A model of pupal water loss in Glossina

Mathematical Biosciences

2015

Self Cite

The temporal aspect of a model of pupal dehydration is improved upon. The observed dependence of pupal transpiration on time is attributed to an alternation between two, essential modes, for which the deposition of a thin, pupal skin inside the puparium and its subsequent demise are thought to be responsible. For each mode of transpiration, the results of the Bursell investigation into pupal dehydration are used as a rudimentary data set. These data are generalised to all temperatures and humidities by invoking the property of multiplicative separability. The problem, then, is that as the temperature varies with time, so does the metabolism and the developmental stages to which the model data pertain, must necessarily warp. The puparial-duration formula of Phelps and Burrows and Hargrove is exploited to facilitate a mapping between the constant-temperature time domain of the data and that of some, more general case at hand. The resulting, Glossina morsitans model is extrapolated to other species using their relative surface areas, their relative protected and unprotected transpiration rates and their different fourth instar excretions (drawing, to a lesser extent, from the data of Buxton and Lewis). In this way the problem of pupal dehydration is formulated as a series of integrals and the consequent survival can be predicted. The discovery of a distinct definition for hygrophilic species, within the formulation, prompts the investigation of the hypothetical effect of a two-day heat wave on pupae. This leads to the conclusion 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.

Section: The Dependence Of Transpiration On Temperature Humidity Andmentioning

confidence: 94%

“…The same transpiration dependences on temperature, humidity and historical water loss are used as in [6]. A brief summary of their derivation follows.…”

Section: The Dependence Of Transpiration On Temperature Humidity Andmentioning

confidence: 99%

Section: Assumptionmentioning

confidence: 99%

Section: Transpiration On Bursell's Time Domainmentioning

confidence: 99%

Section: Transpiration On Bursell's Time Domainmentioning

confidence: 99%

See 3 more Smart Citations

An improved temporal formulation of pupal transpiration in Glossina

Mathematical Biosciences

2015

Self Cite

Theoretical levels of control as a function of mean temperature and spray efficacy in the aerial spraying of tsetse fly

2011

Acta Tropica

Self Cite

The hypothetical impact of aerial spraying on tsetse fly populations is investigated. Spray cycles are scheduled at intervals two days short of the first interlarval period and halted once the last of the female flies that originated from pre-spray-deposited pupae have been sprayed twice. The effect of temperature on the aerial spraying of tsetse, through its reproductive cycle and general population dynamics, is of particular interest, given that cooler weather is preferred for the settling of insecticidal droplets. Spray efficacy is found to come at a price due to the greater number of cycles necessitated by cooler weather. The extra cost is argued to be worth while. Pupae, still in the ground at the end of spraying, are identified as the main threat to a successful operation. They are slightly more vulnerable at the low temperature extreme of tsetse habitat (16°C), when the cumulative, natural pupal mortality is high. One can otherwise base one's expectations on the closeness with which the time to the third last spray approaches one puparial duration. A disparity of anything close to the length of a spray cycle advocates caution, whereas one which comes close to vanishing should be interpreted as being auspicious. Three such key temperatures, just below which one can anticipate an improved outcome and just above which caution should be exercised, are 17.146°C, 19.278°C and 23.645°C. A refinement of the existing formulae for the puparial duration and the first interlarval period might be prudent in the South African context of a sympatric Glossina brevipalpis-Glossina austeni, tsetse population. The resulting aerial spraying strategy would then be formulated using a G. brevipalpis puparial duration and a G. austeni first interlarval period.

A set of discrete formulae for the performance of a tsetse population during aerial spraying

2013

Acta Tropica

Self Cite

A set of discrete formulae that calculates the hypothetical impact of aerial spraying on a tsetse population is derived and the work is thought to be novel. Both the original population and the subsequent generations which survive the aerial spraying, may ultimately be thought of as deriving from two, distinct sources. These origins are, however, neither distinct, nor relevant by the third generation. It is for this reason that the female population is considered to be composed of the following four categories for the purposes of derivation: Original flies which existed as such at the commencement of spraying; original pupae which existed as such at the commencement of spraying; the immediate descendants of both the aforementioned categories, during spraying; third and higher generation descendants. In theory, the latter category is a recurrence relation. In practice, the third generation's pupal stage has hardly come into existence, even by the end of a completed operation. Implicit in the formulae is the assumption of one, temperature-dependent mortality rate for the entire pupal stage, a second for the period between eclosion and ovulation and yet a third for the entire, adult life-span. Gravid female resistance to the insecticide is assumed to be inconsequential. A further assumption of the formulae is that at least one male is always available (degree of sterility variable).