A stochastic rate-calibrated method for time-scaling phylogenies of fossil taxa

1. Applying phylogeny-based analyses of trait evolution and diversification in the fossil record generally involves transforming an unscaled cladogram into a phylogeny scaled to geologic time. Current methods produce single time-scaled phylogenies with no indication of the uncertainty in the temporal relationships and, under some methods, artificial zero-length branches. 2. Here, I present a stochastic algorithm for time-scaling phylogenies of fossil taxa by randomly sampling node ages from a constrained distribution, with the ultimate goal of producing large samples of time-scaled phylogenies for a given data set as the basis for phylogeny-based analyses. I describe how this stochastic approach can be extended to consider potential ancestral relationships and resolve polytomies. 3. The stochastic selection of node ages in this algorithm is weighted by the probability density of the total inferable unobserved evolutionary history at single divergence events in a tree, a distribution dependent on rates of branching, extinction and sampling in the fossil record. 4. The combined time-scaling method must be calibrated with explicit estimates of three rates: branching, extinction and sampling, and thus is named the cal3 time-scaling method, included in the r library paleotree. I test the time-scaling capabilities of the cal3 and older time-scaling methods in simulations. cal3 produces samples of time-scaled trees that better bracket the uncertainty in the true node ages than existing time-scaling methods. This is true even in simulations under a terminal-taxon' model of differentiation that violates many of the assumptions of the cal3 method. 5. The cal3 method provides a new approach for time-scaling palaeontological cladograms, calibrated to estimated sampling and diversification rates, allowing for better estimates of uncertainty in the phylogenetic time-scaling. The cal3 method is robust to relaxation of at least some model assumptions. Additional work is needed to analyse the impact of time-scaling approaches on macroevolutionary analyses and to integrate time-scaling with phylogenetic inference.