Asymptotics for the site frequency spectrum associated with the genealogy of a birth and death process
| Autor: | Schweinsberg, Jason, Shuai, Yubo |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Consider a birth and death process started from one individual in which each individual gives birth at rate $\lambda$ and dies at rate $\mu$, so that the population size grows at rate $r = \lambda - \mu$. Lambert and Harris, Johnston, and Roberts came up with methods for constructing the exact genealogy of a sample of size $n$ taken from this population at time $T$. We use the construction of Lambert, which is based on the coalescent point process, to obtain asymptotic results for the site frequency spectrum associated with this sample. In the supercritical case $r > 0$, our results extend results of Durrett for exponentially growing populations. In the critical case $r = 0$, our results parallel those that Dahmer and Kersting obtained for Kingman's coalescent. Comment: 38 pages, 4 figures |
| Databáze: | arXiv |
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