In-duct flow computation and acoustic propagation using the admittance multimodal formulation

A multimodal method for computing the potential base flow and propagating acoustic perturbations inside axisymmetric ducts is presented. Instead of using the standard modal basis, a polynomial basis is used in the radial direction to reduce the computational cost of the method, but this introduces non-physical high-order modes. The impact of these modes on the stability of the calculation is examined, and for the acoustic computation, a modification of the axial integration is proposed to improve the conditioning of the matrices involved. The flow computation is achieved by applying the method (initially devoted to acoustics) at a zero frequency without convective effects, by modifying the definition of the admittance at the exit of the duct, and by performing an induction process on the density. The method is validated against a finite element method for ducts with hard walls or lined walls. The results show that the proposed multimodal method is very efficient in computing the mean flow and propagating the sound disturbances inside axisymmetric ducts.

Sunflower Hybrids and Inbred Lines Adopt Different Physiological Strategies and Proteome Responses to Cope with Water Deficit

Sunflower is a hybrid crop that is considered moderately drought-tolerant and adapted to new cropping systems required for the agro-ecological transition. Here, we studied the impact of hybridity status (hybrids vs. inbred lines) on the responses to drought at the molecular and eco-physiological level exploiting publicly available datasets. Eco-physiological traits and leaf proteomes were measured in eight inbred lines and their sixteen hybrids grown in the high-throughput phenotyping platform Phenotoul-Heliaphen. Hybrids and parental lines showed different growth strategies: hybrids grew faster in the absence of water constraint and arrested their growth more abruptly than inbred lines when subjected to water deficit. We identified 471 differentially accumulated proteins, of which 256 were regulated by drought. The amplitude of up- and downregulations was greater in hybrids than in inbred lines. Our results show that hybrids respond more strongly to water deficit at the molecular and eco-physiological levels. Because of presence/absence polymorphism, hybrids potentially contain more genes than their parental inbred lines. We propose that detrimental homozygous mutations and the lower number of genes in inbred lines lead to a constitutive defense mechanism that may explain the lower growth of inbred lines under well-watered conditions and their lower reactivity to water deficit.

The genomics of linkage drag in inbred lines of sunflower

Crop wild relatives represent valuable sources of alleles for crop improvement, including adaptation to climate change and emerging diseases. However, introgressions from wild relatives might have deleterious effects on desirable traits, including yield, due to linkage drag. Here, we analyzed the genomic and phenotypic impacts of wild introgressions in inbred lines of cultivated sunflower to estimate the impacts of linkage drag. First, we generated reference sequences for seven cultivated and one wild sunflower genotype, as well as improved assemblies for two additional cultivars. Next, relying on previously generated sequences from wild donor species, we identified introgressions in the cultivated reference sequences, as well as the sequence and structural variants they contain. We then used a ridge-regression best linear unbiased prediction (BLUP) model to test the effects of the introgressions on phenotypic traits in the cultivated sunflower association mapping population. We found that introgression has introduced substantial sequence and structural variation into the cultivated sunflower gene pool, including >3,000 new genes. While introgressions reduced genetic load at protein-coding sequences, they mostly had negative impacts on yield and quality traits. Introgressions found at high frequency in the cultivated gene pool had larger effects than low-frequency introgressions, suggesting that the former likely were targeted by artificial selection. Also, introgressions from more distantly related species were more likely to be maladaptive than those from the wild progenitor of cultivated sunflower. Thus, breeding efforts should focus, as far as possible, on closely related and fully compatible wild relatives.

Gene regulatory network inference methodology for genomic and transcriptomic data acquired in genetically related heterozygote individuals

MOTIVATION

Inferring gene regulatory networks in non-independent genetically related panels is a methodological challenge. This hampers evolutionary and biological studies using heterozygote individuals such as in wild sunflower populations or cultivated hybrids.

RESULTS

First, we simulated 100 datasets of gene expressions and polymorphisms, displaying the same gene expression distributions, heterozygosities and heritabilities as in our dataset including 173 genes and 353 genotypes measured in sunflower hybrids. Secondly, we performed a meta-analysis based on six inference methods [least absolute shrinkage and selection operator (Lasso), Random Forests, Bayesian Networks, Markov Random Fields, Ordinary Least Square and fast inference of networks from directed regulation (Findr)] and selected the minimal density networks for better accuracy with 64 edges connecting 79 genes and 0.35 area under precision and recall (AUPR) score on average. We identified that triangles and mutual edges are prone to errors in the inferred networks. Applied on classical datasets without heterozygotes, our strategy produced a 0.65 AUPR score for one dataset of the DREAM5 Systems Genetics Challenge. Finally, we applied our method to an experimental dataset from sunflower hybrids. We successfully inferred a network composed of 105 genes connected by 106 putative regulations with a major connected component.

AVAILABILITY AND IMPLEMENTATION

Our inference methodology dedicated to genomic and transcriptomic data is available at https://forgemia.inra.fr/sunrise/inference_methods.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Discovery of interesting new polymorphisms in a sugar beet (elite [Formula: see text] exotic) progeny by comparison with an elite panel

KEY MESSAGE

The comparison of QTL detection performed on an elite panel and an (elite [Formula: see text] exotic) progeny shows that introducing exotic germplasm into breeding programs can bring new interesting allelic diversity. Selection of stable varieties producing the highest amount of extractable sugar per hectare (ha), resistant to diseases, and respecting environmental criteria is undoubtedly the main target for sugar beet breeding. As sodium, potassium, and [Formula: see text]-amino nitrogen in sugar beets are the impurities that have the biggest negative impact on white sugar extraction, it is interesting to reduce their concentration in further varieties. However, domestication history and strong selection pressures have affected the genetic diversity needed to achieve this goal. In this study, quantitative trait locus (QTL) detection was performed on two populations, an (elite [Formula: see text] exotic) sugar beet progeny and an elite panel, to find potentially new interesting regions brought by the exotic accession. The three traits linked with impurities content were studied. Some QTLs were detected in both populations, the majority in the elite panel because of most statistical power. Some of the QTLs were colocated and had favorable effect in the progeny since the exotic allele was linked with a decrease in the impurity content. A few number of favorable QTLs were detected in the progeny, only. Consequently, introgressing exotic genetic material into sugar beet breeding programs can allow the incorporation of new interesting alleles.

