Improved estimates for extinction probabilities and times to extinction for populations of tsetse (Glossina spp)

Improved estimates of abortion rates in tsetse (Glossina spp.)

Abortion rates were assessed among 170, 846 tsetse (154,228 Glossina pallidipes and 19,618 Glossina morsitans morsitans) sampled in Zimbabwe in 1988-1999. The study produced improved estimates of abortion rates and how these varied with fly age and size and temperatures experienced during pregnancy. An abortion was diagnosed if the uterus was empty and the largest oocyte <0.82 of the expected mature length. Abortion rates for G. pallidipes and G. m. morsitans were 0.64% (95% ci: 0.59-0.69) and 0.83% (0.62-1.10) for trapped flies and 2.03% (1.77-2.31) and 1.55% (1.20-1.98) for flies from artificial refuges. Abortion rates increased with increasing temperature and decreased with increasing wing length and wing fray. Contrary to laboratory findings, abortion rates did not increase in the oldest flies. Percentages of tsetse with empty uteri, regardless of abortion status, were significantly higher than estimated abortion percentages. For tsetse from traps, 4.01% (95% ci: 3.90-4.13) of G. pallidipes and 2.52% (2.14-2.95) of G. m. morsitans had empty uteri; for flies from artificial refuges, the percentages were 12.69% (12.07-13.34) and 14.90% (13.82-16.02), respectively. Abortion losses are small relative to losses at all other stages of life.

Does Counting Different Life Stages Impact Estimates for Extinction Probabilities for Tsetse (Glossina spp)?

As insect populations decline, due to climate change and other environmental disruptions, there has been an increased interest in understanding extinction probabilities. Generally, the life cycle of insects occurs in well-defined stages: when counting insects, questions naturally arise about which life stage to count. Using tsetse flies (vectors of trypanosomiasis) as a case study, we develop a model that works when different life stages are counted. Previous branching process models for tsetse populations only explicitly represent newly emerged adult female tsetse and use that subpopulation to keep track of population growth/decline. Here, we directly model other life stages. We analyse reproduction numbers and extinction probabilities and show that several previous models used for estimating extinction probabilities for tsetse populations are special cases of the current model. We confirm that the reproduction number is the same regardless of which life stage is counted, and show how the extinction probability depends on which life stage we start from. We demonstrate, and provide a biological explanation for, a simple relationship between extinction probabilities for the different life stages, based on the probability of recruitment between stages. These results offer insights into insect population dynamics and provide tools that will help with more detailed models of tsetse populations. Population dynamics studies of insects should be clear about life stages and counting points.

Modelling optimal timing and frequency of insecticide sprays for eradication or knockdown of closed populations of tsetse flies Glossina spp. (Diptera: Glossinidae)

A population model for tsetse species was used to assess the optimal number and spacing of airborne sprays to reduce or eradicate a tsetse population. It was found that the optimal spray spacing was determined by the time (days) from adult emergence to the first larviposition and, for safety, spacing was assigned to that duration minus 2 days. If sprays killed all adults, then the number of sprays required for eradication is determined by a simple formula. If spray efficiency is less than 100% kill per spray, then a simulation was used to determine the optimal number, which was strongly affected by spray efficiency, mean daily temperature, pupal duration, age to first larviposition and the acceptance threshold for control, rather than eradication. For eradication, it is necessary to have a spray efficiency of greater than 99.9% to avoid requiring an excessive number of sprays. Output from the simulation was compared with the results of two aerial spraying campaigns against tsetse and a least squares analysis estimated that, in both cases, the kill efficiency of the sprays was not significantly less than 100%.

Uncertainty and sensitivity analyses of extinction probabilities suggest that adult female mortality is the weakest link for populations of tsetse (Glossina spp)

Background

A relatively simple life history allows us to derive an expression for the extinction probability of populations of tsetse, vectors of African sleeping sickness. We present the uncertainty and sensitivity analysis of the extinction probability, to offer key insights into factors affecting the control or eradication of tsetse populations.

Methods

We represent tsetse population growth as a branching process, and derive closed form estimates of population extinction from that model. Statistical and mathematical techniques are used to analyse the uncertainties in estimating extinction probability, and the sensitivity of the extinction probability to changes in input parameters representing the natural life history and vital dynamics of tsetse populations.

Results

For fixed values of input parameters, the sensitivity of extinction probability depends on the baseline parameter values. Extinction probability is most sensitive to the probability that a female is inseminated by a fertile male when daily pupal mortality is low, whereas the extinction probability is most sensitive to daily mortality rate for adult females when daily pupal mortality, and extinction probabilities, are high. Global uncertainty and sensitivity analysis show that daily mortality rate for adult females has the highest impact on the extinction probability.

