Solvable Senescence Model Showing a Mortality Plateau

We present some analytic results for the steady states of the Penna model of senescence, generalized to allow genetically identical individuals to die at different ages via an arbitrary survival function. Modeling this with a Fermi function (of modest width) we obtain a clear mortality plateau late in life: something that has so far eluded explanation within such mutation accumulation models. This suggests that factors causing variable mortality within genetically identical subpopulations, which include environmental effects, may be essential to understanding the mortality plateau seen in many real species.

Figure 1

Life span distribution $n\left(l\right)$ for $l_{\max }=20(+),30(\times )$, compared with simulations (boxes). Simulation size ${10}^7$, averaged over 10 runs.

Figure 2

Mortality rate with $l_{\max }=30$ (note log scale).

Figure 3

Mortality rate for Fermi survival functions of different width $w$, and $l_{\max }=30$.

Figure 4

Life span distribution function $C_{T-1}^l{n}_T\left(l\right)$ for $T=4$.

Figure 5

Mortality rate for $T=4$.