Microbiome samples often represent mixtures of communities, where each community is composed of overlapping assemblages of species. Such mixtures are complex, the number of species is huge and abundance information for many species is often sparse. Classical methods have a limited value for identifying complex features within such data. Here, we describe a novel hierarchical model for Bayesian inference of microbial communities (BioMiCo). The model takes abundance data derived from environmental DNA, and models the composition of each sample by a two-level hierarchy of mixture distributions constrained by Dirichlet priors. BioMiCo is supervised, using known features for samples and appropriate prior constraints to overcome the challenges posed by many variables, sparse data, and large numbers of rare species. The model is trained on a portion of the data, where it learns how assemblages of species are mixed to form communities and how assemblages are related to the known features of each sample. Training yields a model that can predict the features of new samples. We used BioMiCo to build models for three serially sampled datasets and tested their predictive accuracy across different time points. The first model was trained to predict both body site (hand, mouth, and gut) and individual human host. It was able to reliably distinguish these features across different time points. The second was trained on vaginal microbiomes to predict both the Nugent score and individual human host. We found that women having normal and elevated Nugent scores had distinct microbiome structures that persisted over time, with additional structure within women having elevated scores. The third was trained for the purpose of assessing seasonal transitions in a coastal bacterial community. Application of this model to a high-resolution time series permitted us to track the rate and time of community succession and accurately predict known ecosystem-level events. BioMiCo provides a framework for learning the structure of microbial communities and for making predictions based on microbial assemblages. By training on carefully chosen features (abiotic or biotic), BioMiCo can be used to understand and predict transitions between complex communities composed of hundreds of microbial species.

Testing model adequacy is important before a DNA substitution model is chosen for phylogenetic inference. Using a mis-specified model can negatively impact phylogenetic inference, for example, the maximum likelihood method can be inconsistent when the DNA sequences are generated under a tree topology which is in the Felsentein Zone and analyzed with a mis-specified or inadequate model. However, model adequacy testing in phylogenetics is underdeveloped. Here we develop a simple, general, powerful and robust model test based on Pearson’s goodness-of-fit test and binning of site patterns. We demonstrate through simulation that this test is robust in its high power to reject the inadequate models for a large range of different ways of binning site patterns while the Type I error is controlled well. In the real data analysis we discovered many cases where models chosen by another method can be rejected by this new test, in particular, our proposed test rejects the most complex DNA model (GTR+I+ Γ) while the Goldman-Cox test fails to reject the commonly used simple models. Model adequacy testing and bootstrap should be used together to assess reliability of conclusions after model selection and model fitting have already been applied to choose the model and fit it. The new goodness-of-fit test proposed in this paper is a simple and powerful model adequacy testing method serving such a regular model checking purpose. We caution against deriving strong conclusions from analyses based on inadequate models. At a minimum, those results derived from inadequate models can now be readly flagged using the new test, and reported as such.

Despite that obesity is associated with many metabolic diseases, a significant proportion (10–30 %) of obese individuals is recognized as ‘metabolically healthy obeses’ (MHOs). The aim of the current study is to characterize the gut microbiome for MHOs as compared to ‘metabolically unhealthy obeses’ (MUOs). We compared the gut microbiome of 172 MHO and 138 MUO individuals from Chongqing (China) (inclined to eat red meat and food with a spicy taste), and performed validation with selected biomarkers in 40 MHOs and 33 MUOs from Quanzhou (China) (inclined to eat seafood and food with a light/bland taste). The genera Alistipes , Faecalibacterium and Odoribacter had increased abundance in both Chongqing and Quanzhou MHOs. We also observed different microbial functions in MUOs compared to MHOs, including an increased abundance of genes associated with glycan biosynthesis and metabolism. In addition, the microbial gene markers identified from the Chongqing cohort bear a moderate accuracy [AUC (area under the operating characteristic curve)=0.69] for classifying MHOs distinct from MUOs in the Quanzhou cohort. These findings indicate that gut microbiome is significantly distinct between MHOs and MUOs, implicating the potential of the gut microbiome in stratification and refined management of obesity.

An excess of nonsynonymous substitutions, over neutrality, is considered evidence of positive Darwinian selection. Inference for proteins often relies on estimation of the nonsynonymous to synonymous ratio (ω = dN/dS) within a codon model. However, to ease computational difficulties, ω is typically estimated assuming an idealized substitution process where (i) all nonsynonymous substitutions have the same rate (regardless of impact on organism fitness) and (ii) instantaneous double and triple (DT) nucleotide mutations have zero probability (despite evidence that they can occur). It follows that estimates of ω represent an imperfect summary of the intensity of selection, and that tests based on the ω > 1 threshold could be negatively impacted. We developed a general-purpose parametric (GPP) modelling framework for codons. This novel approach allows specification of all possible instantaneous codon substitutions, including multiple nonsynonymous rates (MNRs) and instantaneous DT nucleotide changes. Existing codon models are specified as special cases of the GPP model. We use GPP models to implement likelihood ratio tests for ω > 1 that accommodate MNRs and DT mutations. Through both simulation and real data analysis, we find that failure to model MNRs and DT mutations reduces power in some cases and inflates false positives in others. False positives under traditional M2a and M8 models were very sensitive to DT changes. This was exacerbated by the choice of frequency parameterization (GY vs. MG), with rates sometimes > 90% under MG. By including MNRs and DT mutations, accuracy and power was greatly improved under the GPP framework. However, we also find that over-parameterized models can perform less well, and this can contribute to degraded performance of LRTs. We suggest GPP models should be used alongside traditional codon models. Further, all codon models should be deployed within an experimental design that includes (i) assessing robustness to model assumptions, and (ii) investigation of non-standard behaviour of MLEs. As the goal of every analysis is to avoid false conclusions, more work is needed on model selection methods that consider both the increase in fit engendered by a model parameter and the degree to which that parameter is affected by un-modelled evolutionary processes.