Standard Penna Model Research Articles

Numerical solution of the Penna model of biological aging with age-modified mutation rate

In this paper we present results of numerical calculation of the Penna bit-string model of biological aging, modified for the case of a -dependent mutation rate m(a), where a is the parent's age. The mutation rate m(a) is the probability per bit of an extra bad mutation introduced in offspring inherited genome. We assume that m(a) increases with age a. As compared with the reference case of the standard Penna model based on a constant mutation rate m , the dynamics of the population growth shows distinct changes in age distribution of the population. Here we concentrate on mortality q(a), a fraction of items eliminated from the population when we go from age (a) to (a+1) in simulated transition from time (t) to next time (t+1). The experimentally observed q(a) dependence essentially follows the Gompertz exponential law for a above the minimum reproduction age. Deviation from the Gompertz law is however observed for the very old items, close to the maximal age. This effect may also result from an increase in mutation rate m with age a discussed in this paper. The numerical calculations are based on analytical solution of the Penna model, presented in a series of papers by Coe et al. [J. B. Coe, Y. Mao, and M. E. Cates, Phys. Rev. Lett. 89, 288103 (2002)]. Results of the numerical calculations are supported by the data obtained from computer simulation based on the solution by Coe et al.

AN EVOLUTIONARY MODEL BASED ON BIT-STRING WITH INTELLIGENCE

An evolutionary model based on bit-strings with intelligence is set up in this paper. In this model, gene is divided into two parts which relative to health and intelligence. The accumulated intelligence influences the survival process by the effect of food and space restrictions. We modify the Verhulst factor to study this effect. Both asexual and sexual model are discussed in this paper. The results show that after many time steps, stability is reached and the population self-organizes, just like the standard Penna model. The intelligence made the equilibrium to be reached larger both in asexual model and sexual model. Compared with asexual model the population size fluctuates more strongly in the sexual model.

Effect of time slowing in biological ageing

The Penna model which accounts for genetic death was applied in computer simulations of population growth and ageing. In this paper we assume a biological time scale in which time runs faster for younger individuals than for the old ones. This means that we read out the genome's fraction, later used in the life game, at a greater pace of 4 bits per evolution time step for very young individuals, and 1 bit per iteration for the oldest. This new mechanism, likely to be present in nature, yields some new and interesting aspects concerning the final population characteristics. We found that the partial distribution function p ( m ) of ‘bad’ mutations m , for groups of same age a , is altered as compared with the standard Penna model. The tendency is that a young population becomes healthier, that is with a smaller portion of youngsters with many bad mutations. This effect is still present yet less pronounced for older individuals. We expect that the main findings may be statistically significant to be observed in real populations. For a typical set of model parameters, calculations on population of the order of one million items requires about 100 MB memory and execution takes a couple of hours for 2 or 3 thousand iterations on the HP EXEMPLAR machine.

Penna model of biological aging on a lattice

The Penna bit-string model of biological aging is implemented on a square lattice. Hence, there is no need to manipulate the population size by the Verhulst factor. Instead, the spatial lattice relations between neighboring individuals are considered. Mortality obtained in the lattice asexual Penna model is different from the corresponding feature of the standard Penna model.

Biological Ageing with Birth Rate Controlled by Mutations in the Penna Model

Summary Within the Penna model, we assume a modification with a reproduction rate B that depends on the health state of the individual defined by the number of bad mutations. The idea is that biologically weaker individuals has got less chance to produce offsprings. The results obtained from simulations and for typical set of model parameters show that then the mortality rate q(a) is increasing faster with age a. The maximum age is also limited from about 50 percent of the biological maximum lifespan for the standard Penna model, to about 40 percent. We also conclude that bad mutation distribution r(a) is altered so that younger individuals may accommodate significantly more bad mutations, up to 25 percent, as compared with the standard model (5 percent). In summary, it makes sense to force less productivity for older and weaker individuals.

Influence of variations in threshold of bad mutations on age structure of the population

Computer study of population evolution in a modified Penna model is presented, where different thresholds T for bad mutation may be assigned to individuals. The model indicates a possible source of such fluctuations of T due to embryo period of life before birth. Changes in age characteristics of the population, survival rate and mutation distributions at equilibrium are discussed. Results of computer simulation are compared with the standard Penna model with no fluctuation in T. We obtained larger equilibrium population for the same environmental capacity. However, the survival rate is smaller and the age of the oldest individuals also decreases. This is also reflected in age distribution of the population, similar at older populations and with higher decrease rate among younger ones. Also, the mutation accumulation is similar for older ages, yet younger individuals may absorb more mutations as a result of the presence of some items with threshold value above the average T. We conclude that fluctuations in threshold T may alter population characteristics, also in terms of measurable statistics in population such as age distribution or the survival rate.