Evolutionary Dynamics of Oviposition Strategies in Outbreaking Herbivorous Insect Populations: A Stochastic Spatially Explicit PDE Model

Insects show complex dynamics in evading natural enemies. Outbreaking herbivorous insects often spatially aggregate eggs as protection strategy against predators and parasitoids. While this strategy fosters collective defense, it is not common in non-outbreaking species. This study introduces a spatially explicit Partial Differential Equations (PDE) model that includes an inheritable egg aggregation strategy. The main aim is to assess its effectiveness as an Evolutionary Stable Strategy (ESS) and its role in outbreaking dynamics. The model simulates the biological and spatial dynamics of the herbivore population from the egg stage to adult stages, while natural enemies target the eggs. The relationship between egg aggregation and outbreaks was explored through 256 simulations with fixed low (σ=0.1), medium (σ=1.0) and high (σ=10) aggregation, as well as variable inheritable aggregation (σ=0.1–10), under three types of functional response. We tracked changes in herbivore eggs (E), adults (A), and predator/parasitoid (P) populations, considering allele frequency shifts as well. The results indicate that type I response supports low aggregation, stabilising herbivore populations, while type II response leads to instability, making variable aggregation advantageous post-outbreak. Type III responses show intermediate effects. The lower σ spreads the risk, aiding evasion, while the higher σ concentrates the risk, assuming predators/parasitoids have consumption limits on outbreak fringes. This promotes local competition, destabilising populations as risk-spreading individuals are outcompeted.