Fast and accurate joint inference of coancestry parameters for populations and/or individuals.

We introduce a fast, new algorithm for inferring from allele count data the FST parameters describing genetic distances among a set of populations and/or unrelated diploid individuals, and a tree with branch lengths corresponding to FST values. The tree can reflect historical processes of splitting and divergence, but seeks to represent the actual genetic variance as accurately as possible with a tree structure. We generalise two major approaches to defining FST, via correlations and mismatch probabilities of sampled allele pairs, which measure shared and non-shared components of genetic variance. A diploid individual can be treated as a population of two gametes, which allows inference of coancestry coefficients for individuals as well as for populations, or a combination of the two. A simulation study illustrates that our fast method-of-moments estimation of FST values, simultaneously for multiple populations/individuals, gains statistical efficiency over pairwise approaches when the population structure is close to tree-like. We apply our approach to genome-wide genotypes from the 26 worldwide human populations of the 1000 Genomes Project. We first analyse at the population level, then a subset of individuals and in a final analysis we pool individuals from the more homogeneous populations. This flexible analysis approach gives advantages over traditional approaches to population structure/coancestry, including visual and quantitative assessments of long-standing questions about the relative magnitudes of within- and between-population genetic differences.

Improving the use of plant genetic resources to sustain breeding programs' efficiency.

Genetic progress of crop plants is required to face human population growth and guarantee production stability in increasingly unstable environmental conditions. Breeding is accompanied by a loss in genetic diversity, which hinders sustainable genetic gain. Methodologies based on molecular marker information have been developed to manage diversity and proved effective in increasing long-term genetic gain. However, with realistic plant breeding population sizes, diversity depletion in closed programs appears ineluctable, calling for the introduction of relevant diversity donors. Although maintained with significant efforts, genetic resource collections remain underutilized, due to a large performance gap with elite germplasm. Bridging populations created by crossing genetic resources to elite lines prior to introduction into elite programs can manage this gap efficiently. To improve this strategy, we explored with simulations different genomic prediction and genetic diversity management options for a global program involving a bridging and an elite component. We analyzed the dynamics of quantitative trait loci fixation and followed the fate of allele donors after their introduction into the breeding program. Allocating 25% of total experimental resources to create a bridging component appears highly beneficial. We showed that potential diversity donors should be selected based on their phenotype rather than genomic predictions calibrated with the ongoing breeding program. We recommend incorporating improved donors into the elite program using a global calibration of the genomic prediction model and optimal cross selection maintaining a constant diversity. These approaches use efficiently genetic resources to sustain genetic gain and maintain neutral diversity, improving the flexibility to address future breeding objectives.

Portability of genomic predictions trained on sparse factorial designs across two maize silage breeding cycles.

KEY MESSAGE: We validated the efficiency of genomic predictions calibrated on sparse factorial training sets to predict the next generation of hybrids and tested different strategies for updating predictions along generations. Genomic selection offers new prospects for revisiting hybrid breeding schemes by replacing extensive phenotyping of individuals with genomic predictions. Finding the ideal design for training genomic prediction models is still an open question. Previous studies have shown promising predictive abilities using sparse factorial instead of tester-based training sets to predict single-cross hybrids from the same generation. This study aims to further investigate the use of factorials and their optimization to predict line general combining abilities (GCAs) and hybrid values across breeding cycles. It relies on two breeding cycles of a maize reciprocal genomic selection scheme involving multiparental connected reciprocal populations from flint and dent complementary heterotic groups selected for silage performances. Selection based on genomic predictions trained on a factorial design resulted in a significant genetic gain for dry matter yield in the new generation. Results confirmed the efficiency of sparse factorial training sets to predict candidate line GCAs and hybrid values across breeding cycles. Compared to a previous study based on the first generation, the advantage of factorial over tester training sets appeared lower across generations. Updating factorial training sets by adding single-cross hybrids between selected lines from the previous generation or a random subset of hybrids from the new generation both improved predictive abilities. The CDmean criterion helped determine the set of single-crosses to phenotype to update the training set efficiently. Our results validated the efficiency of sparse factorial designs for calibrating hybrid genomic prediction experimentally and showed the benefit of updating it along generations.

