Multiple Quantitative Trait Research Articles

Herkogamy and Its Effects on Mating Patterns in Arabidopsis thaliana

The evolution of mating systems, which exhibit an extraordinary diversity in flowering plants, is of central interest in plant biology. Herkogamy, the spatial separation of sexual organs within flowers, is a widespread floral mechanism that is thought to be an adaptive trait reducing self-pollination in hermaphroditic plants. In contrast with previous studies of herkogamy that focused on plants with relatively large floral displays, we here characterized herkogamy in Arabidopsis thaliana, a model plant with a strong selfing syndrome. Developmental features, reproductive consequences, and genetic architecture of herkogamy were exploited using naturally variable A. thaliana accessions, under both greenhouse and natural conditions. Our results demonstrate that the degree of herkogamy can strongly influence the mating patterns of A. thaliana: approach herkogamy can effectively promote outcrossing, no herkogamy is also capable of enhancing the opportunity for outcrossing, and reverse herkogamy facilitates efficient self-pollination. In addition, we found that the expression of herkogamy in A. thaliana was environment-dependent and regulated by multiple quantitative trait loci. This study reveals how minor modifications in floral morphology may cause dramatic changes in plant mating patterns, provides new insights into the function of herkogamy, and suggests the way for dissecting the genetic basis of this important character in a model plant.

SYMPHONY, an information-theoretic method for gene–gene and gene–environment interaction analysis of disease syndromes

We develop an information-theoretic method for gene-gene (GGI) and gene-environmental interactions (GEI) analysis of syndromes, defined as a phenotype vector comprising multiple quantitative traits (QTs). The K-way interaction information (KWII), an information-theoretic metric, was derived for multivariate normal distributed phenotype vectors. The utility of the method was challenged with three simulated data sets, the Genetic Association Workshop-15 (GAW15) rheumatoid arthritis data set, a high-density lipoprotein (HDL) and atherosclerosis data set from a mouse QT locus study, and the 1000 Genomes data. The dependence of the KWII on effect size, minor allele frequency, linkage disequilibrium, population stratification/admixture, as well as the power and computational time requirements of the novel method was systematically assessed in simulation studies. In these studies, phenotype vectors containing two and three constituent multivariate normally distributed QTs were used and the KWII was found to be effective at detecting GEI associated with the phenotype. High KWII values were observed for variables and variable combinations associated with the syndrome phenotype compared with uninformative variables not associated with the phenotype. The KWII values for the phenotype-associated combinations increased monotonically with increasing effect size values. The KWII also exhibited utility in simulations with non-linear dependence between the constituent QTs. Analysis of the HDL and atherosclerosis data set indicated that the simultaneous analysis of both phenotypes identified interactions not detected in the analysis of the individual traits. The information-theoretic approach may be useful for non-parametric analysis of GGI and GEI of complex syndromes.

A Decision Rule for Quantitative Trait Locus Detection Under the Extended Bayesian LASSO Model

Bayesian shrinkage analysis is arguably the state-of-the-art technique for large-scale multiple quantitative trait locus (QTL) mapping. However, when the shrinkage model does not involve indicator variables for marker inclusion, QTL detection remains heavily dependent on significance thresholds derived from phenotype permutation under the null hypothesis of no phenotype-to-genotype association. This approach is computationally intensive and more importantly, the hypothetical data generation at the heart of the permutation-based method violates the Bayesian philosophy. Here we propose a fully Bayesian decision rule for QTL detection under the recently introduced extended Bayesian LASSO for QTL mapping. Our new decision rule is free of any hypothetical data generation and relies on the well-established Bayes factors for evaluating the evidence for QTL presence at any locus. Simulation results demonstrate the remarkable performance of our decision rule. An application to real-world data is considered as well.

