Exact Solution of an Evolutionary Model without Ageing

TL;DR

This paper presents an exact age-structured evolutionary model incorporating mutations, heredity, and fecundity, revealing complex dynamics such as mutational meltdown and linking fertility to Fibonacci sequences.

Contribution

It introduces a novel exact solution for an age-structured model without ageing, integrating mutations and natural selection through an integral equation.

Findings

Fertility relates to generalized Fibonacci sequences.

Mutations and selection are modeled via an integral equation.

System can exhibit mutational meltdown.

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.