DaTeR: error-correcting phylogenetic chronograms using relative time constraints

Abstract

Motivation: A chronogram is a dated phylogenetic tree whose branch lengths have been scaled to represent time. Such chronograms are computed based on available date estimates (e.g. from dated fossils), which provide absolute time constraints for one or more nodes of an input undated phylogeny, coupled with an appropriate underlying model for evolutionary rates variation along the branches of the phylogeny. However, traditional methods for phylogenetic dating cannot take into account relative time constraints, such as those provided by inferred horizontal transfer events. In many cases, chronograms computed using only absolute time constraints are inconsistent with known relative time constraints.

Results: In this work, we introduce a new approach, Dating Trees using Relative constraints (DaTeR), for phylogenetic dating that can take into account both absolute and relative time constraints. The key idea is to use existing Bayesian approaches for phylogenetic dating to sample posterior chronograms satisfying desired absolute time constraints, minimally adjust or 'error-correct' these sampled chronograms to satisfy all given relative time constraints, and aggregate across all error-corrected chronograms. DaTeR uses a constrained optimization framework for the error-correction step, finding minimal deviations from previously assigned dates or branch lengths. We applied DaTeR to a biological dataset of 170 Cyanobacterial taxa and a reliable set of 24 transfer-based relative constraints, under six different molecular dating models. Our extensive analysis of this dataset demonstrates that DaTeR is both highly effective and scalable and that its application can significantly improve estimated chronograms.

Availability and implementation: Freely available from https://compbio.engr.uconn.edu/software/dater/.

Supplementary information: Supplementary data are available at Bioinformatics online.

Fig. 1.

Chronograms and relative time calibrations. The figure shows two distinct chronograms for the same underlying phylogenetic tree. Each chronogram is dated backward in time, with the six leaves (tips) representing contemporary nodes. Dates assigned to internal nodes are shown italicized within parentheses and are in units of ‘mya’. Implied branch lengths are shown italicized in blue along edges. The dotted red line in each chronogram represents a known HGT event from the edge (y, z) to the edge (v, w). This horizontal transfer provides a relative time calibration, implying that node y must be older than node w. The chronogram on the left is not consistent with this relative time calibration while the chronogram on the right is

Fig. 2.

Illustration of objective functions implemented in DaTeR. (a) An input chronogram which is not consistent with the depicted horizontal transfer event (dotted red line) implying that y should be dated to be at least as old as w. The chronograms shown in parts (b), (c), and (d) are obtained by error-correcting the chronogram in (a) using DaTeR under SBD, SLRB and SDD objective functions, respectively. Observe that each error-corrected chronogram satisfies the relative constraint and that each of the three objective functions results in a slightly different chronogram

Fig. 3.

Average date gap for violated relative constraints. The figure shows the average difference in assigned dates for pairs of nodes corresponding to violated relative constraints in the aggregated input chronograms. A negative difference mean that the constraint is violated (i.e. that the difference in dates is in the wrong direction). Positive differences mean that the constraints are satisfied and the differences in assigned dates are in the correct direction. Results are shown for the aggregated input chronograms and the aggregated chronograms computed using the three objective functions implemented in DaTeR, for each of the six dating models

Fig. 4.

Bar chart of percent change in branch lengths. The number of edges within various percent ranges is shown for aggregated DaTeR-corrected chronograms under the three different objective functions for the CIR_nobd model. All intervals are left-closed and right-open, and a log scale is used for the Y-axis. The total number of edges is 338