A Model of Teneral Dehydration in Glossina
aa r X i v : . [ q - b i o . O T ] O c t A Model of Teneral Dehydration in
Glossina
S. J. Childs
Department of Mathematics and Applied Mathematics, University of the Free State,P.O. Box 339, Bloemfontein, 9300, South Africa.Tel: +27 51 4013386 Email: [email protected]
Acta Tropica, 131: 79–91, 2014
Abstract
The results of a long-established investigation into teneral transpiration are used as a rudi-mentary data set. These data are not complete in that all are at 25 ◦ C and the temperature-dependence cannot, therefore be resolved. An allowance is, nonetheless, made for the out-standing temperature-dependent data. The data are generalised to all humidities, levelsof activity and, in theory, temperatures, by invoking the property of multiplicative separa-bility. In this way a formulation, which is a very simple, first order, ordinary differentialequation, is devised. The model is extended to include a variety of Glossina species by re-sorting to their relative, resting water loss rates in dry air. The calculated, total water lossis converted to the relevant humidity, at 24 ◦ C , that which produced an equivalent waterloss in the pupa, in order to exploit an adaption of an established survival relationship.The resulting computational model calculates total, teneral water loss, consequent mor-tality and adult recruitment. Surprisingly, the postulated race against time, to feed, appliesmore to the mesophilic and xerophilic species, in that increasing order. So much so thatit is reasonable to conclude that, should Glossina brevipalpis survive the pupal phase, itwill almost certainly survive to locate a host, without there being any significant prospectof death from dehydration. With the conclusion of this work comes the revelation that theclassification of species as hygrophilic, mesophilic and xerophilic is largely true only in somuch as their third and fourth instars are and, possibly, the hours shortly before eclosion. Keywords: teneral water loss; transpiration; dehydration; mortality; tsetse; glossina . The teneral stage of the tsetse fly is defined to commence immediately after eclosion and itterminates with the taking of the first blood-meal. Water loss continues after eclosion and1
Childs S.J. dehydration becomes progressively, more critical, up until the moment the teneral fly has itsfirst meal. Once fed, it is essentially no longer in jeopardy. The severely depleted, pupalreserves are replenished and, from then on, dehydration assumes a far lesser importance. Theadult fly is far better equipped to fend for itself and, to a certain extent, is a master of its owndestiny. It can avoid dehydration through behavioural strategies, for example, by modifying itslevel of activity, by temporarily retreating to deep shade, or by locating an host on which tofeed; all activities that the severely depleted reserves of the teneral fly may not allow enoughtime for. Work on adult flies, by Hargrove (2004), is strongly supportive of such reasoningin that humidity was found to be insignificant with regard to adult mortality. Dehydration istherefore a phenomenon usually only associated with the pupal and teneral stages in tsetse. Theultimate toll on a given cohort is cumulative and, likely, best assessed in terms of the proportionof original larvae which still have sufficient reserves to achieve their first feed, as tenerals.Since combined dehydration and fat loss are thought to culminate in massive teneral mortality(Hargrove, 1990), pupal and teneral mortality rates are crucial in deciding the viability of anytsetse population. The vastly different dynamics of water loss during the pupal and teneralphases, however, afford both the status of topics in their own right. It seems likely that thehigh mortality which usually characterises the teneral phase is essentially determined duringthe pupal phase. While teneral water loss rates are generally several times higher than pupalrates, it can be argued that pupal rates prevail many times longer (comparing the Bursell, 1958and 1959, data). To give some idea of the relative importance, while teneral water loss ratesare probably around 40 times sensu strictu pupal-stage rates and around seven times the unpro-tected rates which prevail prior to and immediately following the sensu strictu pupal-stage, theunprotected rates generally prevail six times longer than teneral rates and sensu strictu pupal-stage rates 24 times longer. Thus, any teneral that dies of dehydration could be said, very likely,to have died as a result of pupal water loss. Water loss during the pupal phase can decide thefate of the teneral and one possible criticism of the Bursell (1959) work is that it doesn’t takethe state of the inherited, pupal reserves into account enough.A general model of teneral water loss is developed in the same vein as the pupal water lossmodel of Childs (2013 and 2009). It is largely based on the investigations of one experimen-talist (Bursell, 1959 and 1958) and it otherwise relies heavily on the pupal dehydration modelfor its initial values. The main challenge to exploiting Bursell’s results for the purposes of acomputational model, could be said to be in three, very specific respects: A function for tran-spiration, extending the
Glossina morsitans -based, teneral model to the rest of the
Glossina genus, then formulating a satisfactory criterion for survival that is dependent on total waterloss. In the latter instance, a surprisingly simple solution is found to lie in the form of thepupal emergence data and the challenge then becomes one of utilizing the dependence of pupalsurvival on humidity, at 24 ◦ C , when only the cumulative water loss for the teneral has beencalculated. Transpiration is activity-dependent in the case of the teneral and an allowance forthe future acquisition of temperature-dependent data must be made in generalising transpira-tion to all humidities, activity levels and temperatures. The Bursell (1959) teneral work was allcarried out at 25 ± ◦ C . In the pupal case, the G. morsitans model was extended to otherspecies on the basis of the puparium’s surface area and its transpiration rate per unit of surfacearea, a strategy which predicted the critical water losses of all species with remarkable success eneral Transpiration in
Glossina
G. morsitans -based model must nec-essarily be extended to other species. Extending a
