Conclusions from a dynamic population model for tsetse: response to comments

The critique by Hargrove et al. (Popul Ecol, 2011) of our recently published paper on a tsetse population model (Barclay and Vreysen in Popul Ecol 53:89–110, 2011) has made some good points but has also misinterpreted the intent of some of our results as we presented them. Hargrove et al. rightly say that there is a mismatch between the size of the unit cells in the model (1 ha) and the iteration rate of the model (every 5 days), yielding too low a dispersal rate to simulate reality. However, they have misconstrued several of our results that we presented as examples to imply that those results were a necessary condition for control of tsetse, especially using traps and targets.     

A dynamic population model for tsetse (Diptera: Glossinidae) area-wide integrated pest management

A spatial model of tsetse (Glossina palpalis ssp. and G. pallidipes) life cycle was created in FORTRAN, and four control measures [aerial spraying of non-residual insecticides, traps and targets, insecticide-treated livestock (ITL) and the sterile insect technique] were programmed into the model to assess how much of each of various combinations of these control tactics would be necessary to eradicate the population. The model included density-independent and -dependent mortality rates, temperature-dependent mortality, an age-dependent mortality, two mechanisms of dispersal and a component of aggregation. Sensitivity analyses assessed the importance of various life history features and indicated that female fertility and factors affecting survivorship had the greatest impact on the equilibrium of the female population. The female equilibrium was likewise reduced when dispersal and aggregation were acting together. Sensitivity analyses showed that basic female survivorship, age-dependent and temperature-dependent survivorship of adults, teneral-specific survivorship, daily female fertility, and mean temperature had the greatest effect on the four applied control measures. Time to eradication was reduced by initial knockdown of the population and due to the synergism of certain combinations of methods [e.g., traps-targets and sterile insect technique (SIT); ITL and SIT]. Competitive ability of the sterile males was an important parameter when sterile to wild male overflooding ratios were small. An aggregated wild population reduced the efficiency of the SIT, but increased it with increased dispersal. The model can be used interactively to facilitate decision making during the planning and implementation of operational area-wide integrated pest management programs against tsetse.     

A model for blood meal digestion and fat metabolism in male tsetse flies (Glossinidae)

Abstract. Fat and haematin levels of mature male Glossina morsitans morsitans Westwood were estimated at different times after feeding at temperatures between 15 and 30°C. Flies were kept (largely inactive) in 7.5 × 2.5 cm tubes, or in actograph cages, where flight activity increased with time after feeding. Haematin excretion was modelled as a series of three first order reactions, all with the same rate parameter. The model accounted for > 98% of the variance in mean haematin in each of seven experiments; the rate parameter increased linearly with temperature and activity level. A similar approach was adopted for modelling fat metabolism. The rate coefficients of lipogenesis increased with temperature, and that for lipolysis with temperature, activity level and their interaction. All experiments were analysed simultaneously to provide equations predicting haematin or fat levels for all times, for active or inactive flies, and for temperatures between 15 and 30°C. Haematin exhibited large variations between individuals, but for active flies the expected haematin content at a given time varied little between flies kept at 25 and at 30°C. In inactive flies kept at 25°C, lipogenesis peaked at ≈ 24 h and lipolysis at ≈ 48 h. For active flies the times were 12 and 24 h, respectively; both rates were about twice as high as in inactive flies. Active flies produced (up to 1 mg) more fat out of a given size of blood meal than inactive flies. Curves of fat content against logarithm of haematin content differed little with temperature, and can therefore be useful for comparative studies of field populations of tsetse.     

A parity-structured matrix model for tsetse populations

A matrix model is used to describe the dynamics of a population of female tsetse flies structured by parity (i.e., by the number of larvae laid). For typical parameter values, the intrinsic growth rate of the population is zero when the adult daily survival rate is 0.970, corresponding to an adult life expectancy of 1/0.030 = 33.3 days. This value is plausible and consistent with results found earlier by others. The intrinsic growth rate is insensitive to the variance of the interlarval period. Temperature being a function of the time of the year, a known relationship between temperature and mean pupal and interlarval times was used to produce a time-varying version of the model which was fitted to temperature and (estimated) population data. With well-chosen parameter values, the modeled population replicated at least roughly the population data. This illustrates dynamically the abiotic effect of temperature on population growth. Given that tsetse flies are the vectors of trypanosomiasis ("sleeping sickness") the model provides a framework within which future transmission models can be developed in order to study the impact of altered temperatures on the spread of this deadly disease.     

