Narrow Results

The Penna model of aging predicts the accumulation of defective genes expressed after the organism reaches the minimum reproduction age in the genetic pool of the population. The accumulation of defects in the genomes implicates the specific age structure of the modeled populations. Nevertheless, the fraction of defective alleles at loci switched on before the reproduction period does not depend on exact age when precisely they are switched on, it may be just after conception or after birth. We have modeled the mortality of a population in the period before the minimum reproduction age, even before birth, assuming that sets of genes of different size are switched on in different periods of the life span.

In this paper, we consider a generalization to the asexual version of Penna model for biological aging, where we take a continuous time limit. The genotype associated to each individual is an interval of real numbers over which Dirac δ-functions are defined, representing genetically programmed diseases to be switched on at defined ages of the individual life. We discuss two different continuous limits for the evolution equation and two different mutation protocols, to be implemented during reproduction. Exact stationary solutions are obtained and scaling properties are discussed.

We consider the Penna model for biological aging to investigate correlations between early fertility and late life survival rates in populations at equilibrium. We consider inherited initial reproduction ages together with a reproduction cost translated in a probability that mother and offspring die at birth, depending on the mother age. For convenient sets of parameters, the equilibrated populations present genetic variability in what regards both genetically programmed death age and initial reproduction age. In the asexual Penna model, a negative correlation between early life fertility and late life survival rates naturally emerges in the stationary solutions. In the sexual Penna model, selection experiments are performed where individuals are sorted by initial reproduction age from the equilibrated populations and the separated populations are evolved independently. After a transient, a negative correlation between early fertility and late age survival rates also emerges in the sense that populations that start reproducing earlier present smaller average genetically programmed death age. These effects appear due to the age structure of populations in the steady state solution of the evolution equations. We claim that the same demographic effects may be playing an important role in selection experiments in the laboratory.

We have presented elsewhere a model for computer simulation of a colony of individuals reproducing sexually, by meiotic parthenogenesis and by cloning. Our algorithm takes into account food and space restriction, and attacks of some diseases. Each individual is characterized by a string of L "base" units, each of which can be of four types (quaternary model) or two types (binary model). Our previous report was for the case of L = 12 (quaternary model) and L = 24 (binary model) and contained the result that the fluctuation of population was the lowest for sexual reproduction with four types of base units. The present communication reports that the same conclusion also holds for L = 10 (quaternary model) and L = 20 (binary model), and for L = 8 (quaternary model) and L = 16 (binary model). This model however, suffers from the drawback that it does not show the effect of aging. A modification of the model was attempted to remove this drawback, but the results were not encouraging.

We have simulated the evolution of population using the Penna model of aging. In populations of diploid organisms, without recombination between haplotypes or with low cross-over rate, a specific distribution of defective genes has been established. As an effect, relatively higher mortality is observed during the earliest stages of life. When two independently evolving populations were mixed and co-evolved in one environment without crossbreeding, one population won after several generations and this winning population showed stronger "early" death effect. We conclude that in the environmentally limited size of a population (in the model limit set by Verhulst factor) it is a better strategy to sacrifice younger individuals — higher fractions of such populations reach the reproduction age.

We have simulated the evolution of diploid, sexually reproducing populations using the Penna model of aging. We have noted that diminishing the recombination frequency during the gamete production generates a specific diversity of genomes in the populations. When two populations independently evolving for some time were mixed in one environmental niche of the limited size and crossbreeding between them was allowed, the average lifespan of hybrids was significantly shorter than the lifespan of the individuals of parental lines. Another effect of higher hybrid mortality is the faster elimination of one parental line from the shared environment. The two populations living in one environment co-exist much longer if they are genetically separated — they compete as two species instead of crossbreeding. This effect can be considered as the first step to speciation — any barrier eliminating crossbreeding between these populations, leading to speciation, would favor the populations.

We have simulated the effect of the diversity of the late expressed genes in the genetic pool of population on the phenotypes of individuals in the late ages. Using Penna model based on the Monte Carlo method we have obtained for the oldest fractions of populations lower mortality rates than predicted by the exponential Gompertz function. Such deviations from the expected exponential increase of mortality are the characteristic for populations which are not in equilibrium with the environment, or if a relatively high probability of reversions was assumed, or if the population is heterogeneous. In such populations, the genes expressed in the late ages, are under the very weak selection pressure and thus, highly-polymorphic. As an effect, the probability of the genetically-determined death of the oldest organisms does not grow as fast as predicted by the Gompertz exponential curve describing mortality during earlier periods of life.

We removed from the Penna model for biological aging any random killing Verhulst factor. Deaths are due only to genetic diseases and the population size is fixed, instead of fluctuating around some constant value. We show that these modifications give qualitatively the same results obtained in an earlier paper, where the random killings (used to avoid an exponential increase of the population) were applied only to newborns.

Two aging models were analyzed on whether they can confirm the dauer mutation of the nematode helps to preserve the species. As a result the Penna model shows that populations with dauer larvae survive bad environmental conditions, whereas populations without it die out. In the Stauffer model, the advantage of the dauer mutation for the survival is only given under certain conditions.

The Penna model for biological aging is modified so that the fertility of each individual is determined by means of the number of activated mutations at that time. A new concept of "good" mutation, which makes an individual to mature enough to reproduce, is introduced. It is assumed that each individual can reproduce only during adulthood, which is determined by the number of activated mutations. The results of Monte Carlo calculations using the modified model show that the ranges of the reproductive age are broadened as time goes by, thus showing self-organization in the biological aging to the direction of the maximum self-conservation. In addition, the population, the survival rate, and the average life span were calculated and analyzed by changing the number of new mutations at birth. It is observed that the higher is the considered number of new mutations at birth, the shorter is the obtained average life span. The mortality functions are also calculated and they showed the exponential increase in adulthood, satisfying the Gompertz law.

The efficient usage of parallel computers and workstation clusters for biologically motivated simulations depends first of all on a dynamic redistribution of the workload. For the development of a parallel algorithm for the Penna model of aging we have used a dynamic load balancing library, called PLB. It turns out that PLB manages a nearly balanced load situation during runtime taking only a low communication overhead. We compare different architectures like parallel computers and nondedicated heterogeneous networks, and give some results for large populations.