Extinction probabilities and times to extinction for populations of tsetse flies Glossina spp. (Diptera: Glossinidae) subjected to various control measures

Abstract

A stochastic branching process was used to derive equations for the mean and variance of the probability of, and time to, extinction in tsetse populations. If the remnant population is a single inseminated female, the extinction probability increases linearly with adult mortality and is always certain if this mortality >3.5% per day even for zero pupal mortality. If the latter mortality is 4% per day, certain extinction is only avoided if adult mortality <1.5% per day. For remnant female populations >1, the extinction probability increases in a non-linear manner with adult mortality. Extinction is still certain for adult mortality >3.5% per day but, when the remnant population is >16, extinction is highly unlikely for adult mortality <2.5% per day if all females are inseminated. Extinction probability increases with increasing probability of sterile mating in much the same way as it does with increasing adult mortality. Extinction is assured if the probability of insemination can be reduced to 0.1. The required reduction decreases with increasing adult mortality. For adult mortality = 6-8% per day, the time to extinction increases only by one generation per order of magnitude increase in the starting population. Time to extinction is less sensitive to changes in the pupal than in the adult mortality. Reductions in the probability of insemination only become important when adult mortality is small; if the adult mortality is 8% per day, reducing the insemination probability from 1 to 0.1 only reduces the expected time to extinction by two generations. Conversely, increases in adult mortality produce important reductions in the required time even when the probability of insemination is 0.1. The practical, economic implication for the sterile insect technique is that the low-tech methods used to suppress tsetse populations should not be halted when the release of sterile males is initiated. The sterile insect technique should only be contemplated when it has been demonstrated that the low-tech methods have failed to effect eradication. The theory is shown to be in good accord with the observed results of tsetse control campaigns involving the use of odour-baited targets in Zimbabwe and the sterile insect technique on Unguja Island, Zanzibar.