G. morsitans -based model to other speciesis work that can best be described as exploratory, however, the success of the same approachin the pupal model is cause for optimism. The results at the end make it an interesting andjustifiable exercise, nonetheless. This model takes no account of the vagaries of phenotypicplasticity although there is no reason why relevant data would not facilitate the incorporationof such detail.The final formulation, hence solution to the problem, is predicated on five major assumptionswhich are explicitly stated and explored. Another is taken for granted. It is assumed that theBursell (1958 and 1959) investigations are comprehensive, to the extent that they encapsulateall salient aspects of pupal and teneral water loss. The problem of teneral transpiration is thenreduced to a first order, ordinary differential equation for water loss. Although this equation isin itself extremely simple, the other equations, which constitute the combined pupal and teneralscheme, are both numerous and voluminous and there are issues pertaining to differentiabilityand continuity. This fact and the anticipated accuracy of such models render preferred inte-gration schemes, such as the fourth-order-accurate Runge-Kutta-Fehlberg (RKF45) method,slightly impractical. Since the problem is not intractably large from a computational point ofview, expedience takes precedence over taste and the more pedestrian midpoint rule is the pre-ferred integration technique, in keeping with the pupal-stage model. It is in this way that theresulting problem is transformed from a mathematical one, to a computational one.The goals and broader applications of this work are threefold. In order of priority, the first isthe completion of the most challenging compartment of an early mortality model, the secondis habitat assessment, while the third is a better comprehension of tsetse biology, particularlythe Bursell (1958 and 1959) endeavours. Most of the experimental work needed for a model ofearly stage mortality has long been complete. The main causes of mortality could be summedup as dehydration, fat loss, predation and parasitism. The relationship between pupal fat lossand temperature has been extensively studied by Bursell (1960) and Phelps (1973). A cursoryinspection of that work suggests that a few data points pertaining to teneral fat consumption’sdependence on activity (at either fixed or variable temperature) are required. Quantitative worklinking predation and parasitism to the density at pupal sites has been carried out by Rogersand Randolph (1990), although the topic can almost certainly be predicted to require somestochastic treatment. The completion of this work could be supposed to leave the way open toa comprehensive model of early mortality, based either on a joint probability density function,or, more likely, a Markov chain. Once a model of early stage mortality is completed, mattersshould become a lot simpler. Adult mortality is lower (Hargrove, 1990) and thought to betrivial, likely a simple, linear dependence on temperature with population density becomingrelevant at its higher levels.The question of habitat assessment is a topic of intense interest to entomologists and parasitol-ogists. Although environmental degradation militates against the tsetse fly ever making anysignificant return to its former status, health officials might have become over-reliant on work
Childs S.J. such as Ford and Katondo (1977) and the implications of climate change for traditional habitat(as well as other, geopolitical factors) could find them complacent. The presently perceivedincursion of
G. austeni into previously unrecognised, South African habitat (Hendrickx, 2007),for example, requires an explanation. Accurate determination of a greatly more confined pupaland teneral habitat, as well as early mortality, will facilitate a greatly more effective applicationof the various kinds of control measures contemplated by an integrated approach to pest man-agement (Barclay and Vreysen, 2010), aerial spraying being the possible exception (Childs,2013 and 2011). Habitat assessment and tsetse biology are, of course, intricately entwined.The implications of tsetse biology for the habitat assessment of hygrophilic species in general,as well as South Africa’s two, extant tsetse species,
G. brevipalpis and
G. austeni , are eluci-dated in this work. Certainly there are surprises in store so far as to what truly sets hygrophilicspecies apart from their mesophilic and xerophilic counterparts.
The transpiration rate resorted to in this work is measured in residual dry masses per hour,rather than as a pecentage of the same which was the preferred choice of Bursell (1959). Allother units conform to those of Bursell (1959). Both the level of activity and the relative humid-ity used are percentages and the temperature is in degrees centigrade. Bursell (1959) obtainedone set of transpiration data for variable activity (at 0% r . h . and 80% r . h . ) and another forvariable humidity (at 0% acitivity and 30% activity) during his investigations into teneral waterloss (Fig. 1 of Bursell, 1959). Both data sets were measured at a temperature of 25 ± ◦ C .No temperature-dependent data are presently known to exist, however, this need not precludeone from making provision for such data coming into existence at some stage in the future. Thequestion as to how one generalises these and as yet unknown data to all temperatures, humidi-ties and levels of activity therefore arises. The prospect of some, temperature-dependent dataset coming into existence in the future lends itself favourably to an assumption of multiplicativeseperability.A SSUMPTION Transpiration rate is a multiplicatively, separable function of activity andtemperature. That is, if dk/dt is the transpiration rate, then there exist two functions φ and θ , dependent exclusively on activity and temperature respectively, so that dkdt ( h, a, T ) = φ ( h, a ) θ ( h, T ) , (1) in which a denotes activity, T the temperature and h is the humidity. Such an assumption supposes that transpiration’s dependence on humidity at one temperature,is simply a temperature-dependent multiple of that same dependence at another temperature i.e.that there is no coupling of the independent variables. Simple relationships, such as the transpi-ration rate depicted in Bursell (1959), often lend themselves favourably to such an assumption. eneral Transpiration in
Glossina
The transpiration rate during the teneral phase is approximately steady. It differs little fromthe adult rate, which is marginally lower (comparing Figures 1A and 1B of Bursell, 1959). Anhumidity and activity dependence in keeping with the multiplicative separability assumption isrecognized and the relevant data is that published in Figs. 1A, 1C and 1D of Bursell (1959). Thefigures can be interpreted as transections through a surface which intersect. They suggest a verysimple surface, one which appears to be of no higher order than bi-quadratic, by inspection. Itwas therefore decided to fit a bi-quadratic surface, dkdt ( h, a,
25) = c + c h + c a + c ha + c h + c a , (2)to the transpiration data using the method of least squares and the values of the coefficients,thus obtained, are tabulated in Table 1.coefficient value asymptotic standard error c . × − ± . c − . × − ± . × − c . × − ± . c − . × − ± . × − c − . × − ± . × − c − . × − ± . × − Table 1: Coefficients for a bi-quadratic fit to the Bursell (1959) transpiration data. The sum ofsquares of residuals was . × − .Note that the asymptotic standard errors in Table 1 appear to deny any justification for a termwhich is purely quadratic in activity, although including such a term does result in a marginallyimproved sum of the squares of the residuals. That selfsame observation might also be said topertain to the term which is purely quadratic in humidity. Yet a single glance at Fig. 1C of Childs S.J.