Training set optimization of genomic prediction by means of EthAcc

Genomic prediction is a useful tool for plant and animal breeding programs and is starting to be used to predict human diseases as well. A shortcoming that slows down the genomic selection deployment is that the accuracy of the prediction is not known a priori. We propose EthAcc (Estimated THeoretical ACCuracy) as a method for estimating the accuracy given a training set that is genotyped and phenotyped. EthAcc is based on a causal quantitative trait loci model estimated by a genome-wide association study. This estimated causal model is crucial; therefore, we compared different methods to find the one yielding the best EthAcc. The multilocus mixed model was found to perform the best. We compared EthAcc to accuracy estimators that can be derived via a mixed marker model. We showed that EthAcc is the only approach to correctly estimate the accuracy. Moreover, in case of a structured population, in accordance with the achieved accuracy, EthAcc showed that the biggest training set is not always better than a smaller and closer training set. We then performed training set optimization with EthAcc and compared it to CDmean. EthAcc outperformed CDmean on real datasets from sugar beet, maize, and wheat. Nonetheless, its performance was mainly due to the use of an optimal but inaccessible set as a start of the optimization algorithm. EthAcc's precision and algorithm issues prevent it from reaching a good training set with a random start. Despite this drawback, we demonstrated that a substantial gain in accuracy can be obtained by performing training set optimization.

Heliaphen, an Outdoor High-Throughput Phenotyping Platform for Genetic Studies and Crop Modeling

Heliaphen is an outdoor platform designed for high-throughput phenotyping. It allows the automated management of drought scenarios and monitoring of plants throughout their lifecycles. A robot moving between plants growing in 15-L pots monitors the plant water status and phenotypes the leaf or whole-plant morphology. From these measurements, we can compute more complex traits, such as leaf expansion (LE) or transpiration rate (TR) in response to water deficit. Here, we illustrate the capabilities of the platform with two practical cases in sunflower (Helianthus annuus): a genetic and genomic study of the response of yield-related traits to drought, and a modeling study using measured parameters as inputs for a crop simulation. For the genetic study, classical measurements of thousand-kernel weight (TKW) were performed on a biparental population under automatically managed drought stress and control conditions. These data were used for an association study, which identified five genetic markers of the TKW drought response. A complementary transcriptomic analysis identified candidate genes associated with these markers that were differentially expressed in the parental backgrounds in drought conditions. For the simulation study, we used a crop simulation model to predict the impact on crop yield of two traits measured on the platform (LE and TR) for a large number of environments. We conducted simulations in 42 contrasting locations across Europe using 21 years of climate data. We defined the pattern of abiotic stresses occurring at the continental scale and identified ideotypes (i.e., genotypes with specific trait values) that are more adapted to specific environment types. This study exemplifies how phenotyping platforms can assist the identification of the genetic architecture controlling complex response traits and facilitate the estimation of ecophysiological model parameters to define ideotypes adapted to different environmental conditions.

Comparison of GWAS models to identify non-additive genetic control of flowering time in sunflower hybrids

This study compares five models of GWAS, to show the added value of non-additive modeling of allelic effects to identify genomic regions controlling flowering time of sunflower hybrids. Genome-wide association studies are a powerful and widely used tool to decipher the genetic control of complex traits. One of the main challenges for hybrid crops, such as maize or sunflower, is to model the hybrid vigor in the linear mixed models, considering the relatedness between individuals. Here, we compared two additive and three non-additive association models for their ability to identify genomic regions associated with flowering time in sunflower hybrids. A panel of 452 sunflower hybrids, corresponding to incomplete crossing between 36 male lines and 36 female lines, was phenotyped in five environments and genotyped for 2,204,423 SNPs. Intra-locus effects were estimated in multi-locus models to detect genomic regions associated with flowering time using the different models. Thirteen quantitative trait loci were identified in total, two with both model categories and one with only non-additive models. A quantitative trait loci on LG09, detected by both the additive and non-additive models, is located near a GAI homolog and is presented in detail. Overall, this study shows the added value of non-additive modeling of allelic effects for identifying genomic regions that control traits of interest and that could participate in the heterosis observed in hybrids.

Comparison of GWAS models to identify non-additive genetic control of flowering time in sunflower hybrids

This study compares five models of GWAS, to show the added value of non-additive modeling of allelic effects to identify genomic regions controlling flowering time of sunflower hybrids. Genome-wide association studies are a powerful and widely used tool to decipher the genetic control of complex traits. One of the main challenges for hybrid crops, such as maize or sunflower, is to model the hybrid vigor in the linear mixed models, considering the relatedness between individuals. Here, we compared two additive and three non-additive association models for their ability to identify genomic regions associated with flowering time in sunflower hybrids. A panel of 452 sunflower hybrids, corresponding to incomplete crossing between 36 male lines and 36 female lines, was phenotyped in five environments and genotyped for 2,204,423 SNPs. Intra-locus effects were estimated in multi-locus models to detect genomic regions associated with flowering time using the different models. Thirteen quantitative trait loci were identified in total, two with both model categories and one with only non-additive models. A quantitative trait loci on LG09, detected by both the additive and non-additive models, is located near a GAI homolog and is presented in detail. Overall, this study shows the added value of non-additive modeling of allelic effects for identifying genomic regions that control traits of interest and that could participate in the heterosis observed in hybrids.

