Egg hatching and survival time of soil-dwelling insect larvae: A partial differential equation model and experimental validation

Insect herbivores that have soil-dwelling larval stages usually lay eggs directly or indirectly into the soil. Following egg hatch, emergent larvae must locate host plant roots to avoid starvation and this represents the most vulnerable part of the life cycle. We present a model for this aspect of the life cycle, specifically modelling the egg development rate and survival time of the clover root weevil, Sitona lepidus. The model is based on a partial differential equation, developed from age-structure models that are widely used in ecology. The model incorporates stochastic random variation caused by environmental fluctuation and genetic variation in a population, and treats chronological time and biological age as two independent variables. The average developmental rate and the impact of randomness are described by a first-order and a second-order derivative term, respectively. The significance of this model is that it can combine two biological events (egg development and larval survival time) into a single functional event, a potentially important feature for soil-dwelling insects because their concealed habitat does not permit all biological events to be observed. The model was tested against experimental observations of egg development and larval survival time under different soil conditions, firstly by considering egg development and larval survival time as independent biological events and secondly by combining both into a single functional event. Model simulations and experimental observations were in close agreement in all cases. To further test whether the model could be applied to other insect taxa and incorporate more than two biological events, we compared model simulations with published experimental results for the cereal leaf beetle (Oulema duftschmidi). Simulations of egg hatching and the larval development through several instars compared favourably with all experimental observations, demonstrating that the model has multiple applications.