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Adaptive dynamics for a non-autonomous Lotka–Volterra model with size-selective disturbance

Nonlinear Analysis Real World Applications
DOI: 10.1016/j.nonrwa.2013.09.019


Abstract This paper intends to develop a theoretical framework for investigating the evolutionary impact of size-selective disturbance on an evolving trait of individuals in a non-autonomous Lotka–Volterra competition model. We first construct an invasion fitness function, which involves the average growth rate and settles in a nonequilibrium attractor. Then using methods of adaptive dynamics and critical function analysis we investigate the evolution of body size related traits in a competitive community, and when having size-selective disturbance we obtain the conditions for continuously stable strategy and evolutionary branching. Our results show that (1) heavy harvesting can lead to rapidly stable evolution towards smaller body size, but planting has an opposite effect; (2) smaller harvest pressure can give rise to high levels of polymorphism during evolution; (3) planting can make for evolutionary branching, while harvesting can go against evolutionary branching and promote evolutionary stability. Thus we can conclude, from an evolutionary point of view, that planting can promote species diversity and spatial differentiation among populations; however, harvesting does the opposite.

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