Exploiting Fast-Variables to Understand Population Dynamics and Evolution

George W.A. Constable, Alan J McKane

Research output: Contribution to journalArticle

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.

LanguageEnglish
Pages1-41
Number of pages41
JournalJournal of Statistical Physics
Early online date1 Nov 2017
DOIs
StatusE-pub ahead of print - 1 Nov 2017

Fingerprint

Population Dynamics
Diffusion Approximation
Stochastic Dynamics
Deterministic Model
Probability density function
Continuous Time
Time Scales
Subspace
Methodology
Prediction
probability density functions
Modeling
leaves
methodology
predictions
approximation
Framework
Review

Keywords

  • Effective models
  • Noise-induced selection
  • Population dynamics
  • Population genetics
  • Stochastic models
  • Time-scale separation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Exploiting Fast-Variables to Understand Population Dynamics and Evolution. / Constable, George W.A.; McKane, Alan J.

In: Journal of Statistical Physics, 01.11.2017, p. 1-41.

Research output: Contribution to journalArticle

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