Study of the interactions between Tetranychus urticae, Phytoseiulus persimilis and Macrolophus pygmaeus in a tomato glasshouse: a cross-diffusion model case study with Beddington-DeAngelis response.

Background: The two-spotted spider mite (TSSM), Tetranychus urticae Koch, poses a significant threat to greenhouse tomato production, potentially causing ≤40% yield loss. Although biological control using the specialist predator Phytoseiulus persimilis and generalist predator Macrolophus pygmaeus has proven effective in small-scale studies, their interactions in large commercial glasshouses remain poorly understood. This study develops a mathematical model incorporating spatial dynamics and multispecies interactions to bridge laboratory findings with commercial applications.

Results: Our model incorporating diffusion patterns, plant defense and intraguild predation best predicted population dynamics (MSE: 0.221, 0.125 for T. urticae and P. persimilis, respectively). Spatial diffusion had the strongest impact on model accuracy, whereas all M. pygmaeus-induced effects were minimal in practice. The model achieved 77.2% directional accuracy in 3-week forecasts for T. urticae populations. Simulations revealed that early releases of P. persimilis (0.5 individuals per leaf) could effectively control T. urticae within 4 weeks.

Conclusion: This study demonstrates that many species interactions observed in small-scale experiments may not translate directly to effective biocontrol in commercial settings, which is likely to be a consequence of spatial dilution. We further found that spatial movements outweigh laboratory-observed effects. Lastly, our model enables 3-week advance predictions of T. urticae populations and provides evidence-based guidance for biocontrol agent release strategies, helping growers optimize their pest management decisions. © 2025 Society of Chemical Industry.