The Ancestral Process of Long-Range Seed Bank Models
| Autor: | Dario Spanò, Jochen Blath, Noemi Kurt, Adrián González Casanova |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Most recent common ancestor
Statistics and Probability renewal process General Mathematics 010102 general mathematics Wright‒Fisher model Kingman coalescent long-range interaction 01 natural sciences Coalescent theory 92D15 seed bank Fixation (population genetics) 010104 statistics & probability 60K05 Bounded function Statistics Age distribution Renewal theory 0101 mathematics Statistics Probability and Uncertainty Merge (version control) Mathematical economics Positive probability Mathematics |
| Zdroj: | J. Appl. Probab. 50, no. 3 (2013), 741-759 |
| ISSN: | 1475-6072 0021-9002 |
| DOI: | 10.1017/s0021900200009815 |
| Popis: | 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). |
| Databáze: | OpenAIRE |
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