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, 2 (4), e384

Robust Time Estimation Reconciles Views of the Antiquity of Placental Mammals


Robust Time Estimation Reconciles Views of the Antiquity of Placental Mammals

Yasuhiro Kitazoe et al. PLoS One.


Background: Molecular studies have reported divergence times of modern placental orders long before the Cretaceous-Tertiary boundary and far older than paleontological data. However, this discrepancy may not be real, but rather appear because of the violation of implicit assumptions in the estimation procedures, such as non-gradual change of evolutionary rate and failure to correct for convergent evolution.

Methodology/principal findings: New procedures for divergence-time estimation robust to abrupt changes in the rate of molecular evolution are described. We used a variant of the multidimensional vector space (MVS) procedure to take account of possible convergent evolution. Numerical simulations of abrupt rate change and convergent evolution showed good performance of the new procedures in contrast to current methods. Application to complete mitochondrial genomes identified marked rate accelerations and decelerations, which are not obtained with current methods. The root of placental mammals is estimated to be approximately 18 million years more recent than when assuming a log Brownian motion model. Correcting the pairwise distances for convergent evolution using MVS lowers the age of the root about another 20 million years compared to using standard maximum likelihood tree branch lengths. These two procedures combined revise the root time of placental mammals from around 122 million years ago to close to 84 million years ago. As a result, the estimated distribution of molecular divergence times is broadly consistent with quantitative analysis of the North American fossil record and traditional morphological views.

Conclusions/significance: By including the dual effects of abrupt rate change and directly accounting for convergent evolution at the molecular level, these estimates provide congruence between the molecular results, paleontological analyses and morphological expectations. The programs developed here are provided along with sample data that reproduce the results of this study and are especially applicable studies using genome-scale sequence lengths.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.


Figure 1
Figure 1. Molecular divergence times and evolutionary rates of placental mammals.
A and B show the MVS-FIR and ML-FLOG trees, respectively. The numbers 1–61 denote the ancestral nodes. The red numbers 1–8 indicate the internal nodes with fossil constraints which are as follows: 1, 49–61; 2, 52–58; 3, 45–63; 4, 43–60; 5, <63; 6, >12; 7, 36–55; 8, 54–65 (all in mya) [see 4], . The colors of the branches denote inferred evolutionary rates (in units of ×10−9/site per year) as follows: black, <0.2; dark blue, 0.2–0.3; light blue, 0.3–0.4; green, 0.4–0.5; brown, 0.5–0.6; yellow, 0.6–0.7; and red, >0.7.
Figure 2
Figure 2. Evolutionary rate changes from the root to the fin whale.
Figures A and B, respectively, trace the estimated rates along edges on analyses using MVS and ML branch lengths. The root time of of the FADD analysis in Figure A and B was set at a large value (400 mya) because the numerical calculation continues towards an infinite root time.
Figure 3
Figure 3. Comparing molecular and fossil records of placental diversification.
The blue squares show the rate of the appearance of new species based on the fossil record [adapted from 3]. At present, such quantitative data are limited to the well-studied North American record. The red circles represent the chronological distribution of node density (or splits) on the MVS-FIR tree (Figure 1A). The green triangles represent split frequency on the ML-FLOG tree (Figure 1B). The node density is given by the number of nodes in an 8 myr sliding window. A scaling constant for the molecular frequencies was calculated via a least-squares fit to the fossil data in the period 85–50 mya.
Figure 4
Figure 4. A worked example of the effect of a transient elevation of evolutionary rate upon estimated divergence times.
In this worked example using a symmetric 32-taxon tree (Figure A), a global molecular clock holds, except for a short-term increase in evolutionary rate along one branch (the red line in Figure A). The true root time was set to 80 mya, and the times at the internal nodes are 48, 56, 64, and 72 mya. The deep internal branch (the red line in Figure A) is given an evolutionary rate ten times that of the remaining edges. The various cost functions were minimized subject to two calibrated nodes (the red numbers 1 and 2 in Figure A), using the exact branch lengths of this example as input data. The cost functions FIR, FLOG, and FADD inferred the weighted trees of Figures B, C and D, respectively. Figures E–G show the trace of evolutionary rates along the lineages from the root to taxa numbers 5, 9, and 25 of Figure A, respectively. The inferred age of the root for each cost function is shown with an arrow. The function FIR recovered the original pattern of rate change, whereas the other two functions inferred far more gradual changes, which resulted in a substantial overestimation of the root time.
Figure 5
Figure 5. A simulation of convergent evolution.
Amino acid substitutions were evolved on the shown weighted tree using the JTT model of amino acid substitutions. After this, 30% of sites were swapped between the four lineages indicated by the red lines.
Figure 6
Figure 6. Branch lengths estimated by MVS, NJ, and ML for the example of convergent evolution in figure 5.
The tree topology inferred by these methods was identical to the tree that generated the data, so the estimated branch lengths are plotted against their true values. The blue numbers show the branch index, as used on Figure 5, of outliers. Note, all the outliers are internal branches ancestral to the four lineages undergoing convergent evolution or are ancestral to the sister group to these lineages. Branch lengths ancestral to the groups undergoing convergent evolution are underestimated by the ML and NJ methods, whereas those ancestral to their sister taxa are overestimated.
Figure 7
Figure 7. Log-likelihood profiles of the FIR, FLOG, and FADD cost functions about the estimated ages of the root.
This figure shows the profile of the cost function with respect to the age of the root estimated by three different cost functions. Because the root age estimated by function FADD was going to infinity, it was set to 200 mya for illustrative purposes. Figure A is a single example from a tree simulated under the scenario of random auto-correlated changes of rate moving towards the tips, strongly biased towards a deceleration of evolutionary rates as time progresses (from the set of simulations used for Table 3). The true age of the root was 100 mya. Figure B shows the results using the MVS tree derived from the mitochondrial sequences of placental mammals. The dotted line indicates the 95% confidence interval of the estimated age of the root using the sum-of-squares approach described in Materials and Methods.

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