Persistence and extinction dynamics in a stochastic predator-prey model with emergent Allee effects
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908277711831040 |
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| author | Granados, Carlos Valencia, Leon A. |
| author_facet | Granados, Carlos Valencia, Leon A. |
| contents | The Allee effect describes a decline in population fitness at low densities, potentially leading to extinction. In predator-prey systems, an emergent Allee effect can arise due to interactions such as density-dependent maturation rates and predation constraints. This work studies a stochastic predator-prey model where the prey population is structured into juvenile and adult stages, with maturation following a nonlinear function. We introduce Ito-type stochastic perturbations in mortality rates to account for environmental variability. We first establish the positivity of solutions and derive sufficient conditions for the stability of the trivial equilibrium, prey extinction, and conditional predator extinction. We then analyze prey persistence under specific maturation rate functions. Finally, numerical simulations illustrate the theoretical results and their ecological implications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Persistence and extinction dynamics in a stochastic predator-prey model with emergent Allee effects Granados, Carlos Valencia, Leon A. Populations and Evolution Probability 60K99, 92B05, 60G99 The Allee effect describes a decline in population fitness at low densities, potentially leading to extinction. In predator-prey systems, an emergent Allee effect can arise due to interactions such as density-dependent maturation rates and predation constraints. This work studies a stochastic predator-prey model where the prey population is structured into juvenile and adult stages, with maturation following a nonlinear function. We introduce Ito-type stochastic perturbations in mortality rates to account for environmental variability. We first establish the positivity of solutions and derive sufficient conditions for the stability of the trivial equilibrium, prey extinction, and conditional predator extinction. We then analyze prey persistence under specific maturation rate functions. Finally, numerical simulations illustrate the theoretical results and their ecological implications. |
| title | Persistence and extinction dynamics in a stochastic predator-prey model with emergent Allee effects |
| topic | Populations and Evolution Probability 60K99, 92B05, 60G99 |
| url | https://arxiv.org/abs/2503.17583 |