Tsetse: the limits to population growth

Growth rates of tsetse populations were estimated by calculating the dominant eigenvalues of appropriate Leslie matrices. The individual effects of four variables (pre-adult and adult survival probability, interlarval period and pupal duration), have been investigated by varying each one over a wide range of values, while the other three are held constant. R, the log of the growth rate, was found to vary approximately linearly with adult and pre-adult death rate; a 1% change in the adult death rate causes approximately a 10-fold change in R. R varies linearly with the log of fecundity and of the pupal duration. An increase in the pupal duration results in a decrease in the growth rate for populations which have a positive growth rate, but an increase for populations which have a negative growth rate. For a population at equilibrium, a change in the pupal duration has no effect. Small changes in fecundity have less effect on the growth rate than small changes in the death rate; this fact is advanced as an important contributor to the generally very cautious nature of female tsetse, and their aversion to man, particularly as a potential host. A simple linear model is described which relates R to all four variables and their first order interactions. The model is used to produce a set of graphs which encapsulate the relationship between the growth rate and the vital parameters over a wide range of values. It is also used to draw the loci on one side of which tsetse populations grow, and on the other of which they decline. Population resilience is discussed in relation to the problem of tsetse eradication; it is concluded that if one can impose and sustain an added mortality of 4% per day on any female tsetse population then it must go extinct, regardless of the strength of the density dependent processes; and it seems likely that in most field conditions only an added 2-3% is required. It is pointed out that ground and aerial spraying techniques produce much higher daily mortalities than this, but they may often not be sustained for sufficiently long to achieve eradication. When odour-baited targets are used the increased death rate is much smaller, but it can be sustained as required; recent work in Zimbabwe shows that there is a good correspondence between the calculated imposed death rate and the observed rate of decline of tsetse populations.     

A general model for mortality in adult tsetse (Glossina spp.)

Tsetse exhibit a U-shaped age-mortality curve, with high losses after eclosion and a well-marked ageing process, which is particularly dramatic in males. A three-parameter (k(1) -k(3) ) model for age-dependent adult instantaneous mortality rates was constructed using mark-recapture data for the tsetse fly Glossina morsitans morsitans Westwood (Diptera: Glossinidae). Mortality changed linearly with k(1) over all ages; k(2) affected only losses in roughly the first week of adult life, and k(3) controlled the ageing rate. Mortality pooled over age was twice as sensitive to changes in k(3) as in k(1) . Population growth rate was, however, similarly affected by these two parameters, reflecting the disproportionate effect of k(3) on mortality in the oldest flies that contribute least to the growth rate. Pooled-age mortality and growth rate were insensitive to changes in k(2) . The same model also provided good fits to data for laboratory colonies of female G. m. morsitans and Glossina austeni Newstead and should be applicable to all tsetse of both sexes. The new model for tsetse mortality should be incorporated into models of tsetse and trypanosome population dynamics; it will also inform the estimation of adult female mortality from ovarian dissection data.     

Dispersal in heterogeneous environments drives population dynamics and control of tsetse flies

Spatio-temporally heterogeneous environments may lead to unexpected population dynamics. Knowledge is needed on local properties favouring population resilience at large scale. For pathogen vectors, such as tsetse flies transmitting human and animal African trypanosomosis, this is crucial to target management strategies. We developed a mechanistic spatio-temporal model of the age-structured population dynamics of tsetse flies, parametrized with field and laboratory data. It accounts for density- and temperature-dependence. The studied environment is heterogeneous, fragmented and dispersal is suitability-driven. We confirmed that temperature and adult mortality have a strong impact on tsetse populations. When homogeneously increasing adult mortality, control was less effective and induced faster population recovery in the coldest and temperature-stable locations, creating refuges. To optimally select locations to control, we assessed the potential impact of treating them and their contribution to the whole population. This heterogeneous control induced a similar population decrease, with more dispersed individuals. Control efficacy was no longer related to temperature. Dispersal was responsible for refuges at the interface between controlled and uncontrolled zones, where resurgence after control was very high. The early identification of refuges, which could jeopardize control efforts, is crucial. We recommend baseline data collection to characterize the ecosystem before implementing any measures.     