Genetic control of plasticity of oil yield for combined abiotic stresses using a joint approach of crop modelling and genome-wide association

Understanding the genetic basis of phenotypic plasticity is crucial for predicting and managing climate change effects on wild plants and crops. Here, we combined crop modelling and quantitative genetics to study the genetic control of oil yield plasticity for multiple abiotic stresses in sunflower. First, we developed stress indicators to characterize 14 environments for three abiotic stresses (cold, drought and nitrogen) using the SUNFLO crop model and phenotypic variations of three commercial varieties. The computed plant stress indicators better explain yield variation than descriptors at the climatic or crop levels. In those environments, we observed oil yield of 317 sunflower hybrids and regressed it with three selected stress indicators. The slopes of cold stress norm reaction were used as plasticity phenotypes in the following genome-wide association study. Among the 65 534 tested Single Nucleotide Polymorphisms (SNPs), we identified nine quantitative trait loci controlling oil yield plasticity to cold stress. Associated single nucleotide polymorphisms are localized in genes previously shown to be involved in cold stress responses: oligopeptide transporters, lipid transfer protein, cystatin, alternative oxidase or root development. This novel approach opens new perspectives to identify genomic regions involved in genotype-by-environment interaction of a complex traits to multiple stresses in realistic natural or agronomical conditions.

Genomic Prediction of Sunflower Hybrids Oil Content

Prediction of hybrid performance using incomplete factorial mating designs is widely used in breeding programs including different heterotic groups. Based on the general combining ability (GCA) of the parents, predictions are accurate only if the genetic variance resulting from the specific combining ability is small and both parents have phenotyped descendants. Genomic selection (GS) can predict performance using a model trained on both phenotyped and genotyped hybrids that do not necessarily include all hybrid parents. Therefore, GS could overcome the issue of unknown parent GCA. Here, we compared the accuracy of classical GCA-based and genomic predictions for oil content of sunflower seeds using several GS models. Our study involved 452 sunflower hybrids from an incomplete factorial design of 36 female and 36 male lines. Re-sequencing of parental lines allowed to identify 468,194 non-redundant SNPs and to infer the hybrid genotypes. Oil content was observed in a multi-environment trial (MET) over 3 years, leading to nine different environments. We compared GCA-based model to different GS models including female and male genomic kinships with the addition of the female-by-male interaction genomic kinship, the use of functional knowledge as SNPs in genes of oil metabolic pathways, and with epistasis modeling. When both parents have descendants in the training set, the predictive ability was high even for GCA-based prediction, with an average MET value of 0.782. GS performed slightly better (+0.2%). Neither the inclusion of the female-by-male interaction, nor functional knowledge of oil metabolism, nor epistasis modeling improved the GS accuracy. GS greatly improved predictive ability when one or both parents were untested in the training set, increasing GCA-based predictive ability by 10.4% from 0.575 to 0.635 in the MET. In this scenario, performing GS only considering SNPs in oil metabolic pathways did not improve whole genome GS prediction but increased GCA-based prediction ability by 6.4%. Our results show that GS is a major improvement to breeding efficiency compared to the classical GCA modeling when either one or both parents are not well-characterized. This finding could therefore accelerate breeding through reducing phenotyping efforts and more effectively targeting for the most promising crosses.

Molecular diversity of sunflower populations maintained as genetic resources is affected by multiplication processes and breeding for major traits

SNP genotyping of 114 cultivated sunflower populations showed that the multiplication process and the main traits selected during breeding of sunflower cultivars drove molecular diversity of the populations. The molecular diversity in a set of 114 cultivated sunflower populations was studied by single-nucleotide polymorphism genotyping. These populations were chosen as representative of the 400 entries in the INRA collection received or developed between 1962 and 2011 and made up of land races, open-pollinated varieties, and breeding pools. Mean allele number varied from 1.07 to 1.90. Intra-population variability was slightly reduced according to the number of multiplications since entry but some entries were probably largely homozygous when received. A principal component analysis was used to study inter-population variability. The first 3 axes accounted for 17% of total intra-population variability. The first axis was significantly correlated with seed oil content, more closely than just the distinction between oil and confectionary types. The second axis was related to the presence or absence of restorer genes and the third axis to flowering date and possibly to adaptation to different climates. Our results provide arguments highlighting the effect of the maintenance process on the within population genetic variability as well as on the impact of breeding for major agronomic traits on the between population variability of the collection. Propositions are made to improve sunflower population maintenance procedures to keep maximum genetic variability for future breeding.

Genomic Prediction of Sunflower Hybrids Oil Content

Prediction of hybrid performance using incomplete factorial mating designs is widely used in breeding programs including different heterotic groups. Based on the general combining ability (GCA) of the parents, predictions are accurate only if the genetic variance resulting from the specific combining ability is small and both parents have phenotyped descendants. Genomic selection (GS) can predict performance using a model trained on both phenotyped and genotyped hybrids that do not necessarily include all hybrid parents. Therefore, GS could overcome the issue of unknown parent GCA. Here, we compared the accuracy of classical GCA-based and genomic predictions for oil content of sunflower seeds using several GS models. Our study involved 452 sunflower hybrids from an incomplete factorial design of 36 female and 36 male lines. Re-sequencing of parental lines allowed to identify 468,194 non-redundant SNPs and to infer the hybrid genotypes. Oil content was observed in a multi-environment trial (MET) over 3 years, leading to nine different environments. We compared GCA-based model to different GS models including female and male genomic kinships with the addition of the female-by-male interaction genomic kinship, the use of functional knowledge as SNPs in genes of oil metabolic pathways, and with epistasis modeling. When both parents have descendants in the training set, the predictive ability was high even for GCA-based prediction, with an average MET value of 0.782. GS performed slightly better (+0.2%). Neither the inclusion of the female-by-male interaction, nor functional knowledge of oil metabolism, nor epistasis modeling improved the GS accuracy. GS greatly improved predictive ability when one or both parents were untested in the training set, increasing GCA-based predictive ability by 10.4% from 0.575 to 0.635 in the MET. In this scenario, performing GS only considering SNPs in oil metabolic pathways did not improve whole genome GS prediction but increased GCA-based prediction ability by 6.4%. Our results show that GS is a major improvement to breeding efficiency compared to the classical GCA modeling when either one or both parents are not well-characterized. This finding could therefore accelerate breeding through reducing phenotyping efforts and more effectively targeting for the most promising crosses.

