An approximation of populations on a habitat with large carrying capacity
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911805977133056 |
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| author | Bauman, N. Chigansky, P. Klebaner, F. |
| author_facet | Bauman, N. Chigansky, P. Klebaner, F. |
| contents | We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton-Watson branching process and then its size follows an almost deterministic path until reaching its maximum, sustainable by the habitat. In this paper we put forward an alternative and, in fact, more accurate approximation which suggests that the population size behaves as a special nonlinear transformation of the Galton Watson process from the very beginning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03735 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An approximation of populations on a habitat with large carrying capacity Bauman, N. Chigansky, P. Klebaner, F. Probability 60J80, 92D25 We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton-Watson branching process and then its size follows an almost deterministic path until reaching its maximum, sustainable by the habitat. In this paper we put forward an alternative and, in fact, more accurate approximation which suggests that the population size behaves as a special nonlinear transformation of the Galton Watson process from the very beginning. |
| title | An approximation of populations on a habitat with large carrying capacity |
| topic | Probability 60J80, 92D25 |
| url | https://arxiv.org/abs/2303.03735 |