Modeling Study of Factors Determining Efficacy of Biological Control of Adventive Weeds

Yuri V. Tyutyunov (), Vasily N. Govorukhin and Vyacheslav G. Tsybulin
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Yuri V. Tyutyunov: Southern Scientific Centre of the Russian Academy of Sciences (SSC RAS), 344006 Rostov-on-Don, Russia
Vasily N. Govorukhin: I.I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University (SFedU), 344090 Rostov-on-Don, Russia
Vyacheslav G. Tsybulin: I.I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences, Southern Federal University (SFedU), 344090 Rostov-on-Don, Russia

Mathematics, 2024, vol. 12, issue 1, 1-16

Abstract: We model the spatiotemporal dynamics of a community consisting of competing weed and cultivated plant species and a population of specialized phytophagous insects used as the weed biocontrol agent. The model is formulated as a PDE system of taxis–diffusion–reaction type and computer-implemented for one-dimensional and two-dimensional cases of spatial habitat for the Neumann zero-flux boundary condition. In order to discretize the original continuous system, we applied the method of lines. The obtained system of ODEs is integrated using the Runge–Kutta method with a variable time step and control of the integration accuracy. The numerical simulations provide insights into the mechanism of formation of solitary population waves (SPWs) of the phytophage, revealing the factors that determine the efficacy of combined application of the phytophagous insect (classical biological method) and cultivated plant (phytocenotic method) to suppress weed foci. In particular, the presented results illustrate the stabilizing action of cultivated plants, which fix the SPW effect by occupying the free area behind the wave front so that the weed remains suppressed in the absence of a phytophage.

Keywords: population system; invasive weed; biological control agent; specialized phytophagous insect; cultivated plant; competitive exclusion; indirect prey taxis; spatiotemporal heterogeneity; solitary population wave (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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