Statistical properties and error threshold of quasispecies on single-peak Gaussian-distributed fitness landscapes

TL;DR

This paper investigates how stochastic fluctuations in fitness landscapes affect the error threshold and statistical properties of quasispecies, revealing linear relations and distribution changes near the threshold, which aids antiviral strategy development.

Contribution

It introduces a Gaussian-distributed fitness landscape to analyze error threshold behavior and statistical properties of quasispecies, extending prior models with environmental fluctuations.

Findings

Error threshold width correlates linearly with fitness fluctuation strength.

Relative concentration fluctuations are minimized at the maximum of the average concentration.

Bimodal distribution of relative concentration occurs near the error threshold.

Abstract

The stochastic Eigen model proposed by Feng et al. (Journal of theoretical biology, 246 (2007) 28) showed that error threshold is no longer a phase transition point but a crossover region whose width depends on the strength of the random fluctuation in an environment. The underlying cause of this phenomenon has not yet been well examined. In this article, we adopt a single peak Gaussian distributed fitness landscape instead of a constant one to investigate and analyze the change of the error threshold and the statistical property of the quasi-species population. We find a roughly linear relation between the width of the error threshold and the fitness fluctuation strength. For a given quasi-species, the fluctuation of the relative concentration has a minimum with a normal distribution of the relative concentration at the maximum of the averaged relative concentration, it has however a largest value with a bimodal distribution of the relative concentration near the error threshold. The above results deepen our understanding of the quasispecies and error threshold and are heuristic for exploring practicable antiviral strategies.