Variable selection and regression analysis for graph-structured covariates with an application to genomics

Graphs and networks are common ways of depicting biological information. In biology, many different biological processes are represented by graphs, such as regulatory networks, metabolic pathways and protein--protein interaction networks. This kind of a priori use of graphs is a useful supplement to the standard numerical data such as microarray gene expression data. In this paper we consider the problem of regression analysis and variable selection when the covariates are linked on a graph. We study a graph-constrained regularization procedure and its theoretical properties for regression analysis to take into account the neighborhood information of the variables measured on a graph. This procedure involves a smoothness penalty on the coefficients that is defined as a quadratic form of the Laplacian matrix associated with the graph. We establish estimation and model selection consistency results and provide estimation bounds for both fixed and diverging numbers of parameters in regression models. We demonstrate by simulations and a real data set that the proposed procedure can lead to better variable selection and prediction than existing methods that ignore the graph information associated with the covariates.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS332 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The evolution of genetic architectures underlying quantitative traits

In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in QTL mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher's blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here we develop a simple, population-genetic model for the evolution of genetic architectures. Our model predicts that traits under moderate selection should be encoded by many loci with highly variable effects, whereas traits under either weak or strong selection should be encoded by relatively few loci. We compare these theoretical predictions to qualitative trends in the genetics of human traits, and to systematic data on the genetics of gene expression levels in yeast. Our analysis provides an evolutionary explanation for broad empirical patterns in the genetic basis of traits, and it introduces a single framework that unifies the diversity of observed genetic architectures, ranging from Mendelian to Fisherian.Comment: Minor changes in the text; Added supplementary materia

Negative feedback and transcriptional overshooting in a regulatory network for horizontal gene transfer

Horizontal gene transfer (HGT) is a major force driving bacterial evolution. Because of their ability to cross inter-species barriers, bacterial plasmids are essential agents for HGT. This ability, however, poses specific requisites on plasmid physiology, in particular the need to overcome a multilevel selection process with opposing demands. We analyzed the transcriptional network of plasmid R388, one of the most promiscuous plasmids in Proteobacteria. Transcriptional analysis by fluorescence expression profiling and quantitative PCR revealed a regulatory network controlled by six transcriptional repressors. The regulatory network relied on strong promoters, which were tightly repressed in negative feedback loops. Computational simulations and theoretical analysis indicated that this architecture would show a transcriptional burst after plasmid conjugation, linking the magnitude of the feedback gain with the intensity of the transcriptional burst. Experimental analysis showed that transcriptional overshooting occurred when the plasmid invaded a new population of susceptible cells. We propose that transcriptional overshooting allows genome rebooting after horizontal gene transfer, and might have an adaptive role in overcoming the opposing demands of multilevel selection