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 artificial zero-length branches and no indication of the uncertainty in the temporal relationships. 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 dataset 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 paleontological 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 analyze the impact of time-scaling approaches on macroevolutionary analyses and to integrate time-scaling with phylogenetic inference.

#### R script for methods comparison simulations under budding

This R script will execute the methods comparison simulations shown in the paper under budding differentiation, given that appropriate libraries are installed.

timeTest_budd_r0.1_in5_LAD_11-05-12.R

#### R script for methods comparison simulations under terminal-taxon differentiation

This R script will execute the methods comparison simulations shown in the paper under terminal-taxon differentiation, given that appropriate libraries are installed.

timeTest_candle_r0.1_in5_LAD_11-05-12.R

#### R Workspace for methods comparisons with budding

Workspace file containing methods comparison simulation data generated under budding differentiation.

timeTest_budd_r0.1_in5_LAD_11-05-12.Rdata

#### R Workspace for methods comparisons with terminal-taxon differentiation

Workspace file containing methods comparison simulation data generated under terminal-taxon differentiation.

timeTest_candle_r0.1_in5_LAD_11-05-12.Rdata

#### R script for plotting methods comparison figures

This R script, when executed with the two R workspace files for methods comparisons (see first few lines) will recreate the various methods comparison plots from the paper. Note that the figure numbers in the actual paper have shifted since this script was written, with one figure even being moved to the supplement.

plot_Fig12_Fig13_Fig14_Fig15_11-12-12.R

#### R script for testing Ps derivation with simulations

R script for simulating Ps under various rates to compare to the value calculated by the solved derivation.

testing_Ps_09-21-12.R

#### R Workspace for testing Ps

Workspace file that contains all the simulation data necessary for creating the figure showing the comparison of simulated and calculated values of Ps.

testing_Ps_09-22-12.Rdata

#### R script for plotting Ps comparison figure

R script which, given the workspace file that contains all the simulation data from the Ps comparison, will create the figure showing the comparison of simulated and calculated values of Ps.

plot_testing_Ps.R

#### R script for simulating cap-delta distributions (Budding, set A)

This R script, when executed, generates simulated phylogenies and fossil records under a budding scenario with branching, extinction and sampling rates equal, saving the cap-delta values at the root (as defined in the manuscript).

testing_gap_models_A_09-21-12.R

#### R script for simulating cap-delta distributions (Budding, set B)

This R script, when executed, generates simulated phylogenies and fossil records under a budding scenario with branching and extinction rates greater than sampling rates, saving the cap-delta values at the root (as defined in the manuscript).

testing_gap_models_B_09-21-12.R

#### R script for simulating cap-delta distributions (Budding, set C)

This R script, when executed, generates simulated phylogenies and fossil records under a budding scenario with branching and extinction rates less than sampling rates, saving the cap-delta values at the root (as defined in the manuscript).

testing_gap_models_C_09-21-12.R

#### R script for simulating cap-delta distributions (Bifurcation)

This R script, when executed, generates simulated phylogenies and fossil records under a bifurcating cladogenesis scenario with equal branching, extinction and sampling rates, saving the cap-delta values at the root (as defined in the manuscript).

testing_gap_models_bifurc_09-21-12.R

#### R workspace for simulated cap-delta distributions (Budding, set A)

This contains simulated cap-delta values generated under a budding scenario with equal branching, extinction and sampling rates.

gaptest_data_A_09-22-12.Rdata

#### R workspace for simulated cap-delta distributions (Budding, set B)

This contains simulated cap-delta values generated under a budding scenario with branching and extinction rates greater than the sampling rates.

gaptest_data_B_09-22-12.Rdata

#### R workspace for simulated cap-delta distributions (Budding, set C)

This contains simulated cap-delta values generated under a budding scenario with branching and extinction rates less than the sampling rates.

gaptest_data_C_09-22-12.Rdata

#### R workspace for simulated cap-delta distributions (Bifurcation)

This contains simulated cap-delta values generated under a bifurcating cladogenesis scenario with equal branching, extinction and sampling rates.

gaptest_data_bifurc_09-22-12.Rdata

#### R script for plotting cap-delta comparison figures

This R script, when executed with the four workspaces containing simulated cap-delta values, will generate the histogram and q-q plots shown in the supplement which compare the simulated values against different derivations of the cap-delta function.

plot_gaptest_Fig10_abc&bifurc.R