1 to a cultivar. We report here the characterization of the ms-CW pollen grains and mapping of the restorer gene for ms-CW-type CMS. Pollen grains of the male-sterile plants appeared to be normal and viable based on the fluorochromatic reaction test, but they did not germinate on normal stigmas. The 1:1 segregation of fertile and sterile plants in a BC₁F₁ population from a cross between W1-R and a maintainer line demonstrated that fertility restoration is controlled by a single gene. The fertile seed set of all the F₂ plants examined indicated that the fertility restoration functions gametophytically. We designated the fertility restorer gene Rfcw. Using cleaved amplified polymorphic sequence (CAPS) and simple sequence repeat (SSR) markers, we localized Rfcw to chromosome 4 with a genetic distance of 0.6 cM from the nearest SSR marker.     

Mapping QTLs with epistatic effects and QTL×environment interactions by mixed linear model approaches

A new methodology based on mixed linear models was developed for mapping QTLs with digenic epistasis and QTL×environment (QE) interactions. Reliable estimates of QTL main effects (additive and epistasis effects) can be obtained by the maximum-likelihood estimation method, while QE interaction effects (additive×environment interaction and epistasis×environment interaction) can be predicted by the-best-linear-unbiased-prediction (BLUP) method. Likelihood ratio and t statistics were combined for testing hypotheses about QTL effects and QE interactions. Monte Carlo simulations were conducted for evaluating the unbiasedness, accuracy, and power for parameter estimation in QTL mapping. The results indicated that the mixed-model approaches could provide unbiased estimates for both positions and effects of QTLs, as well as unbiased predicted values for QE interactions. Additionally, the mixed-model approaches also showed high accuracy and power in mapping QTLs with epistatic effects and QE interactions. Based on the models and the methodology, a computer software program (QTLMapper version 1.0) was developed, which is suitable for interval mapping of QTLs with additive, additive×additive epistasis, and their environment interactions. Received: 23 October 1998 / Accepted: 11 May 1999     

一个嵌合型药用野生稻7号染色体单体附加系及其回交后代的分析

对一个药用野生稻(Oryza officinalis Wall ex Watt,基因组型CC)异源单体附加系(monosomic alien addition line,MAAL)及其回交后代进行了分析,应用分子标记技术确定了该异源单体附加系所附加的染色体是一条嵌合的7号染色体,药用野生稻贡献了其长臂部分,而短臂和着丝粒则来源于栽培稻。将该植株与栽培稻亲本回交,得到109株回交后代,考察了回交群体的主要农艺性状并进行了分子标记分析,发现野生稻染色体片段的渗入影响了回交后代的株高、千粒重、结实率、结实密度、叶宽等农艺性状,而且这些性状之间正相关度很大。     

A Dominant Gene for Male Sterility in Salvia miltiorrhiza Bunge

A natural male sterile mutant of Salvia miltiorrhiza (Labiatae, Sh-B) was found during field survey in 2002. Our objective was to analyze its genetic mechanism for producing F1 hybrid seeds and to develop a molecular marker linked to male sterile gene for selection of a hybrid parent line. The segregation ratios of male sterile plants to fertile plants in the progenies of both testcross and backcross were 1:1 in continuous experiments conducted in 2006–2009. The male sterile Sh-B was heterozygous (Msms). The male sterile plants could capture most pollen (2 granule/cm²·24 h) with row ratio (female : male 2 : 1) within 45-cm distance and harvest the largest amount of 6495 g hybrid seeds per hectare. We also developed DNA markers linked to the male sterile gene in a segregating population using bulked segregant analysis (BSA) and amplified fragment length polymorphism (AFLP) techniques. The segregating population was subjected to BSA-AFLP with 128 primer combinations. One out of fourteen AFLP markers (E11/M4208) was identified as tightly linked to the dominant male sterile gene with a recombination frequency of 6.85% and at a distance of 6.89 cM. This marker could be converted to PCR-based assay for large-scale selection of fertile plants in MAS (marker-assisted selection) at the seedling stage. Blastn analysis indicated that the male sterile gene sequence showed higher identity with nucleotides in Arabidopsis chromosome 1–5, and was more likely to encode S-adenosylmethionine-dependent methyltransferase, in which DNA methylation regulated the development of plant gametogenesis.     

