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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Combined phenomic and genomic approaches are required to evaluate the margin of progress of breeding strategies. Here, we analyze 65 years of genetic progress in maize yield, which was similar (101 kg ha−1 year−1) across most frequent environmental scenarios in the European growing area. Yield gains were linked to physiologically simple traits (plant phenology and architecture) which indirectly affected reproductive development and light interception in all studied environments, marked by significant genomic signatures of selection. Conversely, studied physiological processes involved in stress adaptation remained phenotypically unchanged (e.g. stomatal conductance and growth sensitivity to drought) and showed no signatures of selection. By selecting for yield, breeders indirectly selected traits with stable effects on yield, but not physiological traits whose effects on yield can be positive or negative depending on environmental conditions. Because yield stability under climate change is desirable, novel breeding strategies may be needed for exploiting alleles governing physiological adaptive traits. Phenomic and genomic approaches are required to evaluate the progress of breeding strategies. Here, the authors analyse 65 years of genetic progress in maize, showing that breeders have selected traits with stable effects on yield whereas not for adaptive traits key for climate change adaptation. [ABSTRACT FROM AUTHOR]

Key message: Collaborative diversity panels and genomic prediction seem relevant to identify and harness genetic resources for polygenic trait-specific enrichment of elite germplasms. In plant breeding, genetic diversity is important to maintain the pace of genetic gain and the ability to respond to new challenges in a context of climatic and social expectation changes. Many genetic resources are accessible to breeders but cannot all be considered for broadening the genetic diversity of elite germplasm. This study presents the use of genomic predictions trained on a collaborative diversity panel, which assembles genetic resources and elite lines, to identify resources to enrich an elite germplasm. A maize collaborative panel (386 lines) was considered to estimate genome-wide marker effects. Relevant predictive abilities (0.40–0.55) were observed on a large population of private elite materials, which supported the interest of such a collaborative panel for diversity management perspectives. Grain-yield estimated marker effects were used to select a donor that best complements an elite recipient at individual loci or haplotype segments, or that is expected to give the best-performing progeny with the elite. Among existing and new criteria that were compared, some gave more weight to the donor–elite complementarity than to the donor value, and appeared more adapted to long-term objective. We extended this approach to the selection of a set of donors complementing an elite population. We defined a crossing plan between identified donors and elite recipients. Our results illustrated how collaborative projects based on diversity panels including both public resources and elite germplasm can contribute to a better characterization of genetic resources in view of their use to enrich elite germplasm. [ABSTRACT FROM AUTHOR]

Key message: Silage quality traits of maize hybrids between the Dent and Flint heterotic groups mostly involved QTL specific of each parental group, some of them showing unfavorable pleiotropic effects on yield. Maize (Zea mays L.) is commonly used as silage for cattle feeding in Northern Europe. In addition to biomass production, improving whole-plant digestibility is a major breeding objective. To identify loci involved in the general (GCA, parental values) and specific combining ability (SCA, cross-specific value) components of hybrid value, we analyzed an incomplete factorial design of 951 hybrids obtained by crossing inbred lines issued from two multiparental connected populations, each specific to one of the heterotic groups used for silage in Europe ("Dent" and "Flint"). Inbred lines were genotyped for approximately 20K single nucleotide polymorphisms, and hybrids were phenotyped in eight environments for seven silage quality traits measured by near-infrared spectroscopy, biomass yield and precocity (partly analyzed in a previous study). We estimated variance components for GCA and SCA and their interaction with environment. We performed QTL detection using different models adapted to this hybrid population. Strong family effects and a predominance of GCA components compared to SCA were found for all traits. In total, 230 QTL were detected, with only two showing SCA effects significant at the whole-genome level. More than 80% of GCA QTL were specific of one heterotic group. QTL explained individually less than 5% of the phenotypic variance. QTL co-localizations and correlation between QTL effects of quality and productivity traits suggest at least partial pleiotropic effects. This work opens new prospects for improving maize hybrid performances for both biomass productivity and quality accounting for complementarities between heterotic groups. [ABSTRACT FROM AUTHOR]

