Stochastic models of evolution in genetics, ecology and linguistics

Blythe, Richard A.; McKane, Alan J.

doi:10.1088/1742-5468/2007/07/p07018

Cited by 206 publications

(345 citation statements)

References 103 publications

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“…1 Illustration of four systems featuring timescale separation that can be analysed with the methods reviewed in this paper. Top left panel: Phase plot for a haploid Moran model with two alleles on two islands with strong migration (described in Sect.…”

Section: Setting-up the Modelmentioning

confidence: 99%

“…Since we are aiming to be as simple as possible to illustrate the basic ideas, we will assume that this fitness weighting is the same on both islands, though it is simple enough to relax this condition. Therefore we will denote the fitness weighting of allele 1 to be W (1) (n) and of allele 2 to be W (2) (n). Then the four transition rates from state (n 1 , n 2 ) to the new state are…”

Section: Setting-up the Modelmentioning

confidence: 99%

“…(3) the reader is referred to previous discussions in the literature [1,6,43]. If W (1) and W (2) are independent of n, then the selection is known as frequency independent selection. This will be assumed in this pedagogical treatment, and we write…”

Section: Setting-up the Modelmentioning

confidence: 99%

“…, where s is a selection coefficient and α (1) , α (2) are constants. Since s is typically very small, we do not expect it will be necessary to include the order s 2 terms in the expressions for W (1) and W (2) .…”

Section: Setting-up the Modelmentioning

confidence: 99%

“…Since s is typically very small, we do not expect it will be necessary to include the order s 2 terms in the expressions for W (1) and W (2) .…”

Section: Setting-up the Modelmentioning

confidence: 99%

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Exploiting Fast-Variables to Understand Population Dynamics and Evolution

Constable

McKane

2017

J Stat Phys

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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.

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Section: Setting-up the Modelmentioning

confidence: 99%

Section: Setting-up the Modelmentioning

confidence: 99%

Section: Setting-up the Modelmentioning

confidence: 99%

Section: Setting-up the Modelmentioning

confidence: 99%

“…Since s is typically very small, we do not expect it will be necessary to include the order s 2 terms in the expressions for W (1) and W (2) .…”

Section: Setting-up the Modelmentioning

confidence: 99%

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Exploiting Fast-Variables to Understand Population Dynamics and Evolution

Constable

McKane

2017

J Stat Phys

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References

2013

Spatial Simulation

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Molecular Dynamics Investigation of Liquid and Vapor Interactions Near an Evaporating Interface: A Theoretical Genetics Perspective

Montazeri

Hao

Qomi

et al. 2020

Advcd Theory and Sims

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Understanding phase transition between the liquid and gaseous states has gained significant interest, and has been ubiquitously observed in many places ranging from natural systems to water–energy nexus and thermal management applications. Phase transition phenomena at liquid–vapor interfaces are greatly governed by intermolecular‐level kinetics, which requires the use of empirical parameters in continuum‐level relations to explain the discrete nature of molecular particles. Despite its significance, it has been a great challenge to find detailed expressions of empirical parameters such as accommodation coefficients, which represent the probabilities for phase transition of liquid or vapor molecules at the interface. Here, direct statistical measurements of accommodation coefficients are reported by tracking the trajectories of liquid and vapor molecules in molecular simulations. The measurements reveal that evaporation and condensation coefficients are different by ≈50%, whereas they have been assumed to be equal in most previous studies. Then, the indirect measurement method is studied from a perspective of theoretical genetics based on the diffusion approximation. A good agreement between two approaches suggests that diffusion approximation can contribute to provide empirical parameters with a cost‐effective method.

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Stochastic models of evolution in genetics, ecology and linguistics

Cited by 206 publications

References 103 publications

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

References

Molecular Dynamics Investigation of Liquid and Vapor Interactions Near an Evaporating Interface: A Theoretical Genetics Perspective

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