Figure 3

Convergence of the DCFTP-SSA for the bistable gene network (13). (a) As a function of CPU time, we represent ∊ _E , the Euclidean error of the sampled distributions estimated using: the DCFTP-SSA (+), as in Fig. 2 (b); the SSA with T _s = 1000(○), as in Fig. 2 (c); the SSA started from the two modes (*), as in Fig. 2 (d); the SSA started from uniform initial conditions (∇), as in Fig. 2 (e); and the SSA uniformly sampled from a long run (□), as in Fig. 2 (f). For each scheme, we produced N = 100, 316, 1000, 3162 and 10000 samples to show how the error improves as the number of samples increases. The DCFTP-SSA converges to the stationary distribution at the expected N^-1/2 rate, whereas the approximate estimates obtained using the SSA level off in a similar manner as in Fig. 1a. (b) The distribution of coalescence times for the DCFTP-SSA for this network is bimodal with a very long tail for the second mode, indicating the likelihood of long coalescence times. The data presented corresponds to 6000 runs.