Non-fixation in infinite potential

TL;DR

This paper investigates the implications of infinite adaptive peaks caused by genetic drift, extending escape time formulas to non-Gaussian distributions, and providing a comprehensive landscape model for long-term evolutionary dynamics.

Contribution

It introduces a novel extension of Kramers' escape formula to non-Gaussian cases and constructs a global landscape model for understanding long-term evolutionary behaviors.

Findings

Extended Kramers' escape formula to non-Gaussian distributions.

Developed a global landscape model for evolutionary dynamics.

Analyzed escape times from infinite adaptive peaks.

Abstract

Under the effects of strong genetic drift, it is highly probable to observe gene fixation or loss in a population, shown by divergent probability density functions, or infinite adaptive peaks on a landscape. It is then interesting to ask what such infinite peaks imply, with or without combining other biological factors (e.g. mutation and selection). We study the stochastic escape time from the generated infinite adaptive peaks, and show that Kramers' classical escape formula can be extended to the non-Gaussian distribution cases. The constructed landscape provides a global description for system's middle and long term behaviors, breaking the constraints in previous methods.