The utilization of the most prevalent endosymbionts Wolbachia spp. to tackle insect-borne viral diseases is growing rapidly. Understanding how and how often Wolbachia establish in a local population is fundamental to replacement releases but remains unclear. Previous models make the prediction of poor performance of Wolbachia at low frequencies that contradicts the natural ubiquity of those endosymbionts, and the prediction of almost certain fixation of Wolbachia at high frequencies that cannot explain the large fluctuations and collapses of infection in field releases. Here, we investigated whether those paradoxes can be reconciled by the stochasticity originating from fecundity overdispersion within host insects. We first reanalysed published data sets and showed that fecundity was mostly overdispersed in insects. To understand the effects of host fecundity variation on Wolbachia establishment, we further constructed a model accounting for cytoplasmic incompatibility and fecundity cost on infected hosts. Based on the empirical results of fecundity overdispersion, the model predicted not only a biologically relevant probability for Wolbachia to establish from a single infection, but also a large uncertainty of fixation at high frequencies. These findings will enable a better understanding of endosymbiont-insect dynamics and help to design sustainable strategies to control arboviral diseases.

利用最普遍的内共生菌Wolbachia spp。解决昆虫传播的病毒性疾病的发展迅速。了解沃尔巴克氏菌在当地人口中的建立方式和频率是替代释放的基础，但仍不清楚。以前的模型做出的沃尔贝氏体在低频下的不良表现的预测与这些共生共生体的自然普遍性相矛盾，并且预测了沃尔贝希氏菌几乎固定的状态在高频率下无法解释现场释放中感染的巨大波动和崩溃。在这里，我们调查了这些悖论是否可以被宿主昆虫中繁殖力过度分散所产生的随机性所调和。我们首先重新分析了已发布的数据集，并显示了繁殖力大多过度分散在昆虫中。为了了解宿主繁殖力变异对Wolbachia建立的影响，我们进一步构建了一个模型，解释了感染宿主的细胞质不相容性和繁殖力成本。基于繁殖力过度分散的经验结果，该模型不仅预测了沃尔巴克氏菌的生物学相关概率从单个感染确定，但高频固定的不确定性也很大。这些发现将使人们更好地了解共生共生体昆虫的动态，并有助于设计可持续的策略来控制虫媒病毒疾病。