The quasispecies distribution

TL;DR

This paper explores the quasispecies model's mathematical structure, focusing on its stationary solutions and revealing connections to combinatorial numbers like Eulerian and Stirling numbers.

Contribution

It provides a detailed analysis of the stationary solutions of the quasispecies model and uncovers their combinatorial properties.

Findings

Stationary solutions involve Eulerian and Stirling numbers.

The model exhibits a rich combinatorial structure.

Connections to permutation up-down coefficients.

Abstract

The quasispecies model was introduced in 1971 by Manfred Eigen to discuss the first stages of life on Earth. It provides an appealing mathematical framework to study the evolution of populations in biology, for instance viruses. We present briefly the model and we focus on its stationary solutions. These formulae have a surprisingly rich combinatorial structure, involving for instance the Eulerian and Stirling numbers, as well as the up--down coefficients of permutations.