Invasion dynamics of super invaders: Elimination of Allee effects by a strategy at the range boundary
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912265639297024 |
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| author | Du, Yihong Li, Ling Ni, Wenjie Shabgard, Narges |
| author_facet | Du, Yihong Li, Ling Ni, Wenjie Shabgard, Narges |
| contents | Using a reaction-diffusion model with free boundaries in one space dimension for a single population species with density $u(t,x)$ and population range $[g(t), h(t)]$, we demonstrate that the Allee effects can be eliminated if the species maintains its population density at a suitable level at the range boundary by advancing or retreating the fronts. It is proved that with such a strategy at the range edge the species can invade the environment successfully with all admissible initial populations, exhibiting the dynamics of super invaders. Numerical simulations are used to help understand what happens if the population density level at the range boundary is maintained at other levels. If the invading cane toads in Australia used this strategy at the range boundary to become a super invader, then our results may explain why toads near the invading front evolve to have longer legs and run faster. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invasion dynamics of super invaders: Elimination of Allee effects by a strategy at the range boundary Du, Yihong Li, Ling Ni, Wenjie Shabgard, Narges Populations and Evolution Analysis of PDEs 35B40, 35K55, 35R35 Using a reaction-diffusion model with free boundaries in one space dimension for a single population species with density $u(t,x)$ and population range $[g(t), h(t)]$, we demonstrate that the Allee effects can be eliminated if the species maintains its population density at a suitable level at the range boundary by advancing or retreating the fronts. It is proved that with such a strategy at the range edge the species can invade the environment successfully with all admissible initial populations, exhibiting the dynamics of super invaders. Numerical simulations are used to help understand what happens if the population density level at the range boundary is maintained at other levels. If the invading cane toads in Australia used this strategy at the range boundary to become a super invader, then our results may explain why toads near the invading front evolve to have longer legs and run faster. |
| title | Invasion dynamics of super invaders: Elimination of Allee effects by a strategy at the range boundary |
| topic | Populations and Evolution Analysis of PDEs 35B40, 35K55, 35R35 |
| url | https://arxiv.org/abs/2503.06020 |