Lookdown construction for a Moran seed-bank model
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908636660367360 |
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| author | Fittipaldi, Maria Clara Casanova, Adrián González Nava, Julio Ernesto |
| author_facet | Fittipaldi, Maria Clara Casanova, Adrián González Nava, Julio Ernesto |
| contents | We present a lookdown construction for a Moran seed-bank model with variable active and inactive population sizes and we show that the empirical measure of our model coincides with that of the Seed-Bank-Moran Model with latency of Greven, den Hollander and Oomen, 2022. Furthermore, we prove that the time to the most recent common ancestor, starting from $N$ individuals with stationary distribution over its state (active or inactive), has the same asymptotic order as the largest inactivity period. We then obtain an asymptotic distribution of the TMRCA, and use this result to find the first order of the asymptotic distribution of the fixation time of a single beneficial mutant conditioned to invade the whole population, which surprisingly is of order $\ln(N)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_12489 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lookdown construction for a Moran seed-bank model Fittipaldi, Maria Clara Casanova, Adrián González Nava, Julio Ernesto Probability 60K35, 92D15 We present a lookdown construction for a Moran seed-bank model with variable active and inactive population sizes and we show that the empirical measure of our model coincides with that of the Seed-Bank-Moran Model with latency of Greven, den Hollander and Oomen, 2022. Furthermore, we prove that the time to the most recent common ancestor, starting from $N$ individuals with stationary distribution over its state (active or inactive), has the same asymptotic order as the largest inactivity period. We then obtain an asymptotic distribution of the TMRCA, and use this result to find the first order of the asymptotic distribution of the fixation time of a single beneficial mutant conditioned to invade the whole population, which surprisingly is of order $\ln(N)$. |
| title | Lookdown construction for a Moran seed-bank model |
| topic | Probability 60K35, 92D15 |
| url | https://arxiv.org/abs/2305.12489 |