Feller Property and Absorption of Diffusions for Multi-Species Metacommunities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918307448225792 |
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| author | Henry, Benoît Wang, Céline |
| author_facet | Henry, Benoît Wang, Céline |
| contents | We consider individuals of two species distributed over m patches, each with a hosting capacity $d_i N$ , where $d_i \in (0, 1]$. We assume that all the patches are linked by the dispersal of individuals. This work examines how the metacommunity evolves in these patches. The model incorporates Wright-Fisher intra-patch reproduction and a general exchange function representing dispersal. Under minimal assumptions, we demonstrate that as $N$ approaches infinity, the processes converge to a diffusion process for which we establish the Feller property. We prove that the limiting process almost surely reaches the absorbing states in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16616 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Feller Property and Absorption of Diffusions for Multi-Species Metacommunities Henry, Benoît Wang, Céline Probability 60G44, 60G53, 60H10, 60J70, 92D25 We consider individuals of two species distributed over m patches, each with a hosting capacity $d_i N$ , where $d_i \in (0, 1]$. We assume that all the patches are linked by the dispersal of individuals. This work examines how the metacommunity evolves in these patches. The model incorporates Wright-Fisher intra-patch reproduction and a general exchange function representing dispersal. Under minimal assumptions, we demonstrate that as $N$ approaches infinity, the processes converge to a diffusion process for which we establish the Feller property. We prove that the limiting process almost surely reaches the absorbing states in finite time. |
| title | Feller Property and Absorption of Diffusions for Multi-Species Metacommunities |
| topic | Probability 60G44, 60G53, 60H10, 60J70, 92D25 |
| url | https://arxiv.org/abs/2601.16616 |