Performance of Phenological Models Under Variable Temperature Regimes: Consequences of the Kaufmann or Rate Summation Effect

Abstract

Published research concerning insect development rate or phenology models shows that the effect of fluctuating temperature and rate summation on nonlinear and linear model predictions is not well understood. Models of rates of development at constant temperatures of an example insect are compared graphically with predicted rates under artificial and naturally varying temperature regimes. Acceleration of insect development at low temperatures and retardation at high temperatures are shown to be implicit to the assumption of nonlinearity of development. The influence of the diurnal range of the temperature regime on the rate summation effect and the interaction between rate summation and the mathematical structure of a particular development rate model are clearly demonstrated. This study shows that the selection of a development rate function for prescriptive use, based on closeness of fit to developmental data from constant temperature experiments, is meaningless. Nor should selection be based on how well a model derived from constant temperature experiments predicts insect development measured under a narrow range of fluctuating temperatures. Reasons why a nonlinear model fitted directly to rates observed under variable temperature laboratory or field data is inappropriate for subsequent prediction (in theory at least), are clearly demonstrated. An appropriate technique that calculates instantaneous development rate functions from fluctuating temperature development time observations is tested with hypothetical data. This technique failed to give reasonable estimates of the parameters of the instantaneous development rate function that generated the hypothetical data.