Predicting the temperature-driven development of stage-structured insect populations with a Bayesian hierarchical model

Abstract

The management of forest pests relies on an accurate understanding of the species phenology. Thermal performance curves (TPCs) have traditionally been used to model insect phenology; many such models have been proposed and fitted to data from both wild and laboratory-reared populations, most of which have used maximum likelihood estimation (MLE). Analyses typically present point estimates of parameters with confidence intervals, but estimates of the correlations among TPC parameters are rarely provided. Neglecting aspects of model uncertainty such as correlation among parameters may lead to incorrect confidence intervals of predictions. This paper implements a Bayesian hierarchical model of insect phenology incorporating individual variation, quadratic variation in development rates across insects larval stages, and non-parametric adjustment terms that allow for deviations from a parametric TPC. We use Hamiltonian Monte Carlo (HMC) for estimation; the model is fitted to a laboratory-reared spruce budworm population as a case study. We assessed the accuracy of the model using stratified, 10-fold cross-validation. Using the posterior samples, we found prediction intervals for spruce budworm development for a given year.