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%.

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.

Probability models to facilitate a declaration of pest-free status, with special reference to tsetse (Diptera: Glossinidae).

A methodology is presented to facilitate a declaration that an area is 'pest-free' following an eradication campaign against an insect pest. This involves probability models to assess null trapping results and also growth models to help verify, following a waiting period, that pests were not present when control was stopped. Two probability models are developed to calculate the probability of negative trapping results if in fact insects were present. If this probability is sufficiently low, then the hypothesis that insects are present is rejected. The models depend on knowledge of the efficiency and the area of attractiveness of the traps. To verify the results of the probability model, a waiting period is required to see if a rebound occurs. If an incipient but non-detectable population remains after control measures are discontinued, then a rebound should occur. Using a growth model, the rate of increase of an insect population is examined starting from one gravid female or one male and a female. An example is given for tsetse in which both means and confidence limits are calculated for a period of 24 reproductive periods after control is terminated. If no rebound is detected, then a declaration of eradication can be made.

Genetic population replacement for insect control: a new method for estimating fitness and generation time of continuously-breeding competing strains.

A model of complete underdominance that applies to population replacement for insect control by compound autosomes or compound; free arm strains, has been used to develop a new technique for estimating fitness and generation time in continuously-breeding competing populations, without resorting to measurement of birth rate, survivorship etc. The method is statistical and uses successive intervals of various sizes in an estimation equation. Estimates of fitness and generation time are revealed as a result of convergence of data from competitions in which a strain either becomes fixed or is eliminated in a mixed population. The technique has been applied to data from Drosophila melanogaster cage competitions with believable results. Difficulties resulting from the frequency dependence of the estimates over time and the inherent cyclicity of the population competition data are evaluated. Fitness estimates from this method of successive intervals are lower than those from another unstable equilibrium method. The former technique measures fitness in population at carrying capacity in which density-dependence is prominent, whereas the latter method is applicable only to populations in which density-dependence is negligible. The implications to insect control of an estimation procedure which yields fitness values for continuously-breeding populations under conditions of density dependence are discussed.