The age of the root inferred by functions FIR, FLOG, and FADD on simulated data with random auto-correlated rate changes

In these simulations, the length of a branch (on what tree!) is selected randomly proportional to its true duration in time. A rate adjustment (change) factor is then chosen randomly form a uniform distribution and all its descendant branch lengths were then multiplied by this factor. A total of 25 such random rate changes were placed on the tree, then the branch lengths (measured in the product of rate and time) of the weighted tree were passed on to the time estimation procedures. The whole procedure was repeated 600 times to obtain the average root time and standard error. Three different ranges were used for the uniform distribution of rate changes. The first has a range of 0.25 to 1 and represent a strong persistent bias towards rate deceleration. A range of 0.5 to 1.5 gives minimal rate change bias, but retains stochastic fluctuations. Finally a strong acceleration effect is achieved by the use of the range 1.0�C1.75. The function FADD gave an age of the root tending to infinity on 139 of the weighted trees simulated under the deceleration model. In such cases the root time is set to 200 mya in order to allow the mean and standard deviation of this cost function to be calculated.