Modeling Insect Development Time of Two or More Larval Stages in the Field under Variable Temperatures

Abstract

A statistical method is proposed for modeling the relation between development and variable temperature with 2 or more stages. Classical models were built using laboratory data obtained by rearing insects at different constant temperatures; these models could not be simply extrapolated to natural conditions. More recent models incorporate a temperature-dependent development rate and variability between individuals. Generalized linear models applied to estimate rates of several stages require a physiological scale identical for all stages. The method we propose leads to separate stage duration estimates with a different physiological scale per stage. We apply the method to the 4 larval stages of a chestnut curculio, Curculio elephas Gyllenhal, from hatching to larval exit from the chestnut. Data came from experiments done in natural conditions in 1986 and 1992. The physiological scale is represented by degree-days, which leads to a statistically good fit for the 4 stages. Median duration and variability for each stage thus can be derived. Because the base estimate for larval stages of the chestnut weevil does not change with stage, our model can be compared with the continuation ratio model. The 2 approaches gave very similar median estimates, indicating robustness of our method. The advantage of our approach is its flexibility when stages differ according to their physiological base, which is observed, for example, for egg and larval weevil development and frequently with other species. However, the continuation ratio model generally leads to more accurate estimates in the case of a base common to each stage.