Key message: We review and propose easily implemented and affordable indicators to assess the genetic diversity and the potential of a breeding population and propose solutions for its long-term management. Successful plant breeding programs rely on balanced efforts between short-term goals to develop competitive cultivars and long-term goals to improve and maintain diversity in the genetic pool. Indicators of the sustainability of response to selection in breeding pools are of key importance in this context. We reviewed and proposed sets of indicators based on temporal phenotypic and genotypic data and applied them on an early maize grain program implying two breeding pools (Dent and Flint) selected in a reciprocal manner. Both breeding populations showed a significant positive genetic gain summing up to 1.43 qx/ha/year but contrasted evolutions of genetic variance. Advances in high-throughput genotyping permitted the identification of regions of low diversity, mainly localized in pericentromeric regions. Observed changes in genetic diversity were multiple, reflecting a complex breeding system. We estimated the impact of linkage disequilibrium (LD) and of allelic diversity on the additive genetic variance at a genome-wide and chromosome-wide scale. Consistently with theoretical expectation under directional selection, we found a negative contribution of LD to genetic variance, which was unevenly distributed between chromosomes. This suggests different chromosome selection histories and underlines the interest to recombine specific chromosome regions. All three sets of indicators valorize in house data and are easy to implement in the era of genomic selection in every breeding program. [ABSTRACT FROM AUTHOR]

Key message: Population structure affects genomic selection efficiency as well as the ability to forecast accuracy using standard GBLUP.Abstract: 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. [ABSTRACT FROM AUTHOR]

Key message : Genotyping by sequencing is suitable for analysis of global diversity in maize. We showed the distinctiveness of flint maize inbred lines of interest to enrich the diversity of breeding programs. Abstract: Genotyping-by-sequencing (GBS) is a highly cost-effective procedure that permits the analysis of large collections of inbred lines. We used it to characterize diversity in 1191 maize flint inbred lines from the INRA collection, the European Cornfed association panel, and lines recently derived from landraces. We analyzed the properties of GBS data obtained with different imputation methods, through comparison with a 50 K SNP array. We identified seven ancestral groups within the Flint collection (dent, Northern flint, Italy, Pyrenees-Galicia, Argentina, Lacaune, Popcorn) in agreement with breeding knowledge. Analysis highlighted many crosses between different origins and the improvement of flint germplasm with dent germplasm. We performed association studies on different agronomic traits, revealing SNPs associated with cob color, kernel color, and male flowering time variation. We compared the diversity of both our collection and the USDA collection which has been previously analyzed by GBS. The population structure of the 4001 inbred lines confirmed the influence of the historical inbred lines (B73, A632, Oh43, Mo17, W182E, PH207, and Wf9) within the dent group. It showed distinctly different tropical and popcorn groups, a sweet-Northern flint group and a flint group sub-structured in Italian and European flint (Pyrenees-Galicia and Lacaune) groups. Interestingly, we identified several selective sweeps between dent, flint, and tropical inbred lines that co-localized with SNPs associated with flowering time variation. The joint analysis of collections by GBS offers opportunities for a global diversity analysis of maize inbred lines. [ABSTRACT FROM AUTHOR]

Transposable elements are the major component of the maize genome and presumably highly polymorphic yet they have not been used in population genetics and association analyses. Using the Transposon Display method, we isolated and converted into PCR-based markers 33 Miniature Inverted Repeat Transposable Elements (MITE) polymorphic insertions. These polymorphisms were genotyped on a population-based sample of 26 American landraces for a total of 322 plants. Genetic diversity was high and partitioned within and among landraces. The genetic groups identified using Bayesian clustering were in agreement with published data based on SNPs and SSRs, indicating that MITE polymorphisms reflect maize genetic history. To explore the contribution of MITEs to phenotypic variation, we undertook an association mapping approach in a panel of 367 maize lines phenotyped for 26 traits. We found a highly significant association between the marker ZmV1- 9, on chromosome 1, and male flowering time. The variance explained by this association is consistent with a flowering delay of +123 degree-days. This MITE insertion is located at only 289 nucleotides from the 3′ end of a Cytochrome P450-like gene, a region that was never identified in previous association mapping or QTL surveys. Interestingly, we found (i) a non-synonymous mutation located in the exon 2 of the gene in strong linkage disequilibrium with the MITE polymorphism, and (ii) a perfect sequence homology between the MITE sequence and a maize siRNA that could therefore potentially interfere with the expression of the Cytochrome P450-like gene. Those two observations among others offer exciting perspectives to validate functionally the role of this region on phenotypic variation. [ABSTRACT FROM AUTHOR]

