The rate of multi-step evolution in Moran and Wright-Fisher populations

TL;DR

This paper derives the probability of stochastic tunneling in large populations for Moran and Wright-Fisher models, revealing that tunneling is twice as likely in Wright-Fisher populations.

Contribution

It provides a new analytical approach to compute tunneling probabilities for both models, including finite population cases, advancing understanding of multi-step evolution.

Findings

Tunneling probability is twice as high in Wright-Fisher compared to Moran.

Derived analytical formulas for large populations.

Provided methods for efficient numerical computation for finite populations.

Abstract

Several groups have recently modeled evolutionary transitions from an ancestral allele to a beneficial allele separated by one or more intervening mutants. The beneficial allele can become fixed if a succession of intermediate mutants are fixed or alternatively if successive mutants arise while the previous intermediate mutant is still segregating. This latter process has been termed stochastic tunneling. Previous work has focused on the Moran model of population genetics. I use elementary methods of analyzing stochastic processes to derive the probability of tunneling in the limit of large population size for both Moran and Wright-Fisher populations. I also show how to efficiently obtain numerical results for finite populations. These results show that the probability of stochastic tunneling is twice as large under the Wright-Fisher model as it is under the Moran model.