Gompertz mortality law and scaling behavior of the Penna model

The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism's genome is represented by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas [Int. J. Mod. Phys. C 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz law for mortality rates for early ages, which is generally regarded as being empirical.