TY - JOUR
T1 - Dynamics of a single species evolutionary model with Allee effects
AU - Kang, Yun
AU - Udiani, Oyita
N1 - Funding Information:
The authors would like to thank the comments of Professor Jim Cushing for the early draft of this manuscript. The research of Y.K. is partially supported by Simons Collaboration Grants for Mathematicians ( 208902 ), NSF DMS ( 1313312 ) and the internal grant from School of Letters and Sciences ( UC54015 YK ), Arizona State University, USA.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - We investigate the evolutionary outcomes of a single species population subject to Allee effects within the framework of a continuous strategy evolutionary game theory (EGT) model. Our model assumes a single trait creates a phenotypic trade-off between carrying capacity (i.e., competition) and predator evasion ability following a Gaussian distribution. This assumption contributes to one of our interesting findings that evolution prevents extinction even when population exhibits strong Allee effects. However, the extinction equilibrium can be an ESS under some special distributions of anti-predation phenotypes. The ratio of variation in competition and anti-predation phenotypes plays an important role in determining global dynamics of our EGT model: (a) evolution may suppress strong Allee effects for large values of this ratio; (b) evolution may preserve strong Allee effects for small values of this ratio by generating a low density evolutionary stable strategy (ESS) equilibrium which can serve as a potential Allee threshold; and (c) intermediate values of this ratio can result in multiple ESS equilibria.
AB - We investigate the evolutionary outcomes of a single species population subject to Allee effects within the framework of a continuous strategy evolutionary game theory (EGT) model. Our model assumes a single trait creates a phenotypic trade-off between carrying capacity (i.e., competition) and predator evasion ability following a Gaussian distribution. This assumption contributes to one of our interesting findings that evolution prevents extinction even when population exhibits strong Allee effects. However, the extinction equilibrium can be an ESS under some special distributions of anti-predation phenotypes. The ratio of variation in competition and anti-predation phenotypes plays an important role in determining global dynamics of our EGT model: (a) evolution may suppress strong Allee effects for large values of this ratio; (b) evolution may preserve strong Allee effects for small values of this ratio by generating a low density evolutionary stable strategy (ESS) equilibrium which can serve as a potential Allee threshold; and (c) intermediate values of this ratio can result in multiple ESS equilibria.
KW - ESS maximum principle
KW - Evolutionary game theory
KW - Evolutionary stable strategy (ESS)
KW - Strong/weak Allee effects
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U2 - 10.1016/j.jmaa.2014.03.083
DO - 10.1016/j.jmaa.2014.03.083
M3 - Article
AN - SCOPUS:84899901771
SN - 0022-247X
VL - 418
SP - 492
EP - 515
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -