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Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 [F.sub.5] maize testcross progenies evaluated across 12 environments in the U.S.com belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.

In Arabidopsis thaliana, significant efforts to determine the extent of genomic variation between phenotypically divergent accessions are under way, but virtually nothing is known about variation at the transcription level. We used microarrays to examine variation in transcript abundance among three inbred lines and two pairs of reciprocal [F.sub.1] hybrids of the highly self-fertilizing species Arabidopsis. Composite additive genetic effects for gene expression were estimated from pairwise comparisons of the three accessions Columbia (Col), Landsberg erecta (LEO, and Cape Verde Islands (Cvi). For the pair Col and Ler 27.0% of the 4876 genes exhibited additive genetic effects in their expression ([alpha] = 0.001) vs. 32.2 and 37.5% for Cvi with Lerand Col, respectively. Significant differential expression ranged from 32.45 down to 1.10 in fold change and typically differed by a factor of 1.56. Maternal or paternal transmission affected only a few genes, suggesting that the reciprocal effects observed in the two crosses analyzed were minimal. Dominance effects were estimated from the comparisons of hybrids with the corresponding midparent value. The percentage of genes showing dominance at the expression level in the [F.sub.1] hybrids ranged from 6.4 to 21.1% (a = 0.001). Breakdown of these numbers of genes according to the magnitude of the dominance ratio revealed heterosis for expression for on average 9% of the genes. Further advances in the genetic analysis of gene expression variation may contribute to a better understanding of its role in affecting quantitative trait variation at the phenotypic level.

Associations between markers and complex quantitative traits were investigated in a collection of 146 modern two-row spring barley cultivars, representing the current commercial germ plasm in Europe. Using 236 AFLP markers, associations between markers were found for markers as far apart as 10 cM. Subsequently, for the 146 cultivars the complex traits mean yield adaptability, (Finlay-Wilkinson slope), and stability (deviations from regression) were estimated from the analysis of variety trial data. Regression of those trails on individual marker data disclosed marker-trait associations for mean yield and yield stability. Support for identified associations was obtained from association profiles, i.e., from plots of P-values against chromosome positions. In addition, many of the associated markers were located in regions where earlier QTL were found for yield and yield components. To study the oligogenic genetic base of the traits in more detail, multiple linear regression of the traits on markers was carried out, using stepwise selection. By this procedure, 18-20 markers that accounted for 40-58% of the variation were selected. Our results indicate that association mapping approaches can be a viable alternative to classical QTL approaches based on crosses between inbred lines, especially for complex traits with costly measurements.

Construction of genetic linkage maps has become a routine step for mapping quantitative trait loci (QTL), particularly in animal and plant breeding populations. Many multiparental populations have recently been produced to increase genetic diversity and QTL mapping resolution. However, few software packages are available for map construction in these populations. In this paper, we build a general framework for the construction of genetic linkage maps from genotypic data in diploid populations, including bi- and multiparental populations, cross-pollinated (CP) populations, and breeding pedigrees. The framework is implemented as an automatic pipeline called magicMap, where the maximum multilocus likelihood approach utilizes genotypic information efficiently. We evaluate magicMap by extensive simulations and eight real datasets: one biparental, one CP, four multiparent advanced generation intercross (MAGIC), and two nested association mapping (NAM) populations, the number of markers ranging from a few hundred to tens of thousands. Not only is magicMap the only software capable of accommodating all of these designs, it is more accurate and robust to missing genotypes and genotyping errors than commonly used packages. [ABSTRACT FROM AUTHOR]

Many different types of multiparental populations have recently been produced to increase genetic diversity and resolution in QTL mapping. Low-coverage, genotyping-by-sequencing (GBS) technology has become a cost-effective tool in these populations, despite large amounts of missing data in offspring and founders. In this work, we present a general statistical framework for genotype imputation in such experimental crosses from low-coverage GBS data. Generalizing a previously developed hidden Markov model for calculating ancestral origins of offspring DNA, we present an imputation algorithm that does not require parental data and that is applicable to bi- and multiparental populations. Our imputation algorithm allows heterozygosity of parents and offspring as well as error correction in observed genotypes. Further, our approach can combine imputation and genotype calling from sequencing reads, and it also applies to called genotypes from SNP array data. We evaluate our imputation algorithm by simulated and real data sets in four different types of populations: the F2, the advanced intercross recombinant inbred lines, the multiparent advanced generation intercross, and the cross-pollinated population. Because our approach uses marker data and population design information efficiently, the comparisons with previous approaches show that our imputation is accurate at even very low (,13) sequencing depth, in addition to having accurate genotype phasing and error detection. [ABSTRACT FROM AUTHOR]

We present a general hidden Markov model framework called reconstructing ancestry blocks bit by bit (RABBIT) for reconstructing genome ancestry blocks from single-nucleotide polymorphism (SNP) array data, a required step for quantitative trait locus (QTL) mapping. The framework can be applied to a wide range of mapping populations such as the Arabidopsis multiparent advanced generation intercross (MAGIC), the mouse Collaborative Cross (CC), and the diversity outcross (DO) for both autosomes and X chromosomes if they exist. The model underlying RABBIT accounts for the joint pattern of recombination breakpoints between two homologous chromosomes and missing data and allelic typing errors in the genotype data of both sampled individuals and founders. Studies on simulated data of the MAGIC and the CC and real data of the MAGIC, the DO, and the CC demonstrate that RABBIT is more robust and accurate in reconstructing recombination bin maps than some commonly used methods. [ABSTRACT FROM AUTHOR]

The next generation of QTL (quantitative trait loci) mapping populations have been designed with multiple founders, where one to a number of generations of intercrossing are introduced prior to the inbreeding phase to increase accumulated recombinations and thus mapping resolution. Examples of such populations are Collaborative Cross (CC) in mice and Multiparent Advanced Generation Inter-Cross (MAGIC) lines in Arabidopsis. The genomes of the produced inbred lines are fine-grained random mosaics of the founder genomes. In this article, we present a novel framework for modeling ancestral origin processes along two homologous autosomal chromosomes from mapping populations, which is a major component in the reconstruction of the ancestral origins of each line for QTL mapping. We construct a general continuous time Markov model for ancestral origin processes, where the rate matrix is deduced from the expected densities of various types of junctions (recombination breakpoints). The model can be applied to monoecious populations with or without self-fertilizations and to dioecious populations with two separate sexes. The analytic expressions for map expansions and expected junction densities are obtained for mapping populations that have stage-wise constant mating schemes, such as CC and MAGIC. Our studies on the breeding design of MAGIC populations show that the intercross mating schemes do not matter much for large population size and that the overall expected junction density, and thus map resolution, are approximately proportional to the inverse of the number of founders. [ABSTRACT FROM AUTHOR]

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.? [ABSTRACT FROM AUTHOR]