Joint stationary moments of a two-island diffusion model of population subdivision

Kermany, Amir R.; Zhou, Xiaowen; Hickey, Dónal A.

doi:10.1016/j.tpb.2008.07.004

Cited by 9 publications

(9 citation statements)

References 13 publications

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“…The first mechnism, spontaneous switching has been incorporated in [BGCE + 15], [BGCKWB16] into a population model related to Wright's two island model ( [Wri51], [KZH08]), where the islands correspond to the active and the dormant sub-population (with the distinguishing feature that reproduction is blocked in the dormant part). Here, spontaneous switching events correspond to what one would traditionally call migration between the two sub-populations.…”

Section: Introductionmentioning

confidence: 99%

The seed bank coalescent with simultaneous switching

Blath¹,

Casanova²,

Kurt³

et al. 2020

Electron. J. Probab.

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We introduce a new Wright-Fisher type model for seed banks incorporating "simultaneous switching", which is motivated by recent work on microbial dormancy ([LJ11], [SL17]). We show that the simultaneous switching mechanism leads to a new jump-diffusion limit for the scaled frequency processes, extending the classical Wright-Fisher and seed bank diffusion limits. We further establish a new dual coalescent structure with multiple activation and deactivation events of lineages. While this seems reminiscent of multiple merger events in general exchangeable coalescents, it actually leads to an entirely new class of coalescent processes with unique qualitative and quantitative behaviour. To illustrate this, we provide a novel kind of condition for coming down from infinity for these coalescents using recent results of Griffiths [Gri14].

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Section: Introductionmentioning

confidence: 99%

The seed bank coalescent with simultaneous switching

Blath¹,

Casanova²,

Kurt³

et al. 2020

Electron. J. Probab.

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“…The classical Wright-Fisher frequency process with mutation is reversible. However, the diffusion process of the two-island model is not, as shown in [KZH08]. It turns out, that the seed bank diffusion with mutation is not reversible in general, either.…”

Section: Figurementioning

confidence: 97%

“…In this model, there seems to be no explicit characterization of the stationary distribution, though recursion formulas may still be found, see e.g. [NG93,FGH03,KZH08] for results in this direction. We are also not aware of a full boundary classification.…”

Section: Introductionmentioning

confidence: 99%

Structural properties of the seed bank and the two island diffusion

et al. 2019

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We investigate various aspects of the (biallelic) Wright-Fisher diffusion with seed bank in conjunction with and contrast to the two-island model analysed e.g. in [KZH08] and [NG93], including moments, stationary distribution and reversibility, for which our main tool is duality. Further, we show that the Wright-Fisher diffusion with seed bank can be reformulated as a one-dimensional stochastic delay differential equation, providing an elegant interpretation of the age structure in the seed bank also forward in time in the spirit of [KKL01]. We also provide a complete boundary classification for this two-dimensional SDE using martingale-based reasoning known as McKean's argument.

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“…However, analysis by Kermany et al. (2008) allows the construction of the moments of to any desired order, so in principle, we can indeed construct the steady‐state mutual information exactly as a function of N , m and μ (although in an iterative form, not in closed form).…”

Section: Two Technical Questionsmentioning

confidence: 99%

“…However, analysis by Kermany et al (2008) allows the construction of the moments of P p 1 ; p 2 ; s ¼ 1 ð Þto any desired order, so in principle, we can indeed construct the steady-state mutual information hI s¼1 i exactly as a function of N, m and l (although in an iterative form, not in closed form). However, in view of our results, hI T ð Þ s i and hI T ð Þ s¼1 i (eqns 9 and 10) already provide useful analytical approximations to hI s i and hI s¼1 i.…”

Section: Two Technical Questionsmentioning

confidence: 99%

Predictions of single-nucleotide polymorphism differentiation between two populations in terms of mutual information

et al. 2011

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Mutual information (I) provides a robust measure of genetic differentiation for the purposes of estimating dispersal between populations. At present, however, there is little predictive theory for I. The growing importance in population biology of analyses of single-nucleotide and other single-feature polymorphisms (SFPs) is a potent reason for developing an analytic theory for I with respect to a single locus. This study represents a first step towards such a theory. We present theoretical predictions of I between two populations with respect to a single haploid biallelic locus. Dynamical and steady-state forecasts of I are derived from a Wright-Fisher model with symmetrical mutation between alleles and symmetrical dispersal between populations. Analytical predictions of a simple Taylor approximation to I are in good agreement with numerical simulations of I and with data on I from SFP analyses of dispersal experiments on Drosophila fly populations. The theory presented here also provides a basis for the future inclusion of selection effects and extension to multiallelic loci.

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Joint stationary moments of a two-island diffusion model of population subdivision

Cited by 9 publications

References 13 publications

The seed bank coalescent with simultaneous switching

The seed bank coalescent with simultaneous switching

Structural properties of the seed bank and the two island diffusion

Predictions of single-nucleotide polymorphism differentiation between two populations in terms of mutual information

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