Fine Mapping and Candidate Gene Prediction of a Pleiotropic Quantitative Trait Locus for Yield-Related Trait in Zea mays

The yield of maize grain is a highly complex quantitative trait that is controlled by multiple quantitative trait loci (QTLs) with small effects, and is frequently influenced by multiple genetic and environmental factors. Thus, it is challenging to clone a QTL for grain yield in the maize genome. Previously, we identified a major QTL, qKNPR6, for kernel number per row (KNPR) across multiple environments, and developed two nearly isogenic lines, SL57-6 and Ye478, which differ only in the allelic constitution at the short segment harboring the QTL. Recently, qKNPR6 was re-evaluated in segregating populations derived from SL57-6×Ye478, and was narrowed down to a 2.8 cM interval, which explained 56.3% of the phenotypic variance of KNPR in 201 F2∶3 families. The QTL simultaneously affected ear length, kernel weight and grain yield. Furthermore, a large F2 population with more than 12,800 plants, 191 recombinant chromosomes and 10 overlapping recombinant lines placed qKNPR6 into a 0.91 cM interval corresponding to 198Kb of the B73 reference genome. In this region, six genes with expressed sequence tag (EST) evidence were annotated. The expression pattern and DNA diversity of the six genes were assayed in Ye478 and SL57-6. The possible candidate gene and the pathway involved in inflorescence development were discussed.

Iteratively reweighted LASSO for mapping multiple quantitative trait loci

The iteratively reweighted least square (IRLS) method is mostly identical to maximum likelihood (ML) method in terms of parameter estimation and power of quantitative trait locus (QTL) detection. But the IRLS is greatly superior to ML in terms of computing speed and the robustness of parameter estimation. In conjunction with the priors of parameters, ML can analyze multiple QTL model based on Bayesian theory, whereas under a single QTL model, IRLS has very limited statistical power to detect multiple QTLs. In this study, we proposed the iteratively reweighted least absolute shrinkage and selection operator (IRLASSO) for extending IRLS to simultaneously map multiple QTLs. The LASSO with coordinate descent step is employed to efficiently estimate non-zero genetic effect of each locus scanned over entire genome. Simulations demonstrate that IRLASSO has a higher precision of parameter estimation and power to detect QTL than IRLS, and is able to estimate residual variance more accurately than the unweighted LASSO based on LS. Especially, IRLASSO is very fast, usually taking less than five iterations to converge. The barley dataset from the North American Barley Genome Mapping Project is reanalyzed by our proposed method.

Cross Tissue Trait-Pathway Network Reveals the Importance of Oxidative Stress and Inflammation Pathways in Obesity-Induced Diabetes in Mouse

Complex disorders often involve dysfunctions in multiple tissue organs. Elucidating the communication among them is important to understanding disease pathophysiology. In this study we integrate multiple tissue gene expression and quantitative trait measurements of an obesity-induced diabetes mouse model, with databases of molecular interaction networks, to construct a cross tissue trait-pathway network. The animals belong to two strains of mice (BTBR or B6), of two obesity status (obese or lean), and at two different ages (4 weeks and 10 weeks). Only 10 week obese BTBR animals are diabetic. The expression data was first utilized to determine the state of every pathway in each tissue, which is subsequently utilized to construct a pathway co-expression network and to define trait-relevant and trait-linking pathways. Among the six tissues profiled, the adipose contains the largest number of trait-linking pathways. Among the eight traits measured, the body weight and plasma insulin level possess the most number of relevant and linking pathways. Topological analysis of the trait-pathway network revealed that the glycolysis/gluconeogenesis pathway in liver and the insulin signaling pathway in muscle are of top importance to the information flow in the network, with the highest degrees and betweenness centralities. Interestingly, pathways related to metabolism and oxidative stress actively interact with many other pathways in all animals, whereas, among the 10 week animals, the inflammation pathways were preferentially interactive in the diabetic ones only. In summary, our method offers a systems approach to delineate disease trait relevant intra- and cross tissue pathway interactions, and provides insights to the molecular basis of the obesity-induced diabetes.

