  We build upon our previous analytical results for the Penna model of
senescence to include positive mutations. We investigate whether a small but
non-zero positive mutation rate gives qualitatively different results to the
traditional Penna model in which no positive mutations are considered. We find
that the high-lifespan tail of the distribution is radically changed in
structure, but that there is not much effect on the bulk of the population. Th
e mortality plateau that we found previously for a stochastic generalization of
the Penna model is stable to a small positive mutation rate.