On the Accuracy of Genomic Selection

Genomic selection is focused on prediction of breeding values of selection candidates by means of high density of markers. It relies on the assumption that all quantitative trait loci (QTLs) tend to be in strong linkage disequilibrium (LD) with at least one marker. In this context, we present theoretical results regarding the accuracy of genomic selection, i.e., the correlation between predicted and true breeding values. Typically, for individuals (so-called test individuals), breeding values are predicted by means of markers, using marker effects estimated by fitting a ridge regression model to a set of training individuals. We present a theoretical expression for the accuracy; this expression is suitable for any configurations of LD between QTLs and markers. We also introduce a new accuracy proxy that is free of the QTL parameters and easily computable; it outperforms the proxies suggested in the literature, in particular, those based on an estimated effective number of independent loci (M_e). The theoretical formula, the new proxy, and existing proxies were compared for simulated data, and the results point to the validity of our approach. The calculations were also illustrated on a new perennial ryegrass set (367 individuals) genotyped for 24,957 single nucleotide polymorphisms (SNPs). In this case, most of the proxies studied yielded similar results because of the lack of markers for coverage of the entire genome (2.7 Gb).

Genetic diversity, linkage disequilibrium and power of a large grapevine (Vitis vinifera L) diversity panel newly designed for association studies

BACKGROUND

As for many crops, new high-quality grapevine varieties requiring less pesticide and adapted to climate change are needed. In perennial species, breeding is a long process which can be speeded up by gaining knowledge about quantitative trait loci linked to agronomic traits variation. However, due to the long juvenile period of these species, establishing numerous highly recombinant populations for high resolution mapping is both costly and time-consuming. Genome wide association studies in germplasm panels is an alternative method of choice, since it allows identifying the main quantitative trait loci with high resolution by exploiting past recombination events between cultivars. Such studies require adequate panel design to represent most of the available genetic and phenotypic diversity. Assessing linkage disequilibrium extent and panel power is also needed to determine the marker density required for association studies.

RESULTS

Starting from the largest grapevine collection worldwide maintained in Vassal (France), we designed a diversity panel of 279 cultivars with limited relatedness, reflecting the low structuration in three genetic pools resulting from different uses (table vs wine) and geographical origin (East vs West), and including the major founders of modern cultivars. With 20 simple sequence repeat markers and five quantitative traits, we showed that our panel adequately captured most of the genetic and phenotypic diversity existing within the entire Vassal collection. To assess linkage disequilibrium extent and panel power, we genotyped single nucleotide polymorphisms: 372 over four genomic regions and 129 distributed over the whole genome. Linkage disequilibrium, measured by correlation corrected for kinship, reached 0.2 for a physical distance between 9 and 458 Kb depending on genetic pool and genomic region, with varying size of linkage disequilibrium blocks. This panel achieved reasonable power to detect associations between traits with high broad-sense heritability (> 0.7) and causal loci with intermediate allelic frequency and strong effect (explaining > 10 % of total variance).

CONCLUSIONS

Our association panel constitutes a new, highly valuable resource for genetic association studies in grapevine, and deserves dissemination to diverse field and greenhouse trials to gain more insight into the genetic control of many agronomic traits and their interaction with the environment.

Breeding patterns and cultivated beets origins by genetic diversity and linkage disequilibrium analyses

Genetic diversity in worldwide population of beets is strongly affected by the domestication history, and the comparison of linkage disequilibrium in worldwide and elite populations highlights strong selection pressure. Genetic relationships and linkage disequilibrium (LD) were evaluated in a set of 2035 worldwide beet accessions and in another of 1338 elite sugar beet lines, using 320 and 769 single nucleotide polymorphisms, respectively. The structures of the populations were analyzed using four different approaches. Within the worldwide population, three of the methods gave a very coherent picture of the population structure. Fodder beet and sugar beet accessions were grouped together, separated from garden beets and sea beets, reflecting well the origins of beet domestication. The structure of the elite panel, however, was less stable between clustering methods, which was probably because of the high level of genetic mixing in breeding programs. For the linkage disequilibrium analysis, the usual measure (r (2)) was used, and compared with others that correct for population structure and relatedness (r S (2) , r V (2) , r VS (2)). The LD as measured by r (2) persisted beyond 10 cM within the elite panel and fell below 0.1 after less than 2 cM in the worldwide population, for almost all chromosomes. With correction for relatedness, LD decreased under 0.1 by 1 cM for almost all chromosomes in both populations, except for chromosomes 3 and 9 within the elite panel. In these regions, the larger extent of LD could be explained by strong selection pressure.

Genetic architecture of pollination syndrome transition between hummingbird-specialist and generalist species in the genus Rhytidophyllum (Gesneriaceae)

Adaptation to pollinators is a key factor of diversification in angiosperms. The Caribbean sister genera Rhytidophyllum and Gesneria present an important diversification of floral characters. Most of their species can be divided in two major pollination syndromes. Large-open flowers with pale colours and great amount of nectar represent the generalist syndrome, while the hummingbird-specialist syndrome corresponds to red tubular flowers with a less important nectar volume. Repeated convergent evolution toward the generalist syndrome in this group suggests that such transitions rely on few genes of moderate to large effect. To test this hypothesis, we built a linkage map and performed a QTL detection for divergent pollination syndrome traits by crossing one specimen of the generalist species Rhytidophyllum auriculatum with one specimen of the hummingbird pollinated R. rupincola. Using geometric morphometrics and univariate traits measurements, we found that floral shape among the second-generation hybrids is correlated with morphological variation observed between generalist and hummingbird-specialist species at the genus level. The QTL analysis showed that colour and nectar volume variation between syndromes involve each one major QTL while floral shape has a more complex genetic basis and rely on few genes of moderate effect. Finally, we did not detect any genetic linkage between the QTLs underlying those traits. This genetic independence of traits could have facilitated evolution toward optimal syndromes.

