Figure 3. The Error Threshold and Error Catastrophe.
Left: replacement rates of the two genotypes in Figure 1, w 1(1 − μ1) for A 1 (solid black line extending to dashes) and w 2(1 − μ2) for A 2 (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 w 1 > w 2, the constraint on k ensures a higher replacement rate of A 1 than of A 2 at low mutation rates and the reverse at higher mutation rates. The point at which the lines intersect is the error threshold, beyond which A 1 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 A 1 declines as the mutation rate increases until the error threshold is reached. At higher mutation rates, only A 2 is present. The decline in the frequency of A 1 with μ toward the error threshold may be linear (as shown here), concave, or convex, depending on parameter values. (Right side drawn for w 1 = 3.0, w 2 = 2, and k = 2.)