Background

The nucleotide substitution rate matrix is a key parameter of molecular evolution. Several methods for inferring this parameter have been proposed, with different mathematical bases. These methods include counting sequence differences and taking the log of the resulting probability matrices, methods based on Markov triples, and maximum likelihood methods that infer the substitution probabilities that lead to the most likely model of evolution. However, the speed and accuracy of these methods has not been compared.

Results

Different methods differ in performance by orders of magnitude (ranging from 1 ms to 10 s per matrix), but differences in accuracy of rate matrix reconstruction appear to be relatively small. Encouragingly, relatively simple and fast methods can provide results at least as accurate as far more complex and computationally intensive methods, especially when the sequences to be compared are relatively short.

Conclusion

Based on the conditions tested, we recommend the use of method of Gojobori et al. (1982) for long sequences (> 600 nucleotides), and the method of Goldman et al. (1996) for shorter sequences (< 600 nucleotides). The method of Barry and Hartigan (1987) can provide somewhat more accuracy, measured as the Euclidean distance between the true and inferred matrices, on long sequences (> 2000 nucleotides) at the expense of substantially longer computation time. The availability of methods that are both fast and accurate will allow us to gain a global picture of change in the nucleotide substitution rate matrix on a genomewide scale across the tree of life.

Advances in sequencing technologies have enabled novel insights into microbial niche differentiation, from analyzing environmental samples to understanding human diseases and informing dietary studies. However, identifying the microbial taxa that differentiate these samples can be challenging. These issues stem from the compositional nature of 16S rRNA gene data (or, more generally, taxon or functional gene data); the changes in the relative abundance of one taxon influence the apparent abundances of the others. Here we acknowledge that inferring properties of individual bacteria is a difficult problem and instead introduce the concept of balances to infer meaningful properties of subcommunities, rather than properties of individual species. We show that balances can yield insights about niche differentiation across multiple microbial environments, including soil environments and lung sputum. These techniques have the potential to reshape how we carry out future ecological analyses aimed at revealing differences in relative taxonomic abundances across different samples. IMPORTANCE By explicitly accounting for the compositional nature of 16S rRNA gene data through the concept of balances, balance trees yield novel biological insights into niche differentiation. The software to perform this analysis is available under an open-source license and can be obtained at https://github.com/biocore/gneiss. Author Video: An author video summary of this article is available.