Biological Time Scale and Ageing in the Penna Model

Abstract

Computer study of population evolution in a modified Penna model is presented. We introduced biological time scale for which time runs faster for younger individuals than for the old ones. Such mechanism is likely to be present in real organisms. Results of computer simulation are compared with the classical Penna model which accounts for genetic death caused by too many ’bad’ mutations m, and with the simplest logistic model approach which ignores genetic death and accounts only for elimination due to limited environmental capacity. The first conclusion is that the partial distribution function p(m) of ’bad’ mutations m in the population for groups of same age a, is different from the standard Penna model and shows a clear tendency that young population becomes healthier, that is with smaller portion of youngsters with many bad mutations. This effect is less pronounced for older individuals. It may be statistically significant to be observed in real populations. The second important conclusion is that scaling does not hold when we repeat calculations on machine of different number of bits per word, and/or when we code genomes on different number of words. This is a direct consequence of the fact that operations setting up for one evolution cycle do not commute in the limit of discrete age representation. For typical set of model parameters, calculations on population of order of one million items requires about 100MB memory and execution takes couple of hours for 2 or 3 thousand iterations on HP S2000 machine.