Fig. 2.

CPU time versus evolutionary distance for the GY model. In all plots the beginning state is AAA. In the left plot the ending state is AAG, in the middle plot the ending state is AAC, and in the right plot the ending state is TTT. Rejection sampling is most efficient in the situation depicted on the left, but it enters an infinite while loop on the right (and is therefore not shown). Direct sampling and uniformization have similar running times, with uniformization being slightly faster. The solid thick lines show predicted CPU times when the cost of initialization and recursion is fitted to the observed CPU times (see Sections 4.1–4.3). The solid thin lines show predicted CPU times when the cost of initialization and recursion is estimated from a simulation study of reversible rate matrices (see Section 4.4). Finally, the dashed lines show predicted CPU times when the initialization and recursion costs are estimated from a simulation study of sparse rate matrices (see Section 4.4).