Development of a low-cost tsetse trap and odour baits for Glossina pallidipes and G.longipennis in Kenya

Experiments were carried out to improve the NG2B tsetse trap (Brightwell et al., 1987), baited with acetone and cow urine, for use by rural communities to control G.pallidipes Austen and G.longipennis Corti. Modifications included a lower dose rate of acetone, a new cage design and raising the trap about 15-20 cm. Research on different trap cone materials showed that the degree of light transmission of the netting, rather than its colour, was the crucial factor affecting the catch of G.pallidipes. Adding an additional metre of blue cloth to one side of the trap increased catches of females of both species by about 60%. Traps baited with synthetic phenols yielded similar numbers of G.pallidipes and significantly more G.longipennis than those baited with natural cow urine. The latter difference was not apparent when octenol was also used, so cow urine was retained as one of the odour baits in preference to the imported phenols. Although octenol increased catches of G.pallidipes by only about 30%, catches of G.longipennis were increased 2-4-fold, making it a very useful attractant for the latter species. The cost of the trap/odour-bait system was estimated to be US$8.5 per unit per annum. The economics of this method of tsetse control are discussed.     

Effects of age, sex and hunger on the antennal olfactory sensitivity of tsetse flies

Abstract The effects of age on electroantennogram (EAG) responses were investigated in male and female Glossina morsitans morsitans and comparative studies on the effects of starvation and sex on the EAG in G.m. morsitans, G.austeni, G.tachinoides and G.fuscipes fuscipes were made. Stimuli were the vapours of l-octen-3-ol, 4-heptanone, 3-nonanone and acetone. EAG decreased with age in both sexes of G.m.morsitans , responses in 5-day-old flies already being significantly lower than those in 1-day-old flies. In G.m.morsitans and G.tachinoides , EAG responses of males were higher than those of females. In G.austeni and G.f.fuscipes , however, the reverse was found. With increasing starvation EAG sensitivity increased in both sexes of G.m.morsitans and G.tachinoides. In G.austeni and in G.f.fuscipes no clear effects of starvation were observed. Response spectra of the individual species to the four odour substances did not change with increasing hunger. It is concluded that receptor sensitivity may be modulated depending on the insect's needs. Possible mechanisms of regulation and significance of this modulation are discussed.     

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.     

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.     

Modelling the effect of feeding-related mortality on the feeding strategy of tsetse (Diptera: Glossinidae)

Abstract. Free-living haematophagous insects risk death through host grooming responses or through increased susceptibility to predation whenever they take a bloodmeal. In this paper we investigate the effects of these risks on the feeding strategy of tsetse. A model is presented that allows for death of tsetse by starvation if they do not succeed in feeding within a fixed time (set at 6 days in the first instance) and for mortality specifically associated with feeding. In addition there is background mortality that applies to all flies at all times.
The model is used to compute the individual life-time fertility (number of female puparia per female) as a function of the probability of obtaining a meal (indicated by field data to be very high, usually > 0.85 per day) and the day on which flies start to search for a meal. We suggest that the feeding strategy that would be selected for is that which allows the maximum reproductive output. The model shows that this strategy involves making no attempts to feed for 3–4 days after the previous meal and then attempting to feed with the greatest possible probability until a meal is obtained. The predicted feeding interval, obtained independently of any trapping data, agrees closely with all previous estimates from field studies using a variety of methods. Preliminary results from a laboratory experiment reveal an increased risk of predation of recently fed as compared with hungry tsetse. The lower the actual feeding mortality the more frequently will flies be able to feed should conditions so demand. It is adaptive, however, for tsetse to delay attempting to feed for as long as they can, which is made possible by the near certainty of locating and feeding on a host within 1 day, using their sophisticated sensory systems.     

Field experiments on a new method for determining age in tsetse flies (Diptera: Glossinidae)

ABSTRACT.

• 1 Data are presented which suggests that the accurate determination of the age of tsetse flies (Glossina morsitans morsitans Westwood and G. pallidipes Austen) in the field can be achieved by measuring the fluorescence content of the head capsule.
• 2 The way in which this can be achieved and further work which would improve the accuracy of the technique are discussed.

