Epidemiology in evolutionary time: the case of Wolbachia horizontal transmission between arthropod host species

Wolbachia are bacterial endosymbionts that manipulate the reproduction of their arthropod hosts. Although theory suggests that infections are frequently lost within host species due to the evolution of resistance, Wolbachia infect a huge number of species worldwide. This apparent paradox suggests that horizontal transmission between host species has been a key factor in shaping the global Wolbachia pandemic. Because Wolbachia infections are thus acquired and lost like any other infection, we use a standard epidemiological model to analyse Wolbachia horizontal transmission dynamics over evolutionary time. Conceptually modifying the model, we apply it not to transmission between individuals but between species. Because, on evolutionary timescales, infections spread frequently between closely related species and occasionally over large phylogenetic distances, we represent the set of host species as a small-world network that satisfies both requirements. Our model reproduces the effect of basic epidemiological parameters, which demonstrates the validity of our approach. We find that the ratio between transmission rate and recovery rate is crucial for determining the proportion of infected species (incidence) and that, in a given host network, the incidence may still be increasing over evolutionary time. Our results also point to the importance of occasional transmission over long phylogenetic distances for the observed high incidence levels of Wolbachia. In conclusion, we are able to explain why Wolbachia are so abundant among arthropods, although selection for resistance within hosts often leads to infection loss. Furthermore, our unorthodox approach of using epidemiology in evolutionary time can be applied to all symbionts that use horizontal transmission to infect new hosts.