Exact solution of an evolutionary model without aging

Abstract

We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural selection. An exact solution without ageing is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated indicating that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups as many protozoa and coelenterates is discussed.

Heumann-Hötzel model for aging revisited

“…Alleles responsible for lethal diseases that express late in life, escape from the natural selection and accumulate in the population, provoking senescence. However, if the natural selection is too strong then deleterious mutations might not accumulate [9]. The most successful aging theory of the mutational type is the Penna model [10,11].…”

“…The Gompertz law holds in the age interval x ∈[4,9]. The parameters are: F = 0.1, m = 1, |a| = 2, |b| = 0, R min = 4, R max = 15.…”

Time evolution of the Partridge-Barton model

“…Nevertheless, if the natural selection is too strong then deleterious mutations might not accumulate in the population and the eternal youth could be reached. An evolutionary model with such characteristics was recently studied and solved by Onody and de Medeiros [8].…”