Identification of Hypertension Susceptibility Loci on Rat Chromosome 12

Previous studies have identified multiple blood pressure and renal disease quantitative trait loci located on rat chromosome 12. In the present study, we narrowed blood pressure loci using a series of overlapping Dahl salt-sensitive/Mcwi (SS)-12 Brown Norway (BN) congenic lines. We found that transferring 6.1 Mb of SS chromosome 12 (13.4-19.5 Mb) onto the consomic SS-12BN background significantly elevated blood pressure on 1% NaCl (146±6 versus 127±1 mm Hg; P<0.001) and 8% NaCl diets (178±7 versus 144±2 mm Hg; P<0.001). Compared with the SS-12BN consomic, these animals also had significantly elevated albumin (218±31 versus 104±8 mg/d; P<0.001) and protein excretion (347±41 versus 195±12 mg/d; P<0.001) on a 1% NaCl diet. Elevated blood pressure, albuminuria, and proteinuria coincided with greater renal and cardiac damage, demonstrating that SS allele(s) within the 6.1 Mb congenic interval are associated with strong cardiovascular disease phenotypes. Sequence analysis of the 6.1 Mb congenic region revealed 12 673 single nucleotide polymorphisms between SS and BN rats. Of these polymorphisms, 293 lie within coding regions, and 18 resulted in nonsynonymous changes in conserved genes, of which 5 were predicted to be potentially damaging to protein function. Syntenic regions in human chromosome 7 have also been identified in multiple linkage and association studies of cardiovascular disease, suggesting that genetic variants underlying cardiovascular phenotypes in this congenic strain can likely be translated to a better understanding of human hypertension.

Functional Genomic Architecture of Predisposition to Voluntary Exercise in Mice: Expression QTL in the Brain

The biological basis of voluntary exercise is complex and simultaneously controlled by peripheral (ability) and central (motivation) mechanisms. The accompanying natural reward, potential addiction, and the motivation associated with exercise are hypothesized to be regulated by multiple brain regions, neurotransmitters, peptides, and hormones. We generated a large (n = 815) advanced intercross line of mice (G(4)) derived from a line selectively bred for increased wheel running (high runner) and the C57BL/6J inbred strain. We previously mapped multiple quantitative trait loci (QTL) that contribute to the biological control of voluntary exercise levels, body weight, and composition, as well as changes in body weight and composition in response to short-term exercise. Currently, using a subset of the G(4) population (n = 244), we examined the transcriptional landscape relevant to neurobiological aspects of voluntary exercise by means of global mRNA expression profiles from brain tissue. We identified genome-wide expression quantitative trait loci (eQTL) regulating variation in mRNA abundance and determined the mode of gene action and the cis- and/or trans-acting nature of each eQTL. Subsets of cis-acting eQTL, colocalizing with QTL for exercise or body composition traits, were used to identify candidate genes based on both positional and functional evidence, which were further filtered by correlational and exclusion mapping analyses. Specifically, we discuss six plausible candidate genes (Insig2, Socs2, DBY, Arrdc4, Prcp, IL15) and their potential role in the regulation of voluntary activity, body composition, and their interactions. These results develop a potential initial model of the underlying functional genomic architecture of predisposition to voluntary exercise and its effects on body weight and composition within a neurophysiological framework.

Dissecting the Genetic Basis of Extremely Large Grain Shape in Rice Cultivar ‘JZ1560’

Rice grain shape, grain length (GL), width (GW), thickness (GT) and length-to-width ratio (LWR), are usually controlled by multiple quantitative trait locus (QTL). To elucidate the genetic basis of extremely large grain shape, QTL analysis was performed using an F(2) population derived from a cross between a japonica cultivar 'JZ1560' (extremely large grain) and a contrasting indica cultivar 'FAZ1' (small grain). A total number of 24 QTLs were detected on seven different chromosomes. QTLs for GL, GW, GT and LWR explained 11.6%, 95.62%, 91.5% and 89.9% of total phenotypic variation, respectively. Many QTLs pleiotropically controlled different grain traits, contributing complex traits correlation. GW2 and qSW5/GW5, which have been cloned previously to control GW, showed similar chromosomal locations with qGW2-1/qGT2-1/qLWR2-2 and qGW5-2/qLWR5-1 and should be the right candidate genes. Plants pyramiding GW2 and qSW5/GW5 showed a significant increase in GW compared with those carrying one of the two major QTLs. Furthermore, no significant QTL interaction was observed between GW2 and qSW5/GW5. These results suggested that GW2 and qSW5/GW5 might work in independent pathways to regulate grain traits. 'JZ1560' alleles underlying all QTLs contributed an increase in GW and GT and the accumulation of additive effects generates the extremely large grain shape in 'JZ1560'.

