Model derivation, priors, and parameter estimates from Inferring stratified parasitoid dispersal mechanisms and parameters from coarse data using mathematical and Bayesian methods

Biological invasions have movement at the core of their success. However, due to difficulties in collecting data, medium- and long-distance dispersal of small insects has long been poorly understood and likely underestimated. The agricultural release of parasitic hymenoptera, a group of wasps that are critical for biological pest control, represents a rare opportunity to study the spread of insects on multiple spatial scales. As these insects are typically less than 1 mm in size and are challenging to track individually, a first-time biocontrol release will provide a known spatial position and time of initial release for all individuals that are subsequently collected. In this paper, we develop and validate a new mathematical model for parasitoid wasp dispersal from point release, as in the case of biocontrol. The model is derived from underlying stochastic processes but is fully deterministic and admits an analytical solution. Using a Bayesian framework, we then fit the model to an Australian dataset describing the multi-scale wind-borne dispersal pattern of Eretmocerus hayati Zolnerowich & Rose (Hymenoptera: Aphelinidae). Our results confirm that both local movements and long-distance wind dispersal are significant to the movement of parasitoids. The model results also suggest that low velocity winds are the primary indicator of dispersal direction on the field scale shortly after release, and that average wind data may be insufficient to resolve long-distance movement given inherent nonlinearities and heterogeneities in atmospheric flows. The results highlight the importance of collecting wind data when developing models to predict the spread of parasitoids and other tiny organisms.