Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), University of Stellenbosch, Stellenbosch, South Africa.
PLoS Negl Trop Dis. 2020 May 7;14(5):e0007769. doi: 10.1371/journal.pntd.0007769. eCollection 2020 May.
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.
津巴布韦部分地区的采采蝇（ Glossina spp ）数量显著减少，这归因于近几十年来温度的升高。温度的持续升高可能导致采采蝇种群局部灭绝。迄今为止，尚未根据温度估计采采蝇种群灭绝的概率。我们为采采蝇生活在不同固定温度水平的情况开发了一个时间均匀的分支过程模型。我们得出了一个概率分布 pk(T)，该分布表示在其一生中，一只成年雌性采采蝇预计会产生的雌性后代数量，作为她生活的固定温度的函数。我们表明 pk(T)可以表示为几何级数：因此，它的生成函数是分数线性类型。我们获得了灭绝概率、繁殖数、灭绝时间和增长率的表达式。这些结果适用于所有采采蝇，但温度的详细影响将因物种而异。如果长时间暴露在 16°C-32°C 之外的温度下，没有任何 G. m. morsitans 种群能够逃脱灭绝。灭绝概率随着温度接近和超过上限和下限而更快地增加。如果雌性数量足够大，即使在高温（28°C-31°C）下，种群仍然可以存活。分别在 16°C 和 31°C 附近的恒定温度的小的降低或升高，都可能导致采采蝇种群灭绝。需要进一步研究来估计在温度连续变化的野外情况下采采蝇种群的灭绝概率。
