Comparison of Thermal Performance Equations in Describing Temperature-Dependent Developmental Rates of Insects: (I) Empirical Models

Abstract

Temperature greatly affects the developmental duration of insects at their different stages, and many mathematical models exist for describing their temperature-dependent developmental rates. It is important to choose a suitable model to predict outbreaks of pest insects under climate change. However, previous comparisons among these models were usually based on a single species. In the present study, we compared the six nonlinear models (the Briére-1, Briére-2, Lactin, Performance-2, beta, and Ratkowsky models) based on the goodness of fit and the trade-off between the model’s goodness of fit and structural complexity, using 10 temperature-dependent developmental rate datasets on insects to make the conclusions general. We found that the square root model (i.e., the Ratkowsky model) fitted all datasets well, and the curve shape produced by this model also approximates the curve shape of thermodynamically based mathematical models. The square root model was originally derived to be applicable to the growth rates of bacteria, and until now it has been generally ignored in entomology. We were mainly concerned with the predicted results obtained by using this model on observations of temperature-dependent developmental rates. We found that the square root model described well the pooled developmental rates in the low-, mid-, and high-temperature ranges, and we believe that it merits wider use in entomology.