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On the ancestral process of long-range seed bank models
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Spanò, Dario, Blath, J., Kurt, Noemi and Gonzales Casanova, Adrian (2013) On the ancestral process of long-range seed bank models. Journal of Applied Probability, Volume 50 (Number 3). pp. 741-759. ISSN 0021-9002.
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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).
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Journal of Applied Probability | ||||
Publisher: | Applied Probability Trust | ||||
ISSN: | 0021-9002 | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 50 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 741-759 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
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