Comparison of the performance equation with its generalized version in describing the temperature-dependent survival of insects and mites

The performance of various life processes in arthropods is greatly influenced by temperature. The survival of arthropods is temperature-dependent, which must be accounted for when predicting and simulating outbreaks of pest population under global warming scenarios. However, mathematical models for describing temperature-dependent arthropod survival are still lacking. The 5-parameter performance equation (PE), which was originally proposed to describe the influence of temperature on the jumping distance of the green frog, can generate symmetrical and asymmetrical inverted U-shaped curves, and thus is applicable to modeling a broad variety of thermal performance relationships. However, prior studies have not assessed its validity in describing the temperature-dependent survival of arthropods. In this study, we used 16 data sets of insects and mites to test the validities of this PE and its generalized version with 7 parameters (GPE) in fitting temperature-dependent survival data. The PE and GPE were both found to be valid for use in fitting the observed data. However, the estimated values of the PE’s parameters were more robust than those of the GPE. The goodness of fit of the GPE was better than that of the PE for each data set; however, the GPE tended to overfit the data when observations at threshold temperatures were lacking. Overall, the PE is better than the GPE. The present work further confirmed that the temperature-dependent survival of arthropods is an inverse U-shaped curve and provided a useful tool for quantifying the effect of temperature on the survival of arthropods.