Proportion of Trees Showing Support for Temporally-Varying Speciation Model Using Coalescent Approximation.

<p>Results from simulations showing the proportion of phylogenies for which a temporally-varying speciation (TVS) model (Model 4a of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0043348#pone.0043348-Morlon1" target="_blank">[23]</a>) is preferred over a constant-rate birth-death model (BD; Model 3 of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0043348#pone.0043348-Morlon1" target="_blank">[23]</a>) using AIC to select amongst the models. Both the models were formulated according to a coalescent-based approximation of the likelihood <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0043348#pone.0043348-Morlon1" target="_blank">[23]</a>. We used a AIC cutoff of 4 to favor the TVS model when the generating model was a constant-rate process. Extinction rate, , varies across the plots (); speciation rate, , and total tree-depth, are held constant ( and ). All are plotted against the expected number of taxa across the cumulative distribution of probability densities (from 0.99 to 0.01). The dashed vertical line represents the expected value for under the simulating conditions. Each point represents 1000 simulations. (Results for and not shown.)</p

Type-1 Error Rate for the

<p><b>-Statistic.</b> Results from simulations showing the Type-1 error rate for the statisitc, signifying a false inference of a slowdown. All trees were generated under a constant-rate birth-death (or pure-birth) process. We recognize a Type-1 error if the value of (significant at ; one-tailed test). Extinction rate, , varies across the plots (); speciation rate, , and total tree-depth, are held constant ( and ). All are plotted against the expected number of taxa across the cumulative distribution of probability densities (from 0.99 to 0.01). The dashed vertical line represents the expected value for under the simulating conditions. Each point represents 1000 simulations. (Results for and not shown.)</p

Exemplar Lineages-Through-Time Plot.

<p>An example of a lineages-through-time (LTT) plot for a tree (shown on left) drawn from the far right tail of the distribution of tree sizes (5 percent of surviving trees are expected to be this large or larger) for , and . The dotted line is the expected number of lineages under a constant diversification rate. This LTT plot shows the typical signature of an early burst of speciation yet this signature is not captured by the -statistic (; not significant) as the burst is masked by later extinction events.</p

Proportion of Trees Showing Support for Diversity-Dependent Model.

<p>Results from simulations showing the proportion of phylogenies for which a density-dependent (DD) model is preferred over a constant-rate birth-death (BD) model in using AIC to select amongst the models. Only the DD model and a BD model were compared. We used a AIC cutoff of 4 to favor a DD model when the generating model was a constant-rate process. Extinction rate, , varies across the plots (); speciation rate, , and total tree-depth, are held constant ( and ). All are plotted against the expected number of taxa across the cumulative distribution of probability densities (from 0.99 to 0.01). The dashed vertical line represents the expected value for under the simulating conditions. Each point represents 1000 simulations. (Results for and not shown.)</p