Exact Distribution of Divergence Times from Fossil Ages and Tree Topologies

Abstract

Being given a phylogenetic tree of both extant and extinct taxa in which the fossil ages are the only temporal information (namely, in which divergence times are considered unknown), we provide a method to compute the exact probability distribution of any divergence time of the tree with regard to any speciation (cladogenesis), extinction, and fossilization rates under the Fossilized Birth–Death model. We use this new method to obtain a probability distribution for the age of Amniota (the synapsid/sauropsid or bird/mammal divergence), one of the most-frequently used dating constraints. Our results suggest an older age (between about 322 and 340 Ma) than has been assumed by most studies that have used this constraint (which typically assumed a best estimate around 310–315 Ma) and provide, for the first time, a method to compute the shape of the probability density for this divergence time. [Divergence times; fossil ages; fossilized birth–death model; probability distribution.]

Rates and Rocks: Strengths and Weaknesses of Molecular Dating Methods

“…Although the three distributions are not conditioned here on having the same younger bound (i.e., by forcing the three densities to have the same 95% upper quantile for instance), substantial differences in their modes and the variances are observed depending on the value of the fossilization rate. Note however that the uncertainty around the fossilization rate estimated by Didier and Laurin (2020) is much smaller than the two orders of magnitude considered here. Their analysis focused on 109 data points corresponding to a rich collection of fossils.…”

“…The estimation is conditioned here on a particular tree topology, in which Diadectomorpha is placed as outgroup. This topology is one of thousands of equally-most-parsimonious trees obtained from the analysis of a matrix of morphological characters (Didier and Laurin, 2020).…”

“…FIGURE 6 | Distribution of the time of divergence of Amniota under the FBD model for various values of the fossilization rate (ψ). The birth and death rates were set to those given in Didier and Laurin (2020). Stadler et al (2018) recently proposed an extension of the original FBD model that accounts for multiple fossils per species and different modes of speciation.…”

Probabilities of tree topologies with temporal constraints and diversification shifts

“…The probability provided in [3, Supp. Mat., Appendix 2] is actually the same as that just above though it was derived in a different way from [13] and expressed in a slightly different form (see [4,Appendix 1]).…”

“…Last, the approach presented here can be extended in order to take into account fossils. In [4], we started to work in this direction by determining divergence time distributions from tree topologies and fossil ages under the fossilized-birth-death model in order to obtain better node-calibrations for phylogenetic inference.…”