Exploiting fast-variables to understand population dynamics and evolution

TL;DR

This paper introduces a continuous-time stochastic modeling framework for biological populations that leverages slow variables to simplify complex dynamics, highlighting the importance of demographic noise in evolutionary outcomes.

Contribution

It presents a novel approach to model population dynamics using time-scale separation, emphasizing the role of demographic noise in evolutionary predictions.

Findings

Demographic noise can reverse the direction of selection.

Slow variables enable simplified models of complex dynamics.

Retaining demographic noise is crucial for accurate evolutionary analysis.

Abstract

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are caused by individual events while the dynamics are described in terms of the time-evolution of a probability density function. In general, the application of the diffusion approximation still leaves a description that is quite complex. However, in many biological applications one or more of the processes happen slowly relative to the system's other processes, and the dynamics can be approximated as occurring within a slow low-dimensional subspace. We review these time-scale separation arguments and analyse the more simple stochastic dynamics that result in a number of cases. We stress that it is important to retain the demographic noise derived in this way, and emphasise this point by showing that it can alter the direction of selection compared to the prediction made from an analysis of the corresponding deterministic model.