Bursell (1959) will leave little doubt that that nonlinear term indeed exists. A subtle distinctionbetween a term being inappropriate and the quality and quantity of the data was thereforeinvoked to retain all the nonlinear terms. Fortunately, the contentious decision, supported bysomewhat heuristic arguments, is of no consequence for all realistic levels of activity. Onlyfor levels of activity above 50% is there a slight difference in the transpiration rates predictedwhen omitting the somewhat controversial quadratic activity term.The resulting bi-quadratic fit is in
G. morsitans -teneral, residual dry masses per hour and isdepicted in Fig. 1. That surface is nonetheless a surface of transpiration when, instead, onlythe humidity and activity dependence are sought. The multiplicative separability assumptionfacilitates the following manipulation, φ ( h, a ) = c + c h + c a + c ha + c h + c a θ ( h, , (3)and thus, an expression for the combined humidity–activity dependence is obtained. It is in thisway that the model facilitates the future acquisition of temperature-dependent data. Transpiration Rate / Residual Dry Masses H -1 a c t i v i t y / % Figure 1: The fit to the Bursell (1959) Figs. 1A, 1C and 1D data. eneral Transpiration in
Glossina All Bursell (1959) data sets were recorded at a constant temperature of 25 ± ◦ C . Theyprovide no clue as to the dependence of transpiration on temperature. For this reason furtherlaboratory measurements are needed. Measuring activity levels is a tedious task which canprobably be avoided if cognizance is taken of the work of Brady (1972). There is no activity atnight for flies kept continuously in the dark (Brady, 1972). It is generally suspected that the
Glossina genus derives from a common, tropical, rain-forestdwelling ancestor, adjusted to moist, warm climates (Glasgow, 1963). There can be no doubtthat the water reserve is a limiting factor to the pupa (Bursell, 1958) and the young, teneral flyhas not yet had an opportunity to replenish that reserve. Dehydration is therefore a challenge, ifnot the major threat to the teneral fly, when one considers the significance Rogers and Robinson(2004) attach to cold cloud duration (rainfall). One might therefore presume that the tenerals,in all tsetse species, actively pursue the same strategy to minimise water loss for the majorityof modern habitats and have mechanisms preventative of dehydration.Adult transpiration rates in dry air and at room temperature have been measured as a percentageof the residual dry mass for a number of species and are quoted in Table II of Bursell (1959).The residual dry masses, themselves, can be recovered from Fig. 2 of Bursell (1959). Thatsame Bursell (1959) endeavour suggests adult transpiration rates are not significantly differentfrom those of the teneral and should suffice for the teneral model. Transpiration during theteneral phase can therefore also be assumed to be steady and the observation that transpirationin adults is only minutely lower than in tenerals (Bursell, 1959) would seem to vindicate anassumption that the decrease takes place over a relatively long period. The resting transpirationrate per fly, in dry air at room temperature, can therefore be calculated from this data. It is therelevant datum multiplied by the residual dry mass, divided by 100. Under such conditions adimensionless, species conversion factor for teneral transpiration rates can be defined as theratio of the water loss rates of the different species. That is, δ species = p species p morsitans × m species m morsitans , in which p morsitans and p species are the resting water loss rates, in dry air, for G. morsitans and the species in question, respectively; m morsitans and m species are the residual dry massesof G. morsitans and the species in question, respectively. Actual values of δ species for eightdifferent species are tabulated in Table 2. Childs S.J.
Group Species δ morsitans austeni morsitans pallidipes swynnertoni palpalis palpalis fusca brevipalpis fuscipleuris longipennis G. morsitans model, to other species, in a more general context. These factors could enablethe teneral transpiration rate for another species to be extrapolated from
G. morsitans values,based on the following assumption.A
SSUMPTION The relative, resting transpiration rates, in dry air at 25 ◦ C , can be used toextrapolate the hypothetical water loss, in one species, into the water loss of another species,for any given activity level and any set of environmental conditions. Assumption 2 certainly appears to be the most tenuous and one cannot help questioning its va-lidity, wondering whether such a simplistic approach will work. Although no variation in rateswith pronounced changes in temperature and humidity is indicated, it is of some comfort thatthe conversion of the
G. morsitans model to other species involves relative rates. The factorsare a comparative ratio of the species-specific, transpiration-rate-per-fly data. Certainly therewas surprisingly strong evidence to suggest that the analogous assumption worked from the be-havioural point of view, in the pupal case. In the pupal scenario, the relative surface areas andthe relative permeability of the membranes, per unit area of membrane, were used to convert the
G. morsitans water loss to those of another species (Childs, 2013 and 2009). The strategy forthe teneral is the same in that transpiration data are converted to a per-fly value for each species,in order for a relative value to be obtained. In the case of the teneral fly, it is an inescapable factthat there is less scope for biologically different strategies among the tenerals of the differentspecies, than there is for the pupae from which they derive. Transpiration is steady. There areno unprotected third and fourth instars, followed by a protracted transition to a protected, sensustrictu pupal stage etc. Allowance has been made to accommodate the most basic behavioural eneral Transpiration in
Glossina
G brevipalpis data in Fig. 2 of Bursell (1959) appear to be at oddswith Table III of that same publication. Although the
G. brevipalpis residual dry weight isexpected to be approximately in keeping with that of
G. fuscipleuris , it was reasoned, firstly,that
G. brevipalpis has a higher water loss rate prior to eclosion and, secondly, that a singletypographical error is more likely than four, incorrectly plotted coordinates. The relevant,Bursell (1959) Fig. 2 value for
G brevipalpis was accordingly selected over that in Table III ofthe same reference.
The teneral transpiration rate can be formulated by collecting together all prior derivation andthe assumptions to give rise to a single governing equation. The rate formula which followsconstitutes a first order, ordinary differential equation.
Generalising Eqs. 1 and 3 to all species leads to dkdt = (cid:2) c + c h + c a + c ha + c h + c a (cid:3) θ ( h, T ) θ ( h, p species p morsitans m species m morsitans (4)in units of G. morsitans -teneral, residual dry masses per hour (5.43 mg h − ) and in which thecoefficients are those from Table 1. At 25 ◦ C the fraction involving the unknown function, θ ( h,T ) θ ( h, , is unity. The above rate formula constitutes a first order, ordinary differential equation. A fourth orderaccurate Runge-Kutta-Fehlberg method (RKF45) would normally be the preferred method ofintegration as it combines high accuracy with error control. A scheme in keeping with that ofthe pupal model it is used in conjunction with is, however, more convenient.The midpoint rule is usually considered distasteful from the point of view of its error. The localerror per step, of length ∆ t , is O(∆ t ) . Since the required number of steps is proportional to t ,the global error is O(∆ t ) . This is indeed primitive. The real strength of the midpoint rule andother low order methods lies, however, in their robustness at discontinuities and points of non-differentiability; something which is indeed relevant to the pupal models of Childs (2013 and0 Childs S.J.
