We report a new transformation, the LogDet, that is consistent for sequences with differing nucleotide composition and that have arisen under simple but asymmetric stochastic models of evolution. This transformation is required because existing methods tend to group sequences on the basis of their nucleotide composition, irrespective of their evolutionary history. This effect of differing nucleotide frequencies is illustrated by using a tree-selection criterion on a simple distance measure defined solely on the basis of base composition, independent of the actual sequences. The new LogDet transformation uses determinants of the observed divergence matrices and works because multiplication of determinants (real numbers) is commutative, whereas multiplication of matrices is not,except in special symmetric cases. The use of determinants thus allows more general models of evolution with a symmetric rates of nucleotide change. The transformation is illustrated on a theoretical data set (where existing methods select the wrong tree) and with three biological data sets: chloroplasts, birds/mammals (nuclear), and honeybees ( mitochondrial ) . The LogDet transformation reinforces the logical distinction between transformations on the data and tree-selection criteria. The overall conclusions from this study are that irregular A,C,G,T compositions are an important and possible general cause of patterns that can mislead tree-reconstruction methods, even when high bootstrap values are obtained. Consequently, many published studies may need to be reexamined.

It is nearly 20 years since the landmark paper (Saitou and Nei 1987) in Molecular Biology and Evolution introducing Neighbor-Joining (NJ). The method has become the most widely used method for building phylogenetic trees from distances, and the original paper has been cited about 13,000 times (Science Citation Index). Yet the question “what does the NJ method seek to do?” has until recently proved somewhat elusive, leading to some imprecise claims and misunderstanding. However, a rigorous answer to this question has recently been provided by further mathematical investigation, and the purpose of this note is to highlight these results and their significance for interpreting NJ. The origins of this story lie in a paper by Pauplin (2000) though its continuation has unfolded in more mathematically inclined literature. Our aim here is to make these findings more widely accessible.

Molecular evolutionary rate estimates have been shown to depend on the time period over which they are estimated. Factors such as demographic processes, calibration errors, purifying selection, and the heterogeneity of substitution rates among sites (RHAS) are known to affect the accuracy with which rates of evolution are estimated. We use mathematical modeling and Bayesian analyses of simulated sequence alignments to explore how mutational hotspots can lead to time-dependent rate estimates. Mathematical modeling shows that underestimation of molecular rates over increasing time scales is inevitable when RHAS is ignored. Although a gamma distribution is commonly used to model RHAS, we show that when the actual RHAS deviates from a gamma-like distribution, rates can either be under- or overestimated in a time-dependent manner. Simulations performed under different scenarios of RHAS confirm the mathematical modeling and demonstrate the impacts of time-dependent rates on estimates of divergence times. Most notably, erroneous rate estimates can have narrow credibility intervals, leading to false confidence in biased estimates of rates, and node ages. Surprisingly, large errors in estimates of overall molecular rate do not necessarily generate large errors in divergence time estimates. Finally, we illustrate the correlation between time-dependent rate patterns and differential saturation between quickly and slowly evolving sites. Our results suggest that data partitioning or simple nonparametric mixture models of RHAS significantly improve the accuracy with which node ages and substitution rates can be estimated.

Analyses of 55 individual and 31 concatenated protein data sets encoded in Reclinomonas americana and Marchantia polymorpha mitochondrial genomes revealed that current methods for constructing phylogenetic trees are insufficiently sensitive (or artifact-insensitive) to ascertain the sister of mitochondria among the current sample of eight α-proteobacterial genomes using mitochondrially-encoded proteins. However, Rhodospirillum rubrum came as close to mitochondria as any α-proteobacterium investigated. This prompted a search for methods to directly compare eukaryotic genomes to their prokaryotic counterparts to investigate the origin of the mitochondrion and its host from the standpoint of nuclear genes. We examined pairwise amino acid sequence identity in comparisons of 6,214 nuclear protein-coding genes from Saccharomyces cerevisiae to 177,117 proteins encoded in sequenced genomes from 45 eubacteria and 15 archaebacteria. The results reveal that ∼75% of yeast genes having homologues among the present prokaryotic sample share greater amino acid sequence identity to eubacterial than to archaebacterial homologues. At high stringency comparisons, only the eubacterial component of the yeast genome is detectable. Our findings indicate that at the levels of overall amino acid sequence identity and gene content, yeast shares a sister-group relationship with eubacteria, not with archaebacteria, in contrast to the current phylogenetic paradigm based on ribosomal RNA. Among eubacteria and archaebacteria, proteobacterial and methanogen genomes, respectively, shared more similarity with the yeast genome than other prokaryotic genomes surveyed.