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September 2013 The ancestral process of long-range seed bank models
Jochen Blath, Adrián González Casanova, Noemi Kurt, Dario Spanò
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J. Appl. Probab. 50(3): 741-759 (September 2013). DOI: 10.1239/jap/1378401233

Abstract

We present a new model for seed banks, where direct ancestors of individuals may have lived in the near as well as the very far past. The classical Wright‒Fisher model, as well as a seed bank model with bounded age distribution considered in Kaj, Krone and Lascoux (2001) are special cases of our model. We discern three parameter regimes of the seed bank age distribution, which lead to substantially different behaviour in terms of genetic variability, in particular with respect to fixation of types and time to the most recent common ancestor. We prove that, for age distributions with finite mean, the ancestral process converges to a time-changed Kingman coalescent, while in the case of infinite mean, ancestral lineages might not merge at all with positive probability. Furthermore, we present a construction of the forward-in-time process in equilibrium. The mathematical methods are based on renewal theory, the urn process introduced in Kaj, Krone and Lascoux (2001) as well as on a paper by Hammond and Sheffield (2013).

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Jochen Blath. Adrián González Casanova. Noemi Kurt. Dario Spanò. "The ancestral process of long-range seed bank models." J. Appl. Probab. 50 (3) 741 - 759, September 2013. https://doi.org/10.1239/jap/1378401233

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1301.92053
MathSciNet: MR3102512
Digital Object Identifier: 10.1239/jap/1378401233

Subjects:
Primary: 92D15
Secondary: 60K05

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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