Simple SummaryMathematical models are developed to predict key aspects of insects harmful to many crops, including grapevine. Practical applications of these models include forecasting seasonal occurrence and spread over space in order to make decisions about pest management (e.g., timing of insecticide sprays). Many models have recently been developed to evaluate the spread of insect pests on grapevine under a climate change scenario as well as to forecast the possibility that alien species could settle into new environments. To make the published models available to vine-growers and their stakeholders, a holistic approach presenting these models within the frame of a decision support system should be followed.This paper reviews the existing predictive models concerning insects and mites harmful to grapevine. A brief conceptual description is given on the definition of a model and about different types of models: deterministic vs. stochastics, continuous vs. discrete, analytical vs. computer-based, and descriptive vs. data-driven. The main biological aspects of grapevine pests covered by different types of models are phenology, population growth and dynamics, species distribution, and invasion risk. A particular emphasis is put on forecasting epidemics of plant disease agents transmitted by insects with sucking-piercing mouthparts. The most investigated species or groups are the glassy-winged sharpshooter Homalodisca vitripennis (Germar) and other vectors of Xylella fastidiosa subsp. fastidiosa, a bacterium agent of Pierce’s disease; the European grape berry moth, Lobesia botrana (Denis and Schiffermuller); and the leafhopper Scaphoideus titanus Ball, the main vector of phytoplasmas agents of Flavescence dorée. Finally, the present and future of decision-support systems (DSS) in viticulture is discussed.
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