Hierarchical Bayesian state-space model on tritrophic dynamics with cryptic life stages

Mechanistic modelling of tritrophic dynamics is difficult as it must simultaneously address three major challenges: process stochasticity that generates unpredictable temporal fluctuations, cryptic life stages that cannot be directly observed and spatial heterogeneity that induces local variation in ecological processes. Here we apply a hierarchical Bayesian state-space model (HBSSM) to jointly address these challenges in a controlled greenhouse biocontrol system. We deployed aphid (M. persicae) - parasitoid (A. colemani) - predator (M. pygmaeus) assemblages across 14 greenhouse rows where we explicitly incorporated a two-stage model of A. colemani to handle the cryptic adults and observable mummies, Gompertz growth for M. persicae and the facultative phytophagy by M. pygmaeus. Our HBSSM has successfully converged (all demographic parameters < 1.1) with strong predictive performance. It has an average of 75–100% directional accuracy, a normalized root mean square error of 18% across species, and peak timing predictions within ±1 week, while maintaining parameter identifiability. Scenario analysis identified the synergy of M. pygmaeus with A. colemani to reach best biocontrol efficiency. Our results also highlight the significance of early phase specification for modelling and greenhouse, where biological effectiveness for M. pygmaeus and forecast accuracy both depend critically on accurate initial population representation, with misspecification leading to inefficient control and 5.4x forecast error. Yet paradoxically, detectability is density dependent and poorest at low population densities when early-phase inference matters most. Overall, while HBSSM successfully addressed the three modelling challenges, our analysis warrants attention on detectability constraints beyond model structure.