Comparison of average branch length resulting from single-branch and tree evolution, with probability of branching p = 1/2.

This comparison is done time steps ranging from 1 to 6, listed in the first row. Comparison at larger times becomes computationally prohibitive. Second row lists results obtained from theoretical considerations for the evolution of a single branch (see Table 4). Third row lists expected values resulting from the statistics of trees, (e. g. Tables 5 and 6, for t = 3 and t = 4, respectively). Computation of the entries for t = 5 and 6 has been done numerically, generating the tree trees and their corresponding probabilities automatically. Fourth row displays the relative error between these two measures, that is, (Lasingle branch−Latree)/ Lasingle branch. While these estimates are in agreement for small timesteps, Latree consistently underestimates Lasingle branch for timesteps larger than 3. Last row displays the number of trees needed to carry out the calculations for Latree, indicating a factorial explosive growth in the number of trees required to perform the calculations for these estimates.