Extended error threshold mechanism in {\it quasispecies} theory via population dynamics

TL;DR

This paper extends Eigen's quasispecies theory by deriving a new error threshold formula that accounts for multiple copying errors per digit, using a population dynamics approach to better understand genetic information preservation.

Contribution

It introduces a generalized error threshold formula for Eigen's model that considers multiple errors per replication, expanding the traditional single-error threshold analysis.

Findings

Derived a new formula for the error threshold with multiple errors per digit

Demonstrated the model's applicability to various error rates

Enhanced understanding of genetic information stability in evolving populations

Abstract

We investigate Eigen's model for the evolution of the genetic code of microorganisms using a novel method based on population dynamics analysis. This model, for a given number of offspring, determines long-term survival as a function of the "genetic" information length and copy error probability. There exists a maximum threshold for the quantity of information that can be consistently preserved through the process of evolution within a population of perfectly replicating sequences, meaning no errors are allowed. With our formula, we expand upon the traditional error threshold formula of Eigen's theory and introduce a new expression for general cases where the self-reproduction process allows up to any integer number of copying errors per digit per replication step.