Multiple Quantitative Trait Analysis Using Bayesian Networks

Models for genome-wide prediction and association studies usually target a single phenotypic trait. However, in animal and plant genetics it is common to record information on multiple phenotypes for each individual that will be genotyped. Modeling traits individually disregards the fact that they are most likely associated due to pleiotropy and shared biological basis, thus providing only a partial, confounded view of genetic effects and phenotypic interactions. In this article we use data from a Multiparent Advanced Generation Inter-Cross (MAGIC) winter wheat population to explore Bayesian networks as a convenient and interpretable framework for the simultaneous modeling of multiple quantitative traits. We show that they are equivalent to multivariate genetic best linear unbiased prediction (GBLUP) and that they are competitive with single-trait elastic net and single-trait GBLUP in predictive performance. Finally, we discuss their relationship with other additive-effects models and their advantages in inference and interpretation. MAGIC populations provide an ideal setting for this kind of investigation because the very low population structure and large sample size result in predictive models with good power and limited confounding due to relatedness.     

Linkage Disequilibrium with Linkage Analysis of Multiline Crosses Reveals Different Multiallelic QTL for Hybrid Performance in the Flint and Dent Heterotic Groups of Maize

Multiparental designs combined with dense genotyping of parents have been proposed as a way to increase the diversity and resolution of quantitative trait loci (QTL) mapping studies, using methods combining linkage disequilibrium information with linkage analysis (LDLA). Two new nested association mapping designs adapted to European conditions were derived from the complementary dent and flint heterotic groups of maize (Zea mays L.). Ten biparental dent families (N = 841) and 11 biparental flint families (N = 811) were genotyped with 56,110 single nucleotide polymorphism markers and evaluated as test crosses with the central line of the reciprocal design for biomass yield, plant height, and precocity. Alleles at candidate QTL were defined as (i) parental alleles, (ii) haplotypic identity by descent, and (iii) single-marker groupings. Between five and 16 QTL were detected depending on the model, trait, and genetic group considered. In the flint design, a major QTL (R² = 27%) with pleiotropic effects was detected on chromosome 10, whereas other QTL displayed milder effects (R² < 10%). On average, the LDLA models detected more QTL but generally explained lower percentages of variance, consistent with the fact that most QTL display complex allelic series. Only 15% of the QTL were common to the two designs. A joint analysis of the two designs detected between 15 and 21 QTL for the five traits. Of these, between 27 for silking date and 41% for tasseling date were significant in both groups. Favorable allelic effects detected in both groups open perspectives for improving biomass production.     

Efficiently Tracking Selection in a Multiparental Population: The Case of Earliness in Wheat

Multiparental populations are innovative tools for fine mapping large numbers of loci. Here we explored the application of a wheat Multiparent Advanced Generation Inter-Cross (MAGIC) population for QTL mapping. This population was created by 12 generations of free recombination among 60 founder lines, following modification of the mating system from strict selfing to strict outcrossing using the ms1b nuclear male sterility gene. Available parents and a subset of 380 SSD lines of the resulting MAGIC population were phenotyped for earliness and genotyped with the 9K i-Select SNP array and additional markers in candidate genes controlling heading date. We demonstrated that 12 generations of strict outcrossing rapidly and drastically reduced linkage disequilibrium to very low levels even at short map distances and also greatly reduced the population structure exhibited among the parents. We developed a Bayesian method, based on allelic frequency, to estimate the contribution of each parent in the evolved population. To detect loci under selection and estimate selective pressure, we also developed a new method comparing shifts in allelic frequency between the initial and the evolved populations due to both selection and genetic drift with expectations under drift only. This evolutionary approach allowed us to identify 26 genomic areas under selection. Using association tests between flowering time and polymorphisms, 6 of these genomic areas appeared to carry flowering time QTL, 1 of which corresponds to Ppd-D1, a major gene involved in the photoperiod sensitivity. Frequency shifts at 4 of 6 areas were consistent with earlier flowering of the evolved population relative to the initial population. The use of this new outcrossing wheat population, mixing numerous initial parental lines through multiple generations of panmixia, is discussed in terms of power to detect genes under selection and association mapping. Furthermore we provide new statistical methods for use in future analyses of multiparental populations.     