Maize ( Zea mays L. ssp. mays) was domesticated from one wild species ancestor, the Balsas teosinte ( Zea mays ssp. parviglumis) about 9000 years ago. Higher levels of gene diversity are found in teosinte taxa compared to maize, following domestication and selection bottlenecks. Diversity in maize can be increased via gene flow from teosinte, which has certainly occurred from various taxa, but the rate of flow from different teosinte taxa and the final impact on maize evolution has been difficult to measure. One hundred populations from six Zea taxa, both domesticated (maize) and wild (teosinte), including domesticated landraces from Asia, Africa, and the Americas, were genotyped with 17 SSR markers using 15 individuals per population. Overall levels of diversity were high, and populations could be distinguished based on markers. Relationships between populations followed most published reports, or can now help resolve previously conflicting reports. Gene flow into maize from different teosinte groups, and gene flow between different teosintes, was estimated. Evidence for contributions from the Balsas teosintes and from Chalco teosintes ( Z. mays ssp. mexicana) to the maize gene pool was found, as well as from Chalco into ssp. mexicana race “Durango” and Z. mays ssp. huehuetenengensis. These contributions are almost certainly the result of post-domestication (and ongoing) exchanges. This information must give more impetus to in situ conservation of teosinte species, and use of these teosintes to continue to direct the evolution of maize, especially in response to new diseases, insect pests, and other biotic and abiotic stresses. [ABSTRACT FROM AUTHOR]

ociation 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. [ABSTRACT FROM AUTHOR]

Many studies already investigated marker-assisted selection (MAS) efficiency but mainly in biparental populations. Connected multiparental populations address a broader diversity and confer a gain of power for QTL detection which must be beneficial for MAS. Our objective was to compare multiparental connected designs to biparental populations taken separately for MAS and phenotypic selection. We first detected QTL for flowering time and grain yield in an experimental maize design involving four parental inbred lines crossed to produce six different biparental populations and confirmed the advantage of multiparental connected designs over biparental populations for QTL detection. Based on these results we performed stochastic simulations to evaluate the expected efficiency of four generations of MAS and phenotypic selection. Different parameters were considered: trait heritability, genetic architecture and whether QTL were assumed to be known or have to be detected. Genetic gains were higher in the multiparental design than on average over the biparental populations considered separately, especially when favourable alleles were equally distributed among parental lines. When QTL detection was included in the simulation process, we found that type I error risk considered for declaring QTL as significant should be adapted to the design. Type I error risks leading to the best response were higher for the biparental populations than for the multiparental design. Besides addressing a broader diversity, multiparental designs increase the power of QTL detection, which reinforces their superiority over biparental designs for MAS. Application of MAS to multiparental designs therefore appears promising to accelerate genetic gain in plant breeding programs. [ABSTRACT FROM AUTHOR]

Only a few mutations affecting flowering time have been detected in maize. We analyzed a spontaneous early mutation, vgt-f7p, which appeared during production of the inbred line F7. This mutation shortens the time from planting to flowering by about 100 growing degree days (GDD), and reduces the number of nodes. It therefore seems to affect the timing of meristem differentiation from a vegetative to a reproductive state. It was mapped to a 6 cM confidence interval on chromosome 8, using a QTL mapping approach. QTL analysis of a mapping population generated by crossing the mutant F7 line (F7p) and the Gaspé flint population showed that vgt-f7p is probably allelic to vgt1, a QTL described in previous studies, and affects earliness more strongly than the Gaspé allele at vgt1. Global analysis of the QTL in the region suggested that there may be two consensus QTL, vgt1 and vgt2. These two QTL have contrasting allelic effects: rare alleles conferring extremely early flowering at vgt1 vs. greater diversity and milder effects at locus vgt2. Finally, detailed syntenic analysis showed that the vgt1 region displays a highly conserved duplicated region on chromosome 6, which also plays an important role in maize flowering time variation. The cloning of vgt1 should, therefore, also facilitate the analysis of the molecular basis of variation due to this second region. [ABSTRACT FROM AUTHOR]