It is logical to assume that the same level of depletion that was fatal to the pupa before eclosion,only a few hours before, will likewise be fatal to the newly-eclosed, teneral fly. Since thenewly-eclosed, teneral has not yet fed, one can reasonably argue that it inherits the pupa’sremaining reserves and will die off in the same cumulative proportions, as dehydration becomesprogressively more critical. The failure of the pupa to eclode is simply a measure of mortality.It is a symptom of the same water reserve which the teneral inherits, becoming depleted tocritical levels.A
SSUMPTION The same cumulative water loss, which would have killed the organism at,or before, the time of eclosion, will kill the as yet unfed, teneral fly.
The assumption is that the total, cumulative water loss since parturition, can be interpreted asif it were solely a pupal water loss to predict survival up until the first meal. By using the pupalformulae alone, that water loss can be redefined in terms of a soil humidity value at 24 ◦ C and,consequently, a measure of survival as per Fig. 2; in spite of the different teneral mode oftranspiration having contributed to that total cumulative water loss.The format in which the only available emergence data was originally produced necessitatesthat pupal emergence be taken to be that for the pertinent soil humidity at 24 ◦ C , that whichproduced an identical pupal water loss (Childs, 2013 and 2009).A SSUMPTION The survival for a given water loss, is the same as the pupal emergence forthe steady humidity at 24oC, that produced an equivalent total water loss.
To determine survival, water loss was re-expressed as an humidity which produced an identical,total water loss in the pupa at 24 ◦ C . The percentage emergence is therefore given by somefunction, E ( h ( k pupal )) , where h is the humidity, at 24 ◦ C , which gives rise to an identical eneral Transpiration in Glossina k pupal , to that calculated to have been incurred by the teneral under theconditions in question.Lastly, the same explanation for the pupal emergence data as in Childs (2013 and 2009) wasassumed. Some pupae will be slightly bigger, have slightly bigger reserves and more compe-tent integuments. Yet others will be slightly smaller, have slightly smaller reserves and lesscompetent integuments. This justifies the following interpretation of the Bursell (1958) andBuxton and Lewis (1934) pupal emergence data.A SSUMPTION The relationship between pupal emergence and humidity, at 24 ◦ C , is aGaussian curve, or a part thereof. The parameters in E ( h ) = a exp (cid:20) − ( h − b ) c (cid:21) , for each species, are provided in Table 3.group species a b c morsitans austeni .
663 73 . . morsitans . . . pallidipes . . . submorsitans . . . swynnertoni . . . palpalis palpalis . . . tachinoides . . . fusca brevipalpis . . . Table 3: Parameters for the fit of a Gaussian curve to the Bursell (1959) and Buxton and Lewis(1934) pupal emergence data for a variety of species (Childs, 20013 and 2009). All are at24 ◦ C , except G. tachinoides (30 ◦ C ).The assumption produced a pleasing result (Fig. 2), how ever correct, or otherwise, the un-derlying reasoning. Note that no attempt has been made to accommodate the Bursell (1958)opinion that all Fig. 2 curves should be shifted to the left by approximately 10% r . h . , due tothe slightly inferior quality of the pupal material he used.2 Childs S.J. e m e r gen c e / % relative humidity / % G. austeniG. brevipalpisG. longipennisG. morsitansG. pallidipesG. palpalisG. submorsitansG. swynnertoniG. tachinoides
Figure 2: Percentage emergence data (Bursell, 1958, and Buxton and Lewis, 1934) modelledas a Gaussian curve (Childs, 20013 and 2009) for a variety of species. All are at 24 ◦ C , except G. tachinoides (30 ◦ C ). G. longipennis is the single exception (a straight line had to be fitted tothe only two data points).
Fig. 3 explores the effect of activity on
G. morsitans water loss. The Figs. 4–8 compositesshow, firstly, the combined pupal-teneral response to both an atmosphere and soil of identicalhumidity, at 25 ◦ C and a 20% activity level, for each species. The temperature of the pupalenvironment is then raised to 30 ◦ C to produce a second plot for each species. Such scenariosare, nonetheless, probably not very realistic, especially in the case of more specialized species.The fate of pupae from a single pupal environment really needs to be considered in order toexamine the nature of the teneral stage in isolation. It is for this reason that, in the case ofthe hygrophilic species, additional results are plotted for pupae subjected to the drier extremeof pupal habitat from which tenerals should survive, as well as for those from the ideal pupalenvironment. eneral Transpiration in Glossina Survival of
G. morsitans
Larvae / % 90 70 50 30 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. morsitans
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. morsitans
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. morsitans
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s Figure 3: The effect of activity on survival, since parturition, in
G. morsitans tenerals: At topleft, a 10% activity level at 25 ◦ C . At top right, a 30% activity level at 25 ◦ C . At bottom left, a10% activity level at 30 ◦ C . At bottom right, a 30% activity level at 30 ◦ C .4 Childs S.J.
Survival of
G. morsitans
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. morsitans
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. pallidipes
Larvae / % 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. pallidipes
Larvae / % 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s Figure 4: Survival, since parturition, in tenerals at 25 ◦ C and a 20% activity level. At topleft, for a pupal phase at 25 ◦ C in G. morsitans . At top right, for a pupal phase at 30 ◦ C in G. morsitans . At bottom left, for a pupal phase at 25 ◦ C in G. pallidipes . At bottom right, fora pupal phase at 30 ◦ C in G. pallidipes . eneral Transpiration in Glossina Survival of
G. austeni
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. austeni
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. austeni
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. austeni
Larvae / % 90 70 50 30 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s Figure 5: Survival, since parturition, in
G. austeni tenerals at 25 ◦ C and a 20% activity level.At top left, for a pupal phase at 25 ◦ C . At top right, for a pupal phase at 30 ◦ C . At bottomleft, for a pupal phase at 25 ◦ C and 60% r . h . . At bottom right, for a pupal phase at 25 ◦ C and75% r . h . Childs S.J.
Survival of
G. palpalis
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. palpalis
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. palpalis
Larvae / % 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. palpalis
Larvae / % 90 70 50 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s Figure 6: Survival, since parturition, in
G. palpalis tenerals at 25 ◦ C and a 20% activity level.At top left, for a pupal phase at 25 ◦ C . At top right, for a pupal phase at 30 ◦ C . At bottomleft, for a pupal phase at 25 ◦ C and 65% r . h . . At bottom right, for a pupal phase at 25 ◦ C and80% r . h . eneral Transpiration in Glossina Survival of
G. brevipalpis
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. brevipalpis
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. brevipalpis
Larvae / % 50 30 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. brevipalpis
Larvae / % 90 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s Figure 7: Survival, since parturition, in
G. brevipalpis tenerals at 25 ◦ C and a 20% activitylevel. At top left, for a pupal phase at 25 ◦ C . At top right, for a pupal phase at 30 ◦ C . Atbottom left, for a pupal phase at 25 ◦ C and 71% r . h . . At bottom right, for a pupal phase at25 ◦ C and 85% r . h . Childs S.J.