Saturated Molecular Map of the Rice Genome Based on an Interspecific Backcross Population

A molecular map has been constructed for the rice genome comprised of 726 markers (mainly restriction fragment length polymorphisms; RFLPs). The mapping population was derived from a backcross between cultivated rice, Oryza sativa, and its wild African relative, Oryza longistaminata. The very high level of polymorphism between these species, combined with the use of polymerase chain reaction-amplified cDNA libraries, contributed to mapping efficiency. A subset of the probes used in this study was previously used to construct an RFLP map derived from an inter subspecific cross, providing a basis for comparison of the two maps and of the relative mapping efficiencies in the two crosses. In addition to the previously described PstI genomic rice library, three cDNA libraries from rice (Oryza), oat (Avena) and barley (Hordeum) were used in this mapping project. Levels of polymorphism detected by each and the frequency of identifying heterologous sequences for use in rice mapping are discussed. Though strong reproductive barriers isolate O. sativa from O. longistaminata, the percentage of markers showing distorted segregation in this backcross population was not significantly different than that observed in an intraspecific F(2) population previously used for mapping. The map contains 1491 cM with an average interval size of 4.0 cM on the framework map, and 2.0 cM overall. A total of 238 markers from the previously described PstI genomic rice library, 250 markers from a cDNA library of rice (Oryza), 112 cDNA markers from oat (Avena), and 20 cDNA markers from a barley (Hordeum) library, two genomic clones from maize (Zea), 11 microsatellite markers, three telomere markers, eleven isozymes, 26 cloned genes, six RAPD, and 47 mutant phenotypes were used in this mapping project. Applications of a molecular map for plant improvement are discussed.     

Nonparametric Method for Genomics-Based Prediction of Performance of Quantitative Traits Involving Epistasis in Plant Breeding

Genomic selection (GS) procedures have proven useful in estimating breeding value and predicting phenotype with genome-wide molecular marker information. However, issues of high dimensionality, multicollinearity, and the inability to deal effectively with epistasis can jeopardize accuracy and predictive ability. We, therefore, propose a new nonparametric method, pRKHS, which combines the features of supervised principal component analysis (SPCA) and reproducing kernel Hilbert spaces (RKHS) regression, with versions for traits with no/low epistasis, pRKHS-NE, to high epistasis, pRKHS-E. Instead of assigning a specific relationship to represent the underlying epistasis, the method maps genotype to phenotype in a nonparametric way, thus requiring fewer genetic assumptions. SPCA decreases the number of markers needed for prediction by filtering out low-signal markers with the optimal marker set determined by cross-validation. Principal components are computed from reduced marker matrix (called supervised principal components, SPC) and included in the smoothing spline ANOVA model as independent variables to fit the data. The new method was evaluated in comparison with current popular methods for practicing GS, specifically RR-BLUP, BayesA, BayesB, as well as a newer method by Crossa et al., RKHS-M, using both simulated and real data. Results demonstrate that pRKHS generally delivers greater predictive ability, particularly when epistasis impacts trait expression. Beyond prediction, the new method also facilitates inferences about the extent to which epistasis influences trait expression.     

Genetic models to estimate additive and non-additive effects of marker-associated QTL using multiple regression techniques

Summary The development of molecular markers has recently raised expectations for their application in selection programs. However, some questions related to quantitative trait loci (QTL) identification are still unanswered. The objectives of this paper are (1) to develop statistical genetic models for detecting and locating on the genome multi-QTL with additive, dominance and epistatic effects using multiple linear regression analysis in the backcross and F_n generations from the cross of two inbred lines; and (2) to discuss the bias caused by linked and unlinked QTL on the genetic estimates. Non-linear models were developed for different backcross and F_n generations when both epistasis and no epistasis were assumed. Generation analysis of marked progenies is suggested as a way of increasing the number of observations for the estimates without additional cost for molecular scoring. Some groups of progenies can be created in different generations from the same scored individuals. The non-linear models were transformed into approximate multivariate linear models to which combined stepwise and standard regression analysis could be applied. Expressions for the biases of the marker classes from linked QTL were obtained when no epistasis was assumed. When epistasis was assumed, these expressions increased in complexity, and the biases were caused by both linked and unlinked QTL.