A population of 300 F3:4 lines derived from the cross between maize inbred lines F2 and F252 was evaluated for testcross value in a large range of environmental conditions (11 different locations in 2 years: 1995 and 1996) in order to study (1) the magnitude of genotype × environment and (2) the stability of quantitative trait loci (QTL) effects. Several agronomic traits were measured: dry grain yield (DGY), kernel weight, average number of kernels per plant, silking date (SD) and grain moisture at harvest. A large genotype × environment interaction was found, particularly for DGY. A hierarchical classification of trials and an additive main effects and multiplicative interaction (AMMI) model were carried out. Both methods led to the conclusion that trials could be partitioned into three groups consistent with (1) the year of experiment and (2) the water availability (irrigated vs non-irrigated) for the trials sown in 1995. QTL detection was carried out for all the traits in the different groups of trials. Between 9 and 15 QTL were detected for each trait. QTL × group and QTL × trial effects were tested and proved significant for a large proportion of QTL. QTL detection was also performed on coordinates on the first two principal components (PC) of the AMMI model. PC QTL were generally detected in areas where QTL × group and QTL × trial interactions were significant. A region located on chromosome 8 near an SD QTL seemed to play a key role in DGY stability. Our results confirm the key role of water availability and flowering earliness on grain yield stability in maize. [ABSTRACT FROM AUTHOR]

Molecular markers bring new information on the determinism of trait variation and the organisation of genetic diversity within plant species of agricultural interest. We review here how this information can be used to increase the efficiency of plant breeding programs, considering both theoretical analyses and recent experimental data. Use of mapping information to assemble alleles of interest is discussed first, considering an increasing complexity in trait determinism and its consequences on the breeding schemes. Experimental data now confirm the efficiency of these approaches. They call however, for (i) a better modelling of phenotype determinism, to better anticipate the final effect of marker assisted selection and (ii) studies that would address trait variation determinism within a broad diversity, to increase the probability to identify alleles of key interest and identify stable marker-trait associations. Recent promising developments in genetic diversity analysis are discussed with respect to these last objectives. [ABSTRACT FROM AUTHOR]

We analyzed the variability of a large maize ( Zea mays L.) collection of152 tropical populations for photoperiod sensitivity and grain productivityunder long-day conditions to investigate their potential adaptation to temperateconditions. A multilocal experimental design was used: one location withshort-day conditions (Guadeloupe), one location with medium-day conditions (latesowing in the south of France) and two locations with long-day conditions (earlysowing in both the North and South of France). The photoperiod sensitivity wasestimated by the slope of the regression of thermal time from sowing to 50%anthesis on photoperiod. We found highly significant effects of latitude andaltitude of the collecting site of the population on photoperiod sensitivity anda significant but small interaction between these two factors. Populationsoriginated from low altitudes and low latitudes are highly sensitive tophotoperiod, whereas highland populations never display a high photoperiodsensitivity, whatever the latitude of origin. Grain productivity under long-dayconditions was not highly correlated with photoperiod sensitivity. Andeanpopulations were little sensitive to photoperiod and exhibited poor grainproduction under long-day conditions. In contrast, some populations from theCaribbean such as populations from Cuban Flint and Early Caribbean racesexhibited a good grain production although sensitive to photoperiod. The goodadaptation of some Caribbean material to temperate conditions is consistent withthe hypothesis of the successful introduction of Caribbean germplasm in southernregions of the Old World. [ABSTRACT FROM AUTHOR]

Numerous studies have aimed at assessing the relationships between (i) distances computed from phenotypic data, (ii) distances computed from marker data and (iii) heterosis, for pairs of individuals or populations. The conflicting results obtained illustrate that these relationships are far from simple. In this paper, we investigate the effect on these relationships of (i) the polygenic inheritance of phenotypic traits and (ii) the structure of linkage disequilibrium between genetic markers and the loci involved in the variation of quantitative traits (QTLs). Both theoretical and experimental results showed that the relationship between marker distances and phenotypic distances computed from quantitative traits displays a triangular shape: low marker distances are systematically associated with low phenotypic distances, whereas high marker distances correspond to either low or high phenotypic distances. Because of this property, the linear coefficient of correlation between both distances decreases as the number of QTLs involved in the variation of the traits considered for phenotypic distance computation increases. Similar properties are expected for the relationship between heterosis and phenotypic distances. [ABSTRACT FROM AUTHOR]