Three epochs on estimating the parameter values of thermodynamic Sharpe-Schoolfield-Ikemoto (SSI) model describing the relation of temperature and insect development rate

Abstract

The SSI model describes the relationship between temperature and development rate of insect based on the laws of thermodynamics. The greatest feature of the SSI model curve is that it defines the “Intrinsic optimum temperature for the development of ectotherms”. However, this model has 8 parameters, it was extremely difficult to estimate the values of these parameters from experimental data. This is because the curve fitting of experimental data yields multiple curves depending on the initial conditions. In the first epoch of estimating parameter values, the difficulties were overcome by clarifying the model and applying all the knowledge gained about the model, but it took several days to determine the model. In the second epoch, the OptimSSI-program, which incorporates a basic optimization function, was developed, making it possible to obtain parameter values instantaneously after inputting experimental data. Although this program mostly runs automatically on a PC, a manual calculation remains to be carried outs so that the obtained model curves do not deviate from Arrhenius’ law. Afterward, a new program was suggested. This new program called DEoptim.sqrt not only incorporates an optimization function available on the internet but also was completely different from OptimSSI-P in terms of the design concept. Users had hoped that this new program would be start of the third epoch; however, when we examined the output values, there were serious problems, and we were back in the state before the first epoch. After all, OptimSSI-P of the second epoch was decided to be more reliable.