Genetic Regulation of Zfp30, CXCL1, and Neutrophilic Inflammation in Murine Lung

Allergic asthma is a complex disease characterized in part by granulocytic inflammation of the airways. In addition to eosinophils, neutrophils (PMN) are also present, particularly in cases of severe asthma. We sought to identify the genetic determinants of neutrophilic inflammation in a mouse model of house dust mite (HDM)-induced asthma. We applied an HDM model of allergic asthma to the eight founder strains of the Collaborative Cross (CC) and 151 incipient lines of the CC (preCC). Lung lavage fluid was analyzed for PMN count and the concentration of CXCL1, a hallmark PMN chemokine. PMN and CXCL1 were strongly correlated in preCC mice. We used quantitative trait locus (QTL) mapping to identify three variants affecting PMN, one of which colocalized with a QTL for CXCL1 on chromosome (Chr) 7. We used lung eQTL data to implicate a variant in the gene Zfp30 in the CXCL1/PMN response. This genetic variant regulates both CXCL1 and PMN by altering Zfp30 expression, and we model the relationships between the QTL and these three endophenotypes. We show that Zfp30 is expressed in airway epithelia in the normal mouse lung and that altering Zfp30 expression in vitro affects CXCL1 responses to an immune stimulus. Our results provide strong evidence that Zfp30 is a novel regulator of neutrophilic airway inflammation.     

Characterizing Uncertainty in High-Density Maps from Multiparental Populations

Multiparental populations are of considerable interest in high-density genetic mapping due to their increased levels of polymorphism and recombination relative to biparental populations. However, errors in map construction can have significant impact on QTL discovery in later stages of analysis, and few methods have been developed to quantify the uncertainty attached to the reported order of markers or intermarker distances. Current methods are computationally intensive or limited to assessing uncertainty only for order or distance, but not both simultaneously. We derive the asymptotic joint distribution of maximum composite likelihood estimators for intermarker distances. This approach allows us to construct hypothesis tests and confidence intervals for simultaneously assessing marker-order instability and distance uncertainty. We investigate the effects of marker density, population size, and founder distribution patterns on map confidence in multiparental populations through simulations. Using these data, we provide guidelines on sample sizes necessary to map markers at sub-centimorgan densities with high certainty. We apply these approaches to data from a bread wheat Multiparent Advanced Generation Inter-Cross (MAGIC) population genotyped using the Illumina 9K SNP chip to assess regions of uncertainty and validate them against the recently released pseudomolecule for the wheat chromosome 3B.     

Reconstruction of Genome Ancestry Blocks in Multiparental Populations

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.     

The Genetic Basis of Natural Variation in Seed Size and Seed Number and Their Trade-Off Using Arabidopsis thaliana MAGIC Lines

Offspring number and size are key traits determining an individual’s fitness and a crop’s yield. Yet, extensive natural variation within species is observed for these traits. Such variation is typically explained by trade-offs between fecundity and quality, for which an optimal solution is environmentally dependent. Understanding the genetic basis of seed size and number, as well as any possible genetic constraints preventing the maximization of both, is crucial from both an evolutionary and applied perspective. We investigated the genetic basis of natural variation in seed size and number using a set of Arabidopsis thaliana multiparent advanced generation intercross (MAGIC) lines. We also tested whether life history affects seed size, number, and their trade-off. We found that both seed size and seed number are affected by a large number of mostly nonoverlapping QTL, suggesting that seed size and seed number can evolve independently. The allele that increases seed size at most identified QTL is from the same natural accession, indicating past occurrence of directional selection for seed size. Although a significant trade-off between seed size and number is observed, its expression depends on life-history characteristics, and generally explains little variance. We conclude that the trade-off between seed size and number might have a minor role in explaining the maintenance of variation in seed size and number, and that seed size could be a valid target for selection.     

Rapid Identification of Major-Effect Genes Using the Collaborative Cross

The Collaborative Cross (CC) was designed to facilitate rapid gene mapping and consists of hundreds of recombinant inbred lines descended from eight diverse inbred founder strains. A decade in production, it can now be applied to mapping projects. Here, we provide a proof of principle for rapid identification of major-effect genes using the CC. To do so, we chose coat color traits since the location and identity of many relevant genes are known. We ascertained in 110 CC lines six different coat phenotypes: albino, agouti, black, cinnamon, and chocolate coat colors and the white-belly trait. We developed a pipeline employing modifications of existing mapping tools suitable for analyzing the complex genetic architecture of the CC. Together with analysis of the founders’ genome sequences, mapping was successfully achieved with sufficient resolution to identify the causative genes for five traits. Anticipating the application of the CC to complex traits, we also developed strategies to detect interacting genes, testing joint effects of three loci. Our results illustrate the power of the CC and provide confidence that this resource can be applied to complex traits for detection of both qualitative and quantitative trait loci.     

