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.

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.

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.

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.

Approximate thresholds of interval mapping tests for QTL detection.

A general method is proposed for calculating approximate thresholds of interval mapping tests for quantitative trait loci (QTL) detection. Simulation results show that this method, when applied to backcross and F2 populations, gives good approximations and is useful for any situation. Programs which calculate these thresholds for backcross, recombinant inbreds and F2 for any given level and any chromosome with any given distribution of codominant markers were written in Fortran 77 and are available under request. The approach presented here could be used to obtain, after suitable calculations, thresholds for most segregating populations used in QTL mapping experiments.

Constructing confidence intervals for QTL location.

We describe a method for constructing the confidence interval of the QTL location parameter. This method is developed in the local asymptotic framework, leading to a linear model at each position of the putative QTL. The idea is to construct a likelihood ratio test, using statistics whose asymptotic distribution does not depend on the nuisance parameters and in particular on the effect of the QTL. We show theoretical properties of the confidence interval built with this test, and compare it with the classical confidence interval using simulations. We show in particular, that our confidence interval has the correct probability of containing the true map location of the QTL, for almost all QTLs, whereas the classical confidence interval can be very biased for QTLs having small effect.

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.

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.

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.

The genetic basis of heterosis: multiparental quantitative trait loci mapping reveals contrasted levels of apparent overdominance among traits of agronomical interest in maize (Zea mays L.).

Understanding the genetic bases underlying heterosis is a major issue in maize (Zea mays L.). We extended the North Carolina design III (NCIII) by using three populations of recombinant inbred lines derived from three parental lines belonging to different heterotic pools, crossed with each parental line to obtain nine families of hybrids. A total of 1253 hybrids were evaluated for grain moisture, silking date, plant height, and grain yield. Quantitative trait loci (QTL) mapping was carried out on the six families obtained from crosses to parental lines following the "classical" NCIII method and with a multiparental connected model on the global design, adding the three families obtained from crosses to the nonparental line. Results of the QTL detection highlighted that most of the QTL detected for grain yield displayed apparent overdominance effects and limited differences between heterozygous genotypes, whereas for grain moisture predominance of additive effects was observed. For plant height and silking date results were intermediate. Except for grain yield, most of the QTL identified showed significant additive-by-additive epistatic interactions. High correlation observed between heterosis and the heterozygosity of hybrids at markers confirms the complex genetic basis and the role of dominance in heterosis. An important proportion of QTL detected were located close to the centromeres. We hypothesized that the lower recombination in these regions favors the detection of (i) linked QTL in repulsion phase, leading to apparent overdominance for heterotic traits and (ii) linked QTL in coupling phase, reinforcing apparent additive effects of linked QTL for the other traits.

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.

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.

Optimal structure of protocol designs for building genetic linkage maps in livestock.

We investigated protocol designs for gene mapping in livestock. The optimization of the population structure was based on the empirical variance of the recombination rate estimator. We concluded that a mixture of half-sib and full-sib families is preferred to half-sib families; a knowledge of parental phases does not improve the quality of the estimation for typical livestock families with five offspring or more; and measurements of the genotype of the mates in half-sib families are not useful. Graphs and algebraic approximations for the practical choice of family size and structure are given.

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.