The role of Allee effects for Gaussian and Lévy dispersals in an environmental niche
type: Item
instance of: scholarly article
title: The role of Allee effects for Gaussian and Lévy dispersals in an environmental niche
zbMATH Open document ID: 1547.35693
author: Serena Dipierro
author: Edoardo Proietti Lippi
author: Enrico Valdinoci
published in: Journal of Mathematical Biology
publication date: 2024-08-06T00:00:00Z
review text: This work presents a comprehensive analysis of the influence of spatial stochastic dispersal on the population dynamics, which takes into account the Allee effect. The paper is supplied with a clear and substantial discussion of the biological and mathematical backgrounds of the considered phenomenon, which is followed by the rigorous mathematical consideration of spatial and spatiotemporal effects. Among the principal results are the analysis of stationary spatial solutions (an elliptic problem), which characterizes the survival chances of a dispersed population, and spatiotemporal problems, which take into account not only Brownian random walks leading to the classical diffusion but also anomalous random walk process in the form of superdiffusive Lévy flights revealed actually in the modern investigation of animal movements.
reviewed by: Eugene Postnikov
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92D50
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7893154
zbMATH Keywords: Allee effect
zbMATH Keywords: mixed Gaussian and Lévy diffusion
zbMATH Keywords: survival thresholds
MaRDI profile type: Publication
cites work: Getting acquainted with the fractional Laplacian
cites work: The Neumann problem for the fractional Laplacian: regularity up to the boundary
cites work: Q4748596
cites work: Hitchhiker's guide to the fractional Sobolev spaces
cites work: Linear theory for a mixed operator with Neumann conditions
cites work: (Non)local logistic equations with Neumann conditions
cites work: Some maximum principles for parabolic mixed local/nonlocal operators
cites work: Nonlocal problems with Neumann boundary conditions
cites work: Description of an ecological niche for a mixed local/nonlocal dispersal: an evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes
cites work: Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics
cites work: A probabilistic approach to a non‐local quadratic form and its connection to the Neumann boundary condition problem
cites work: Q5244856
DOI: 10.1007/S00285-024-02106-8
description: scientific article; zbMATH DE number 7893154