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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.02809 |
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| _version_ | 1866909387102093312 |
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| author | Videla, Leonardo Tejo, Mauricio Quiñinao, Cristóbal Marquet, Pablo A. Rebolledo, Rolando |
| author_facet | Videla, Leonardo Tejo, Mauricio Quiñinao, Cristóbal Marquet, Pablo A. Rebolledo, Rolando |
| contents | We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the $N$-replicator system and the existence of invariant distributions for a class of associated McKean-Vlasov dynamics. In particular, our results show that, unlike typical models of neutral ecology, fitness equivalence does not need to be assumed but emerges as a condition for the persistence of the system. Further, neutrality is associated with a unique Dirichlet invariant probability measure. We illustrate our findings with some simple case studies, provide numerical results, and discuss our conclusions in the light of Neutral Theory in ecology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02809 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Persistence and neutrality in interacting replicator dynamics Videla, Leonardo Tejo, Mauricio Quiñinao, Cristóbal Marquet, Pablo A. Rebolledo, Rolando Probability Mathematical Physics 60H10, 92D25 We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the $N$-replicator system and the existence of invariant distributions for a class of associated McKean-Vlasov dynamics. In particular, our results show that, unlike typical models of neutral ecology, fitness equivalence does not need to be assumed but emerges as a condition for the persistence of the system. Further, neutrality is associated with a unique Dirichlet invariant probability measure. We illustrate our findings with some simple case studies, provide numerical results, and discuss our conclusions in the light of Neutral Theory in ecology. |
| title | Persistence and neutrality in interacting replicator dynamics |
| topic | Probability Mathematical Physics 60H10, 92D25 |
| url | https://arxiv.org/abs/2310.02809 |