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.
| Language | English |
|---|---|
| Pages | 1-41 |
| Number of pages | 41 |
| Journal | Journal of Statistical Physics |
| Early online date | 1 Nov 2017 |
| DOIs | |
| Status | E-pub ahead of print - 1 Nov 2017 |
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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 journal › Article
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TY - JOUR
T1 - Exploiting Fast-Variables to Understand Population Dynamics and Evolution
AU - Constable, George W.A.
AU - McKane, Alan J
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
KW - Effective models
KW - Noise-induced selection
KW - Population dynamics
KW - Population genetics
KW - Stochastic models
KW - Time-scale separation
UR - http://www.scopus.com/inward/record.url?scp=85032789905&partnerID=8YFLogxK
U2 - 10.1007/s10955-017-1900-1
DO - 10.1007/s10955-017-1900-1
M3 - Article
SP - 1
EP - 41
JO - Journal of Statistical Physics
T2 - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
ER -