Haplotype reconstruction in connected tetraploid F1 populations

In diploid species, many multiparental populations have been developed to increase genetic diversity and quantitative trait loci (QTL) mapping resolution. In these populations, haplotype reconstruction has been used as a standard practice to increase the power of QTL detection in comparison with the marker-based association analysis. However, such software tools for polyploid species are few and limited to a single biparental F1 population. In this study, a statistical framework for haplotype reconstruction has been developed and implemented in the software PolyOrigin for connected tetraploid F1 populations with shared parents, regardless of the number of parents or mating design. Given a genetic or physical map of markers, PolyOrigin first phases parental genotypes, then refines the input marker map, and finally reconstructs offspring haplotypes. PolyOrigin can utilize single nucleotide polymorphism (SNP) data coming from arrays or from sequence-based genotyping; in the latter case, bi-allelic read counts can be used (and are preferred) as input data to minimize the influence of genotype calling errors at low depth. With extensive simulation we show that PolyOrigin is robust to the errors in the input genotypic data and marker map. It works well for various population designs with ≥30 offspring per parent and for sequences with read depth as low as 10x. PolyOrigin was further evaluated using an autotetraploid potato dataset with a 3 × 3 half-diallel mating design. In conclusion, PolyOrigin opens up exciting new possibilities for haplotype analysis in tetraploid breeding populations.     

Bayesian Modeling of Haplotype Effects in Multiparent Populations

A general Bayesian model, Diploffect, is described for estimating the effects of founder haplotypes at quantitative trait loci (QTL) detected in multiparental genetic populations; such populations include the Collaborative Cross (CC), Heterogeneous Socks (HS), and many others for which local genetic variation is well described by an underlying, usually probabilistically inferred, haplotype mosaic. Our aim is to provide a framework for coherent estimation of haplotype and diplotype (haplotype pair) effects that takes into account the following: uncertainty in haplotype composition for each individual; uncertainty arising from small sample sizes and infrequently observed haplotype combinations; possible effects of dominance (for noninbred subjects); genetic background; and that provides a means to incorporate data that may be incomplete or has a hierarchical structure. Using the results of a probabilistic haplotype reconstruction as prior information, we obtain posterior distributions at the QTL for both haplotype effects and haplotype composition. Two alternative computational approaches are supplied: a Markov chain Monte Carlo sampler and a procedure based on importance sampling of integrated nested Laplace approximations. Using simulations of QTL in the incipient CC (pre-CC) and Northport HS populations, we compare the accuracy of Diploffect, approximations to it, and more commonly used approaches based on Haley–Knott regression, describing trade-offs between these methods. We also estimate effects for three QTL previously identified in those populations, obtaining posterior intervals that describe how the phenotype might be affected by diplotype substitutions at the modeled locus.     

Usefulness of Multiparental Populations of Maize (Zea mays L.) for Genome-Based Prediction

The efficiency of marker-assisted prediction of phenotypes has been studied intensively for different types of plant breeding populations. However, one remaining question is how to incorporate and counterbalance information from biparental and multiparental populations into model training for genome-wide prediction. To address this question, we evaluated testcross performance of 1652 doubled-haploid maize (Zea mays L.) lines that were genotyped with 56,110 single nucleotide polymorphism markers and phenotyped for five agronomic traits in four to six European environments. The lines are arranged in two diverse half-sib panels representing two major European heterotic germplasm pools. The data set contains 10 related biparental dent families and 11 related biparental flint families generated from crosses of maize lines important for European maize breeding. With this new data set we analyzed genome-based best linear unbiased prediction in different validation schemes and compositions of estimation and test sets. Further, we theoretically and empirically investigated marker linkage phases across multiparental populations. In general, predictive abilities similar to or higher than those within biparental families could be achieved by combining several half-sib families in the estimation set. For the majority of families, 375 half-sib lines in the estimation set were sufficient to reach the same predictive performance of biomass yield as an estimation set of 50 full-sib lines. In contrast, prediction across heterotic pools was not possible for most cases. Our findings are important for experimental design in genome-based prediction as they provide guidelines for the genetic structure and required sample size of data sets used for model training.     

A General Modeling Framework for Genome Ancestral Origins in Multiparental Populations

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.     

High-Resolution Genetic Mapping of Complex Traits from a Combined Analysis of F2 and Advanced Intercross Mice

Genetic influences on anxiety disorders are well documented; however, the specific genes underlying these disorders remain largely unknown. To identify quantitative trait loci (QTL) for conditioned fear and open field behavior, we used an F₂ intercross (n = 490) and a 34th-generation advanced intercross line (AIL) (n = 687) from the LG/J and SM/J inbred mouse strains. The F₂ provided strong support for several QTL, but within wide chromosomal regions. The AIL yielded much narrower QTL, but the results were less statistically significant, despite the larger number of mice. Simultaneous analysis of the F₂ and AIL provided strong support for QTL and within much narrower regions. We used a linear mixed-model approach, implemented in the program QTLRel, to correct for possible confounding due to familial relatedness. Because we recorded the full pedigree, we were able to empirically compare two ways of accounting for relatedness: using the pedigree to estimate kinship coefficients and using genetic marker estimates of “realized relatedness.” QTL mapping using the marker-based estimates yielded more support for QTL, but only when we excluded the chromosome being scanned from the marker-based relatedness estimates. We used a forward model selection procedure to assess evidence for multiple QTL on the same chromosome. Overall, we identified 12 significant loci for behaviors in the open field and 12 significant loci for conditioned fear behaviors. Our approach implements multiple advances to integrated analysis of F₂ and AILs that provide both power and precision, while maintaining the advantages of using only two inbred strains to map QTL.     