Assessing the potential of genetic resource introduction into elite germplasm: a collaborative multiparental population for flint maize.

KEY MESSAGE: Implementing a collaborative pre-breeding multi-parental population efficiently identifies promising donor x elite pairs to enrich the flint maize elite germplasm. Genetic diversity is crucial for maintaining genetic gains and ensuring breeding programs' long-term success. In a closed breeding program, selection inevitably leads to a loss of genetic diversity. While managing diversity can delay this loss, introducing external sources of diversity is necessary to bring back favorable genetic variation. Genetic resources exhibit greater diversity than elite materials, but their lower performance levels hinder their use. This is the case for European flint maize, for which elite germplasm has incorporated only a limited portion of the diversity available in landraces. To enrich the diversity of this elite genetic pool, we established an original cooperative maize bridging population that involves crosses between private elite materials and diversity donors to create improved genotypes that will facilitate the incorporation of original favorable variations. Twenty donor × elite BC1S2 families were created and phenotyped for hybrid value for yield related traits. Crosses showed contrasted means and variances and therefore contrasted potential in terms of selection as measured by their usefulness criterion (UC). Average expected mean performance gain over the initial elite material was 5%. The most promising donor for each elite line was identified. Results also suggest that one more generation, i.e., 3 in total, of crossing to the elite is required to fully exploit the potential of a donor. Altogether, our results support the usefulness of incorporating genetic resources into elite flint maize. They call for further effort to create fixed diversity donors and identify those most suitable for each elite program.

High-dimensional multi-omics measured in controlled conditions are useful for maize platform and field trait predictions.

KEY MESSAGE: Transcriptomics and proteomics information collected on a platform can predict additive and non-additive effects for platform traits and additive effects for field traits. The effects of climate change in the form of drought, heat stress, and irregular seasonal changes threaten global crop production. The ability of multi-omics data, such as transcripts and proteins, to reflect a plant's response to such climatic factors can be capitalized in prediction models to maximize crop improvement. Implementing multi-omics characterization in field evaluations is challenging due to high costs. It is, however, possible to do it on reference genotypes in controlled conditions. Using omics measured on a platform, we tested different multi-omics-based prediction approaches, using a high dimensional linear mixed model (MegaLMM) to predict genotypes for platform traits and agronomic field traits in a panel of 244 maize hybrids. We considered two prediction scenarios: in the first one, new hybrids are predicted (CV-NH), and in the second one, partially observed hybrids are predicted (CV-POH). For both scenarios, all hybrids were characterized for omics on the platform. We observed that omics can predict both additive and non-additive genetic effects for the platform traits, resulting in much higher predictive abilities than GBLUP. It highlights their efficiency in capturing regulatory processes in relation to growth conditions. For the field traits, we observed that the additive components of omics only slightly improved predictive abilities for predicting new hybrids (CV-NH, model MegaGAO) and for predicting partially observed hybrids (CV-POH, model GAOxW-BLUP) in comparison to GBLUP. We conclude that measuring the omics in the fields would be of considerable interest in predicting productivity if the costs of omics drop significantly.

Genotyping of DNA pools identifies untapped landraces and genomic regions to develop next-generation varieties.

