On the stability of sequences inserted into viral genomes

Willemsen, Anouk; Zwart, Mark P

At the start of each passage, to simulate the bottleneck we draw the number I from a Binomial distribution with a size a and success probability f D from the previous time point, and then D ¼ a À I. To illustrate the effects of bottlenecks we chose the parameters in Table 2 , set the initial f D to zero, and considered various values of a. The difference in fitness between the virus with insertion and without is large (x I =x D ¼ 0:8). The simulation data illustrate how under these conditions narrow bottlenecks can lead to stable inserted sequence (Fig. 2) . During each round of passaging the frequency of the deletion variant comes up, but as it does not reach a frequency near 1/a this variant is not sampled during the bottleneck. Only when the bottleneck is wider is the probability of sampling the virus variant with a deletion large enough for this to occur regularly. Once a deletion variant has been sampled during the bottleneck, it rapidly goes to fixation as it has a much higher fitness than the full-length virus. Figure 1 provides a simple illustration of the same principle.