Stochastic slowdown in evolutionary processes

TL;DR

This paper investigates how advantageous mutants in evolutionary models can take longer to fixate than neutral ones, revealing a stochastic slowdown effect in birth-death and Wright-Fisher processes with state-dependent transition probabilities.

Contribution

It demonstrates that even with a fitness advantage, the fixation time can increase due to stochastic effects, and provides a simplified model for better understanding of this phenomenon.

Findings

Fixation time can increase with advantageous mutants due to stochastic slowdown.

The effect occurs for weak but non-zero selection bias in transition rates.

The slowdown phenomenon is also observed in Wright-Fisher models, not just birth-death processes.

Abstract

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but non--vanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.