Landraces, that is, traditional varieties, have a large diversity that is underexploited in modern breeding. A novel DNA pooling strategy was implemented to identify promising landraces and genomic regions to enlarge the genetic diversity of modern varieties. As proof of concept, DNA pools from 156 American and European maize landraces representing 2340 individuals were genotyped with an SNP array to assess their genome-wide diversity. They were compared to elite cultivars produced across the 20th century, represented by 327 inbred lines. Detection of selective footprints between landraces of different geographic origin identified genes involved in environmental adaptation (flowering times, growth) and tolerance to abiotic and biotic stress (drought, cold, salinity). Promising landraces were identified by developing two novel indicators that estimate their contribution to the genome of inbred lines: (i) a modified Roger's distance standardized by gene diversity and (ii) the assignation of lines to landraces using supervised analysis. It showed that most landraces do not have closely related lines and that only 10 landraces, including famous landraces as Reid's Yellow Dent, Lancaster Surecrop and Lacaune, cumulated half of the total contribution to inbred lines. Comparison of ancestral lines directly derived from landraces with lines from more advanced breeding cycles showed a decrease in the number of landraces with a large contribution. New inbred lines derived from landraces with limited contributions enriched more the haplotype diversity of reference inbred lines than those with a high contribution. Our approach opens an avenue for the identification of promising landraces for pre-breeding.

Identifying QTLs involved in hybrid performance and heterotic group complementarity: new GWAS models applied to factorial and admixed diallel maize hybrid panels.

KEY MESSAGE: An original GWAS model integrating the ancestry of alleles was proposed and allowed the detection of background specific additive and dominance QTLs involved in heterotic group complementarity and hybrid performance. Maize genetic diversity is structured into genetic groups selected and improved relative to each other. This process increases group complementarity and differentiation over time and ensures that the hybrids produced from inter-group crosses exhibit high performances and heterosis. To identify loci involved in hybrid performance and heterotic group complementarity, we introduced an original association study model that disentangles allelic effects from the heterotic group origin of the alleles and compared it with a conventional additive/dominance model. This new model was applied on a factorial between Dent and Flint lines and a diallel between Dent-Flint admixed lines with two different layers of analysis: within each environment and in a multiple-environment context. We identified several strong additive QTLs for all traits, including some well-known additive QTLs for flowering time (in the region of Vgt1/2 on chromosome 8). Yield trait displayed significant non-additive effects in the diallel panel. Most of the detected Yield QTLs exhibited overdominance or, more likely, pseudo-overdominance effects. Apparent overdominance at these QTLs contributed to a part of the genetic group complementarity. The comparison between environments revealed a higher stability of additive QTL effects than non-additive ones. Several QTLs showed variations of effects according to the local heterotic group origin. We also revealed large chromosomic regions that display genetic group origin effects. Altogether, our results illustrate how admixed panels combined with dedicated GWAS modeling allow the identification of new QTLs that could not be revealed by a classical hybrid panel analyzed with traditional modeling.

Efficient ReML inference in variance component mixed models using a Min-Max algorithm.

Since their introduction in the 50's, variance component mixed models have been widely used in many application fields. In this context, ReML estimation is by far the most popular procedure to infer the variance components of the model. Although many implementations of the ReML procedure are readily available, there is still need for computational improvements due to the ever-increasing size of the datasets to be handled, and to the complexity of the models to be adjusted. In this paper, we present a Min-Max (MM) algorithm for ReML inference and combine it with several speed-up procedures. The ReML MM algorithm we present is compared to 5 state-of-the-art publicly available algorithms used in statistical genetics. The computational performance of the different algorithms are evaluated on several datasets representing different plant breeding experimental designs. The MM algorithm ranks among the top 2 methods in almost all settings and is more versatile than many of its competitors. The MM algorithm is a promising alternative to the classical AI-ReML algorithm in the context of variance component mixed models. It is available in the MM4LMM R-package.

Disentangling group specific QTL allele effects from genetic background epistasis using admixed individuals in GWAS: An application to maize flowering.

