On a mathematical relation between the Eigen model and the asexual Wright-Fisher model

TL;DR

This paper establishes a unified stochastic framework linking the Eigen and Wright-Fisher models, clarifying their differences, and extends the concept of the error threshold to sexual diploids, highlighting its relevance in population genetics.

Contribution

It introduces a unified stochastic model that derives both Eigen and Wright-Fisher models as limits, and applies this to analyze error thresholds in sexual diploid populations.

Findings

Eigen and Wright-Fisher models are special cases of a unified stochastic model.

Error threshold and quasispecies concepts are valid in population genetics.

Error threshold for sexual diploids is derived and compared to asexual populations.

Abstract

We show that the Eigen model and the asexual Wright-Fisher model can be obtained as different limit cases of a unique stochastic model. This derivation makes clear which are the exact differences between these two models. The two key concepts introduced with the Eigen model, the error threshold and the quasispecies, are not affected by these differences, so that they are naturally present also in population genetics models. According to this fact, in the last part of the paper, we use the classical diploid mutation-selection equation and the single peak fitness approximation to obtain the error threshold for sexual diploids. Finally, we compare the results with the asexual case.