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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.20825 |
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| _version_ | 1866908858374422528 |
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| author | Jeddi, Anouar |
| author_facet | Jeddi, Anouar |
| contents | In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first, the case of critical or subcritical branching population processes in a regime combining a discretization of the trait space, small mutations, large time and large initial population size, where we are able to characterize using a Hamilton-Jacobi approach, the survival set of the population, and the asymptotic of the logarithmic scaling of subpopulation sizes. Second, we generalize by a direct method the convergence to the classical Hamilton-Jacobi equation obtained in the super-critical branching regime considered in \cite{CMMT} to a more general trait space and under weaker assumptions. Moreover, we establish that the stochastic and the deterministic dynamics are asymptotically equivalent in large population. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20825 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of some stochastic models in population dynamics: a Hamilton-Jacobi approach Jeddi, Anouar Probability Analysis of PDEs In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first, the case of critical or subcritical branching population processes in a regime combining a discretization of the trait space, small mutations, large time and large initial population size, where we are able to characterize using a Hamilton-Jacobi approach, the survival set of the population, and the asymptotic of the logarithmic scaling of subpopulation sizes. Second, we generalize by a direct method the convergence to the classical Hamilton-Jacobi equation obtained in the super-critical branching regime considered in \cite{CMMT} to a more general trait space and under weaker assumptions. Moreover, we establish that the stochastic and the deterministic dynamics are asymptotically equivalent in large population. |
| title | Asymptotic behavior of some stochastic models in population dynamics: a Hamilton-Jacobi approach |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2602.20825 |