Generalized linear mixed models for mapping multiple quantitative trait loci

Many biological traits are discretely distributed in phenotype but continuously distributed in genetics because they are controlled by multiple genes and environmental variants. Due to the quantitative nature of the genetic background, these multiple genes are called quantitative trait loci (QTL). When the QTL effects are treated as random, they can be estimated in a single generalized linear mixed model (GLMM), even if the number of QTL may be larger than the sample size. The GLMM in its original form cannot be applied to QTL mapping for discrete traits if there are missing genotypes. We examined two alternative missing genotype-handling methods: the expectation method and the overdispersion method. Simulation studies show that the two methods are efficient for multiple QTL mapping (MQM) under the GLMM framework. The overdispersion method showed slight advantages over the expectation method in terms of smaller mean-squared errors of the estimated QTL effects. The two methods of GLMM were applied to MQM for the female fertility trait of wheat. Multiple QTL were detected to control the variation of the number of seeded spikelets.

Improved LASSO priors for shrinkage quantitative trait loci mapping

Recently, the Bayesian least absolute shrinkage and selection operator (LASSO) has been successfully applied to multiple quantitative trait loci (QTL) mapping, which assigns the double-exponential prior and the Student's t prior to QTL effect that lead to the shrinkage estimate of QTL effect. However, as reported by many researchers, the Bayesian LASSO usually cannot effectively shrink the effects of zero-effect QTL very close to zero. In this study, the double-exponential prior and Student's t prior are modified so that the estimate of the effect for zero-effect QTL can be effectively shrunk toward zero. It is also found that the Student's t prior is virtually the same as the Jeffreys' prior, since both the shape and scale parameters of the scaled inverse Chi-square prior involved in the Student's t prior are estimated very close to zero. Besides the two modified Bayesian Markov chain Monte Carlo (MCMC) algorithms, an expectation-maximization (EM) algorithm with use of the modified double-exponential prior is also adapted. The results shows that the three new methods perform similarly on true positive rate and false positive rate for QTL detection, and all of them outperform the Bayesian LASSO.

How do genetic correlations affect species range shifts in a changing environment?

Species may be able to respond to changing environments by a combination of adaptation and migration. We study how adaptation affects range shifts when it involves multiple quantitative traits evolving in response to local selection pressures and gene flow. All traits develop clines shifting in space, some of which may be in a direction opposite to univariate predictions, and the species tracks its environmental optimum with a constant lag. We provide analytical expressions for the local density and average trait values. A species can sustain faster environmental shifts, develop a wider range and greater local adaptation when spatial environmental variation is low (generating low migration load) and multitrait adaptive potential is high. These conditions are favoured when nonlinear (stabilising) selection is weak in the phenotypic direction of the change in optimum, and genetic variation is high in the phenotypic direction of the selection gradient.

A genomics approach to understanding the role of auxin in apple (Malus x domestica)fruit size control

BackgroundAuxin is an important phytohormone for fleshy fruit development, having been shown to be involved in the initial signal for fertilisation, fruit size through the control of cell division and cell expansion, and ripening related events. There is considerable knowledge of auxin-related genes, mostly from work in model species. With the apple genome now available, it is possible to carry out genomics studies on auxin-related genes to identify genes that may play roles in specific stages of apple fruit development.ResultsHigh amounts of auxin in the seed compared with the fruit cortex were observed in 'Royal Gala' apples, with amounts increasing through fruit development. Injection of exogenous auxin into developing apples at the start of cell expansion caused an increase in cell size. An expression analysis screen of auxin-related genes involved in auxin reception, homeostasis, and transcriptional regulation showed complex patterns of expression in each class of gene. Two mapping populations were phenotyped for fruit size over multiple seasons, and multiple quantitative trait loci (QTLs) were observed. One QTL mapped to a region containing an Auxin Response Factor (ARF106). This gene is expressed during cell division and cell expansion stages, consistent with a potential role in the control of fruit size.ConclusionsThe application of exogenous auxin to apples increased cell expansion, suggesting that endogenous auxin concentrations are at least one of the limiting factors controlling fruit size. The expression analysis of ARF106 linked to a strong QTL for fruit weight suggests that the auxin signal regulating fruit size could partially be modulated through the function of this gene. One class of gene (GH3) removes free auxin by conjugation to amino acids. The lower expression of these GH3 genes during rapid fruit expansion is consistent with the apple maximising auxin concentrations at this point.

