Peter Carbonetto

Polygenic modeling with bayesian sparse linear mixed models.

Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling in genome-wide association studies. These two approaches make very different assumptions, so are expected to perform well in different situations. However, in practice, for a given dataset one typically does not know which assumptions will be more accurate. Motivated by this, we consider a hybrid of the two, which we refer to as a “Bayesian sparse linear mixed model” (BSLMM) that includes both these models as special cases. We address several key computational and statistical issues that arise when applying BSLMM, including appropriate prior specification for the hyper-parameters and a novel Markov chain Monte Carlo algorithm for posterior inference. We apply BSLMM and compare it with other methods for two polygenic modeling applications: estimating the proportion of variance in phenotypes explained (PVE) by available genotypes, and phenotype (or breeding value) prediction. For PVE estimation, we demonstrate that BSLMM combines the advantages of both standard LMMs and sparse regression modeling. For phenotype prediction it considerably outperforms either of the other two methods, as well as several other large-scale regression methods previously suggested for this problem. Software implementing our method is freely available from http://stephenslab.uchicago.edu/software.html.

Scalable Variational Inference for Bayesian Variable Selection in Regression, and Its Accuracy in Genetic Association Studies

The Bayesian approach to variable selection in regression is a powerful tool for tackling many scientiflc problems. Inference for variable selection models is usually implemented using Markov chain Monte Carlo (MCMC). Because MCMC can impose a high computational cost in studies with a large number of variables, we assess an alternative to MCMC based on a simple variational approximation. Our aim is to retain useful features of Bayesian variable selection at a reduced cost. Using simulations designed to mimic genetic association studies, we show that this simple variational approximation yields posterior inferences in some settings that closely match exact values. In less restrictive (and more realistic) conditions, we show that posterior probabilities of inclusion for individual variables are often incorrect, but variational estimates of other useful quantities|including posterior distributions of the hyperparameters|are remarkably accurate. We illustrate how these results guide the use of variational inference for a genome-wide association study with thousands of samples and hundreds of thousands of variables.

Integrated Enrichment Analysis of Variants and Pathways in Genome-Wide Association Studies Indicates Central Role for IL-2 Signaling Genes in Type 1 Diabetes, and Cytokine Signaling Genes in Crohn's Disease

Pathway analyses of genome-wide association studies aggregate information over sets of related genes, such as genes in common pathways, to identify gene sets that are enriched for variants associated with disease. We develop a model-based approach to pathway analysis, and apply this approach to data from the Wellcome Trust Case Control Consortium (WTCCC) studies. Our method offers several benefits over existing approaches. First, our method not only interrogates pathways for enrichment of disease associations, but also estimates the level of enrichment, which yields a coherent way to promote variants in enriched pathways, enhancing discovery of genes underlying disease. Second, our approach allows for multiple enriched pathways, a feature that leads to novel findings in two diseases where the major histocompatibility complex (MHC) is a major determinant of disease susceptibility. Third, by modeling disease as the combined effect of multiple markers, our method automatically accounts for linkage disequilibrium among variants. Interrogation of pathways from eight pathway databases yields strong support for enriched pathways, indicating links between Crohns disease (CD) and cytokine-driven networks that modulate immune responses; between rheumatoid arthritis (RA) and “Measles” pathway genes involved in immune responses triggered by measles infection; and between type 1 diabetes (T1D) and IL2-mediated signaling genes. Prioritizing variants in these enriched pathways yields many additional putative disease associations compared to analyses without enrichment. For CD and RA, 7 of 8 additional non-MHC associations are corroborated by other studies, providing validation for our approach. For T1D, prioritization of IL-2 signaling genes yields strong evidence for 7 additional non-MHC candidate disease loci, as well as suggestive evidence for several more. Of the 7 strongest associations, 4 are validated by other studies, and 3 (near IL-2 signaling genes RAF1, MAPK14, and FYN) constitute novel putative T1D loci for further study.

Mapping of Craniofacial Traits in Outbred Mice Identifies Major Developmental Genes Involved in Shape Determination.