Survival of
G. swynnertoni
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. swynnertoni
Larvae / % 90 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s Figure 8: Survival, since parturition, in tenerals at 25 ◦ C and a 20% activity level. At left, for apupal phase at 25 ◦ C in G. swynnertoni . At right, for a pupal phase at 30 ◦ C in G. swynnertoni . There is no numerical error associated with the integration in the steady-humidity and steady-activity context of these results. This is since the time derivative is a factor in the formulafor truncation error. The tolerance in the half interval search, used to determine the levelof survival, is several decimal places. All numerical error otherwise derives from the pupalstage. There are, doubtless, a multifarious bevy of other errors, their sources ranging fromthe sparseness and errors in the data itself, to the functions fitted, the formula for the puparialduration and, very likely, Assumptions 1 and 2 in particular. The standard error in the Bursell(1959) estimates is around 10%, there is a 2% error incurred in equating weight loss to waterloss and there is the discrepancy in the
G brevipalpis data already mentioned. The aboveresults are also rooted in the unmodified, Bursell (1958) data. No attempt has been made toaccommodate the opinion that the pupae were of a slightly inferior quality and that all Fig. 2curves should consequently be shifted to the left by approximately 10% r . h . There are many other sources of error. It should, however, be pointed out that some errors com-pensate for others and there are many reasons to believe that the overall error in the results does eneral Transpiration in
Glossina
While the survival level at the average time to feed could be interpreted as the number of origi-nal larvae which survive the teneral phase to adulthood, the following is a more rigorous methodbased, instead, on the probability of the teneral feeding. I am indebted to Dr. Neil Muller forassisting me with statistical aspects of what follows.
Suppose one defines a value E = E ( min { b, h ( k pupal ) } ) , in which b is the mean for E ( h ) , listed in Table 3. Thus, the cumulative density function forthe tenerals, were they never to feed and thereby become adults, would be E ( h ( k ( t ) + k pupal )) E for h ≤ b, where the function k ( t ) is the cumulative water loss since eclosion. Since a certain number oftenerals do manage to feed and in so doing become surviving adults, this cumulative densityfunction is of no use as it stands. A probability density function, ǫ , defined by ǫ ( t ) = c E dEdt is, instead, what is required, c being a normalisation constant. Since c Z ∞ t ǫ ( t ) dt = c (0 −
1) = 1 ⇒ ǫ ( t ) = 1 E a ( h − b ) c e − ( h − b ) / c dh dk dkdt , in which t is the time associated with the water loss, in turn associated with the humiditydefining E (if t = 0 then the integrand is defined as on [0 , t ) ). This is the probability of asingle fly not dying due to dehydration over some time interval.If one devises a similar probability density function for flies not feeding, say p ( t ) , then theprobability of a teneral still being a teneral, over some interval in time, is the number thatneither fed, nor died over that time interval. If one defines f ( t ) = p ( t )1 E a ( h − b ) c e − ( h − b ) / c (cid:18) dkdh (cid:19) − dkdt p ( t ) for h > bh ≤ b , Childs S.J. where dkdt is given by Eq. 4 and dkdh is the rate of change of pupal water loss with humidity at24 ◦ C , then tenerals ( t ) = Z t f ( t ′ ) × E ( h ( k pupal )) dt ′ , in which “tenerals” is used to denote the number of tenerals. Note that numerical values of k need to be calculated for various values of h and a curve fitted so that a dkdh relation for eachspecies might be determined. This is the probability of those that have survived without feeding, now feeding. If p ( t ) is theprobability density function for not feeding, then − p ( t ) is the probability density functionfor feeding and therefore adulthood. The number of adults which result isadults ( t ) = Z t (1 − p ( t ′ )) × tenerals ( t ′ ) dt ′ = Z t (1 − p ( t ′ )) "Z t ′ f ( t ′′ ) × E ( h ( k pupal )) dt ′′ dt ′ . The final tally of adults is consequentlytotal adults = Z ∞ (1 − p ( t )) (cid:20)Z t f ( t ′ ) × E ( h ( k pupal )) dt ′ (cid:21) dt. High water loss rates are a consequence of high levels of teneral activity in dry air and, it isassumed, high temperature. Such conditions lead to a dehydration of the teneral fly which canbe fatal. By knowing the average time to the first blood-meal, the percentage of original larvaewhich survive to become adults can be estimated. Some pupae eclode in the late afternoonand feed at sunset, however, most are thought to eclode in the evening (Vale et. al. 1976)and, considering that the exoskeleton needs a few hours to harden first, one might surmisethat the newly-eclosed, teneral fly usually has to wait through the night, until dawn, to feed(nocturnal species such as
G. longipalpis being the exception, according to Parker, 2009). InFigs. 4–8, the angle between the contours and the time-axis is a measure of the susceptibility tofurther dehydration during the teneral phase. Surprisingly, the postulated race against time toreplenish fluid reserves appears to apply rather more to the mesophilic and xerophilic species,in that increasing order. Very little evidence of the same phenomenon exists in the case ofhygrophilic species for which the atmosphere and soil have an identical humidity. Only for
G. austeni (Fig. 5) is there some evidence of a motive for the teneral to expedite under theaforementioned circumstances. eneral Transpiration in
Glossina
G. pallidipes to G. austeni . G. austeni appears not to simplybe a more extreme adaption of
G. pallidipes . In addition to the clear limitations water losssets for the pupae of each species, Rogers and Robinson (2004) found that cold cloud duration(rainfall) was far and away the most frequently occurring variable in their top five for determin-ing the distribution of both the fusca and palpalis groups using satellite imagery. Normalizeddifference vegetation index (NDVI) ranked second by a significant margin in those two groupsand only just beat cold cloud duration for the morsitans group. It is not too great a stretch of theimagination to entertain the possibility that cold cloud duration and NDVI translate directly intohumidity, as might elevation in the context of low-lying, coastal deltas, through which riversmeander, often terminating in estuaries. Rogers and Robinson (2004) also found that rainfallwas even more relevant when it came to abundance, as opposed to distribution. From theseand other facts, it is clear that the classification of species as hygrophilic, mesophilic and xe-rophilic is certainly not irrelevant. As to what it is that really defines a species as hygrophilic, aknowledge of