Registration of Maize Germplasm Lines Tx736, Tx739, and Tx740 for Reducing Preharvest Aflatoxin Accumulation

Maize (Zea mays L.) production in Texas, the southern United States, and much of the developing world is constrained by preharvest contamination from aflatoxins—potent mycotoxins produced by the fungus Aspergillus flavus. When consumed, aflatoxin can lead to impaired growth, liver cancer, or death of both humans and livestock. Because of these effects, the presence of this mycotoxin is tightly regulated in the U.S. food supply. No complete resistance to A. flavus or aflatoxin is known to exist in maize; however, multiple quantitative traits and some sources of resistance have been identified. We propose the release of three maize lines that demonstrate reduced preharvest aflatoxin accumulation. Tx736 (Reg. No. GP‐578, PI 662937) is a germplasm line derived from modified pedigree selection of a cross between Tx772, a line with reduced aflatoxin accumulation, and T246, a temperate line with good yield and Texas adaptation, backcrossed to Tx772 once. Lines Tx739 (Reg. No. GP‐579, PI 662938) and Tx740 (Reg. No. GP‐580, PI 662939) were selected by pedigree methods from S3 plants selfed out of heterotic groups A, C, and E from Agricomseeds (Santa Cruz, Bolivia). These three lines were field tested as lines per se and as testcross hybrids with introduced inoculation in multienvironmental field trials. In trials, these lines and hybrids had between 30 and 73% lower aflatoxin content than commercial checks. These germplasm lines will serve as unique sources for novel traits and alleles that reduce aflatoxin in elite temperate and subtropical maize.

Methods for adjusting population structure and familial relatedness in association test for collective effect of multiple rare variants on quantitative traits

Because of the low frequency of rare genetic variants in observed data, the statistical power of detecting their associations with target traits is usually low. The collapsing test of collective effect of multiple rare variants is an important and useful strategy to increase the power; in addition, family data may be enriched with causal rare variants and therefore provide extra power. However, when family data are used, both population structure and familial relatedness need to be adjusted for the possible inflation of false positives. Using a unified mixed linear model and family data, we compared six methods to detect the association between multiple rare variants and quantitative traits. Through the analysis of 200 replications of the quantitative trait Q2 from the Genetic Analysis Workshop 17 data set simulated for 697 subjects from 8 extended families, and based on quantile-quantile plots under the null and receiver operating characteristic curves, we compared the false-positive rate and power of these methods. We observed that adjusting for pedigree-based kinship gives the best control for false-positive rate, whereas adjusting for marker-based identity by state slightly outperforms in terms of power. An adjustment based on a principal components analysis slightly improves the false-positive rate and power. Taking into account type-1 error, power, and computational efficiency, we find that adjusting for pedigree-based kinship seems to be a good choice for the collective test of association between multiple rare variants and quantitative traits using family data.

