Quasispecies distribution of Eigen model

TL;DR

This paper investigates the distribution of quasispecies in the Eigen model's sharp peak landscape using novel tools like Hamming distance variance and similarity networks, revealing insights into error thresholds and local optima.

Contribution

It introduces two new analytical tools to study quasispecies distribution, providing detailed insights into the Eigen model's behavior near the error threshold.

Findings

Identification of three regimes of copying fidelity $q$

Distribution of clustering coefficient $C(k)$ follows a lognormal distribution

Clustering coefficient $C$ versus $d_{0}$ shows linear behavior near the threshold

Abstract

We study sharp peak landscapes (SPL) of Eigen model from a new perspective about how the quasispecies distribute in the sequence space. To analyze the distribution more carefully, we bring forth two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how the configuration of the distribution varies with copying fidelity $q$ in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance $d_{0}$, by which we can get a visual and in-depth result about how the sequences distribute. We find that there are several local optima around the center (global optimum) in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient $C(k)$ follows lognormal distribution and the curve of clustering coefficient $C$ of the network versus $d_{0}$ appears as linear behavior near the threshold.