Marcos Malosetti

A Mixed-Model Approach to Association Mapping Using Pedigree Information With an Illustration of Resistance to Phytophthora infestans in Potato

Association or linkage disequilibrium (LD)-based mapping strategies are receiving increased attention for the identification of quantitative trait loci (QTL) in plants as an alternative to more traditional, purely linkage-based approaches. An attractive property of association approaches is that they do not require specially designed crosses between inbred parents, but can be applied to collections of genotypes with arbitrary and often unknown relationships between the genotypes. A less obvious additional attractive property is that association approaches offer possibilities for QTL identification in crops with hard to model segregation patterns. The availability of candidate genes and targeted marker systems facilitates association approaches, as will appropriate methods of analysis. We propose an association mapping approach based on mixed models with attention to the incorporation of the relationships between genotypes, whether induced by pedigree, population substructure, or otherwise. Furthermore, we emphasize the need to pay attention to the environmental features of the data as well, i.e., adequate representation of the relations among multiple observations on the same genotypes. We illustrate our modeling approach using 25 years of Dutch national variety list data on late blight resistance in the genetically complex crop of potato. As markers, we used nucleotide binding-site markers, a specific type of marker that targets resistance or resistance-analog genes. To assess the consistency of QTL identified by our mixed-model approach, a second independent data set was analyzed. Two markers were identified that are potentially useful in selection for late blight resistance in potato.

A multi-trait multi-environment QTL mixed model with an application to drought and nitrogen stress trials in maize (Zea mays L.)

Despite QTL mapping being a routine procedure in plant breeding, approaches that fully exploit data from multi-trait multi-environment (MTME) trials are limited. Mixed models have been proposed both for multi-trait QTL analysis and multi-environment QTL analysis, but these approaches break down when the number of traits and environments increases. We present models for an efficient QTL analysis of MTME data with mixed models by reducing the dimensionality of the genetic variance–covariance matrix by structuring this matrix using direct products of relatively simple matrices representing variation in the trait and environmental dimension. In the context of MTME data, we address how to model QTL by environment interactions and the genetic basis of heterogeneity of variance and correlations between traits and environments. We illustrate our approach with an example including five traits across eight stress trials in CIMMYT maize. We detected 36 QTLs affecting yield, anthesis-silking interval, male flowering, ear number, and plant height in maize. Our approach does not require specialised software as it can be implemented in any statistical package with mixed model facilities.

Mixed models including environmental covariables for studying QTL by environment interaction

The study of the phenotypic responses of a set of genotypes in their dependence on the environment has always been an important area of research in plant breeding. Non-parallelism of those responses is called genotype by environment interaction (GEI). GEI especially affects plant breeding strategies, when the phenotypic superiority of genotypes changes in relation to the environment. The study of the genetic basis of GEI involves the modelling of quantitative trait locus (QTL) expression in its dependence on environmental factors. We present a modelling framework for studying the interaction between QTL and environment, using regression models in a mixed model context. We integrate regression models for QTL main effect expression with factorial regression models for genotype by environment interaction, and, in addition, take care to model adequately the residual genetic variation. Factorial regression models describe GEI as differential genotypic sensitivity to one or more environmental covariables. We show how factorial regression models can be generalized to make also QTL expression dependent on environmental covariables. As an illustrative example, we reanalyzed yield data from the North American Barley Genome Project. QTL by environment interaction for yield, as identified at the 2H chromosome could be described as QTL expression in relation to the magnitude of the temperature range during heading.

The statistical analysis of multi-environment data: modeling genotype-by-environment interaction and its genetic basis.

Genotype-by-environment interaction (GEI) is an important phenomenon in plant breeding. This paper presents a series of models for describing, exploring, understanding, and predicting GEI. All models depart from a two-way table of genotype by environment means. First, a series of descriptive and explorative models/approaches are presented: Finlay–Wilkinson model, AMMI model, GGE biplot. All of these approaches have in common that they merely try to group genotypes and environments and do not use other information than the two-way table of means. Next, factorial regression is introduced as an approach to explicitly introduce genotypic and environmental covariates for describing and explaining GEI. Finally, QTL modeling is presented as a natural extension of factorial regression, where marker information is translated into genetic predictors. Tests for regression coefficients corresponding to these genetic predictors are tests for main effect QTL expression and QTL by environment interaction (QEI). QTL models for which QEI depends on environmental covariables form an interesting model class for predicting GEI for new genotypes and new environments. For realistic modeling of genotypic differences across multiple environments, sophisticated mixed models are necessary to allow for heterogeneity of genetic variances and correlations across environments. The use and interpretation of all models is illustrated by an example data set from the CIMMYT maize breeding program, containing environments differing in drought and nitrogen stress. To help readers to carry out the statistical analyses, GenStat® programs, 15th Edition and Discovery® version, are presented as “Appendix.”

Genotype x environment interaction QTL mapping in plants: lessons from Arabidopsis

Plant growth and development are influenced by the genetic composition of the plant (G), the environment (E), and the interaction between them (G×E). To produce suitable genotypes for multiple environments, G×E should be accounted for and assessed in plant-breeding programs. Here, we review the genetic basis of G×E and its consequence for quantitative trait loci (QTL) mapping in biparental and genome-wide association (GWA) mapping populations. We also consider the implications of G×E for understanding plant fitness trade-offs and evolutionary ecology.

