title: Patchy Invasion of Stage-Structured Alien Species with Short-Distance and Long-Distance Dispersal.
abstract: Understanding of spatiotemporal patterns arising in invasive species spread is necessary for successful management and control of harmful species, and mathematical modeling is widely recognized as a powerful research tool to achieve this goal. The conventional view of the typical invasion pattern as a continuous population traveling front has been recently challenged by both empirical and theoretical results revealing more complicated, alternative scenarios. In particular, the so-called patchy invasion has been a focus of considerable interest; however, its theoretical study was restricted to the case where the invasive species spreads by predominantly short-distance dispersal. Meanwhile, there is considerable evidence that the long-distance dispersal is not an exotic phenomenon but a strategy that is used by many species. In this paper, we consider how the patchy invasion can be modified by the effect of the long-distance dispersal and the effect of the fat tails of the dispersal kernels.
authors.affiliation: Departamento de Matemática, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil.
authors.forename: Luiz Alberto Díaz
authors.initials: LA
authors.lastname: Rodrigues
authors.affiliation: Departamento de Matemática, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil.
authors.forename: Diomar Cristina
authors.initials: DC
authors.lastname: Mistro
authors.affiliation: Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil.
authors.forename: Elisa Regina
authors.initials: ER
authors.lastname: Cara
authors.affiliation: School of Mathematics, University of Birmingham, Birmingham, UK.
authors.forename: Natalia
authors.initials: N
authors.lastname: Petrovskaya
authors.affiliation: Department of Mathematics, University of Leicester, Leicester, UK. sp237@le.ac.uk.
authors.forename: Sergei
authors.initials: S
authors.lastname: Petrovskii
mesh_terms: D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D058865:Introduced Species; D055641:Mathematical Concepts; D008954:Models, Biological; D011157:Population Dynamics
keywords: Allee effect; Biological invasion; Cauchy kernel; Integro-difference equation; Predator–prey system