Propensity score analysis in the Genetic Analysis Workshop 17 simulated data set on independent individuals

Genetic Analysis Workshop 17 provided simulated phenotypes and exome sequence data for 697 independent individuals (209 case subjects and 488 control subjects). The disease liability in these data was influenced by multiple quantitative traits. We addressed the lack of statistical power in this small data set by limiting the genomic variants included in the study to those with potential disease-causing effect, thereby reducing the problem of multiple testing. After this adjustment, we could readily detect two common variants that were strongly associated with the quantitative trait Q1 (C13S523 and C13S522). However, we found no significant associations with the affected status or with any of the other quantitative traits, and the relationship between disease status and genomic variants remained obscure. To address the challenge of the multivariate phenotype, we used propensity scores to combine covariates with genetic risk factors into a single risk factor and created a new phenotype variable, the probability of being affected given the covariates. Using the propensity score as a quantitative trait in the case-control analysis, we again could identify the two common single-nucleotide polymorphisms (C13S523 and C13S522). In addition, this analysis captured the correlation between Q1 and the affected status and reduced the problem of multiple testing. Although the propensity score was useful for capturing and clarifying the genetic contributions of common variants to the disease phenotype and the mediating role of the quantitative trait Q1, the analysis did not increase power to detect rare variants.

Multiple quantitative trait loci for cortical and trabecular bone regulation map to mid-distal mouse chromosome 4 that shares linkage homology to human chromosome 1p36

The mid-distal region of mouse chromosome 4 (Chr 4) is homologous with human Chr 1p36. Previously, we reported that mouse Chr 4 carries a quantitative trait locus (QTL) with strong regulatory effect on volumetric bone mineral density (vBMD). The intent of this study is to utilize nested congenic strains to decompose the genetic complexity of this gene-rich region. Adult females and males from 18 nested congenic strains carrying discrete C3H sequences were phenotyped for femoral mineral and volume by pQCT and for trabecular bone volume (BV), tissue volume (TV), trabecular number (Trab.no), and trabecular thickness (Trab.thk) by MicroCT 40. Our data show that the mouse Chr 4 region consists of at least 10 regulatory QTL regions that affected either or both pQCT and MicroCT 40 phenotypes. The pQCT phenotypes were typically similar between sexes, whereas the MicroCT 40 phenotypes were divergent. Individual congenic strains contained one to seven QTL regions. These regions conferred large positive or negative effects in some congenic strains, depending on the particular bone phenotype. The QTL regions II to X are syntenic with human 1p36, containing from 1 to 102 known genes. We identified 13 candidate genes that can be linked to bone within these regions. Six of these genes were linked to osteoblasts, three linked to osteoclasts, and two linked to skeletal development. Three of these genes have been identified in Genome Wide Association Studies (GWAS) linked to 1p36. In region III, there is only one gene, Lck, which conferred negative pQCT and MicroCT 40 phenotypes in both sexes. This gene is important to development and functioning of T cells, has been associated with osteoclast activity, and represents a novel bone regulatory gene that merits further experimental evaluation. In summary, congenic strains are powerful tools for identifying regulatory regions that influence bone biology and offer models for testing hypotheses about gene-gene and gene-environment interactions that are not available to experimental work in humans.

Revisiting the quantitative trait loci for milk production traits on BTA6

A parallel association study was performed in two independent cattle populations based on 41 validated, targeted single nucleotide polymorphisms (SNPs) and four microsatellite markers to re-evaluate the multiple quantitative trait loci (QTL) architecture for milk performance on bovine chromosome 6 (BTA6). Two distinct QTL located in the vicinity of the middle region of BTA6, but differing unambiguously regarding their effects on milk composition and yield traits were validated in the German Holstein population. A highly significant association of the protein variant ABCG2 p.Tyr581Ser with milk composition traits reconfirmed the causative molecular relevance of the ABCG2 gene in QTL region 1, whereas in QTL region 2, significant and tentative associations between gene variants RW070 and RW023 (located in the promoter region and exon 9 of the PPARGC1A gene for milk yield traits) were detected. For the German Fleckvieh population, only RW023 showed a tentative association with milk yield traits, whereas those loci with significant effects in German Holsteins (ABCG2 p.Tyr581Ser, RW070) showed fixed alleles. Even though our new data highlight two variants in the PPARGC1A gene (RW023, RW070) in QTL region 2, based on the results of our study, currently no unequivocal conclusion about the causal background of this QTL affecting milk yield traits can be drawn. Notably, the German Holstein and Fleckvieh populations, known for their divergent degree of dairy type, differ substantially in their allele frequencies for the growth-associated NCAPG p.Ile442Met locus.