Conclusions

The high correlation between extinction probability and daily female adult mortality gives a strong argument that control techniques which increase daily female adult mortality may be the single most effective means of ensuring eradication of tsetse population.

Tsetse flies (Glossina spp.) are vectors of African trypanosomiasis, a deadly disease commonly called sleeping sickness in humans and nagana in livestock. The relatively simple life history of tsetse enabled us to model its population growth as a stochastic branching process. We derived a closed-form expression for the probability that a population of tsetse goes extinct, as a function of death, birth, development and insemination rates in female tsetse. We analyzed the sensitivity of the extinction probability to the different input parameters, in a bid to identify parameters with the highest impact on extinction probability. This information can, potentially, inform policy direction for tsetse control/elimination. In all the scenarios we considered for the global sensitivity analysis, the daily mortality rate for adult females had the greatest impact on the magnitude of extinction probability. Our findings suggest that the mortality rate in the adult females is the weakest link in tsetse life history, and this fact should be exploited in achieving tsetse population control, or even eradication.

Extinction probabilities as a function of temperature for populations of tsetse (Glossina spp.)

Significant reductions in populations of tsetse (Glossina spp) in parts of Zimbabwe have been attributed to increases in temperature over recent decades. Sustained increases in temperature might lead to local extinctions of tsetse populations. Extinction probabilities for tsetse populations have not so far been estimated as a function of temperature. We develop a time-homogeneous branching process model for situations where tsetse live at different levels of fixed temperature. We derive a probability distribution pk(T) for the number of female offspring an adult female tsetse is expected to produce in her lifetime, as a function of the fixed temperature at which she is living. We show that pk(T) can be expressed as a geometric series: its generating function is therefore a fractional linear type. We obtain expressions for the extinction probability, reproduction number, time to extinction and growth rates. The results are valid for all tsetse, but detailed effects of temperature will vary between species. No G. m. morsitans population can escape extinction if subjected, for extended periods, to temperatures outside the range 16°C-32°C. Extinction probability increases more rapidly as temperatures approach and exceed the upper and lower limits. If the number of females is large enough, the population can still survive even at high temperatures (28°C-31°C). Small decreases or increases in constant temperature in the neighbourhoods of 16°C and 31°C, respectively, can drive tsetse populations to extinction. Further study is needed to estimate extinction probabilities for tsetse populations in field situations where temperatures vary continuously.

The continental atlas of tsetse and African animal trypanosomosis in Nigeria

Tsetse-transmitted trypanosomosis remains a major animal health problem in Nigeria, in a context where changes in land cover, climate and control interventions are modifying its epidemiological patterns. Evidence-based decision making for the progressive control of the disease requires spatially-explicit information on its occurrence and prevalence, as well as on the distribution and abundance of the tsetse vector. In the framework of the continental Atlas of tsetse and African animal trypanosomosis (AAT), a geo-referenced database was assembled for Nigeria, based on the systematic review of 133 scientific publications (period January 1990 - March 2019). The three main species of trypanosomes responsible for the disease (i.e. Trypanosoma vivax, T. congolense and T. brucei) were found to be widespread, thus posing a national-level problem. Their geographic distribution extends beyond the tsetse-infested belt, owing to the combined effect of animal movement and mechanical transmission by non-tsetse vectors. T. simiae, the major trypanosomal pathogen in pigs, T. godfreyi and the human-infective T. brucei gambiense were also reported. AAT was reported in a number of susceptible host species, including cattle, sheep, goats, pigs, camels, horses, donkeys and dogs, while no study on wildlife was identified. Estimates of prevalence are heavily influenced by the sensitivity of the diagnostic techniques, ranging from an average of 3.5% for blood films to 31.0% for molecular techniques. Two riverine tsetse species (i.e. Glossina palpalis palpalis and G. tachinoides) were found to have the broadest geographical range, as they were detected in all six geopolitical zones of Nigeria. By contrast, the distribution of savannah species (i.e. G. morsitans submorsitans and G. longipalpis) appears to be highly fragmented, and limited to protected areas. Very little information is available for forest species, with one single paper reporting on G. fusca congolensis and G. nigrofusca nigrofusca in the Niger Delta region. The future development of a national Atlas of tsetse and AAT, relying on both published and unpublished information, could improve on the present review and provide further epidemiological evidence for decision making.