Dynamical phases in growing populations: understanding recovery from bottlenecks

TL;DR

This paper investigates how the rate of population growth after a bottleneck influences long-term demographic outcomes, revealing that different growth rates can lead to distinct evolutionary trajectories due to intrinsic fluctuations.

Contribution

It introduces a novel framework linking growth rate, mutation, and fluctuations to dynamical phases in recovering populations, highlighting critical thresholds affecting evolution.

Findings

Growth rate critically influences post-bottleneck outcomes.

Fluctuations decrease with increasing population size, affecting dynamics.

Distinct regimes of demographic behavior emerge at critical population sizes.

Abstract

Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given population bottleneck remain poorly understood. In this context, we show that long-term post-bottleneck outcomes can depend crucially on the rate at which a diminished population grows whilst recovering. That is, two otherwise identical populations, each having undergone the same bottleneck, can fixate on dramatically different demographics due to different rates of post-bottleneck growth. This behaviour is moreover shown to change non-trivially with different levels of mutation. The underlying mechanism can be traced to intrinsic fluctuations whose standard deviation decreases in time with the inverse square root of the growing population size. Crucially, such decreasing fluctuations couple to the underlying dynamics and result in distinct regimes of (non-equilibrium) demographic behaviour, delimited by abrupt transitions at critical population sizes. Seen through this lens, growth and mutation alter evolutionary outcomes by changing the duration and character of dynamical phases; a feature that we speculate may be of generic importance across many systems.