Clusthaplo: a plug-in for MCQTL to enhance QTL detection using ancestral alleles in multi-cross design

We enhance power and accuracy of QTL mapping in multiple related families, by clustering the founders of the families on their local genomic similarity. MCQTL is a linkage mapping software application that allows the joint QTL mapping of multiple related families. In its current implementation, QTLs are modeled with one or two parameters for each parent that is a founder of the multi-cross design. The higher the number of parents, the higher the number of model parameters which can impact the power and the accuracy of the mapping. We propose to make use of the availability of denser and denser genotyping information on the founders to lessen the number of MCQTL parameters and thus boost the QTL discovery. We developed clusthaplo, an R package ( http://cran.r-project.org/web/packages/clusthaplo/index.html ), which aims to cluster haplotypes using a genomic similarity that reflects the probability of sharing the same ancestral allele. Computed in a sliding window along the genome and followed by a clustering method, the genomic similarity allows the local clustering of the parent haplotypes. Our assumption is that the haplotypes belonging to the same class transmit the same ancestral allele. So their putative QTL allelic effects can be modeled with the same parameter, leading to a parsimonious model, that is plugged in MCQTL. Intensive simulations using three maize data sets showed the significant gain in power and in accuracy of the QTL mapping with the ancestral allele model compared to the classical MCQTL model. MCQTL_LD (clusthaplo outputs plug in MCQTL) is a versatile and powerful tool for QTL mapping in multiple related families that makes use of linkage and linkage disequilibrium (web site http://carlit.toulouse.inra.fr/MCQTL/ ).

Combined linkage and linkage disequilibrium QTL mapping in multiple families of maize (Zea mays L.) line crosses highlights complementarities between models based on parental haplotype and single locus polymorphism

Advancements in genotyping are rapidly decreasing marker costs and increasing marker density. This opens new possibilities for mapping quantitative trait loci (QTL), in particular by combining linkage disequilibrium information and linkage analysis (LDLA). In this study, we compared different approaches to detect QTL for four traits of agronomical importance in two large multi-parental datasets of maize (Zea mays L.) of 895 and 928 testcross progenies composed of 7 and 21 biparental families, respectively, and genotyped with 491 markers. We compared to traditional linkage-based methods two LDLA models relying on the dense genotyping of parental lines with 17,728 SNP: one based on a clustering approach of parental line segments into ancestral alleles and one based on single marker information. The two LDLA models generally identified more QTL (60 and 52 QTL in total) than classical linkage models (49 and 44 QTL in total). However, they performed inconsistently over datasets and traits suggesting that a compromise must be found between the reduction of allele number for increasing statistical power and the adequacy of the model to potentially complex allelic variation. For some QTL, the model exclusively based on linkage analysis, which assumed that each parental line carried a different QTL allele, was able to capture remaining variation not explained by LDLA models. These complementarities between models clearly suggest that the different QTL mapping approaches must be considered to capture the different levels of allelic variation at QTL involved in complex traits.

Combined linkage and association mapping of flowering time in Sunflower (Helianthus annuus L.)

Association mapping and linkage mapping were used to identify quantitative trait loci (QTL) and/or causative mutations involved in the control of flowering time in cultivated sunflower Helianthus annuus. A panel of 384 inbred lines was phenotyped through testcrosses with two tester inbred lines across 15 location × year combinations. A recombinant inbred line (RIL) population comprising 273 lines was phenotyped both per se and through testcrosses with one or two testers in 16 location × year combinations. In the association mapping approach, kinship estimation using 5,923 single nucleotide polymorphisms was found to be the best covariate to correct for effects of panel structure. Linkage disequilibrium decay ranged from 0.08 to 0.26 cM for a threshold of 0.20, after correcting for structure effects, depending on the linkage group (LG) and the ancestry of inbred lines. A possible hitchhiking effect is hypothesized for LG10 and LG08. A total of 11 regions across 10 LGs were found to be associated with flowering time, and QTLs were mapped on 11 LGs in the RIL population. Whereas eight regions were demonstrated to be common between the two approaches, the linkage disequilibrium approach did not detect a documented QTL that was confirmed using the linkage mapping approach.

Genes involved in muscle lipid composition in 15 European Bos taurus breeds

Consumers demand healthy and palatable meat, both factors being affected by fat composition. However, red meat has relatively high concentration of saturated fatty acids and low concentration of the beneficial polyunsaturated fatty acids. To select animals prone to produce particular fat types, it is necessary to identify the genes influencing muscle lipid composition. This paper describes an association study in which a large panel of candidate genes involved in adipogenesis, lipid metabolism and energy homoeostasis was tested for effects on fat composition in 15 European cattle breeds. Sixteen genes were found to have significant effects on different lipid traits, and among these, CFL1 and MYOZ1 were found to have large effects on the ratio of 18:2/18:3, CRI1 on the amount of neutral adrenic acid (22:4 n-6), MMP1 on docosahexaenoic acid (22:6 n-3) and conjugated linoleic acid, PLTP on the ratio of n-6:n-3 and IGF2R on flavour. Several genes - ALDH2, CHRNE, CRHR2, DGAT1, IGFBP3, NEB, SOCS2, SUSP1, TCF12 and FOXO1 - also were found to be associated with both lipid and organoleptic traits although with smaller effect. The results presented here help in understanding the genetic and biochemical background underlying variations in fatty acid composition and flavour in beef.

Novel measures of linkage disequilibrium that correct the bias due to population structure and relatedness

Among the several linkage disequilibrium measures known to capture different features of the non-independence between alleles at different loci, the most commonly used for diallelic loci is the r(2) measure. In the present study, we tackled the problem of the bias of r(2) estimate, which results from the sample structure and/or the relatedness between genotyped individuals. We derived two novel linkage disequilibrium measures for diallelic loci that are both extensions of the usual r(2) measure. The first one, r(S)(2), uses the population structure matrix, which consists of information about the origins of each individual and the admixture proportions of each individual genome. The second one, r(V)(2), includes the kinship matrix into the calculation. These two corrections can be applied together in order to correct for both biases and are defined either on phased or unphased genotypes.We proved that these novel measures are linked to the power of association tests under the mixed linear model including structure and kinship corrections. We validated them on simulated data and applied them to real data sets collected on Vitis vinifera plants. Our results clearly showed the usefulness of the two corrected r(2) measures, which actually captured 'true' linkage disequilibrium unlike the usual r(2) measure.

Gene regulatory network reconstruction using Bayesian networks, the Dantzig Selector, the Lasso and their meta-analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth "Dialogue for Reverse Engineering Assessments and Methods" (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on "Systems Genetics" proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the 16 teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics.

