Mathematical Model for Two-Spotted Spider Mites System: Verification and Validation

Abstract

This paper presents and compares four mathematical models with unique spatial effects for a prey-predator system, with Tetranychus urticae as prey and Phytoseiulus persimilis as predator. Tetranychus urticae, also known as two-spotted spider mite, is a harmful plant-feeding pest that causes damage to over 300 species of plants. Its predator, Phytoseiulus persimilis, a mite in the Family Phytoseiidae, effectively controls spider mite populations. In this study, we compared four mathematical models using a numerical simulation. These models include two known models: self-diffusion, and cross-diffusion, and two new models: chemotaxis effect model, and integro diffusion model, all with a Beddington-De Angelis functional response. The modeling results were validated by fitting experimental data. Results demonstrate that interaction scheme plays an important role in the prey-predator system and that the crossdiffusion model fits the real system best. The main contribution of this paper is in the two new models developed, as well as the validation of all the models using experimental data.

Simplified modelling enhances biocontrol decision making in tomato greenhouses for three important pest species

“…Figure 1 clearly shows a dramatic drop of both predator and prey on all plants, causing local extinctions of spider mites and/or predatory mites. In addition, the "hump" caused by the carrying capacity of the crop was expected (Rosenzweig & MacArthur 1963), as it was included in other spider mite models (Kozlova et al 2005;Kuang et al 2017), but was not observed.…”

“…A good example of this is the well-studied predatory mite Phytoseiulus persimilis (Athias-Henriot) (Acari: Phytoseiidae) and its prey, two-spotted spider mite Tetranychus urticae (Koch) (Acari: Tetranychidae). Several predator-prey models have been developed in the past (Bernstein 1985;Bancroft and Margolies, 1999;Kozlova et al 2005;Kuang et al 2017), but validation in practical conditions is missing. E.g.…”

Spatial-temporal structures in the active predator-passive prey model

“…Отметим, что в настоящее время гипотеза о пропорциональности ускорения хищников градиенту плотности жертв успешно используется во многих исследованиях [4][5][6][7][8][9][10]. Модели, построенные на данном предположении, демонстрируют сложную пространственновременную динамику [4][5][6][7][8][9][10].…”

“…Отметим, что в настоящее время гипотеза о пропорциональности ускорения хищников градиенту плотности жертв успешно используется во многих исследованиях [4][5][6][7][8][9][10]. Модели, построенные на данном предположении, демонстрируют сложную пространственновременную динамику [4][5][6][7][8][9][10]. Обратим внимание, что рассматриваемая модель относится к системам с кросс-диффузией, в которых волновые явления существенно отличаются от поведения волн в системах типа "реакция-диффузия" [11][12], и которые активно используются для изучения процессов структурообразования в последнее время [13][14][15].…”