A comparison of different thermal performance functions describing temperature-dependent development rates

Abstract

The impact of temperature on developmental duration of insects has been long kept a high profile in the studies of insect pests. The relationship between developmental rate, which is the reciprocal of developmental duration, is generally represented by a straight line over a range of moderate temperature; over two ranges of extreme temperature (i.e., low temperatures and high temperatures), the relationship cannot be accurately reflected by a straight line ( Campbell et al., 1974). For describing the effect of constant temperature on developmental rate over the full range of temperature, some non-linear models were proposed. To analyze the effect of temperature on ectothermic performance, twelve non-linear functions, including Gaussian, Logan1, Logan2, Performance, Wang–Lan–Ding, Sharpe–Schoolfield, Ratkowsky, Brière1, Brière2, Weibull, modified Gaussian and exponentially modified Gaussian functions, are compared using the coefficient of determination, adjusted coefficient of determination, Akaike information criterion (AIC), Bayesian information criterion (BIC), corrected Akaike information criterion (AICC) and a new method best on a weighted average of the five listed indicators. These models were compared using the development rate data of two species of insects at the egg stage. We found that the Performance, Brière1 and Brière2 functions are all very suitable for explaining temperature-dependent development rates. The three functions both belong to the asymmetrical skew thermal performance curves, and show better goodness-of-fit than the symmetrical Gaussian function. The Performance function might be the best function, because it can reflect the linearity between temperatures and developmental rates below the optimal developmental temperature.