Estimating tsetse fertility: daily averaging versus periodic larviposition

When computing mean daily fertility in adult female tsetse, the common practice of taking the reciprocal of the interlarval period (called averaged fertility) was compared with the method of taking the sum of the products of daily fertility and adult survivorship divided by the sum of daily survivorships (called periodic fertility). The latter method yielded a consistently higher measure of fertility (approximately 10% for tsetse) than the former method. A conversion factor was calculated to convert averaged fertility to periodic fertility. A feasibility criterion was determined for the viability of a tsetse population. Fertility and survivorship data from tsetse populations on Antelope Is. and Redcliff Is., both in Zimbabwe, were used to illustrate the feasibility criterion, as well as the limitations imposed by survivorship and fertility on the viability of tsetse populations. The 10% difference in fertility between the two methods of calculation makes the computation of population feasibility with some parameter combinations sometimes result in a wrong answer. It also underestimates both sterile male release rates required to eradicate a pest population, as well as the speed of resurgence if an eradication attempt fails.     

Estimating tsetse population parameters: application of a mathematical model with density-dependence

A density-dependent model is used to describe the dynamics of an open population of tsetse flies (Diptera: Glossinidae). Immigration (or emigration) takes place when the total population is below (or above) a biologically determined threshold value. The population is also subjected to birth and death rates, as well as to the risk of being trapped (continuously or intermittently). During trapping the population decreases toward a 'low' equilibrium population and when trapping ceases the population starts recovering and increases toward a 'high' equilibrium. The model is fitted using data collected on trapped flies in four experiments. The first one was conducted with 'intermittent trapping' (i.e. several trapping-recovery cycles) on Glossina fuscipes fuscipes Newstead in the Central African Republic (Bangui area). In the other experiments, trapping data on Glossina palpalis palpalis (Robineau-Desvoidy) was collected in 'aggregate' form over several days at a time. Two of these were in Congo-Brazzaville (Bouenza area) and one in the Ivory Coast (Vavoua focus). Estimates are derived for the low and high equilibrium values as well as the trapping rate. The estimated effect of sustained trapping is to reduce the population to low equilibrium values that are 85-87% lower than the levels without trapping. The effects of the natural intrinsic growth and of the migration flows cannot be estimated separately because in the model they are mathematically indistinguishable.     

A matrix model for studying tsetse fly populations

Some characteristics of tsetse fly population dynamics were investigated using a matrix model. To take into account the peculiarities of the tsetse fly life cycle, the classic Leslie model was modified. Our model integrated the physiological age group of Glossina females, the pupal and adult survival rate and the pupal life span. The limit of the growth rate was studied and the results were satisfactory when compared with data of tsetse fly mass rearing. The effect of adult and pupal survival rates on the growth rate was examined and confirmed the importance of adult survival. The sensitivity analysis showed that the growth rate was particularly sensitive to change in the survival rate of young nulliparous females. This matrix model, directly accessible to the experimenter, enhanced our understanding of tsetse population dynamics.     

Are tsetse fly populations close to equilibrium?

Glossina or tsetse flies, the vectors of sleeping sickness, form a unique group of insects with remarkable characteristics. They are viviparous with a slow rhythm of reproduction (one larva approximately every 10 days) determined by the regular ovulation of alternate ovaries. This unusual physiology enables the age of the females to be estimated by examining the ovaries.The resulting ovarian age structure of tsetse fly populations has been used to develop research into the demography of tsetse flies. Several authors have proposed methods of estimating population growth rates from ovarian age distribution data. However, such methods are applicable only when the growth rate () is equal to 1 (i.e. the intrinsic rate of increase r is equal to 0). In fact, in this type of estimation, the adult survival rate a (or equivalently the mortality rate) cannot be dissociated from the growth rate.Other independently determined demographic parameters must be used to remove this lack of identiflability. We have built a matrix model of the dynamics of tsetse fly populations which enables the growth rate to be calculated from the pupal survival rate, the pupal period and the adult survival rate. Assuming that the age-groups of the population studied have reached a stable distribution, it is possible to calculate the probabilities for the observed sample of belonging to each of the age-groups, to construct a likelihood function and thus to obtain an estimate of the apparent survival rate = a/ If the pupal survival rate and the pupal period are known, a and can then be calculated from .The application of this method to data collected for over two annual cycles in a savannah habitat (Burkina-Faso) showed a high overall stability in the populations of Glossina palpalis gambiensis. Seasonal fluctuations could be easily interpreted as being the result of climatic changes between the dry and rainy seasons.     