Effect of population structure corrections on the results of association mapping tests in complex maize diversity panels

Association mapping of sequence polymorphisms underlying the phenotypic variability of quantitative agronomical traits is now a widely used method in plant genetics. However, due to the common presence of a complex genetic structure within the plant diversity panels, spurious associations are expected to be highly frequent. Several methods have thus been suggested to control for panel structure. They mainly rely on ad hoc criteria for selecting the number of ancestral groups; which is often not evident for the complex panels that are commonly used in maize. It was thus necessary to evaluate the effect of the selected structure models on the association mapping results. A real maize data set (342 maize inbred lines and 12,000 SNPs) was used for this study. The panel structure was estimated using both Bayesian and dimensional reduction methods, considering an increasing number of ancestral groups. Effect on association tests depends in particular on the number of ancestral groups and on the trait analyzed. The results also show that using a high number of ancestral groups leads to an over-corrected model in which all causal loci vanish. Finally the results of all models tested were combined in a meta-analysis approach. In this way, robust associations were highlighted for each analyzed trait.

Does probabilistic modelling of linkage disequilibrium evolution improve the accuracy of QTL location in animal pedigree?

Background

Since 2001, the use of more and more dense maps has made researchers aware that combining linkage and linkage disequilibrium enhances the feasibility of fine-mapping genes of interest. So, various method types have been derived to include concepts of population genetics in the analyses. One major drawback of many of these methods is their computational cost, which is very significant when many markers are considered. Recent advances in technology, such as SNP genotyping, have made it possible to deal with huge amount of data. Thus the challenge that remains is to find accurate and efficient methods that are not too time consuming. The study reported here specifically focuses on the half-sib family animal design. Our objective was to determine whether modelling of linkage disequilibrium evolution improved the mapping accuracy of a quantitative trait locus of agricultural interest in these populations. We compared two methods of fine-mapping. The first one was an association analysis. In this method, we did not model linkage disequilibrium evolution. Therefore, the modelling of the evolution of linkage disequilibrium was a deterministic process; it was complete at time 0 and remained complete during the following generations. In the second method, the modelling of the evolution of population allele frequencies was derived from a Wright-Fisher model. We simulated a wide range of scenarios adapted to animal populations and compared these two methods for each scenario.

Results

Our results indicated that the improvement produced by probabilistic modelling of linkage disequilibrium evolution was not significant. Both methods led to similar results concerning the location accuracy of quantitative trait loci which appeared to be mainly improved by using four flanking markers instead of two.

Conclusions

Therefore, in animal half-sib designs, modelling linkage disequilibrium evolution using a Wright-Fisher model does not significantly improve the accuracy of the QTL location when compared to a simpler method assuming complete and constant linkage between the QTL and the marker alleles. Finally, given the high marker density available nowadays, the simpler method should be preferred as it gives accurate results in a reasonable computing time.

QTL detection by multi-parent linkage mapping in oil palm (Elaeis guineensis Jacq.)

A quantitative trait locus (QTL) analysis designed for a multi-parent population was carried out and tested in oil palm (Elaeis guineensis Jacq.), which is a diploid cross-fertilising perennial species. A new extension of the MCQTL package was especially designed for crosses between heterozygous parents. The algorithm, which is now available for any allogamous species, was used to perform and compare two types of QTL search for small size families, within-family analysis and across-family analysis, using data from a 2 x 2 complete factorial mating experiment involving four parents from three selected gene pools. A consensus genetic map of the factorial design was produced using 251 microsatellite loci, the locus of the Sh major gene controlling fruit shell presence, and an AFLP marker of that gene. A set of 76 QTLs involved in 24 quantitative phenotypic traits was identified. A comparison of the QTL detection results showed that the across-family analysis proved to be efficient due to the interconnected families, but the family size issue is just partially solved. The identification of QTL markers for small progeny numbers and for marker-assisted selection strategies is discussed.

Developmental genes have pleiotropic effects on plant morphology and source capacity, eventually impacting on seed protein content and productivity in pea

Increasing pea (Pisum sativum) seed nutritional value and particularly seed protein content, while maintaining yield, is an important challenge for further development of this crop. Seed protein content and yield are complex and unstable traits, integrating all the processes occurring during the plant life cycle. During filling, seeds are the main sink to which assimilates are preferentially allocated at the expense of vegetative organs. Nitrogen seed demand is satisfied partly by nitrogen acquired by the roots, but also by nitrogen remobilized from vegetative organs. In this study, we evaluated the respective roles of nitrogen source capacity and sink strength in the genetic variability of seed protein content and yield. We showed in eight genotypes of diverse origins that both the maximal rate of nitrogen accumulation in the seeds and nitrogen source capacity varied among genotypes. Then, to identify the genetic factors responsible for seed protein content and yield variation, we searched for quantitative trait loci (QTL) for seed traits and for indicators of sink strength and source nitrogen capacity. We detected 261 QTL across five environments for all traits measured. Most QTL for seed and plant traits mapped in clusters, raising the possibility of common underlying processes and candidate genes. In most environments, the genes Le and Afila, which control internode length and the switch between leaflets and tendrils, respectively, determined plant nitrogen status. Depending on the environment, these genes were linked to QTL of seed protein content and yield, suggesting that source-sink adjustments depend on growing conditions.

Connected populations for detecting quantitative trait loci and testing for epistasis: an application in maize

Quantitative trait loci (QTL) detection experiments have often been restricted to large biallelic populations. Use of connected multiparental crosses has been proposed to increase the genetic variability addressed and to test for epistatic interactions between QTL and the genetic background. We present here the results of a QTL detection performed on six connected F(2) populations of 150 F(2:3) families each, derived from four maize inbreds and evaluated for three traits of agronomic interest. The QTL detection was carried out by composite interval mapping on each population separately, then on the global design either by taking into account the connections between populations or not. Epistatic interactions between loci and with the genetic background were tested. Taking into account the connections between populations increased the number of QTL detected and the accuracy of QTL position estimates. We detected many epistatic interactions, particularly for grain yield QTL (R(2) increase of 9.6%). Use of connections for the QTL detection also allowed a global ranking of alleles at each QTL. Allelic relationships and epistasis both contribute to the lack of consistency for QTL positions observed among populations, in addition to the limited power of the tests. The potential benefit of assembling favorable alleles by marker-assisted selection are discussed.

