Modelling development time of Lipaphis erysimi (Hemiptera: Aphididae) at constant and variable temperatures

The development period from birth to adult of virginoparae of the turnip aphid, Lipaphis erysimi (Kaltenbach), at 14 constant, 15 alternating and 15 natural temperature regimes were modelled to determine mathematical functions for simulating aphid development under a wide range of natural conditions. The day-degree model, the logistic equation, and the Wang model were used to describe the relationships between temperature and development rate at constant and alternating temperatures. The three models were then used with a Weibull function describing the distribution of development times, to simulate the development of individuals of cohorts at natural temperature regimes. Comparison of the observed with simulated distributions of adult emergence indicates that all three models can simulate the development of L. erysimi equally well when temperature does not go below 6 degrees C (the notional low temperature threshold of the day-degree model) or above 30 degrees C. When accumulation of temperatures below 6 degrees C becomes substantial, only the logistic curve offers accurate simulations; the other two models give falsely longer durations of development. When accumulation of temperatures above 30 degrees C becomes substantial, the logistic curve and the Wang model offer more accurate simulations than the day-degree model, which tends to produce shorter durations of development. Further analysis of the data reveals that development rate of this aphid at a given unfavourable high temperature may vary with time. Methods for accurately simulating the development time of L. erysimi in the field are suggested. The significance of modelling insect development at low and high temperatures by non-linear models is discussed.