Quasispecies Made Simple
Figure 3
The Error Threshold and Error Catastrophe
Left: replacement rates of the two genotypes in Figure 1, w1(1 − μ1) for A1 (solid black line extending to dashes) and w2(1 − μ2) for A2 (gray line). Here we let μ1 = kμ and μ2 = μ, with k > 1 so the two replacement rates can be plotted as lines in the same plane. Since w1 > w2, the constraint on k ensures a higher replacement rate of A1 than of A2 at low mutation rates and the reverse at higher mutation rates. The point at which the lines intersect is the error threshold, beyond which A1 is absent, hence the use of dashes for this part of its replacement rate function. If replacement rate drops below unity, the population goes extinct, so the functions are not extended below one on the vertical axis.
Right: the frequency of A1 declines as the mutation rate increases until the error threshold is reached. At higher mutation rates, only A2 is present. The decline in the frequency of A1 with μ toward the error threshold may be linear (as shown here), concave, or convex, depending on parameter values. (Right side drawn for w1 = 3.0, w2 = 2, and k = 2.)