Population dynamics of stable flies Stomoxys calcitrans (Diptera: Muscidae) at an organic dairy farm in Denmark based on mark-recapture with destructive sub-sampling

A population of stable flies, Stomoxys calcitrans (L.), was studied on a Danish cattle farm in two successive years. Flies were captured monthly by sweep nettings and marked with fluorescent dust. Absolute population size, dilution rate, loss rate, and adult longevity were estimated by means of a modified version of Bailey's triple catch method. In both years, the abundance of flies peaked in July. Using a statistical model, we were able to explain 86.6% of the variation in the per capita growth rate r as a function of current temperature, precipitation, and population size. Omitting precipitation from the model, it still explained 69.3%. The model predicts that stable flies have a temperature optimum at 21.8°C, and that no development will take place when temperatures inside the stable are below 10.2°C or above 33.5°C. At the optimal temperature the intrinsic rate of natural increase is 0.070 d(-1). The per capita dilution rate increased with temperature and decreased with population size, whereas no effect of these factors on the per capita loss rate could be shown. Mean adult survival time was estimated to 6.3 d with 95% CL ranging from 4.3 to 11.1 d. The study points at the possibility of developing predictive models as tools for achieving better, and more environmentally sound, control of stable flies.     

Comment on Barclay and Vreysen: Published dynamic population model for tsetse cannot fit field data

The structure, and assumed parameter values, of a recent dynamic population model for tsetse (Diptera: Glossinidae) render it unable to fit published data on tsetse control programs using odor-baited targets, insecticide-treated cattle and the sterile insect technique (SIT). The underlying problem is a mismatch between the small size of the mapped cells (1 ha) and the long time-step, which allows flies to move only once every 5 days, and then only to an adjacent cell. Assumed rates of tsetse dispersal and killing by odor-baited targets are consequently at least an order of magnitude lower than observed in the field. Suggestions that Glossina pallidipes could be eradicated more rapidly with SIT, than using hundreds of targets per km², is contradicted both by the field data and by three other independent modeling studies.     

A theoretical study of the invasion of cleared areas by tsetse flies (Diptera: Glossinidae)

Large-scale eradication campaigns against tsetse flies Glossina spp. are giving way to smaller operations aimed at disease and vector containment. There has been little discussion of the effects of these changes in policy. This study estimates the rate at which tsetse re-infect treated areas after the termination of control efforts. Movement is modelled as a diffusion process with a daily root mean square displacement (lambda) of 0.2-1 km-1/2 and population growth as logistic with a growth rate (r) < or =1.5% day-1. Invasion fronts move as the product of lambda and radicalr. For r = 0.75% day-1 a front advances at 2.5 km year-1 for each 100 m increment in lambda. If there are 0.001% survivors in 10% of the treated area, the population recovers to within 1% of the carrying capacity (K) within three years. If the control area is subject to invasion from all sides, a treated block of 10,000 km2 is effectively lost within two years - except at the lowest values of lambda and r. Cleared areas of 100 km2 are lost in a year, as observed in a community-based suppression programme in Kenya. If the treated area is closed to re-invasion, but if there is a block where tsetse survive at 0.0001-0.1% of K, the population recovers within 3-4 years for up to 20 km outside the surviving block. If the surviving flies are more widely spread, re-infection is even more rapid. The deterministic approach used here over-estimates re-invasion rates at low density, but comparisons between control scenarios are still valid. Stochastic modelling would estimate more exactly rates of re-infection at near-zero population densities.     

Effect of host packed cell volume on the bloodmeal size of male tsetse flies, Glossina pallidipes

aematin contents of engorged, male tsetse flies, Glossina pallidipes Austen, were compared with the packed cell volumes of oxen on which they had fed. Haematin contents icnreased with packed cell volume up to packed cell volumes of approximately 30%. Haematin contents appeared to level off or decline with further increase in packed cell volume. These results support a model of blood-feeding in tsetse flies in which the rate of blood consumption decreases as packed cell volume increases, because of increase in blood viscosity, and tsetse are unable to compensate for the decrease in consumption rate by feeding for a longer time. After allowing for the effects of packed cell volume, bloodmeal sizes of tsetse increased with ox body temperature.     

