Reduced oviposition period promotes blowfly population extinction in Nicholson’s model

Blowflies use open wounds or the accumulation of feces or urine in wool to lay their eggs. The larvae that emerge cause lesions in the host sheep, which can lead to death. They are found in Australia, New Zealand, and the United Kingdom. Nicholson’s model describes the population dynamics of the Australian blowfly (Lucilia Cuprina). It incorporates environmental variation. The extinction of these flies depends on the time to oviposition and the time between generations. The Lyapunov function, which is positive with a negative derivative, provides the condition for the stability of the equilibrium point: the oviposition period must be sufficiently short, because the shorter it is, the more it favors the extinction of the species. The zero solution is the only equilibrium point, synonymous with the extinction of the population. Another species of blowfly, Lucilia Sericata, also attacks sheep in Australia. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to share same mitochondrial DNA sequences, although the two species are distinct. Presumably to avoid competition between them. the egg-laying time of each species does not occur at the same time of year: L. Sericata prefers warmer months, thus in summer, while L. Cuprina is mainly active in autumn. Laying of eggs in different months allows avoiding competition between these species. This also binds them together. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations, provided they do not adapt.