Viral Evolution and Adaptation as a Multivariate Branching Process

TL;DR

This paper models RNA virus evolution as a multivariate branching process, providing exact solutions and insights into lethal mutagenesis, relaxation time, and population dynamics across different regimes.

Contribution

It introduces a solvable stochastic model for virus evolution, linking it to prior branching process theories and deriving key evolutionary criteria.

Findings

Proof of lethal mutagenesis criterion within the model

Introduction of a quantitative relaxation time concept

Description of expected value evolution in four regimes

Abstract

In the present work we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process in close relation with the branching process advanced by Demetrius, Schuster and Sigmund ("Polynucleotide evolution and branching processes", Bull. Math. Biol. 46 (1985) 239-262), in their study of polynucleotide evolution. We show that in the absence of beneficial forces the model is exactly solvable. As a result it is possible to prove several key results directly related to known typical properties of these systems like (i) proof, in the context of the theory of branching processes, of the lethal mutagenesis criterion proposed by Bull, Sanju\'an and Wilke ("Theory of lethal mutagenesis for viruses", J. Virology 18 (2007) 2930-2939); (ii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation and (iii) the quantitative description of the evolution of the expected values in four distinct regimes: transient, "stationary" equilibrium, extinction threshold and lethal mutagenesis. Moreover, new insights on the dynamics of evolving virus populations can be foreseen.