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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 |

### Keywords:

adaptive dynamics; critical function analysis; periodic disturbance; singular strategy; speciation
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\textit{X. Meng} and \textit{L. Zhang}, Math. Methods Appl. Sci. 39, No. 2, 177--188 (2016; Zbl 1342.92192)

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