A Sense of Self: Exploring the Selfing Syndrome in Capsella

Over the course of angiosperm evolution, inbreeding or selfing lineages have evolved independently numerous times from selfincompatible outbreeding ancestors. One of the driving forces of the evolution of selfing is thought to be limited pollinator and/or mate availability under low population densities (Lloyd, 1992). The breakdown in self-incompatibility that occurs during the transition to selfing typically is accompanied by specific changes in flower morphology and function, known as the selfing syndrome. Compared with their outbreeding relatives, selfing species tend to have smaller flowers that open less, develop a shorter distance between stigma and anthers, and produce less pollen, nectar, and scent (reviewed in Sicard and Lenhard, 2011). New work by Sicard et al. (2011) explores the genetic and molecular basis of these selfing syndrome traits in the genus Capsella, a close relative of Arabidopsis, through genetic mapping of a recombinant inbred line population from a cross between the selfing species Capsella rubella and outbreeding Capsella grandiflora. C. rubella exhibits many of the typical selfing syndrome traits, such as smaller size and opening angle of petals, shorter distance between stigma and anthers, and reduced pollen-to-ovule ratio (see figure). Analysis of the recombinant inbred line population led to the identification of multiple independent quantitative trait loci influencing these traits, suggesting independent evolution of different traits. The authors concluded that the selfing syndrome in Capsella has a complex genetic basis resulting fromthe accumulated effects of mutations at multiple genetic loci. An assessment of a variety of flower, leaf, and growth traits indicated that the main difference between the two species is in their flower morphology, and the floral differences are independent from differences in vegetative growth and development. The morphological traits associated with the selfing syndrome have been proposed to increase the efficiency of self-pollination relative to the outbreeder. The authors tested this hypothesis using an elegant approach by introgressing the S-locus of C. rubella into C. grandiflora. This resulted in introgression lines that were fully selfcompatible but with floral morphology very similar to the C. grandiflora outbreeder. Experiments with these lines suggested that flower morphology in C. rubella, and in particular the reduction in flower opening, is more conducive to efficient self-pollination than that of C. grandiflora. Thus, selfing syndrome flower traits may be selected for directly because of their positive effect on efficient self-pollination. Analysis of different C. rubella accessions showed that the small flower size and opening angle of petals are fixed traits within the species, consistent with a single origin for these traits. This is of interest as C. rubella is geographically far more widespread than C. grandiflora. Further studies, including the identification of genes underlying quantitative trait loci associated with the selfing syndrome in Capsella species, are necessary to determine the timing of the breakdown in self-incompatibility versus the evolution of morphological traits and the primary forces driving evolution.

Optimal selection for multiple quantitative trait loci and contributions of individuals using genetic algorithm

Two methods (Scheme A and Scheme B) were developed to optimize the relative weights on quantitative trait loci (QTL) and contributions of selected individuals simultaneously to maximize selection response while constraining the rate of inbreeding to the rate observed in gene assisted selection (GAS). In Scheme A, both the relative weights give to QTL and contributions of the selected individuals were optimized using a genetic algorithm. The possible solutions for relative weights of QTL and contributions of the selected individuals were encoded simultaneously. A physical selection population was used to evaluate the fitness of each encoded solution using stochastic simulation with 50 replicates. The fitness of each solution was the mean of all replicates for accumulative discounted sum of genetic means of all generations in physical selection population. In Scheme B, the optimization for relative weights on QTL was similar to Scheme A, and also was implemented based on a genetic algorithm. However, unlike Scheme A, an optimal contribution algorithm (OC) was used to optimize contributions of selection candidates. When compared with GAS, Schemes A and B resulted in up to 15.88 and 22.26% extra discounted sum of genetic value of all generations in a long planning horizon, respectively. Compared GAS+OC and Scheme B, most of the increase (about 78%) in genetic gain was produced by only optimizing contributions of selected individuals. The optimization for relative weight given to QTL just avoided the long-term loss (about 22%) observed in GAS scheme.