The spreading front of invasive species in favorable habitat or unfavorable habitat
By Chengxia Lei, Zhigui Lin, Qunying Zhang. 2013
74 citations recorded by the source corpus.
Spatial heterogeneity and habitat characteristic are shown to determine the asymptotic profile of the solution to a reaction-diffusion model with free boundary, which describes the moving front of the invasive species. A threshold value $R_0^{Fr}(D,t)$ is introduced to determine the spreading and vanishing of the invasive species. We prove that if $R_0^{Fr}(D,t_0)\geq 1$ for some $t_0\geq 0$, the spreading must happen; while if $R_0^{Fr}(D,0)<1$, the spreading is also possible. Our results show that the species in the favorable habitat can establish itself if the diffusion is slow or the occupying habitat is large. In an unfavorable habitat, the species dies out if the initial value of the species is small. However, big initial number of the species is benefit for the species to survive. When the species spreads in the whole habitat, the asymptotic spreading speed is given. Some implications of these theoretical results are also discussed.
Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science
View Paper: https://www.semanticscholar.org/paper/6013b437ebe19f8820b792fcf1cfa34a0cc118bf
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In Genetics
In Public Health, Environmental and Occupational Health
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Citations in the corpus
- Invasion by an inferior or superior competitor: A diffusive competition model with a free boundary in a heterogeneous environment (2015, background): “[15], we set λ as the eigenvalue of ⎨⎩−d1Δψ − 1 2 ′ = λψ, 0 < r < 1, ψ′(0) = ψ(1) = 0, with the corresponding eigenfunction ψ > 0, ψ′ ≤ 0 in [0, 1), and ‖ψ‖L∞([0,1)) = 1.”