DOI: 10.1101/463067Nov 5, 2018Paper

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

BioRxiv : the Preprint Server for Biology
Damian KajunguriJ W Hargrove


A published study used a stochastic branching process to derive equations for the mean and variance of the probability of, and time to, extinction in population of tsetse flies (Glossina spp) as a function of adult and pupal mortality, and the probabilities that a female is inseminated by a fertile male. The original derivation was partially heuristic and provided no proofs for inductive results. We provide these proofs, together with a more compact way of reaching the same results. We also show that, while the published equations hold good for the case where tsetse produce male and female offspring in equal proportion, a different solution is required for the more general case where the probability (beta) that an offspring is female lies anywhere in the interval (0,1). We confirm previous results obtained for the special case where beta = 0:5 and show that extinction probability is at a minimum for beta > 0:5 by an amount that increases with increasing adult female mortality. Sensitivity analysis showed that the extinction probability was affected most by changes in adult female mortality, followed by the rate of production of pupae. Because females only produce a single offspring approximately every 10 days, imposing a death ...Continue Reading

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