Linkage disequilibrium interval mapping of quantitative trait loci

BACKGROUND

For many years gene mapping studies have been performed through linkage analyses based on pedigree data. Recently, linkage disequilibrium methods based on unrelated individuals have been advocated as powerful tools to refine estimates of gene location. Many strategies have been proposed to deal with simply inherited disease traits. However, locating quantitative trait loci is statistically more challenging and considerable research is needed to provide robust and computationally efficient methods.

RESULTS

Under a three-locus Wright-Fisher model, we derived approximate expressions for the expected haplotype frequencies in a population. We considered haplotypes comprising one trait locus and two flanking markers. Using these theoretical expressions, we built a likelihood-maximization method, called HAPim, for estimating the location of a quantitative trait locus. For each postulated position, the method only requires information from the two flanking markers. Over a wide range of simulation scenarios it was found to be more accurate than a two-marker composite likelihood method. It also performed as well as identity by descent methods, whilst being valuable in a wider range of populations.

CONCLUSION

Our method makes efficient use of marker information, and can be valuable for fine mapping purposes. Its performance is increased if multiallelic markers are available. Several improvements can be developed to account for more complex evolution scenarios or provide robust confidence intervals for the location estimates.

MCQTL: multi-allelic QTL mapping in multi-cross design

The aim of the MCQTL software package is to perform QTL mapping in multi-cross designs. It allows the analysis of the usual populations derived from inbred lines and can link the families by assuming that the QTL locations are the same in all of them. Moreover, a diallel modelling of the QTL genotypic effects is allowed in multiple related families. The implemented model is a linear regression model. A composite interval mapping and an iterative QTL mapping are implemented to deal with multiple QTL models. Marker cofactor selections by forward or backward stepwise methods are implemented as well as computation of threshold test value by permutation.

AVAILABILITY

The program is available on request after signing a licence agreement; free of charge for academic and non-profit organizations at http://www.genoplante.org (Bioinformatics products).

BioMercator: integrating genetic maps and QTL towards discovery of candidate genes

SUMMARY

Breeding programs face the challenge of integrating information from genomics and from quantitative trait loci (QTL) analysis in order to identify genomic sequences controlling the variation of important traits. Despite the development of integrative databases, building a consensus map of genes, QTL and other loci gathered from multiple maps remains a manual and tedious task. Nevertheless, this is a critical step to reveal co-locations between genes and QTL. Another important matter is to determine whether QTL linked to same traits or related ones is detected in independent experiments and located in the same region, and represents a single locus or not. Statistical tools such as meta-analysis can be used to answer this question. BioMercator has been developed to automate map compilation and QTL meta-analysis, and to visualize co-locations between genes and QTL through a graphical interface.

AVAILABILITY

Available upon request (http://moulon/~bioinfo/BioMercator/). Free of charge for academic use.

A comparison between methods for linkage disequilibrium fine mapping of quantitative trait loci

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.

ERECTA, an LRR receptor-like kinase protein controlling development pleiotropically affects resistance to bacterial wilt

Bacterial wilt, one of the most devastating bacterial diseases of plants worldwide, is caused by Ralstonia solanacearum and affects many important crop species. We show that several strains isolated from solanaceous crops in Europe are pathogenic in different accessions of Arabidopsis thaliana. One of these strains, 14.25, causes wilting symptoms in A. thaliana accession Landsberg erecta (Ler) and no apparent symptoms in accession Columbia (Col-0). Disease development and bacterial multiplication in the susceptible Ler accession depend on functional hypersensitive response and pathogenicity (hrp) genes, key elements for bacterial pathogenicity. Genetic analysis using Ler x Col-0 recombinant inbred lines showed that resistance is governed by at least three loci: QRS1 (Quantitative Resistance to R. solanacearum) and QRS2 on chromosome 2, and QRS3 on chromosome 5. These loci explain about 90% of the resistance carried by the Col-0 accession. The ERECTA gene, which encodes a leucine-rich repeat receptor-like kinase (LRR-RLK) and affects development of aerial organs, is dimorphic in our population and lies close to QRS1. Susceptible Ler plants transformed with a wild-type ERECTA gene, and the LER line showed increased disease resistance to R. solanacearum as indicated by reduced wilt symptoms and impaired bacterial growth, suggesting unexpected cross-talk between resistance and developmental pathways.

Nod genes and Nod signals and the evolution of the Rhizobium legume symbiosis

The establishment of the nitrogen-fixing symbiosis between rhizobia and legumes requires an exchange of signals between the two partners. In response to flavonoids excreted by the host plant, rhizobia synthesize Nod factors (NFs) which elicit, at very low concentrations and in a specific manner, various symbiotic responses on the roots of the legume hosts. NFs from several rhizobial species have been characterized. They all are lipo-chitooligosaccharides, consisting of a backbone of generally four or five glucosamine residues N-acylated at the non-reducing end, and carrying various O-substituents. The N-acyl chain and the other substituents are important determinants of the rhizobial host specificity. A number of nodulation genes which specify the synthesis of NFs have been identified. All rhizobia, in spite of their diversity, possess conserved nodABC genes responsible for the synthesis of the N-acylated oligosaccharide core of NFs, which suggests that these genes are of a monophyletic origin. Other genes, the host specific nod genes, specify the substitutions of NFs. The central role of NFs and nod genes in the Rhizobium-legume symbiosis suggests that these factors could be used as molecular markers to study the evolution of this symbiosis. We have studied a number of NFs which are N-acylated by alpha,beta-unsaturated fatty acids. We found that the ability to synthesize such NFs does not correlate with taxonomic position of the rhizobia. However, all rhizobia that produce NFs such nodulate plants belonging to related tribes of legumes, the Trifolieae, Vicieae, and Galegeae, all of them being members of the so-called galegoid group. This suggests that the ability to recognize the NFs with alpha-beta-unsaturated fatty acids is limited to this group of legumes, and thus might have appeared only once in the course of legume evolution, in the galegoid phylum.