Statistical models for genotype by environment data: from conventional ANOVA models to eco-physiological QTL models

To study the performance of genotypes under different growing conditions, plant breeders evaluate their germplasm in multi-environment trials. These trials produce genotype × environment data. We present statistical models for the analysis of such data that differ in the extent to which additional genetic, physiological, and environmental information is incorporated into the model formulation. The simplest model in our exposition is the additive 2-way analysis of variance model, without genotype × environment interaction, and with parameters whose interpretation depends strongly on the set of included genotypes and environments. The most complicated model is a synthesis of a multiple quantitative trait locus (QTL) model and an eco-physiological model to describe a collection of genotypic response curves. Between those extremes, we discuss linear-bilinear models, whose parameters can only indirectly be related to genetic and physiological information, and factorial regression models that allow direct incorporation of explicit genetic, physiological, and environmental covariables on the levels of the genotypic and environmental factors. Factorial regression models are also very suitable for the modelling of QTL main effects and QTL × environment interaction. Our conclusion is that statistical and physiological models can be fruitfully combined for the study of genotype × environment interaction.

QTL methodology for response curves on the basis of non-linear mixed models, with an illustration to senescence in potato

The improvement of quantitative traits in plant breeding will in general benefit from a better understanding of the genetic basis underlying their development. In this paper, a QTL mapping strategy is presented for modelling the development of phenotypic traits over time. Traditionally, crop growth models are used to study development. We propose an integration of crop growth models and QTL models within the framework of non-linear mixed models. We illustrate our approach with a QTL model for leaf senescence in a diploid potato cross. Assuming a logistic progression of senescence in time, two curve parameters are modelled, slope and inflection point, as a function of QTLs. The final QTL model for our example data contained four QTLs, of which two affected the position of the inflection point, one the senescence progression-rate, and a final one both inflection point and rate.

Marker-Based Estimation of Heritability in Immortal Populations

Heritability is a central parameter in quantitative genetics, from both an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within- and between-genotype variability. This approach estimates broad-sense heritability and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker-based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human genetics but are rarely reported for plant traits. A major obstacle is that current methodology and software assume a single phenotypic value per genotype, hence requiring genotypic means. An alternative that we propose here is to use mixed models at the individual plant or plot level. Using statistical arguments, simulations, and real data we investigate the feasibility of both approaches and how these affect genomic prediction with the best linear unbiased predictor and genome-wide association studies. Heritability estimates obtained from genotypic means had very large standard errors and were sometimes biologically unrealistic. Mixed models at the individual plant or plot level produced more realistic estimates, and for simulated traits standard errors were up to 13 times smaller. Genomic prediction was also improved by using these mixed models, with up to a 49% increase in accuracy. For genome-wide association studies on simulated traits, the use of individual plant data gave almost no increase in power. The new methodology is applicable to any complex trait where multiple replicates of individual genotypes can be scored. This includes important agronomic crops, as well as bacteria and fungi.

Studying the genetic basis of drought tolerance in sorghum by managed stress trials and adjustments for phenological and plant height differences

Managed environments in the form of well watered and water stressed trials were performed to study the genetic basis of grain yield and stay green in sorghum with the objective of validating previously detected QTL. As variations in phenology and plant height may influence QTL detection for the target traits, QTL for flowering time and plant height were introduced as cofactors in QTL analyses for yield and stay green. All but one of the flowering time QTL were detected near yield and stay green QTL. Similar co-localization was observed for two plant height QTL. QTL analysis for yield, using flowering time/plant height cofactors, led to yield QTL on chromosomes 2, 3, 6, 8 and 10. For stay green, QTL on chromosomes 3, 4, 8 and 10 were not related to differences in flowering time/plant height. The physical positions for markers in QTL regions projected on the sorghum genome suggest that the previously detected plant height QTL, Sb-HT9-1, and Dw2, in addition to the maturity gene, Ma5, had a major confounding impact on the expression of yield and stay green QTL. Co-localization between an apparently novel stay green QTL and a yield QTL on chromosome 3 suggests there is potential for indirect selection based on stay green to improve drought tolerance in sorghum. Our QTL study was carried out with a moderately sized population and spanned a limited geographic range, but still the results strongly emphasize the necessity of corrections for phenology in QTL mapping for drought tolerance traits in sorghum.

Genome-wide association mapping of frost tolerance in barley ( Hordeum vulgare L.)

BackgroundFrost tolerance is a key trait with economic and agronomic importance in barley because it is a major component of winter hardiness, and therefore limits the geographical distribution of the crop and the effective transfer of quality traits between spring and winter crop types. Three main frost tolerance QTL (Fr-H1, Fr-H2 and Fr-H3) have been identified from bi-parental genetic mapping but it can be argued that those mapping populations only capture a portion of the genetic diversity of the species. A genetically broad dataset consisting of 184 genotypes, representative of the barley gene pool cultivated in the Mediterranean basin over an extended time period, was genotyped with 1536 SNP markers. Frost tolerance phenotype scores were collected from two trial sites, Foradada (Spain) and Fiorenzuola (Italy) and combined with the genotypic data in genome wide association analyses (GWAS) using Eigenstrat and kinship approaches to account for population structure.ResultsGWAS analyses identified twelve and seven positive SNP associations at Foradada and Fiorenzuola, respectively, using Eigenstrat and six and four, respectively, using kinship. Linkage disequilibrium analyses of the significant SNP associations showed they are genetically independent. In the kinship analysis, two of the significant SNP associations were tightly linked to the Fr-H2 and HvBmy loci on chromosomes 5H and 4HL, respectively. The other significant kinship associations were located in genomic regions that have not previously been associated with cold stress.ConclusionsHaplotype analysis revealed that most of the significant SNP loci are fixed in the winter or facultative types, while they are freely segregating within the un-adapted spring barley genepool. Although there is a major interest in detecting new variation to improve frost tolerance of available winter and facultative types, from a GWAS perspective, working within the un-adapted spring germplasm pool is an attractive alternative strategy which would minimize statistical issues, simplify the interpretation of the data and identify phenology independent genetic determinants of frost tolerance.