Body sizes of species determining the success of biological control in a three-level food chain

Biological control in plant-insect systems represents a fundamental challenge in theoretical ecology, particularly within agricultural systems. This challenge is amplified by climate change, which, through increasing temperatures, has induced variations in insect body size, altering their ecological interactions and, consequently, their abundance. Although allometric relationships provide a static description of the relationship between body size, metabolism, and population density, dynamic models are needed to adequately simulate agroecological systems. In this context, incorporating body size as a dynamic parameter in trophic models offers an analytic approach to linking climate-induced morphological changes with the effectiveness of biological control and the indirect effects on plants. The main objective of this study is to develop a mathematical model based on a three-level food chain (plant-pest-biological control), where body size is incorporated as a key parameter in the dynamics of the plant-pest biological control system. Specifically, the goals are to: 1) Identify the relationships between the body sizes of species that limit population densities and prevent coexistence. 2) Determine the body size relationships that promote the success of biological control. 3) Model the trophic cascade effect as a function of body size and analyze its indirect impact on plants. Through theoretical analysis, indicators based on body sizes are proposed to evaluate the effectiveness of biological control strategies. The results suggest that allometric relationships between body sizes can modify the qualitative behavior of the system, offering a potential tool for evaluating biological control strategies based on these indicators. This study offers a tool for evaluating biological control strategies based on key indicators, complementing experimental designs and advancing integrated pest management through an interdisciplinary framework in which biomathematical models serve as a foundation for digital agriculture.