A Model of Teneral Dehydration in Glossina

TL;DR

This paper develops a simple mathematical model to predict water loss and survival in teneral Glossina flies, considering species differences and environmental factors, to better understand their dehydration risks and development.

Contribution

It introduces a first-order differential equation model for teneral dehydration, incorporating species-specific water loss rates and environmental conditions, extending previous empirical data.

Findings

Model predicts total water loss and mortality in teneral Glossina.

Xerophilic species survive dehydration longer than hygrophilic ones.

Species classification relates mainly to late instar and pre-eclosion stages.

Abstract

The results of a long-established investigation into teneral transpiration are used as a rudimentary data set. These data are not complete in that all are at 25 $^\circ\mathrm{C}$ and the temperature-dependence cannot, therefore be resolved. An allowance is, nonetheless, made for the outstanding temperature-dependent data. The data are generalised to all humidities, levels of activity and, in theory, temperatures, by invoking the property of multiplicative separability. In this way a formulation, which is a very simple, first order, ordinary differential equation, is devised. The model is extended to include a variety of Glossina species by resorting to their relative, resting water loss rates in dry air. The calculated, total water loss is converted to the relevant humidity, at 24 $^\circ\mathrm{C}$, that which produced an equivalent water loss in the pupa, in order to exploit an adaption of an established survival relationship. The resulting computational model calculates total, teneral water loss, consequent mortality and adult recruitment. Surprisingly, the postulated race against time, to feed, applies more to the mesophilic and xerophilic species, in that increasing order. So much so that it is reasonable to conclude that, should Glossina brevipalpis survive the pupal phase, it will almost certainly survive to locate a host, without there being any significant prospect of death from dehydration. With the conclusion of this work comes the revelation that the classification of species as hygrophilic, mesophilic and xerophilic is largely true only in so much as their third and fourth instars are and, possibly, the hours shortly before eclosion.