Solvable senescence model with positive mutations

We build upon our previous analytical results for the Penna model of senescence to include positive mutations. We investigate whether a small but nonzero 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. The mortality plateau that we found previously for a stochastic generalization of the Penna model is stable to a small positive mutation rate.

Figure 1

Birth rate $b$ is plotted against the trucated genetic lifespan $l_c$ for $\alpha =0.001(\times )$ and $\alpha =0.005(+)$. In both cases $\beta =\frac{1}{30}$. Genetic lifespan is measured in time steps.

Figure 2

Lifespan distributions for a Penna model with positive mutations in which $\alpha =0.005(\times )$ and $\alpha =0.001(+)$ and without positive mutations $(☉)$. In each case $\beta =\frac{1}{30}$. Genetic lifespan is measured in time steps.

Figure 3

Mortality rates for a Penna model with positive mutations and Fermi-like survivability function in which $w=0.12$, $\alpha =0.005(\times )$, and $\alpha =0.001(+)$ and without positive mutations $(☉)$. In each case $\beta =\frac{1}{30}$. Age is measured in time steps.