G. brevipalpis ’ environment, then experimenting with the model provides a clue.To be fair in the case of the hygrophilic species, one really needs to consider the fate of pu-pae from a single pupal environment in order to examine the nature of the teneral stage inisolation. It is only in this context that the teneral phase can be considered free of the fatal-ities suffered during the pupal stage. The 50% survival level might loosely be interpreted asdemarcating the survival of a single fly. More than half the
G. austeni pupae still eclode forpupal environments as dry as 40% r . h . (Childs, 2013). Despite this, only those from pupalenvironments as moist as 60% r . h . are resilient enough for general survival through the night,until dawn (Fig. 5). For those that feed before sunset and those that eclode into a very humidatmosphere, even drier pupal substrates than this might be tolerable (Fig. 9). Those G. austeni pupae from 40–60% r . h . pupal substrates are in jeopardy for atmospheric conditions that areanything less than ideal. For ideal pupal substrates of around 75% r . h . there is no chance ofthe newly-eclosed, G. austeni teneral succumbing to dehydration (Fig. 5) at room temperature.The postulated race against time to replenish fluid reserves does not exist for
G. austeni , underthose circumstances. This value is validated by the fact that Onderstepoort Veterinary Insti-tute (O.V.I.) keep their
G. austeni colony at 75% r . h . (De Beer, 2013). That their specimensexperience problems below 60% r . h . is probably too much of a short term effect to claim as val-idation, one which has more to do with adult flies and the regularity with which they are fed. G.palpalis is considered hygrophilic to an even greater degree than
G. austeni . More than half the
G. palpalis pupae still eclode for environments as dry as 50% r . h . (Childs, 2013). Despite this,only those from environments as moist as 65% r . h . are resilient enough for general survivalthrough the night, until dawn (Fig. 6). For those that feed before sunset and those that eclodeinto a very humid atmosphere, drier pupal substrates might be tolerable (Fig. 9). Those G. pal-palis pupae from 50–65% r . h . pupal substrates are in jeopardy for atmospheric conditions thatare anything less than ideal. For ideal pupal substrates of around 80% r . h . there is no chance ofthe newly-eclosed, G. palpalis teneral succumbing to dehydration (Fig. 6) at room temperature.The postulated race against time to replenish fluid reserves does not exist for
G. palpalis undersuch circumstances.
G. brevipalpis is, in turn, considered to be even more hygrophilic than2
Childs S.J.
G. palpalis . More than half the
G. brevipalpis pupae still eclode for pupal environments as dryas 67% r . h . (Childs, 2013). Those from the slightly more humid, 71% r . h . , pupal environmentare resilient enough for general survival through the night until dawn (Fig. 7). For those thatfeed before sunset and those that eclode into a very humid atmosphere, pupal substrates onlyminutely drier might be tolerable and the fact that O.V.I. keep their G. brevipalpis colony at75% r . h . (De Beer, 2013) does not in any way contradict the aforementioned values. For idealsubstrates of around 85% r . h . there is no chance of the newly-eclosed teneral succumbing todehydration (Fig. 7) at room temperature. The postulated race against time to replenish fluidreserves does not exist for G. brevipalpis under those and most other circumstances. Only atthe very driest limit of eclosion does the
G. brevipalpis teneral succumb to dehydration, thedomain of jeopardy being an extremely narrow band of humidity. One can therefore state that,for hygrophilic species, the teneral’s fate at room temperature is substantially determined bythe conditions which existed in the pupal environment from which it eclosed. So much so, thatit is reasonable to conclude that, should
G. brevipalpis survive to eclode into atmospheric con-ditions which match those of the soil, it will almost certainly survive to locate a host, withoutthere being any significant prospect of death from dehydration (Fig. 7).
Survival of
G. austeni
Larvae / % 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s G. palpalis
Larvae / % 70 50 30 10 0 10 20 30 40 50 60 70 80 90 100relative humidity / % 0 5 10 15 20 t i m e s i n c e e c l o s i on / hou r s Figure 9: Survival, since parturition, at 25 ◦ C and a 20% activity level. At left, in G. austeni tenerals, for a pupal phase at 55% r . h . . At right, in G. palpalis tenerals, for a pupal phase at60% r . h . eneral Transpiration in Glossina
G. longipennis , whereas the allegedly-hygrophilic, adult
G. brevipalpis is even more xerophilicthan adult
G. swynnertoni and adult
G. pallidipes ! There is, furthermore, very little differencein the relative losses suffered by the latter three species as adults; or even
G. palpalis , for thatmatter. Had Bursell (1959), himself, not remarked on his data, one might find it difficult tobelieve he hadn’t confused his samples. A simple inspection of Table 2 reveals that, while
G. austeni is only a little greater than half the size of
G. morsitans , it loses the same amount ofwater. In contrast,
G. brevipalpis only loses twice as much water as
G. morsitans , this beingin keeping with their relative sizes. An adult
G. brevipalpis might therefore be considered asxerophilic as
G. morsitans whereas an adult
G. austeni doesn’t stand a chance in dry climates.For the first time it becomes clear why
G. austeni is a relatively sedentary (Childs, 2010)denizen of low-lying, often coastal, vleis and estuaries, whereas the highly mobile
G. bre-vipalpis (Childs, 2010) is also associated with drainage lines in the atmospherically-drier re-gions of the hinterland.
G. austeni only needs to larviposit where it feeds while
G. brevipalpis can strike out into drier, surrounding country to feed, in spite of its pupa requiring the mosthumid substrate of all. For the first time it becomes clear why Rogers and Robinson (2004)found that the predominant variables in determining the distribution of these two hygrophilicspecies were NDVI, in the case of
G. brevipalpis , and elevation in the case of
G. austeni . As anadult,
G. austeni still requires an humid atmosphere in which to survive, whereas
G. brevipalpis only requires a humid substrate in which to larviposit. Hence, the frequent association of
G. brevipalpis with drainage lines, remote from their catchment areas and of which NDVI isthe only trace.
G. austeni is always going to be disadvantaged by its small size, with all thelack of hydrational inertia that a high surface-area-to-volume ratio implies.
