phenModel: A temperature-dependent phenology/voltinism model for a herbivorous insect incorporating facultative diapause and budburst

Abstract A comprehensive phenology/voltinism model was developed for Phratora vulgatissima, an important pest of bioenergy crops. The model, phenModel, was developed based on development times of different life cycle stages (eggs, larvae, pupae, pre-oviposition, oviposition, sexual maturation) obtained from constant temperature laboratory experiments. As part of this study, a number of linear and non-linear models which describe the temperature-dependent development rate (inverse of development time) for each of the different life cycle stages were fitted. Based on the criteria of model parsimony and model fit, the non-linear Lactin-2 model was chosen as the optimum model to describe temperature-driven development in P. vulgatissima. To account for the variation in development times between individuals, an important but often ignored aspect in phenology models, a number of stochastic models (2- and 3- parameter Weibull and logistic models) were evaluated, based on the assumption that normalised development times conform to a similar shaped ('same shape') distribution. Novel aspects of the phenology model include the incorporation of a biologically relevant biofix, based on a budburst model for Salix viminalis, and a photoperiod threshold to induce facultative diapause. The model, which is written in R for accessibility, requires inputs of daily minimum and maximum temperature and site latitude and produces outputs describing the timing of completion of developmental stages for specified proportions of the population. It was evaluated against available field data and found to largely reproduce the observations providing a measure of its potential utility. A key component of the model allows for a sensitivity analysis of the model parameters. The model is structured so that it can easily be adapted for other leaf-feeding beetles which display a facultative reproductive diapause cued by photoperiod, and where the onset of oviposition is dependent on budburst, assuming relevant life cycle stage parameters are available.