Figure 4

Identification of the error-thresholds. (A) The difference between the greatest and the second greatest eigen value (Δλ) is plotted against the error rate (1 - q). The error rate for which Δλ is minimum can be identified as the error-threshold, ν = 50 and f _d = 0.99^d. The value of κ is indicated in the graph. [The actual value of κ is determined in the same way as in Fig. 3, and this is true in this figure unless otherwise stated.] For κ = 1, the line is thicker. (B) The average Hamming distance of the ancestor distribution from the fittest genotype, ${\displaystyle {\sum }_{d=0}^{\nu }{a}_d\left(\infty ,\infty \right)}$, is plotted against 1 - q. The figure depicts the genealogical delocalization of the population from the fittest genotype for high error rates irrespective of the lethality of mutants, and the clear existence of the error-threshold for high lethality of mutants. The thick solid line is for κ = 0.05. The other solid lines are for κ = 1, 0.3, 0.2, respectively from left to right. The stars represent the average Hamming distance between the common ancestors and the fittest genotype obtained from the finite population model (see text). Note that the ancestors from the early simulation (< 10000) steps were discarded to consider the system only at an equilibrium. κ = 0.05. The arrow represents a simulation run which is depicted in (C). (C) The Hamming distance of the common ancestors is plotted against the time step at which the common ancestors were born. The meta-stability is observed as random switching between two modes. The plot was obtained from the simulation run indicated by the arrow in (B). 1 - q = 0.025.