     

Age‐specific changes in sperm levels among female tsetse (Glossina spp.) with a model for the time course of insemination

The age, insemination and ovulation status of tsetse flies Glossina pallidipes Austen (n = 154369) and Glossina morsitans morsitans Westwood (n = 19659), captured over 11 years in Zimbabwe, are assessed by ovarian dissection. Instantaneous rates of insemination increase exponentially with age in both species; 90% insemination levels are reached after 5 days post‐emergence in G. m. morsitans and 7 days in G. pallidipes, varying little with season. More than 95% of both species have ovulated by the age of 8 days and 99% by 12 days. Older flies that have not ovulated are > 100‐fold more likely to be caught in October and November than in other months. A 500‐fold decrease in trap catches did not result in any detectible decrease in the probability of females being inseminated. The proportion of partially filled spermathecae rises for approximately 6 days then declines, consistent with some flies having mated more than once. For flies caught on electric nets, with wings undamaged during capture, wing‐fray data are used to extend ovarian age estimates up to 11 ovulations. Among these flies, the volume of sperm in the spermathecae declines little in flies that have ovulated up to seven times; thereafter, it declines by approximately 1% per ovulation. The time course of insemination and the mating frequency of females are important considerations in modelling tsetse fly populations, as well as for the dynamics of interventions involving the release of genetically‐modified insects, which should not be seriously compromised by the limited levels of polyandry currently observed.     

Insecticide-treated cattle for tsetse control: the power and the problems

Trypanosomiasis control increasingly involves financial input from livestock owners and their active participation. If control is carried out on smaller scales than in the past, methods such as aerial and ground spraying and sterile insect techniques will have reduced application. There will be increased reliance on trypanocidal drugs, and bait methods of tsetse control--where flies are attracted to point sources and killed. If drug resistance develops, cheap and simple bait methods offer the only means of disease control that might be applied, and paid for, by stockowners themselves. The methods have been effective in some circumstances, but not in others, and it is important to understand the reasons for the successes and the failures. Analysis is presented of the results of two Tanzanian tsetse control campaigns involving the use of insecticide-treated cattle. Between 1991 and 1996, following the introduction of widespread dipping in the Kagera Region, trypanosomiasis declined from >19000 cases to <2400 and deaths from >4000 to 29. On four ranches in the region, tsetse have been almost eliminated and trypanosomiasis prophylaxis is no longer used. Similarly aggressive use of pyrethroids on Mkwaja Ranch in Tanga Region has not had such dramatic effects. Tsetse and trypanosomiasis are still common, despite high levels of prophylaxis and the deployment of approximately 200 odour-baited targets. The difference in the results is attributed to a combination of the much smaller area covered by treated animals at Mkwaja, a greater susceptibility to re-invasion and a more suitable habitat for the flies. A better understanding of the dynamics of the use of insecticide-treated cattle is needed before we can predict confidently the outcome of particular control operations.     

A model for the relationship between wing fray and chronological and ovarian ages in tsetse (Glossina spp)

Age-dependent mortality changes in haematophagous insects are difficult to measure but are important determinants of population dynamics and vectorial capacity. A Markov process was used to model age-dependent changes in wing fray in tsetse (Glossina spp), calibrated using published mark–recapture data for male G. m. morsitans in Tanzania. The model was applied to female G. m. morsitans, captured in Zimbabwe using a vehicle-mounted electric net and subjected to ovarian dissection and wing fray analysis. Rates of fray increased significantly with age in males but not females, where the rate was constant for ovarian categories 0–3. A jump in mean fray between ovarian categories 3 and 4 + 4n is consistent with the latter category including flies that have ovulated 4, 8, 12, 16 times and so on. The magnitude of the jump could, theoretically, facilitate improved mortality estimates. In practice, although knowledge of fly mortality was required for modelling wing fray, mortality estimates derived from ovarian dissection data are independent of patterns and rates of change in wing fray. Significantly better fits to ovarian age data resulted when age-specific mortality was modelled as the sum of two exponentials, with high mortality in young and old flies, than when mortality was constant at 2.3% per day.     

