Mathematical Modeling Applied to Biological Control of Ceratitis capitata (Wiedemann) (Diptera: Tephritidae), by Diachasmimorpha longicaudata (Ashmed) (Hymenoptera: Braconidae) in Citrus

• Published in: Neotropical entomology 2005-04, Vol.34 (2), p.281-289
• Main Authors: Freire, Rodrigo M, Pregnolatto, Silvio, Walder, Julio MM, Von Zuben, Claudio J
• Format: Article
• Language: Portuguese
• Subjects: Braconidae; Ceratitis capitata; Citrus; Diptera; Hymenoptera; Tephritidae
• ISSN: 1519-566X
• DOI: 10.1590/S1519-566X2005000200016

The mathematical model proposed has the objectives: (1) to simulate the population dynamics of a tritrophic system composed by the Mediterranean-fruit-fly Ceratitis capitata (Wiedemann), the braconid wasp Diachasmimorpha longicaudata (Ashmed) and citric fruits; (2) help to better understand the main biological and ecological factors affecting the population interactions and (3) contribute to more efficient biological control programs. The methodology was based on the formulation of different equation systems, which described the interaction processes of the trophic system. Numerical resolutions and graphical representation of these equation systems were produced, using the computational program Matlab, version 6.1. The biological and ecological data necessary to formulate the mathematical equations were provided by specialists in C. capitata control, and on the literature related to the biological control of fruit flies in citrus cultivars in Brazil, mainly with parasitoid wasps, such as D. longicaudata. The simulation results suggest that the proposed model describes suitably the ecological system considered, and permit a better comprehension of its main biological and ecological characteristics. Consequently the model may help to choose the best way and moment to liberate the parasitoid wasps aiming to a more effective control of C. capitata.