The vertebrate cranium is a prime example of the high evolvability of complex traits. While evidence of genes and developmental pathways underlying craniofacial shape determination is accumulating, we are still far from understanding how such variation at the genetic level is translated into craniofacial shape variation. Here we used 3D geometric morphometrics to map genes involved in shape determination in a population of outbred mice (Carworth Farms White, or CFW). We defined shape traits via principal component analysis of 3D skull and mandible measurements. We mapped genetic loci associated with shape traits at ~80,000 candidate single nucleotide polymorphisms in ~700 male mice. We found that craniofacial shape and size are highly heritable, polygenic traits. Despite the polygenic nature of the traits, we identified 17 loci that explain variation in skull shape, and 8 loci associated with variation in mandible shape. Together, the associated variants account for 11.4% of skull and 4.4% of mandible shape variation, however, the total additive genetic variance associated with phenotypic variation was estimated in ~45%. Candidate genes within the associated loci have known roles in craniofacial development; this includes 6 transcription factors and several regulators of bone developmental pathways. One gene, Mn1, has an unusually large effect on shape variation in our study. A knockout of this gene was previously shown to affect negatively the development of membranous bones of the cranial skeleton, and evolutionary analysis shows that the gene has arisen at the base of the bony vertebrates (Eutelostomi), where the ossified head first appeared. Therefore, Mn1 emerges as a key gene for both skull formation and within-population shape variation. Our study shows that it is possible to identify important developmental genes through genome-wide mapping of high-dimensional shape features in an outbred population.

Genome-wide association study of behavioral, physiological and gene expression traits in outbred CFW mice

Although mice are the most widely used mammalian model organism, genetic studies have suffered from limited mapping resolution due to extensive linkage disequilibrium (LD) that is characteristic of crosses among inbred strains. Carworth Farms White (CFW) mice are a commercially available outbred mouse population that exhibit rapid LD decay in comparison to other available mouse populations. We performed a genome-wide association study (GWAS) of behavioral, physiological and gene expression phenotypes using 1,200 male CFW mice. We used genotyping by sequencing (GBS) to obtain genotypes at 92,734 SNPs. We also measured gene expression using RNA sequencing in three brain regions. Our study identified numerous behavioral, physiological and expression quantitative trait loci (QTLs). We integrated the behavioral QTL and eQTL results to implicate specific genes, including Azi2 in sensitivity to methamphetamine and Zmynd11 in anxiety-like behavior. The combination of CFW mice, GBS and RNA sequencing constitutes a powerful approach to GWAS in mice.

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.

Discovery and refinement of muscle weight QTLs in B6 × D2 advanced intercross mice

The genes underlying variation in skeletal muscle mass are poorly understood. Although many quantitative trait loci (QTLs) have been mapped in crosses of mouse strains, the limited resolution inherent in these conventional studies has made it difficult to reliably pinpoint the causal genetic variants. The accumulated recombination events in an advanced intercross line (AIL), in which mice from two inbred strains are mated at random for several generations, can improve mapping resolution. We demonstrate these advancements in mapping QTLs for hindlimb muscle weights in an AIL (n = 832) of the C57BL/6J (B6) and DBA/2J (D2) strains, generations F8-F13. We mapped muscle weight QTLs using the high-density MegaMUGA SNP panel. The QTLs highlight the shared genetic architecture of four hindlimb muscles and suggest that the genetic contributions to muscle variation are substantially different in males and females, at least in the B6D2 lineage. Out of the 15 muscle weight QTLs identified in the AIL, nine overlapped the genomic regions discovered in an earlier B6D2 F2 intercross. Mapping resolution, however, was substantially improved in our study to a median QTL interval of 12.5 Mb. Subsequent sequence analysis of the QTL regions revealed 20 genes with nonsense or potentially damaging missense mutations. Further refinement of the muscle weight QTLs using additional functional information, such as gene expression differences between alleles, will be important for discerning the causal genes.

