Growing Probability of Additional Offspring with a Beneficial Reversal Allele in the Decoupled Continuous-time Mutation-selection Model

TL;DR

This study analyzes the probability of beneficial alleles spreading in populations using a decoupled continuous-time mutation-selection model, revealing how various parameters influence growth probabilities in an asymmetric landscape.

Contribution

It introduces a theoretical framework connecting the decoupled continuous-time model with the Moran two-allele model for predicting allele growth probabilities.

Findings

Growing probability inversely proportional to measuring parameter when C<1/Ns*

Saturation of growing probability occurs when C>1/Ns*

Selective advantage ratio decreases with increasing sequence length

Abstract

The growing probabilities of additional offspring with the beneficial reversal allele for various population sizes, $N$, sequence lengths, $L$, selective advantages, $s$, fitness parameters, $k$, and measuring parameters, $C$, were calculated in an asymmetric sharply-peaked landscape using the decoupled continuous-time mutation-selection model. The growing probability in the stochastic region was inversely proportional to the measuring parameter when $C<1/Ns^*$, bent when $C\approx 1/Ns^*$ and became saturated when $C>1/Ns^*$, where $s^*$ is the effective selective advantage. The saturated growing probability in the stochastic region was approximately the effective selective advantage when $C\gg 1/Ns^*$ and $s^*\ll 1$. The present study suggests that the growing probability in the stochastic region in an asymmetric sharply-peaked landscape in the decoupled continuous-time mutation-selection model can be described using the theoretical formula for the growing probability in the Moran two-allele model. The selective advantage ratio, which represents the ratio of the effective selective advantage to the selective advantage, does not depend on the population size, selective advantage, measuring parameter, and fitness parameter; instead the selective advantage ratio decreases with increasing the sequence length.