Thermal tolerance in a south-east African population of the tsetse fly Glossina pallidipes (Diptera, Glossinidae): implications for forecasting climate change impacts

For tsetse (Glossina spp.), the vectors of human and animal trypanosomiases, the physiological mechanisms linking variation in population dynamics with changing weather conditions have not been well established. Here, we investigate high- and low-temperature tolerance in terms of activity limits and survival in a natural population of adult Glossina pallidipes from eastern Zambia. Due to increased interest in chilling flies for handling and aerial dispersal in sterile insect technique control and eradication programmes, we also provide further detailed investigation of low-temperature responses. In wild-caught G. pallidipes, the probability of survival for 50% of the population at low-temperatures was at 3.7, 8.9 and 9.6 degrees C (95% CIs: +/-1.5 degrees C) for 1, 2 and 3 h treatments, respectively. At high temperatures, it was estimated that treatments at 37.9, 36.2 and 35.6 degrees C (95% CIs: +/-0.5 degrees C) would yield 50% population survival for 1, 2 and 3 h, respectively. Significant effects of time and temperature were detected at both temperature extremes (GLZ, p<0.05 in all cases) although a time-temperature interaction was only detected at high temperatures (p<0.0001). We synthesized data from four other Kenyan populations and found that upper critical thermal limits showed little variation among populations and laboratory treatments (range: 43.9-45.0 degrees C; 0.25 degrees C/min heating rate), although reduction to more ecologically relevant heating rates (0.06 degrees C/min) reduce these values significantly from approximately 44.4 to 40.6 degrees C, thereby providing a causal explanation for why tsetse distribution may be high-temperature limited. By contrast, low-temperature limits showed substantial variation among populations and acclimation treatments (range: 4.5-13.8 degrees C; 0.25 degrees C/min), indicating high levels of inter-population variability. Ecologically relevant cooling rates (0.06 degrees C/min) suggest tsetses are likely to experience chill coma temperatures under natural conditions (approximately 20-21 degrees C). The results from acute hardening experiments in the Zambian population demonstrate limited ability to improve low-temperature tolerance over short (hourly) timescales after non-lethal pre-treatments. In flies which survived chilling, recovery times were non-linear with plateaus between 2-6 and 8-12 degrees C. Survival times ranged between 4 and 36 h and did not vary between flies which had undergone chill coma by comparison with flies which had not, even after factoring body condition into the analyses (p>0.5 in all cases). However, flies with low chill coma values had the highest body water and fat content, indicating that when energy reserves are depleted, low-temperature tolerance may be compromised. Overall, these results suggest that physiological mechanisms may provide insight into tsetse population dynamics, hence distribution and abundance, and support a general prediction for reduced geographic distribution under future climate warming scenarios.     

A global sensitivity analysis for African sleeping sickness

African sleeping sickness is a parasitic disease transmitted through the bites of tsetse flies of the genus Glossina. We constructed mechanistic models for the basic reproduction number, R0, of Trypanosoma brucei gambiense and Trypanosoma brucei rhodesiense, respectively the causative agents of West and East African human sleeping sickness. We present global sensitivity analyses of these models that rank the importance of the biological parameters that may explain variation in R0, using parameter ranges based on literature, field data and expertize out of Uganda. For West African sleeping sickness, our results indicate that the proportion of bloodmeals taken from humans by Glossina fuscipes fuscipes is the most important factor, suggesting that differences in the exposure of humans to tsetse are fundamental to the distribution of T. b. gambiense. The second ranked parameter for T. b. gambiense and the highest ranked for T. b. rhodesiense was the proportion of Glossina refractory to infection. This finding underlines the possible implications of recent work showing that nutritionally stressed tsetse are more susceptible to trypanosome infection, and provides broad support for control strategies in development that are aimed at increasing refractoriness in tsetse flies. We note though that for T. b. rhodesiense the population parameters for tsetse - species composition, survival and abundance - were ranked almost as highly as the proportion refractory, and that the model assumed regular treatment of livestock with trypanocides as an established practice in the areas of Uganda experiencing East African sleeping sickness.     

Negative density‐dependent dispersal in tsetse (Glossina spp): red flag or red herring?