When handling a structured population in association mapping, group-specific allele effects may be observed at quantitative trait loci (QTLs) for several reasons: (i) a different linkage disequilibrium (LD) between SNPs and QTLs across groups, (ii) group-specific genetic mutations in QTL regions, and/or (iii) epistatic interactions between QTLs and other loci that have differentiated allele frequencies between groups. We present here a new genome-wide association (GWAS) approach to identify QTLs exhibiting such group-specific allele effects. We developed genetic materials including admixed progeny from different genetic groups with known genome-wide ancestries (local admixture). A dedicated statistical methodology was developed to analyze pure and admixed individuals jointly, allowing one to disentangle the factors causing the heterogeneity of allele effects across groups. This approach was applied to maize by developing an inbred "Flint-Dent" panel including admixed individuals that was evaluated for flowering time. Several associations were detected revealing a wide range of configurations of allele effects, both at known flowering QTLs (Vgt1, Vgt2 and Vgt3) and new loci. We found several QTLs whose effect depended on the group ancestry of alleles while others interacted with the genetic background. Our GWAS approach provides useful information on the stability of QTL effects across genetic groups and can be applied to a wide range of species.

The INCREASE project: Intelligent Collections of food-legume genetic resources for European agrofood systems.

Food legumes are crucial for all agriculture-related societal challenges, including climate change mitigation, agrobiodiversity conservation, sustainable agriculture, food security and human health. The transition to plant-based diets, largely based on food legumes, could present major opportunities for adaptation and mitigation, generating significant co-benefits for human health. The characterization, maintenance and exploitation of food-legume genetic resources, to date largely unexploited, form the core development of both sustainable agriculture and a healthy food system. INCREASE will implement, on chickpea (Cicer arietinum), common bean (Phaseolus vulgaris), lentil (Lens culinaris) and lupin (Lupinus albus and L. mutabilis), a new approach to conserve, manage and characterize genetic resources. Intelligent Collections, consisting of nested core collections composed of single-seed descent-purified accessions (i.e., inbred lines), will be developed, exploiting germplasm available both from genebanks and on-farm and subjected to different levels of genotypic and phenotypic characterization. Phenotyping and gene discovery activities will meet, via a participatory approach, the needs of various actors, including breeders, scientists, farmers and agri-food and non-food industries, exploiting also the power of massive metabolomics and transcriptomics and of artificial intelligence and smart tools. Moreover, INCREASE will test, with a citizen science experiment, an innovative system of conservation and use of genetic resources based on a decentralized approach for data management and dynamic conservation. By promoting the use of food legumes, improving their quality, adaptation and yield and boosting the competitiveness of the agriculture and food sector, the INCREASE strategy will have a major impact on economy and society and represents a case study of integrative and participatory approaches towards conservation and exploitation of crop genetic resources.

Querying multiple sets of P-values through composed hypothesis testing.

MOTIVATION: Combining the results of different experiments to exhibit complex patterns or to improve statistical power is a typical aim of data integration. The starting point of the statistical analysis often comes as a set of P-values resulting from previous analyses, that need to be combined flexibly to explore complex hypotheses, while guaranteeing a low proportion of false discoveries. RESULTS: We introduce the generic concept of composed hypothesis, which corresponds to an arbitrary complex combination of simple hypotheses. We rephrase the problem of testing a composed hypothesis as a classification task and show that finding items for which the composed null hypothesis is rejected boils down to fitting a mixture model and classifying the items according to their posterior probabilities. We show that inference can be efficiently performed and provide a thorough classification rule to control for type I error. The performance and the usefulness of the approach are illustrated in simulations and on two different applications. The method is scalable, does not require any parameter tuning, and provided valuable biological insight on the considered application cases. AVAILABILITY AND IMPLEMENTATION: The QCH methodology is available in the qch package hosted on CRAN. Additionally, R codes to reproduce the Einkorn example are available on the personal webpage of the first author: https://www6.inrae.fr/mia-paris/Equipes/Membres/Tristan-Mary-Huard. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Genomic prediction of hybrid performance: comparison of the efficiency of factorial and tester designs used as training sets in a multiparental connected reciprocal design for maize silage.

