Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory

Biological temperature-dependent rate models based on Arrhenius' and Eyring's equations have been formulated by Johnson & Lewin (1946), Hultin (1955), and Sharpe & DeMichele (1977). The original formulation of Sharpe and DeMichele is poorly suited for non-linear regression. Very high correlations of parameter estimators occassionally make regression with their equation impossible using Marquardt's algorithm (1963).This analysis describes a new formulation of Sharpe and DeMichele's model that greatly alleviates the non-linear regression problem. It is partly based on Hultin's formulation (1955). Biological and graphical interpretation of the model parameters is discussed. Regression suitability is illustrated with a typical data set. Similar modifications to the equations of Hultin (1955) and Johnson & Lewin (1946) are described.