A deterministic model of the distribution of tsetse flies (Glossina spp) was used to assess the extent to which the efficacy of control operations would be affected by three different modes of density dependence in per capita adult dispersal: (i) density‐independent dispersal which has been commonly adopted in previous models, (ii) positive density‐dependent dispersal which has occasionally been discussed in the tsetse literature, (iii) negative density‐dependent dispersal (NDDD). The last has recently been suggested, from genetic studies, to change the dispersal rate of tsetse by up to 200‐fold, thereby posing a severe risk for the success of tsetse control operations. Modelling outputs showed that NDDD poses no such risk, provided the mean daily dispersal of tsetse is below about 1 km, which is greater than any rate actually recorded in the field or indicated by the genetic studies. NDDD can be problematic only if tsetse disperse at rates that appear highly unlikely, or even impossible, on energetic grounds. Under some circumstances these high rates would help rather than hinder the control officer. NDDD is not necessary to explain the results of control operations, and not sufficient to explain the results of successful control programmes.     

Lectin and peritrophic membrane development in the gut of Glossina m.morsitans and a discussion of their role in protecting the fly against trypanosome infection

Newly emerged Glossina m.morsitans Westwood tsetse flies lack a peritrophic membrane which develops to fully line the midgut after c. 80-90 h. Midgut lectins are mainly associated with the peritrophic membrane. Lectin levels in the blood-free gut of adult flies rise slowly up to 8 days and then rapidly to at least 14 days post-eclosion (when the last of our recordings was made). Despite starving flies for 4 days prior to the agglutination assay, gut lectin levels in older flies are 100-200 times more than those in newly ecloded flies. This is inconsistent with the idea that there is a simple relationship between lectins and the protection of tsetse flies against trypanosome infection. Various theories put forward to account for age-dependent variation in the ability of tsetse to become infected with trypanosomes are discussed in the light of these findings.     

The effect of starvation on the susceptibility of teneral and non-teneral tsetse flies to trypanosome infection

Transmission of vector-borne diseases depends largely on the ability of the insect vector to become infected with the parasite. In tsetse flies, newly emerged or teneral flies are considered the most likely to develop a mature, infective trypanosome infection. This was confirmed during experimental infections where laboratory-reared Glossina morsitans morsitans Westwood (Diptera: Glossinidae) were infected with Trypanosoma congolense or T. brucei brucei. The ability of mature adult tsetse flies to become infected with trypanosomes was significantly lower than that of newly emerged flies for both parasites. However, the nutritional status of the tsetse at the time of the infective bloodmeal affected its ability to acquire either a T. congolense or T. b. brucei infection. Indeed, an extreme period of starvation (3-4 days for teneral flies, 7 days for adult flies) lowers the developmental barrier for a trypanosome infection, especially at the midgut level of the tsetse fly. Adult G. m. morsitans became at least as susceptible as newly emerged flies to infection with T. congolense. Moreover, the susceptibility of adult flies, starved for 7 days, to an infection with T. b. brucei was also significantly increased, but only at the level of maturation of an established midgut infection to a salivary gland infection. The outcome of these experimental infections clearly suggests that, under natural conditions, nutritional stress in adult tsetse flies could contribute substantially to the epidemiology of tsetse-transmitted trypanosomiasis.     

Nutritional stress affects the tsetse fly's immune gene expression

Tsetse-transmitted trypanosomiasis poses a serious threat to human and animal health in sub-Saharan Africa. The majority of tsetse flies ( Glossina spp.) in a natural population will not develop a mature infection of either Trypanosoma congolense or Trypanosoma brucei sp. because of refractoriness, a phenomenon that is affected by different factors, including the tsetse fly's immune defence. Starvation of tsetse flies significantly increases their susceptibility to the establishment of a trypanosome infection. This paper reports the effects of nutritional stress (starvation) on (a) uninduced baseline levels of gene expression of the antimicrobial peptides attacin, defensin and cecropin in the tsetse fly, and (b) levels of expression induced in response to bacterial ( Escherichia coli ) or trypanosomal challenge. In newly emerged, unfed tsetse flies, starvation significantly lowers baseline levels of antimicrobial peptide gene expression, especially for attacin and cecropin. In response to trypanosome challenge, only non-starved older flies showed a significant increase in antimicrobial peptide gene expression within 5 days of ingestion of a trypanosome-containing bloodmeal, especially with T. brucei bloodstream forms. These data suggest that a decreased expression of immune genes in newly hatched flies or a lack of immune responsiveness to trypanosomes in older flies, both occurring as a result of fly starvation, may be among the factors contributing to the increased susceptibility of nutritionally stressed tsetse flies to trypanosome infection.     