KEY MESSAGE: Calibrating a genomic selection model on a sparse factorial design rather than on tester designs is advantageous for some traits, and equivalent for others. In maize breeding, the selection of the candidate inbred lines is based on topcross evaluations using a limited number of testers. Then, a subset of single-crosses between these selected lines is evaluated to identify the best hybrid combinations. Genomic selection enables the prediction of all possible single-crosses between candidate lines but raises the question of defining the best training set design. Previous simulation results have shown the potential of using a sparse factorial design instead of tester designs as the training set. To validate this result, a 363 hybrid factorial design was obtained by crossing 90 dent and flint inbred lines from six segregating families. Two tester designs were also obtained by crossing the same inbred lines to two testers of the opposite group. These designs were evaluated for silage in eight environments and used to predict independent performances of a 951 hybrid factorial design. At a same number of hybrids and lines, the factorial design was as efficient as the tester designs, and, for some traits, outperformed them. All available designs were used as both training and validation set to evaluate their efficiency. When the objective was to predict single-crosses between untested lines, we showed an advantage of increasing the number of lines involved in the training set, by (1) allocating each of them to a different tester for the tester design, or (2) reducing the number of hybrids per line for the factorial design. Our results confirm the potential of sparse factorial designs for genomic hybrid breeding.

Phenomic selection in wheat breeding: prediction of the genotype-by-environment interaction in multi-environment breeding trials.

KEY MESSAGE: Phenomic prediction of wheat grain yield and heading date in different multi-environmental trial scenarios is accurate. Modelling the genotype-by-environment interaction effect using phenomic data is a potentially low-cost complement to genomic prediction. The performance of wheat cultivars in multi-environmental trials (MET) is difficult to predict because of the genotype-by-environment interactions (G × E). Phenomic selection is supposed to be efficient for modelling the G × E effect because it accounts for non-additive effects. Here, phenomic data are near-infrared (NIR) spectra obtained from plant material. While phenomic selection has recently been shown to accurately predict wheat grain yield in single environments, its accuracy needs to be investigated for MET. We used four datasets from two winter wheat breeding programs to test and compare the predictive abilities of phenomic and genomic models for grain yield and heading date in different MET scenarios. We also compared different methods to model the G × E using different covariance matrices based on spectra. On average, phenomic and genomic prediction abilities are similar in all different MET scenarios. Better predictive abilities were obtained when G × E effects were modelled with NIR spectra than without them, and it was better to use all the spectra of all genotypes in all environments for modelling the G × E. To facilitate the implementation of phenomic prediction, we tested MET designs where the NIR spectra were measured only on the genotype-environment combinations phenotyped for the target trait. Missing spectra were predicted with a weighted multivariate ridge regression. Intermediate predictive abilities for grain yield were obtained in a sparse testing scenario and for new genotypes, which shows that phenomic selection is an efficient and practicable prediction method for dealing with G × E.

Independent introductions and admixtures have contributed to adaptation of European maize and its American counterparts.

Through the local selection of landraces, humans have guided the adaptation of crops to a vast range of climatic and ecological conditions. This is particularly true of maize, which was domesticated in a restricted area of Mexico but now displays one of the broadest cultivated ranges worldwide. Here, we sequenced 67 genomes with an average sequencing depth of 18x to document routes of introduction, admixture and selective history of European maize and its American counterparts. To avoid the confounding effects of recent breeding, we targeted germplasm (lines) directly derived from landraces. Among our lines, we discovered 22,294,769 SNPs and between 0.9% to 4.1% residual heterozygosity. Using a segmentation method, we identified 6,978 segments of unexpectedly high rate of heterozygosity. These segments point to genes potentially involved in inbreeding depression, and to a lesser extent to the presence of structural variants. Genetic structuring and inferences of historical splits revealed 5 genetic groups and two independent European introductions, with modest bottleneck signatures. Our results further revealed admixtures between distinct sources that have contributed to the establishment of 3 groups at intermediate latitudes in North America and Europe. We combined differentiation- and diversity-based statistics to identify both genes and gene networks displaying strong signals of selection. These include genes/gene networks involved in flowering time, drought and cold tolerance, plant defense and starch properties. Overall, our results provide novel insights into the evolutionary history of European maize and highlight a major role of admixture in environmental adaptation, paralleling recent findings in humans.

