Abstract
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.
Highlights
A bite from a tsetse fly (Glossina spp.) infected with a parasite of the genus Trypanosoma may cause Human African Trypanosomiasis (HAT), commonly called sleeping sickness in humans, or Animal African Trypanosomiasis (AAT), commonly called nagana in livestock
Temperature plays a key role in tsetse population dynamics: no population of G. m. morsitans can escape extinction at constant temperatures < 16 ̊C or > 32 ̊C
High temperatures due to climate change may alter the distribution of tsetse populations in Africa
Summary
A bite from a tsetse fly (Glossina spp.) infected with a parasite of the genus Trypanosoma may cause Human African Trypanosomiasis (HAT), commonly called sleeping sickness in humans, or Animal African Trypanosomiasis (AAT), commonly called nagana in livestock. These tropical diseases have ravaged the African continent for centuries. Excessively high, or low, temperatures are lethal for them [5, 6] This is a serious concern for tsetse because, unlike other insects, the genus Glossina is characterized by birth rates that do not exceed about 4% per day. Extinction could result from increases in mortality consequent on environmental changes, including increases in temperature
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