Multivariate Analysis

BackgroundThe dramatic progress in sequencing technologies offers unprecedented prospects for deciphering the organization of natural populations in space and time. However, the size of the datasets generated also poses some daunting challenges. In particular, Bayesian clustering algorithms based on pre-defined population genetics models such as the STRUCTURE or BAPS software may not be able to cope with this unprecedented amount of data. Thus, there is a need for less computer-intensive approaches. Multivariate analyses seem particularly appealing as they are specifically devoted to extracting information from large datasets. Unfortunately, currently available multivariate methods still lack some essential features needed to study the genetic structure of natural populations.ResultsWe introduce the Discriminant Analysis of Principal Components (DAPC), a multivariate method designed to identify and describe clusters of genetically related individuals. When group priors are lacking, DAPC uses sequential K-means and model selection to infer genetic clusters. Our approach allows extracting rich information from genetic data, providing assignment of individuals to groups, a visual assessment of between-population differentiation, and contribution of individual alleles to population structuring. We evaluate the performance of our method using simulated data, which were also analyzed using STRUCTURE as a benchmark. Additionally, we illustrate the method by analyzing microsatellite polymorphism in worldwide human populations and hemagglutinin gene sequence variation in seasonal influenza.ConclusionsAnalysis of simulated data revealed that our approach performs generally better than STRUCTURE at characterizing population subdivision. The tools implemented in DAPC for the identification of clusters and graphical representation of between-group structures allow to unravel complex population structures. Our approach is also faster than Bayesian clustering algorithms by several orders of magnitude, and may be applicable to a wider range of datasets.

It is challenging to associate features such as human health outcomes, diet, environmental conditions, or other metadata to microbial community measurements, due in part to their quantitative properties. Microbiome multi-omics are typically noisy, sparse (zero-inflated), high-dimensional, extremely non-normal, and often in the form of count or compositional measurements. Here we introduce an optimized combination of novel and established methodology to assess multivariable association of microbial community features with complex metadata in population-scale observational studies. Our approach, MaAsLin 2 (Microbiome Multivariable Associations with Linear Models), uses generalized linear and mixed models to accommodate a wide variety of modern epidemiological studies, including cross-sectional and longitudinal designs, as well as a variety of data types (e.g., counts and relative abundances) with or without covariates and repeated measurements. To construct this method, we conducted a large-scale evaluation of a broad range of scenarios under which straightforward identification of meta-omics associations can be challenging. These simulation studies reveal that MaAsLin 2's linear model preserves statistical power in the presence of repeated measures and multiple covariates, while accounting for the nuances of meta-omics features and controlling false discovery. We also applied MaAsLin 2 to a microbial multi-omics dataset from the Integrative Human Microbiome (HMP2) project which, in addition to reproducing established results, revealed a unique, integrated landscape of inflammatory bowel diseases (IBD) across multiple time points and omics profiles.

Environmental microbiology is undergoing a dramatic revolution due to the increasing accumulation of biological information and contextual environmental parameters. This will not only enable a better identification of diversity patterns, but will also shed more light on the associated environmental conditions, spatial locations, and seasonal fluctuations, which could explain such patterns. Complex ecological questions may now be addressed using multivariate statistical analyses, which represent a vast potential of techniques that are still underexploited. Here, well-established exploratory and hypothesis-driven approaches are reviewed, so as to foster their addition to the microbial ecologist toolbox. Because such tools aim at reducing data set complexity, at identifying major patterns and putative causal factors, they will certainly find many applications in microbial ecology.

Identifying gene expression differences in heterogeneous tissues across conditions is a fundamental biological task, enabled by multi-condition single-cell RNA sequencing (RNA-seq). Current data analysis approaches divide the constituent cells into clusters meant to represent cell types, but such discrete categorization tends to be an unsatisfactory model of the underlying biology. Here, we introduce latent embedding multivariate regression (LEMUR), a model that operates without, or before, commitment to discrete categorization. LEMUR (1) integrates data from different conditions, (2) predicts each cell's gene expression changes as a function of the conditions and its position in latent space and (3) for each gene, identifies a compact neighborhood of cells with consistent differential expression. We apply LEMUR to cancer, zebrafish development and spatial gradients in Alzheimer's disease, demonstrating its broad applicability.