A model of pupal water loss in Glossina

The results of a long-established investigation into pupal transpiration are used as a rudimentary data set. These data are then generalised to all temperatures and humidities by invoking the property of multiplicative separability, as well as by converting established relationships in terms of constant humidity at fixed temperature, to alternatives in terms of a calculated water loss. In this way a formulation which is a series of very simple, first order, ordinary differential equations is devised. The model is extended to include a variety of Glossina species using their relative surface areas, their relative pupal and puparial loss rates and their different 4th instar excretions. The resulting computational model calculates total, pupal water loss, consequent mortality and emergence. Remaining fat reserves are a more tenuous result. The model suggests that, while conventional wisdom is often correct in dismissing variability in transpiration-related pupal mortality as insignificant, the effects of transpiration can be profound under adverse conditions and for some species, in general. The model demonstrates how two gender effects, the more significant one at the drier extremes of tsetse fly habitat, might arise. The agreement between calculated and measured critical water losses suggests very little difference in the behaviour of the different species.