A highly recombined,high‐density,eight‐founder wheat MAGIC map reveals extensive segregation distortion and genomic locations of introgression segments

Multiparent Advanced Generation Intercross (MAGIC) mapping populations offer unique opportunities and challenges for marker and QTL mapping in crop species. We have constructed the first eight‐parent MAGIC genetic map for wheat, comprising 18 601 SNP markers. We validated the accuracy of our map against the wheat genome sequence and found an improvement in accuracy compared to published genetic maps. Our map shows a notable increase in precision resulting from the three generations of intercrossing required to create the population. This is most pronounced in the pericentromeric regions of the chromosomes. Sixteen percent of mapped markers exhibited segregation distortion (SD) with many occurring in long (>20 cM) blocks. Some of the longest and most distorted blocks were collinear with noncentromeric high‐marker‐density regions of the genome, suggesting they were candidates for introgression fragments introduced into the bread wheat gene pool from other grass species. We investigated two of these linkage blocks in detail and found strong evidence that one on chromosome 4AL, showing SD against the founder Robigus, is an interspecific introgression fragment. The completed map is available from http://www.niab.com/pages/id/326/Resources .     

Patterns and mechanisms of sex ratio distortion in the Collaborative Cross mouse mapping population

In species with single-locus, chromosome-based mechanisms of sex determination, the laws of segregation predict an equal ratio of females to males at birth. Here, we show that departures from this Mendelian expectation are commonplace in the 8-way recombinant inbred Collaborative Cross (CC) mouse population. More than one-third of CC strains exhibit significant sex ratio distortion (SRD) at wean, with twice as many male-biased than female-biased strains. We show that these pervasive sex biases persist across multiple breeding environments, are stable over time, and are not mediated by random maternal effects. SRD exhibits a heritable component, but QTL mapping analyses fail to nominate any large effect loci. These findings, combined with the reported absence of sex ratio biases in the CC founder strains, suggest that SRD manifests from multilocus combinations of alleles only uncovered in recombined CC genomes. We explore several potential complex genetic mechanisms for SRD, including allelic interactions leading to sex-biased lethality, genetic sex reversal, chromosome drive mediated by sex-linked selfish elements, and incompatibilities between specific maternal and paternal genotypes. We show that no one mechanism offers a singular explanation for this population-wide SRD. Instead, our data present preliminary evidence for the action of distinct mechanisms of SRD at play in different strains. Taken together, our work exposes the pervasiveness of SRD in the CC population and nominates the CC as a powerful resource for investigating diverse genetic causes of biased sex chromosome transmission.     

An Overview of the Development,Status, and Application of Equilibrium Partitioning Sediment Benchmarks for PAH Mixtures

This article provides an overview of the development, theoretical basis, regulatory status, and application of the U.S. Environmental Protection Agency's (USEPA's) Equilibrium Partitioning Sediment Benchmarks (ESBs) for PAH mixtures. ESBs are compared to other sediment quality guidelines (SQGs) for PAHs. Data that examine the ability of the ESB approach to predict toxic effects to invertebrates are discussed. A USEPA draft methodology for the development of site-specific ESBs that takes into account the limited bioavailability of PAHs at certain sites is discussed. Research is presented that compares the ability of ESBs and site-specific ESBs to predict the toxicity of sediments collected from manufactured gas plants (MGPs). Site-specific ESBs that accounted for adsorption of PAHs onto black carbon were better predictors of the toxicity of sediments from MGP sites than ESBs that did not account for adsorption to black carbon.     

A Hybrid Approach for Assessing the Multi‐Scale Impacts of Urban Resource Use: Transportation in Phoenix,Arizona

Life cycle assessment (LCA) and urban metabolism (UM) are popular approaches for urban system environmental assessment. However, both approaches have challenges when used across spatial scales. LCA tends to decompose systemic information into micro‐level functional units that mask complexity and purpose, whereas UM typically equates aggregated material and energy flows with impacts and is not ideal for revealing the mechanisms or alternatives available to reduce systemic environmental risks. This study explores the value of integrating UM with LCA, using vehicle transportation in the Phoenix metropolitan area as an illustrative case study. Where other studies have focused on the use of LCA providing upstream supply‐chain impacts for UM, we assert that the broader value of the integrated approach is in (1) the ability to cross scales (from micro to macro) in environmental assessment and (2) establishing an analysis that captures function and complexity in urban systems. The results for Phoenix show the complexity in resource supply chains and critical infrastructure services, how impacts accrue well beyond geopolitical boundaries where activities occur, and potential system vulnerabilities.