A bit-string model for biological aging

Abstract

We present a simple model for biological aging. We studied it through computer simulations and we have found this model to reflect some features of real populations. Keywords:Aging, Monte Carlo Simulationsto appear in Journal of Statistical Physics * Electronic address: gfitjpp@vmhpo.uff.br 1The problem of aging has been studied recently [1] also by computer simulations, useful in understanding how the survival rates for younger and older individuals evolve in time and affect the preservation of the species [2]- [4]. The lowering of survival rates as time goes by is called senescence. Mutations play an important role in senescence modifying the survival rates either increasing them (helpful mutations) or decreasing them (deleterious mutations). In this paper we introduce a simple model for aging using the so-called "bit string strategy". This approach has been applied to other biological systems [5]. Our model is particularly suited for implementation in computers, although analytical results may be obtained providing some approximations. Since it is based on Boolean variables, bit-handling techniques have been used [6]. A complete description of our code will be presented elsewhere [7].Let us consider a population of N(t) individuals, at the time t, each one characterized by a genome which contains the information when a mutation will occur in the lifetime of a given individual. We consider the time as a discrete variable (t = 1, 2, . . . , B) as suited for implementation on computers. Hötzel [8] simulated the largest number of ages simulated up to now (five ages). We denote each time step as one generation since births can occur at each time step. Here, we will treat only hereditary mutations, although somatic mutations can be incorporated without great additional effort. Hence, a genome is a string of B bits defined in the birth and kept unchanged during the individual lifetime. The genome is built as follows: if an individual has the i-th bit in genome set to one it will suffer a deleterious mutation at age i. The parameter T represents a threshold, i.e., the maximum number of deleterious mutations that an individual can suffer and stay alive. In order to include the effect of food and space restrictions and to keep the population within the computer memory limits, we imposed the age-independent Verhulst factor. Hence, an individual which has passed the threshold test only stays alive with a probability (1 − N(t)/N max ). The next step is the birth: an individual whose age is larger than the reproduction age R generates one baby. As far as we know, this is the first model for biological aging where the reproduction age appears as a parameter. Although sex is not a difficulty neither for us nor for our model, we chose to work with asexual populations, for the sake of simplicity -sexual reproduction can be introduced, for example, by mixing the bit strings of two individuals (crossing over). Thus, the baby's genome will be the same as the parent, except by a fraction M of 2 randomly changed bits (mutat...

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