Relaxed phylogenetics and dating with confidence

Abstract

In phylogenetics, the unrooted model of phylogeny and the strict molecular clock model are two extremes of a continuum. Despite their dominance in phylogenetic inference, it is evident that both are biologically unrealistic and that the real evolutionary process lies between these two extremes. Fortunately, intermediate models employing relaxed molecular clocks have been described. These models open the gate to a new field of "relaxed phylogenetics." Here we introduce a new approach to performing relaxed phylogenetic analysis. We describe how it can be used to estimate phylogenies and divergence times in the face of uncertainty in evolutionary rates and calibration times. Our approach also provides a means for measuring the clocklikeness of datasets and comparing this measure between different genes and phylogenies. We find no significant rate autocorrelation among branches in three large datasets, suggesting that autocorrelated models are not necessarily suitable for these data. In addition, we place these datasets on the continuum of clocklikeness between a strict molecular clock and the alternative unrooted extreme. Finally, we present analyses of 102 bacterial, 106 yeast, 61 plant, 99 metazoan, and 500 primate alignments. From these we conclude that our method is phylogenetically more accurate and precise than the traditional unrooted model while adding the ability to infer a timescale to evolution.

Figure 1. The Rooted Binary Tree Used for Simulating Sequence Evolution

The timescale is drawn in arbitrary time units. Apart from the branch leading to the outgroup, sequence O, all branches are five time units in length.

Figure 2. A Tree of 69 Influenza A Virus Sequences Drawn Randomly from the Posterior Distribution

The divergence times correspond to the mean posterior estimate of their age in years. The yellow bars represent the 95% HPD interval for the divergence time estimates. Both the mean and 95% HPD of the divergence times were calculated conditional on the existence of the clade defined by the divergence. Each node in the tree that has a posterior probability greater than 0.5 is labeled with its posterior probability. The sampling times of the tips were assumed to be known exactly. Branches colored in red had a posterior rate greater than the average rate, whereas branches colored in blue had a lower-than-average rate.

Figure 3. The Analysis of 17 Marsupials and Seven Placental Mammals

(A) The combined prior distribution of divergence times for the MAP tree topology. The green bars represent the 95% HPD interval for the divergence times. (B) The posterior distribution of the divergence times. The divergence times correspond to the mean posterior estimate of their age in millions of years. The yellow bars represent the 95% HPD interval for the divergence time estimates. Both the mean and 95% HPD of the divergence times were calculated conditional on the existence of the clade defined by the divergence. Each node in the tree is labeled with its posterior probability if it is greater than 0.5. The three nodes with normally distributed calibration priors are indicated by orange bars. Branches colored in red had a posterior rate greater than the average rate, whereas branches colored in blue had a lower-than-average rate.

Figure 4. The “True” Phylogenies for the Large Datasets

The datasets are as follows: (A) bacterial, (B) yeast, (C) plant, (D) metazoan, and (E) primate.

Figure 5. A Lognormal Distribution Discretized into 12 Rate Categories

Each of the 12 categories has equal probability ( p = 1/12). The i ^th rate category (numbered from left to right) corresponds to the (I − 0.5)/12 quantile of the lognormal distribution.