An Analytic Model for Description of Temperature Dependent Rate Phenomena in Arthropods1

A new description of temperature-dependent, rate phenomena was deduced to describe developmental time and ovipositional data for the McDaniel spider mite, Tetranychus mcdanieli McGregor. The derived equation accounted for asymmetry about optimum temperature and was of particular utility for description of systems operating at or above optimum temperatures. Ovipositional and developmental rate functions were used in a temperature-driven, discrete-time, simulation model describing McDaniel spider mite population dynamics. Temperature dependence of the instantaneous population growth rate was determined by fitting the derived rate-temperature function to data generated through simulation at various fixed temperatures. The functional relationship of important population parameters to temperature provided the mechanism for inclusion of phenological effects on mite populations in a synoptic apple pest management model. Two derived functions were fit to several published rate-temperature data sets. Adequacy of description (as indicated by R 2 values) indicated general applicability of both functions for description of temperature-controlled, biological processes. Further, it was concluded that the singular perturbation method of matched asymptotes has potentially wide application in ecology, and an Appendix detailing the application of this method is included.