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Evolutionary dynamics in a Lotka-Volterra competition model with impulsive periodic disturbance. (English) Zbl 1342.92192

Summary: In this paper, we develop a theoretical framework to investigate the influence of impulsive periodic disturbance on the evolutionary dynamics of a continuous trait, such as body size, in a general Lotka-Volterra-type competition model. The model is formulated as a system of impulsive differential equations. First, we derive analytically the fitness function of a mutant invading the resident populations when rare in both monomorphic and dimorphic populations. Second, we apply the fitness function to a specific system of asymmetric competition under size-selective harvesting and investigate the conditions for evolutionarily stable strategy and evolutionary branching by means of critical function analysis. Finally, we perform long-term simulation of evolutionary dynamics to demonstrate the emergence of high-level polymorphism. Our analytical results show that large harvesting effort or small impulsive harvesting period inhibits branching, while large impulsive harvesting period promotes branching.

MSC:

92D25 Population dynamics (general)
92D15 Problems related to evolution
34D23 Global stability of solutions to ordinary differential equations
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