Integration of genome-wide association and extant brain expression QTL identifies candidate genes influencing prepulse inhibition in inbred F1 mice

Genetic association mapping in structured populations of model organisms can offer a fruitful complement to human genetic studies by generating new biological hypotheses about complex traits. Here we investigated prepulse inhibition (PPI), a measure of sensorimotor gating that is disrupted in a number of psychiatric disorders. To identify genes that influence PPI, we constructed a panel of half‐sibs by crossing 30 females from common inbred mouse strains with inbred C57BL/6J males to create male and female F1 offspring. We used publicly available single nucleotide polymorphism (SNP) genotype data from these inbred strains to perform a genome‐wide association scan using a dense panel of over 150 000 SNPs in a combined sample of 604 mice representing 30 distinct F1 genotypes. We identified two independent PPI‐associated loci on Chromosomes 2 and 7, each of which explained 12–14% of the variance in PPI. Searches of available databases did not identify any plausible causative coding polymorphisms within these loci. However, previously collected expression quantitative trait locus (eQTL) data from hippocampus and striatum indicated that the SNPs on Chromosomes 2 and 7 that showed the strongest association with PPI were also strongly associated with expression of several transcripts, some of which have been implicated in human psychiatric disorders. This integrative approach successfully identified a focused set of genes which can be prioritized for follow‐up studies. More broadly, our results show that F1 crosses among common inbred strains can be used in combination with other informatics and expression datasets to identify candidate genes for complex behavioral traits.

Replication and discovery of musculoskeletal QTLs in LG/J and SM/J advanced intercross lines

The genetics underlying variation in health‐related musculoskeletal phenotypes can be investigated in a mouse model. Quantitative trait loci (QTLs) affecting musculoskeletal traits in the LG/J and SM/J strain lineage remain to be refined and corroborated. The aim of this study was to map muscle and bone traits in males (n = 506) of the 50th filial generation of advanced intercross lines (LG/SM AIL) derived from the two strains. Genetic contribution to variation in all musculoskeletal traits was confirmed; the SNP heritability of muscle mass ranged between 0.46 and 0.56; and the SNP heritability of tibia length was 0.40. We used two analytical software, GEMMA and QTLRel, to map the underlying QTLs. GEMMA required substantially less computation and recovered all the QTLs identified by QTLRel. Seven significant QTLs were identified for muscle weight (Chr 1, 7, 11, 12, 13, 15, and 16), and two for tibia length, (Chr 1 and 13). Each QTL explained 4–5% of phenotypic variation. One muscle and both bone loci replicated previous findings; the remaining six were novel. Positional candidates for the replicated QTLs were prioritized based on in silico analyses and gene expression in muscle tissue. In summary, we replicated existing QTLs and identified novel QTLs affecting muscle weight, and replicated bone length QTLs in LG/SM AIL males. Heritability estimates substantially exceed the cumulative effect of the QTLs, hence a richer genetic architecture contributing to muscle and bone variability could be uncovered with a larger sample size.

Accurate genomic prediction of Coffea canephora in multiple environments using whole-genome statistical models

Genomic selection has been proposed as the standard method to predict breeding values in animal and plant breeding. Although some crops have benefited from this methodology, studies in Coffea are still emerging. To date, there have been no studies describing how well genomic prediction models work across populations and environments for different complex traits in coffee. Considering that predictive models are based on biological and statistical assumptions, it is expected that their performance vary depending on how well these assumptions align with the true genetic architecture of the phenotype. To investigate this, we used data from two recurrent selection populations of Coffea canephora, evaluated in two locations, and single nucleotide polymorphisms identified by Genotyping-by-Sequencing. In particular, we evaluated the performance of 13 statistical approaches to predict three important traits in the coffee—production of coffee beans, leaf rust incidence and yield of green beans. Analyses were performed for predictions within-environment, across locations and across populations to assess the reliability of genomic selection. Overall, differences in the prediction accuracy of the competing models were small, although the Bayesian methods showed a modest improvement over other methods, at the cost of more computation time. As expected, predictive accuracy for within-environment analysis, on average, were higher than predictions across locations and across populations. Our results support the potential of genomic selection to reshape traditional plant breeding schemes. In practice, we expect to increase the genetic gain per unit of time by reducing the length cycle of recurrent selection in coffee.