Heterogeneity in symbiotic effects facilitates Wolbachia establishment in insect populations

Facultative vertically transmitted bacterial symbionts often manipulate its host’s reproductive biology and thus facilitate their persistence. Wolbachia is one such symbiont where frequency-dependent reproductive benefits are opposed by frequency-independent fitness costs leading to bistable dynamics. Introduction of carriers does not assure invasion unless the initial frequency is above a threshold determined by the balance of costs and benefits. Recent laboratory experiments have uncovered that Wolbachia also protects their hosts from pathogens. The expected consequence of this phenotype in natural environments is to lower the invasion threshold by a factor that increases with the extent of pathogen exposure. Here, we introduce a series of mathematical models to address how pathogen protection affects Wolbachia invasion. First, under homogeneous symbiotic effects, we obtain an analytical expression for the invasion threshold in terms of pathogen exposure, and find a regime where symbiont releases may result in elimination of the entire host population provided that abundance of virulent pathogens is high. Second, we distribute Wolbachia effects such that some carriers are totally protected and others not at all, and explore how this interplays with different pathogen intensities, to conclude that heterogeneity further lowers the threshold for Wolbachia invasion. Third, we replicate the analysis using a realistic distribution of protective effects and confirm that heterogeneity increases system resilience by reducing the odds of population collapse.