Open AccessDiffusion as a strategy for survival in an invasion predator–prey model
Author(s) -
OlmosLiceaga Daniel,
VillavicencioPulido Geiser,
AcuñaZegarra Manuel Adrian
Publication year - 2017
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/nrm.12135
Subject(s) - allee effect , predation , extinction (optical mineralogy) , predator , linepithema , biology , ecology , habitat , argentine ant , ecosystem , diffusion , introduced species , physics , population , paleontology , demography , sociology , thermodynamics
In some ecosystems, the invasion of species may lead to extinction or displacement of the local species that are in the medium. In this work, we present a theoretical predator–prey model based on reaction diffusion equations, where each species has a strong Allee effect. We use the diffusion coefficients as parameters in a one‐dimensional environment to show that prey can either survive or become extinct from its habitat. When the results are extended to two spatial dimensions, diffusion alone is no longer a sufficient condition in order to assure extinction or survival of the prey species; in this case, the geometry of the propagation front plays an essential role in the dynamics. Finally, a discussion about strategies for survival and extinction of the prey species is considered. The results can be useful in understanding invasion for species such as the Argentine ant Linepithema humile or to help to find control strategies for unwanted species in an ecosystem by introducing a predator.