Genomic selection efficiency and a priori estimation of accuracy in a structured dent maize panel.

KEY MESSAGE: Population structure affects genomic selection efficiency as well as the ability to forecast accuracy using standard GBLUP. Genomic prediction models usually assume that the individuals used for calibration belong to the same population as those to be predicted. Most of the a priori indicators of precision, such as the coefficient of determination (CD), were derived from those same models. But genetic structure is a common feature in plant species, and it may impact genomic selection efficiency and the ability to forecast prediction accuracy. We investigated the impact of genetic structure in a dent maize panel ("Amaizing Dent") using different scenarios including within- or across-group predictions. For a given training set size, the best accuracies were achieved when predicting individuals using a model calibrated on the same genetic group. Nevertheless, a diverse training set representing all the groups had a certain predictive efficiency for all the validation sets, and adding extra-group individuals was almost always beneficial. It underlines the potential of such a generic training set for dent maize genomic selection applications. Alternative prediction models, taking genetic structure explicitly into account, did not improve the prediction accuracy compared to GBLUP. We also investigated the ability of different indicators of precision to forecast accuracy in the within- or across-group scenarios. There was a global encouraging trend of the CD to differentiate scenarios, although there were specific combinations of target populations and traits where the efficiency of this indicator proved to be null. One hypothesis to explain such erratic performances is the impact of genetic structure through group-specific allele diversity at QTLs rather than group-specific allele effects.

Cytonuclear interactions affect adaptive traits of the annual plant Arabidopsis thaliana in the field.

Although the contribution of cytonuclear interactions to plant fitness variation is relatively well documented at the interspecific level, the prevalence of cytonuclear interactions at the intraspecific level remains poorly investigated. In this study, we set up a field experiment to explore the range of effects that cytonuclear interactions have on fitness-related traits in Arabidopsis thaliana To do so, we created a unique series of 56 cytolines resulting from cytoplasmic substitutions among eight natural accessions reflecting within-species genetic diversity. An assessment of these cytolines and their parental lines scored for 28 adaptive whole-organism phenotypes showed that a large proportion of phenotypic traits (23 of 28) were affected by cytonuclear interactions. The effects of these interactions varied from slight but frequent across cytolines to strong in some specific parental pairs. Two parental pairs accounted for half of the significant pairwise interactions. In one parental pair, Ct-1/Sha, we observed symmetrical phenotypic responses between the two nuclear backgrounds when combined with specific cytoplasms, suggesting nuclear differentiation at loci involved in cytonuclear epistasis. In contrast, asymmetrical phenotypic responses were observed in another parental pair, Cvi-0/Sha. In the Cvi-0 nuclear background, fecundity and phenology-related traits were strongly affected by the Sha cytoplasm, leading to a modified reproductive strategy without penalizing total seed production. These results indicate that natural variation in cytoplasmic and nuclear genomes interact to shape integrative traits that contribute to adaptation, thereby suggesting that cytonuclear interactions can play a major role in the evolutionary dynamics ofA. thaliana.

Sequence analysis of European maize inbred line F2 provides new insights into molecular and chromosomal characteristics of presence/absence variants.

BACKGROUND: Maize is well known for its exceptional structural diversity, including copy number variants (CNVs) and presence/absence variants (PAVs), and there is growing evidence for the role of structural variation in maize adaptation. While PAVs have been described in this important crop species, they have been only scarcely characterized at the sequence level and the extent of presence/absence variation and relative chromosomal landscape of inbred-specific regions remain to be elucidated. RESULTS: De novo genome sequencing of the French F2 maize inbred line revealed 10,044 novel genomic regions larger than 1 kb, making up 88 Mb of DNA, that are present in F2 but not in B73 (PAV). This set of maize PAV sequences allowed us to annotate PAV content and to analyze sequence breakpoints. Using PAV genotyping on a collection of 25 temperate lines, we also analyzed Linkage Disequilibrium in PAVs and flanking regions, and PAV frequencies within maize genetic groups. CONCLUSIONS: We highlight the possible role of MMEJ-type double strand break repair in maize PAV formation and discover 395 new genes with transcriptional support. Pattern of linkage disequilibrium within PAVs strikingly differs from this of flanking regions and is in accordance with the intuition that PAVs may recombine less than other genomic regions. We show that most PAVs are ancient, while some are found only in European Flint material, thus pinpointing structural features that may be at the origin of adaptive traits involved in the success of this material. Characterization of such PAVs will provide useful material for further association genetic studies in European and temperate maize.

