Comparison of Thermal Performance Equations in Describing Temperature-Dependent Developmental Rates of Insects: (III) Phenological Applications

Abstract

The developmental times of poikilotherms at different stages are significantly affected by temperature. Most mathematical models describing the temperature-dependent developmental rates of poikilotherms are built according to the experimental data at various constant temperatures. However, these models can also be applied to the developmental rates at variable temperatures. It is more meaningful to use models to predict the occurrence times of pest insects that actually represent the completion for a particular developmental stage (e.g., hatching, pupation, eclosion) under a natural thermal environment. For some developmental stages, insects might experience a period of high temperatures. In this case, skewed bell-shaped nonlinear models are more reasonable than the linear and exponential models because in the high-temperature region the developmental rate decreases with temperature increasing. We used the accumulated developmental progress method that combines three representative nonlinear models to compare the model validity in predicting the egg\'s earliest hatching date of bamboo locust in different years. We found that for the springtime phenological event the simple Arrhenius\' equation obtains the best goodness of fit. This study also provides a general R function that permits users to employ nonlinear parametric models to predict the occurrence times of insect phenology. In fact, if the investigation data cannot reflect the temperature-based phenological models proposed here, we have to consider whether the data set is reliable or whether the temperature is the crucial factor that determines the occurrence time of interest. The present study is valuable for the integrated management of pest insects because the biological or chemical control timing relies on the prediction on the occurrence time of phenological events.