Sparse and Compositionally Robust Inference of Microbial Ecological Networks

Abstract

16S ribosomal RNA (rRNA) gene and other environmental sequencing techniques provide snapshots of microbial communities, revealing phylogeny and the abundances of microbial populations across diverse ecosystems. While changes in microbial community structure are demonstrably associated with certain environmental conditions (from metabolic and immunological health in mammals to ecological stability in soils and oceans), identification of underlying mechanisms requires new statistical tools, as these datasets present several technical challenges. First, the abundances of microbial operational taxonomic units (OTUs) from amplicon-based datasets are compositional. Counts are normalized to the total number of counts in the sample. Thus, microbial abundances are not independent, and traditional statistical metrics (e.g., correlation) for the detection of OTU-OTU relationships can lead to spurious results. Secondly, microbial sequencing-based studies typically measure hundreds of OTUs on only tens to hundreds of samples; thus, inference of OTU-OTU association networks is severely under-powered, and additional information (or assumptions) are required for accurate inference. Here, we present SPIEC-EASI (SParse InversE Covariance Estimation for Ecological Association Inference), a statistical method for the inference of microbial ecological networks from amplicon sequencing datasets that addresses both of these issues. SPIEC-EASI combines data transformations developed for compositional data analysis with a graphical model inference framework that assumes the underlying ecological association network is sparse. To reconstruct the network, SPIEC-EASI relies on algorithms for sparse neighborhood and inverse covariance selection. To provide a synthetic benchmark in the absence of an experimentally validated gold-standard network, SPIEC-EASI is accompanied by a set of computational tools to generate OTU count data from a set of diverse underlying network topologies. SPIEC-EASI outperforms state-of-the-art methods to recover edges and network properties on synthetic data under a variety of scenarios. SPIEC-EASI also reproducibly predicts previously unknown microbial associations using data from the American Gut project.

Network modules and hubs in plant-root fungal biomes

“…Interface 13: 20151097 tandem repeats and compositional biases introduced in PCRamplification processes than analyses based on presence/absence information [50]. However, because relative abundance information was used across samples as detailed previously [48], our SparCC and SPIEC-EASI results were unlikely to be affected greatly by those potential read-count biases.…”

“…In the SPIEC-EASI analysis, the Meinshausen and Bü hlmann (MB) algorithm [49] was applied. As these composition-based methods are usually applied to data matrices without rare species [47,48], the 52 fungal species analysed in the togetherness/checkerboard tests were screened from the original data matrix ('592-OTU.matrix' in the electronic supplementary material, data S1). We also screened samples with sufficient compositional (read-count) information by removing those with less than 5000 sequencing reads.…”

Compositional analysis: a valid approach to analyze microbiome high-throughput sequencing data

“…As noted above, spurious correlation is a very large problem in microbiome data sets. Therefore, analyses that report correlations using traditional methods, such as Pearson's or Spearman's correlations, Kendall's , or Partial correlations are likely to be wrong (Friedman and Alm 2012;Lovell et al 2015, Kurtz et al 2015. However, there are a number of approaches that use a compositional data analytic approach to correlation.…”

“…So, for example, when the last value is dropped from each sample, the correlation between taxa 1 and 2 is positive (0.43), and the correlation between taxa 2 and 3 is even more strongly negative at -0.79. Thus, a correlation determined from compositional data has the potential to be wildly wrong, and normal approaches to determine correlation cannot be used (Friedman and Alm 2012;Lovell et al 2015;Kurtz et al 2015). It is worth noting that any method of determining correlation (including Spearman, Kendall, etc.)…”

“…will suffer from the same problems. Thus, the current tools used to examine the analysis goals give results that may be inconsistent, difficult to interpret, and in many cases completely wrong (Filzmoser et al 2009;Friedman and Alm 2012;Fernandes et al 2013, Lovell et al 2015Kurtz et al 2015).…”