Evolutionary stable strategies of a single species model with carry-over effects due to fear Evolutionary stable strategies of a single species model with carry-over effects due to fear

• Published in: Nonlinear dynamics Vol. 113; no. 4; pp. 3919 - 3941
• Main Authors: Mondal, Santana, Khajanchi, Subhas
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2025; Springer Nature B.V
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Behavior; Biological evolution; Birth rate; Classical Mechanics; Control; Dynamical Systems; Game theory; Maximum principle; Normal distribution; Physics; Physics and Astronomy; Predation; Statistical Physics and Dynamical Systems; Vibration; Carry-over effect; ESS maximum principle; Allee effect; Evolutionary game theory; Evolutionary stable strategy
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-024-10400-9

We propose and analyze a single-species population model subject to fear and its carry-over effect with the help of evolutionary game theory (EGT). We incorporate fear and carry-over cost in the growth of a single species resource population and the extensive analysis of our non-evolutionary model suggests that it can exhibit both weak and strong Allee effects. From the game theoretical viewpoint, we assume that the intrinsic growth rate r of the resource population and the attack rate a of the consumer population are functions of a mean phenotypic trait ( u ) of the resource, following a Normal distribution. Evolutionary stable strategies (ESS) are determined by using ESS maximum principle. Our study of ESS suggests that species extinction may be avoided as a result of evolution, though the extinct equilibrium can also be an ESS under certain conditions. The ratio of variation in the intrinsic growth rate and the attack rate plays a significant role in the ESS conditions of different equilibria as well as the global dynamics of our EGT model. Numerical simulations are performed to support our theoretical analysis.