SegCorr a statistical procedure for the detection of genomic regions of correlated expression.

BACKGROUND: Detecting local correlations in expression between neighboring genes along the genome has proved to be an effective strategy to identify possible causes of transcriptional deregulation in cancer. It has been successfully used to illustrate the role of mechanisms such as copy number variation (CNV) or epigenetic alterations as factors that may significantly alter expression in large chromosomal regions (gene silencing or gene activation). RESULTS: The identification of correlated regions requires segmenting the gene expression correlation matrix into regions of homogeneously correlated genes and assessing whether the observed local correlation is significantly higher than the background chromosomal correlation. A unified statistical framework is proposed to achieve these two tasks, where optimal segmentation is efficiently performed using dynamic programming algorithm, and detection of highly correlated regions is then achieved using an exact test procedure. We also propose a simple and efficient procedure to correct the expression signal for mechanisms already known to impact expression correlation. The performance and robustness of the proposed procedure, called SegCorr, are evaluated on simulated data. The procedure is illustrated on cancer data, where the signal is corrected for correlations caused by copy number variation. It permitted the detection of regions with high correlations linked to epigenetic marks like DNA methylation. CONCLUSIONS: SegCorr is a novel method that performs correlation matrix segmentation and applies a test procedure in order to detect highly correlated regions in gene expression.

Estimation of the relatedness coefficients from biallelic markers, application in plant mating designs.

The problem of inferring the relatedness distribution between two individuals from biallelic marker data is considered. This problem can be cast as an estimation task in a mixture model: at each marker the latent variable is the relatedness state, and the observed variable is the genotype of the two individuals. In this model, only the prior proportions are unknown, and can be obtained via ML estimation using the EM algorithm. When the markers are biallelic and the data unphased, the identifiability of the model is known not to be guaranteed. In this article, model identifiability is investigated in the case of phased data generated from a crossing design, a classical situation in plant genetics. It is shown that identifiability can be guaranteed under some conditions on the crossing design. The adapted ML estimator is implemented in an R package called Relatedness. The performance of the ML estimator is evaluated and compared to that of the benchmark moment estimator, both on simulated and real data. Compared to its competitor, the ML estimator is shown to be more robust and to provide more realistic estimates.

GEM2Net: from gene expression modeling to -omics networks, a new CATdb module to investigate Arabidopsis thaliana genes involved in stress response.

CATdb (http://urgv.evry.inra.fr/CATdb) is a database providing a public access to a large collection of transcriptomic data, mainly for Arabidopsis but also for other plants. This resource has the rare advantage to contain several thousands of microarray experiments obtained with the same technical protocol and analyzed by the same statistical pipelines. In this paper, we present GEM2Net, a new module of CATdb that takes advantage of this homogeneous dataset to mine co-expression units and decipher Arabidopsis gene functions. GEM2Net explores 387 stress conditions organized into 18 biotic and abiotic stress categories. For each one, a model-based clustering is applied on expression differences to identify clusters of co-expressed genes. To characterize functions associated with these clusters, various resources are analyzed and integrated: Gene Ontology, subcellular localization of proteins, Hormone Families, Transcription Factor Families and a refined stress-related gene list associated to publications. Exploiting protein-protein interactions and transcription factors-targets interactions enables to display gene networks. GEM2Net presents the analysis of the 18 stress categories, in which 17,264 genes are involved and organized within 681 co-expression clusters. The meta-data analyses were stored and organized to compose a dynamic Web resource.