The γ statistic does, however, provide a powerful method to validate pure-birth tree simulation algorithms.
The intervals between cladogenic events for a pure-birth tree can be simulated by random sampling from an exponential distribution, with the rate increasing as a function of the number of lineages present at a given time.
The mean of dj is the mean time that j nodes are present based upon simulated pure-birth trees.
Using the command episodic, pure-birth trees were simulated with birth = 3, followed by birth = 1 after a given number of taxa had been simulated.
Pure-birth trees simulated in Phylogen include the entirety of the most recent branch length, resulting in the desired statistical properties for γ (mean = 0, σ2 = 1).
The distribution of tree deviations (TD) based on simulated pure-birth trees was used to identify trees that occurred below the 0.05 quantile, as these trees tend to be those with early, rapid accumulation of lineages (Figure 4B).
The null distribution for the 'tree deviation' was calculated from 1 million simulated pure-birth trees with incomplete taxon sampling.
1,000 pure-birth trees were simulated with n/ f tips for f values ranging from 0.018 to 0.5.
The Cyt b LTT plot for the focal clade lay largely outside the 95% confidence intervals for nearly the entire history of 10,000 simulated pure-birth trees.
Our null distributions of γ were obtained using 10000 simulated pure-birth trees with taxon sampling generated with the program Phylogen [ 76].
These fits were derived from comparisons to 10000 simulated pure-birth trees with taxon sampling generated by the program Phylogen [ 76].