Measuring the fit of sequence data to phylogenetic model: allowing for missing data

It is fundamentally important to assess the fit of data to model in phylogenetic and evolutionary studies. Phylogenetic methods using molecular sequences typically start with a multiple alignment. It is possible to measure the fit of data to model expectations of data, for example, via the likelihood-ratio (G) test or the X(2) test, if all sites in all sequences have an unambiguous residue. However, nearly all alignments of interest contain sites (columns of the alignment) with missing data, that is, ambiguous nucleotides, gaps, or unsequenced regions, which must presently be removed before using the above tests. Unfortunately, this is often either undesirable or impractical, as it will discard much of the data. Here, we show how iterative ML estimators may directly estimate the site-pattern probabilities for columns with missing data, given only standard i.i.d. assumptions. The optimization may use an EM or Newton algorithm, or any other hill-climbing approach. The resulting optimal likelihood under the unconstrained or multinomial model may be compared directly with the likelihood of the data coming from the model (a G statistic). Alternatively the modified observed and the expected frequencies of site patterns may be compared using a X(2) test. The distribution of such statistics is best assessed using appropriate simulations. The new method is applicable to models using codons or paired sites. The methods are also useful with Hadamard conjugations (spectral analysis) and are illustrated with these and with ML evolutionary models that allow site-rate variability.     

A dynamic water quality index model based on functional data analysis

A water quality index (WQI) incorporates two shortcomings in the dynamic assessment of water quality, namely: (1) the sampling time series must be identical for each indicator and no missing data should occur, and (2) stationary weights cannot represent the changes in the pollutant importance. To solve these problems, the present study introduces the functional data analysis method into WQI research and establishes a dynamic WQI (D-WQI) model. D-WQI is a generalization of the conventional WQI. In the D-WQI model, the changes of water quality and pollutant importance are represented in the form of dynamic functional curves. The generation methods of the concentration curves, sub-index curves, dynamic weight curves, and WQI curves are discussed. As an illustration, the D-WQI model is applied in the water quality assessment of the Changjiang River in Sanjiangying in 2012. Result shows that the river can be classified as II (good) throughout the year, which can satisfy the requirement of the Chinese South-to-North Water Diversion Project.     

A dynamic model of darkness tolerance for phytoplankton: model description

To analyze various effects of prolonged darkness on phytoplankton population dynamics, we developed a dynamic model of darkness tolerance for phytoplankton and investigated its characteristics. To construct the basic concepts of the model, we categorized various changes in abundance of phytoplankton both during prolonged darkness and after reillumination into several patterns, and then considered the physiological processes producing these patterns. The nature of darkness tolerance was considered to incorporate previously experienced light conditions, including darkness, as a physiological activity, and members of the same phytoplankton species exhibit different dynamics even in identical light conditions due to such career effects. Taking this into consideration, we developed a cell quota model in relation to darkness tolerance. State variables for abundance were indicated by cell numbers, and physiological condition by three intracellular carbon pools with different physiological functions. Using our model, we analyzed the various changes in abundance of phytoplankton in relation to exposure to prolonged darkness. Various responses in terms of phytoplankton abundance to prolonged darkness and after reillumination were successfully reproduced by the model that simply assumed that deterioration of physiological mechanics, such as photosynthetic functions, was due to a prolonged dark condition. On the basis of the results of calculation and assumptions for the model, we discuss the limitations, problems, and effectiveness of the model. Handling editor: Luigi Naselli-Flores     

Interactions between cattle and biting flies: effects on the feeding rate of tsetse

In Zimbabwe, studies were made of the effect of host behaviour on the feeding success of Glossina pallidipes Austen and G. morsitans morsitans Westwood (Diptera: Glossinidae) attracted to cattle of different age and sex. The mean feeding rates for male and female G. pallidipes attracted to oxen were 60% and 58%, respectively, compared to 33% and 53% for male and female G. m. morsitans. The feeding rate of G. pallidipes varied between oxen and was inversely correlated with a host's rate of defensive leg movements, which, in turn, was positively correlated with the density of Stomoxys spp. (Diptera: Muscidae) caught in the vicinity of the host. Tsetse were significantly less successful in feeding from young cattle. For G. pallidipes, the feeding rate on calves (<6 months) was 11%, whereas for male and female G. m. morsitans the rates were 12% and 20%, respectively. Significantly lower feeding rates were apparent for cattle aged up to 2 years, when the feeding rate for G. pallidipes (31%) was still significantly less than that on mature oxen (68%). Feeding rates for G. pallidipes on adult female cattle were lower than those on oxen (45% vs. 61%). The lower feeding rates in young animals were attributed to higher rates of defensive movements. The results suggest that higher rates of defensive activities by young cattle reduce the risk of them contracting trypanosomiasis.