Tsetse Fly (G.f. fuscipes) Distribution in the Lake Victoria Basin of Uganda

Tsetse flies transmit trypanosomes, the causative agent of human and animal African trypanosomiasis. The tsetse vector is extensively distributed across sub-Saharan Africa. Trypanosomiasis maintenance is determined by the interrelationship of three elements: vertebrate host, parasite and the vector responsible for transmission. Mapping the distribution and abundance of tsetse flies assists in predicting trypanosomiasis distributions and developing rational strategies for disease and vector control. Given scarce resources to carry out regular full scale field tsetse surveys to up-date existing tsetse maps, there is a need to devise inexpensive means for regularly obtaining dependable area-wide tsetse data to guide control activities. In this study we used spatial epidemiological modelling techniques (logistic regression) involving 5000 field-based tsetse-data (G. f. fuscipes) points over an area of 40,000 km², with satellite-derived environmental surrogates composed of precipitation, temperature, land cover, normalised difference vegetation index (NDVI) and elevation at the sub-national level. We used these extensive tsetse data to analyse the relationships between presence of tsetse (G. f. fuscipes) and environmental variables. The strength of the results was enhanced through the application of a spatial autologistic regression model (SARM). Using the SARM we showed that the probability of tsetse presence increased with proportion of forest cover and riverine vegetation. The key outputs are a predictive tsetse distribution map for the Lake Victoria basin of Uganda and an improved understanding of the association between tsetse presence and environmental variables. The predicted spatial distribution of tsetse in the Lake Victoria basin of Uganda will provide significant new information to assist with the spatial targeting of tsetse and trypanosomiasis control.     

Periodic dynamics in a two-stage Allee effect model are driven by tension between stage equilibria

Single species difference population models can show complex dynamics such as periodicity and chaos under certain circumstances, but usually only when rates of intrinsic population growth or other life history parameter are unrealistically high. Single species models with Allee effects (positive density dependence at low density) have also been shown to exhibit complex dynamics when combined with over-compensatory density dependence or a narrow fertility window. Here we present a simple two-stage model with Allee effects which shows large amplitude periodic fluctuations for some initial conditions, without these requirements. Periodicity arises out of a tension between the critical equilibrium of each stage, i.e. when the initial population vector is such that the adult stage is above the critical value, while the juvenile stage is below the critical value. Within this area of parameter space, the range of initial conditions giving rise to periodic dynamics is driven mainly by adult mortality rates. Periodic dynamics become more important as adult mortality increases up to a certain point, after which periodic dynamics are replaced by extinction. This model has more realistic life history parameter values than most 'chaotic' models. Conditions for periodic dynamics might arise in some marine species which are exploited (high adult mortality) leading to recruitment limitation (low juvenile density) and might be an additional source of extinction risk.     

Temperature-dependence of metabolic rate in Glossina morsitans morsitans (Diptera, Glossinidae) does not vary with gender, age, feeding, pregnancy or acclimation

While variation in metabolic rate at a single temperature can occur for a variety of reasons and the effect of temperature is well established in insects, within-generation variation of metabolic rate-temperature relationships has been relatively poorly explored. In this study, we investigate the effects of gender, age, feeding and pregnancy, as well as three acclimation temperatures (19, 24, 29 degrees C), on standard metabolic rate and its temperature-dependence within post-developmental (i.e. non-teneral) adult G. morsitans morsitans. Although most of the independent variables influenced metabolic rate at a single test temperature (P<0.001 in most cases), and cold-acclimation resulted in significant up-regulation of metabolic rate at all test temperatures relative to 24 and 29 degrees C acclimation (P<0.0001), mass-independent metabolic rate-temperature relationships were surprisingly invariant over all experimental groups (P>0.05 in all cases). Slopes of log10 metabolic rate (ml CO2h(-1)) against temperature ( degrees C) ranged from a minimum of 0.03035 (+/-S.E.=0.003) in young fasted females to a maximum of 0.03834 (+/-0.004) in mature fasted males. These findings have implications for predicting the metabolic responses of tsetse flies to short-term temperature variation and may also have applications for modelling tsetse population dynamics as a function of temperature.