G. brevipalpis isalways going to have an advantage over other species for diametrically opposite arguments.On the other hand,
G. austeni eclodes much earlier, leaving
G. brevipalpis to bear the bruntof density-dependent predation and parasitism (Rogers and Randolph, 1990). In this way
G. austeni may compete with
G. brevipalpis in the many environments which facilitate a sym-patric,
G. brevipalpis - G. austeni population (Childs, 2010).While it is tempting to assert that
G. brevipalpis and
G. austeni are the fusca and morsitans groups’ answer to
G. palpalis -type environments, they are in many ways more specialized. If
G. palpalis is to be regarded as a compromise between
G. brevipalpis and
G. austeni , it is un-fortunate that there is little, known water-loss data on other members of the palpalis group. Thesteeper terrain on the eastern side of the Rift Valley generally gives rise to younger geomor-phologies characterized by more clearly differentiated river profiles, consequently to two, morespecialized species. In contrast, much of west Africa is at a relatively low elevation, giving rise4
Childs S.J. to less energetic rivers, typically associated with a more mature geomorphology. Some of theserivers are associated with river basins of a low elevation. Most meander through coastal deltasbefore terminating in estuaries. This fact coupled with an higher rainfall, gives rise to soilenvironments which generally tend to be more humid than those in the vicinity of the valleythicket, vleis and estuaries to which
G. austeni is restricted, as an adult. A drier climate andbetter drainage on the eastern side of the Rift Valley ultimately mean that
G. austeni pupaemust tolerate drier soils and, as an adult, never stray too far inland from the coastal plains withtheir moist ocean air, in South Africa. A wider distribution of moist soils and climates in WestAfrica means the habitats of palpalis -group flies tend to be more two-dimensional and lessfragmented than those of
G. austeni and
G. brevipalpis . G. palpalis can successfully larvipositcloser to where it feeds than
G. brevipalpis sometimes needs to.
G. brevipalpis must generallylarviposit in the immediate vicinity of water explaining its frequent occurrence in and aroundriverine forests. The Rogers and Robinson (2004) study found NDVI to be the second, mostpredominant variable in determining the distribution of
G. tachinoides . This, coupled with ahabitat positioned inland from the coast, might be taken to suggest it is the member of the pal-palis group with the environment most similar to
G. brevipalpis . G. tachinoides is, however, ofsimilar size to
G. austeni and it would appear to flourish in pupal substrates with an even lowermoisture content.One further, general remark can be made with regard to the limited collection of results pre-sented. That is the existence of an optimum humidity common to all species at dawn, as wellas a very narrow envelope containing the optima for all species at the time of eclosion. If pupaeeclode in the late afternoon and feed at sunset, the survival optima for all species lie withinan approximately 15% r . h . interval of each other, or less; all other variables being equal. Ifpupae eclode in the late afternoon and feed at sunset, the differences in optimal survival couldbe consistent with different habitats. If, however, one compares the lower levels of survival, forexample the 50% level (which might loosely be interpreted to demarcate survival for a singlefly), then the differences in the ranges of survival conditions for each species are enormous andthere can be no doubt that the species have different habitats. Pupae are, however, thought toeclode in the evening (Vale et. al. 1976) and, considering that the exoskeleton needs a fewhours to harden first, one might surmise that the newly-eclosed fly has to wait through thenight, until dawn, to feed. At around 12 hours after eclosion, an optimal, steady humidity (airand soil) for the survival of all species turns out to exist at around 85% r . h . (for a 20% activitylevel at 25 ◦ C ; Figs. 4–8). A slightly lower, 90% survival contour also exists for all species,at around the 70% r . h . level. A different optimum, common to all species, appears to exist forthe case when the temperature of the pupal substrate and the atmosphere differ. Habitat anddistribution might therefore not be determined by optimal conditions of survival, instead, bythe conditions for which survival is marginal. One problem with such a conclusion is that itwould have been drawn from a limited number of scenarios in which the humidity of the soildoes not differ from that of the air.The model formulated was obviously intended for more ambitious purposes than mere interpre-tation and a visualization of data. There are, nonetheless, many examples which demonstratethat it is an invaluable tool in the interpretation and visualization of the Bursell (1958 and1959) work, to the point of novel biological insight. For example, on assessing his findings, eneral Transpiration in Glossina
G. palpalis and
G. austeni , there is reason tosuppose that the soil humidity never drops far below saturation”. By “never drops far” it mightbe assumed that a drop of somewhere around 10% r . h . is indicated. Figures 5 and 6 suggest that“never drops far” is ideally a drop of around 20% r . h . in the humidity of both the atmosphereand the pupal substrate, however, an average teneral (with survival loosely defined as beingdemarcated by the 50% survival contour) should still, generally survive at around 65% r . h . , for G. palpalis , and 60% r . h . , for G. austeni , not taking other causes of mortality into account. Ifthe atmosphere is very humid at the time of eclosion, in the latter case, soils as dry as 55% r . h . might be tolerated (Fig. 9). In the case of G. austeni , “never drops far below saturation” couldbe referring to a value as dry as 55% r . h . and the value thus concluded ignores the possibil-ity that the Bursell (1958) pupae may have been of a slightly inferior quality. Has the modelmisinterpreted the data? Is there a mistake? No, the model’s prediction is corroborated by, forexample, the conditions under which O.V.I. keep their tsetse colonies. “Never drops far belowsaturation” could, indeed, mean a pupal substrate as dry as 55% r . h . in the case of G. austeni .Of course, other causes of mortality in the wild would adjust survival downward and, underthese circumstances, the minimum humidity would need to be revised upward. Of course, ifthe temperature of the pupal substrate departs substantially from room temperature then thesame would apply. The point is that
