Modeling winter moth <i>Operophtera brumata</i> egg phenology:Nonlinear effects of temperature and developmental stage on developmental rate

Understanding the relationship between an insect's developmental rate and temperature is crucial to forecast insect phenology under climate change. In the winter moth Operophtera brumata timing of egg-hatching has severe fitness consequences on growth and reproduction as egg-hatching has to match bud burst of the host tree. In the winter moth, as in many insect species, egg development is strongly affected by ambient temperatures. Here we use laboratory experiments to show for the first time that the effect of temperature on developmental rate depends on the stage of development of the eggs. Building on this experimental finding, we present a novel physiological model to describe winter moth egg development in response to temperature. Our model, a modification of the existing Sharpe-Schoolfield biophysical model, incorporates the effect of developmental stage on developmental rate. Next we validate this model using a 13-year data-set from winter moth eggs kept under ambient conditions and compared this validation with a degree day model and with the Sharpe-Schoolfield model, which lacks the interaction between temperature and developmental stage on developmental rate. We show that accounting for the interaction between temperature and developmental stage improved the predictive power of the model and contributed to our understanding of annual variation in winter moth egg phenology. As climate change leads to unequal changes in temperatures throughout the year, a description of insect development in response to realistic patterns of temperature rather than an invariable degree-day approach will help us to better predict future responses of insect phenology, and thereby insect fitness, to climate change.