Nod genes and Nod signals and the evolution of the Rhizobium legume symbiosis

The establishment of the nitrogen-fixing symbiosis between rhizobia and legumes requires an exchange of signals between the two partners. In response to flavonoids excreted by the host plant, rhizobia synthesize Nod factors (NFs) which elicit, at very low concentrations and in a specific manner, various symbiotic responses on the roots of the legume hosts. NFs from several rhizobial species have been characterized. They all are lipo-chitooligosaccharides, consisting of a backbone of generally four or five glucosamine residues N-acylated at the non-reducing end, and carrying various O-substituents. The N-acyl chain and the other substituents are important determinants of the rhizobial host specificity. A number of nodulation genes which specify the synthesis of NFs have been identified. All rhizobia, in spite of their diversity, possess conserved nodABC genes responsible for the synthesis of the N-acylated oligosaccharide core of NFs, which suggests that these genes are of a monophyletic origin. Other genes, the host specific nod genes, specify the substitutions of NFs. The central role of NFs and nod genes in the Rhizobium-legume symbiosis suggests that these factors could be used as molecular markers to study the evolution of this symbiosis. We have studied a number of NFs which are N-acylated by alpha,beta-unsaturated fatty acids. We found that the ability to synthesize such NFs does not correlate with taxonomic position of the rhizobia. However, all rhizobia that produce NFs such nodulate plants belonging to related tribes of legumes, the Trifolieae, Vicieae, and Galegeae, all of them being members of the so-called galegoid group. This suggests that the ability to recognize the NFs with alpha-beta-unsaturated fatty acids is limited to this group of legumes, and thus might have appeared only once in the course of legume evolution, in the galegoid phylum.

Resistance of tomato line Hawaii7996 to Ralstonia solanacearum Pss4 in Taiwan is controlled mainly by a major strain-specific locus

Bacterial wilt caused by the soilborne bacterium Ralstonia solanacearum attacks hundreds of plant species, including many agriculturally important crops. Natural resistance to this disease has been found in some species and is usually inherited as a polygenic trait. In tomato, a model crop plant, genetic analysis previously revealed the involvement of several QTL (quantitative trait loci) controlling resistance and, in all of these studies with different strains of the pathogen, loci on chromosome 6 played the predominant role in controlling this trait. Using quantitative data collected from a greenhouse test F3 population, we identified a new locus on chromosome 12 that appears to be active specifically against a race 1 biovar 3 Pss4 bacterial strain endemic to Taiwan. Chromosome 6 still contributes significantly to the control of the resistance, and weaker associations of the trait to other regions of the genome are observed. These results are discussed in the context of current molecular knowledge about the strain specificity of disease resistance genes.

Temporal and multiple quantitative trait loci analyses of resistance to bacterial wilt in tomato permit the resolution of linked loci

Ralstonia solanacearum is a soil-borne bacterium that causes the serious disease known as bacterial wilt in many plant species. In tomato, several QTL controlling resistance have been found, but in different studies, markers spanning a large region of chromosome 6 showed strong association with the resistance. By using two different approaches to analyze the data from a field test F3 population, we show that at least two separate loci approximately 30 cM apart on this chromosome are most likely involved in the resistance. First, a temporal analysis of the progression of symptoms reveals a distal locus early in the development of the disease. As the disease progresses, the maximum LOD peak observed shifts toward the proximal end of the chromosome, obscuring the distal locus. Second, although classical interval mapping could only detect the presence of one locus, a statistical "two-QTL model" test, specifically adapted for the resolution of linked QTL, strongly supported the hypothesis for the presence of two loci. These results are discussed in the context of current molecular knowledge about disease resistance genes on chromosome 6 and observations made by tomato breeders during the production of bacterial wilt-resistant varieties.

A composite genetic map of the parasitoid wasp Trichogramma brassicae based on RAPD markers

Three linkage maps of the genome of the microhymenopteran Trichogramma brassicae were constructed from the analysis of segregation of random amplified polymorphic DNA markers in three F2 populations. These populations were composed of the haploid male progeny of several virgin F1 females, which resulted from the breeding of four parental lines that were nearly fixed for different random amplified polymorphic DNA markers and that were polymorphic for longevity and fecundity characters. As the order of markers common to the three mapping populations was found to be well conserved, a composite linkage map was constructed. Eighty-four markers were organized into five linkage groups and two pairs. The mean interval between two markers was 17.7 cM, and the map spanned 1330 cM.

A method to measure genetic distance between allogamous populations of alfalfa (Medicago sativa) using RAPD molecular markers

Alfalfa (Medicago sativa L.) is a forage legume of world-wide importance whose both allogamous and autotetraploid nature maximizes the genetic diversity within natural and cultivated populations. This genetic diversity makes difficult the discrimination between two related populations. We analyzed this genetic diversity by screening DNA from individual plants of eight cultivated and natural populations of M. sativa and M.  falcata using the RAPD method. A high level of genetic variation was found within and between populations. Using five primers, 64 intense bands were scored as present or absent across all populations. Most of the loci were revealed to be highly polymorphic whereas very few population-specific polymorphisms were identified. From these observations, we adopted a method based on the Roger's genetic distance between populations using the observed frequency of bands to discriminate populations pairwise. Except for one case, the between-population distances were all significantly different from zero. We have also determined the minimal number of bands and individuals required to test for the significance of between-population distances.

Comparing power of different methods for QTL detection

We compared the powers of two methods for detection of quantitative trait loci (QTL) using genetic markers, in the simple case of an interval between two codominant markers and a backcross population. The first method is the interval mapping approach, based on the use of likelihood ratio tests performed in many positions within the interval considered and the second is the classical analysis of variance (ANOVA) testing only on the positions of the two markers. For both approaches we took into account the correlation between tests performed at different markers or positions in the interval. Appropriate thresholds and powers of tests were then calculated using analytical formulations. Simulations were also done to check the validity of the approximations used to calculate the power of the interval mapping test. Results show that the interval mapping test is slightly more powerful (about 5%) than ANOVA for small intervals (less than 20 cM) and that, for quite large effects of the QTL, the advantage of interval mapping increases as the distance between markers increases. It is more than 30% for intervals of about 70 cM.