G. austeni can probably survive in soils a lot drier thanare usually claimed.
G. austeni is probably as much limited by atmospheric humidity as theconditions which prevailed in its pupal environment. The point is that verbal communicationis often too vague. It does not lead to a precise understanding and can even be misleading.One should never lose sight of the fact that the results presented in this work are projections.They are a substitute which comes a far second to the lab results which would take a life time ofwork, at considerable cost. Not everyone is happy with the predictive potential of such models,phenotypic plasticity being just one of the reasons. Consider, however, that if a model is able tobe adapted and successfully make certain predictions with respect to other species, how muchmore suitable must it be for adaption within a given species. To a certain extent it can be saidthat if one is not happy with the model, then one is really not happy with the data. Anothercomplaint is that there is not enough data. Of course, there is never enough data and once thereis, a model is no longer necessary. In this case, the acquisition of the outstanding temperature-dependent data is, however, a priority. There is presently so little data that the only way theteneral model can be validated is to observe that the Bursell (1959) Figs. 1A, 1C and 1D canbe recovered from Fig. 1, that the conclusions with regard to the habitats of
G. austeni and
G. brevipalpis appear to be consistent with the observations of Hendrickx (2007) and that thereis no disparity with the conditions under which O.V.I. keep their tsetse colonies. There is noway to validate the assumption that the relative transpiration rates of the different species do notchange when no longer at rest and in humid environments. It is otherwise hoped that the modelbrings a certain degree of closure to the question of early mortality due to dehydration in tsetse,outstanding temperature-dependent data aside. The prognosis for the simplistic experimentalmodel would seem to be better than expected (given that issues such as inferior quality pupae,differing puparial durations and the shortage of statistically significant data can be corrected atsome stage).This work, in conjunction with Childs (2013), claims to bring about a revision of the con-6
Childs S.J. ventional wisdom on what truly determines the classification of species as either hygrophilic,mesophilic or xerophilic. Such classification has little to do with the tolerance of the eclosedfly to adversely hot and dry conditions and one possible criticism of the Bursell (1959) conclu-sion is that it doesn’t take the state of the inherited, pupal reserves into account enough. Theplots presented in this work point to the fact that the sites for larviposition in some species arevery much confined in the dry season,
G. brevipalpis being a case in point. It must larvipositin close proximity to water. These would be obvious places in which to concentrate controlmeasures and one immediate application of this work. Barriers of the type modelled in Childs(2010) might be far more efficacious if placed around sites of larviposition than when usedfor containment. Unfortunately, in the case of
G. brevipalpis , recent work by Motloang et. al.(2009) suggests the species is not a vector of trypanosomiasis and Childs (2010) also pointsto limited evidence that it could, in fact, be in competition with
G. austeni . G. palpalis and
G. austeni are most definitely vectors of trypanosomiasis, although their pupal sites appear notto be as severely restricted within their adult environments.
The author is indebted to Dr. Neil Muller for advising him on statistical aspects of the prob-abilistic formulation. The author is indebted to Schalk Schoombie, Johan Meyer and Eleanorvan der Westhuizen of the University of the Free State for hosting this work.
References [1] H. J. Barclay and M. J. B. Vreysen. A dynamic population model for tsetse (Diptera:Glossinidae) area–wide integrated pest management.
Population Ecology , 53(1):89–100,2010.[2] J. Brady. Spontaneous, circadian components of tsetse fly activity.
Journal of InsectPhysiology , 18:471–484, 1972.[3] E. Bursell. The water balance of tsetse pupae.
Philosophical Transactions of the RoyalSociety of London , 241(B):179–210, 1958.[4] E. Bursell. The water balance of tsetse flies.
Transactions of the Royal EntomologicalSociety London , 111:205–235, 1959.[5] E. Bursell. The effect of temperature on the consumption of fat during pupal developmentin glossina.
Bulletin of Entomological Research , 51(3):583–598, 1960.[6] P. A. Buxton and D. J. Lewis. Climate and tsetse flies: laboratory studies upon glossinasubmorsitans and tachinoides.
Philosophical Transactions , 224(B):175–240, 1934.[7] S. J. Childs. A model of pupal water loss in
Glossina . Mathematical Biosciences , 221:77–90, 2009. eneral Transpiration in
Glossina
Mathematical Biosciences ,227:29–43, 2010.[9] S. J. Childs. Theoretical levels of control as a function of mean temperature and sprayefficacy in the aerial spraying of tsetse fly.
Acta Tropica , 117:171–182, 2011.[10] S. J. Childs. An improved temporal formulation of pupal transpiration in
Glossina . Inreview , 2013.[11] S. J. Childs. A set of discrete formulae for the performance of a tsetse population duringaerial spraying.
Acta Tropica , 125:202–213, 2013.[12] C. De Beer.
By communication . 2013.[13] J. Ford and K. M. Katondo. The distribution of tsetse flies in Africa (3 maps).
OAU, Cook,Hammond & Kell, Nairobi , 1977.[14] J. P. Glasgow.
The Distribution and Abundance of Tsetse . International Series of Mono-graphs on Pure and Applied Biology. Pergamon Press, 1963.[15] J. W. Hargrove. Age–dependent changes in the probabilities of survival and capture ofthe tsetse, glossina morsitans morsitans westwood.
Insect Science and its Applications ,11(3):323–330, 1990.[16] J. W. Hargrove.
Tsetse population dynamics . Editors: I. Maudlin, P. H. Holmes and P. H.Miles. CABI publishing, Oxford, U.K., 2004.[17] Guy Hendrickx. Tsetse in Kwazulu Natal – an update –. Technical report, Agriculturaland Veterinary Intelligence Analysis, 2007.[18] M. Y. Motloang, J. Masumu, P. Van Den Bossche, P. A. O. Majiwa, and A. A. Latif.Vector competance of field and colony
Glossina austeni and
Glossina brevipalpis fortrypanosome species in KwaZulu–Natal.
Journal of the South African Veterinary Associ-ation , 80(2):126–140, 2009.[19] A. Parker.
By communication . 2009.[20] R. J. Phelps. The effect of temperature on fat consumption during the puparial stages ofglossina morsitans morsitans westw. (dipt. glossinidae) under laboratory conditions, andits implication in the field.
Bulletin of Entomological Research , 62:423–438, 1973.[21] D. J. Rogers and T. P. Robinson.
The Trypanosomiases . Editors: I. Maudlin, P. H. Holmesand P. H. Miles. CABI publishing, Oxford, U.K., 2004.[22] David J. Rogers and Sarah E. Randolph. Estimation of rates of predation on tsetse.
Med-ical and Veterinary Entomology , 4:195–204, 1990.8
Childs S.J. [23] G. A. Vale, J. W. Hargrove, A. M. Jordan, P.A. Langley, and A. R. Mews. Survivaland behaviour of tsetse flies (
Diptera , Glossinidae ) released in the field: a comparisonbetween wild flies and animal-fed and in vitro -fed laboratory-reared flies.