A Modified Program for Estimating the Parameters of the SSI Model

Temperature has a significant influence on the development rates of poikilotherms. There are many nonlinear mathematical models for describing temperature-dependent development rates. Among these models, the Sharpe-Schoolfield (SS) model with six parameters may be the most popular one. The reciprocal of the denominator in the SS model represents the probability of enzyme being in the active state. There is a reference temperature, 25 degrees C, which was defined as a temperature at which the probability of enzyme being in the active state reaches its maximum. However, several examples of using the SS model to fit experimental data display that the probability of enzyme being in the active state does not reach its maximum at 25 degrees C. For different taxonomic groups, the temperatures at which the probability of enzyme being in the active state reaches its maximum might be different. Thus, Ikemoto modified the SS model to a new model (i.e., the SSI model) which can meet the condition that at a particular temperature the probability of enzyme being in the active state can reach its maximum. In addition, Ikemoto related the SSI model to the linear model and devised an algorithm to estimate model parameters; however, that original program of Ikemoto is so time-consuming that it limits the use of the SSI model. We provide a new program for a faster estimation of the parameters in the SSI model. One complete run of the new program takes less than 1 min (using R 2.10.1). This new program allows investigators to use the SSI model more readily. In addition, we test the linear approximation of the SSI model over three temperature ranges: low, middle, and high temperatures. We also provide a method for calculating the tangent at any point in the SSI model.