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Title: On the Allee effect and directed movement on the whole space
It is well known that relocation strategies in ecology can make the difference between extinction and persistence. We consider a reaction-advection-diffusion framework to analyze movement strategies in the context of species which are subject to a strong Allee effect. The movement strategies we consider are a combination of random Brownian motion and directed movement through the use of an environmental signal. We prove that a population can overcome the strong Allee effect when the signals are super-harmonic. In other words, an initially small population can survive in the long term if they aggregate sufficiently fast. A sharp result is provided for a specific signal that can be related to the Fokker-Planck equation for the Orstein-Uhlenbeck process. We also explore the case of pure diffusion and pure aggregation and discuss their benefits and drawbacks, making the case for a suitable combination of the two as a better strategy.  more » « less
Award ID(s):
2042413
PAR ID:
10505674
Author(s) / Creator(s):
;
Publisher / Repository:
AIMS Press
Date Published:
Journal Name:
Mathematical Biosciences and Engineering
Volume:
20
Issue:
5
ISSN:
1551-0018
Page Range / eLocation ID:
8010 to 8030
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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