A hierarchical Bayesian approach to estimate endosymbiont infection rates

Endosymbionts may play an important role in the evolution of the Insecta. Bacteria such as Wolbachia, Cardinium, and Rickettsia are known to manipulate host reproduction to facilitate their own. Indeed, there are many documented cases where Wolbachia (Alphaproteobacteria: Rickettsiaceae) induces one of four manipulative phenotypes (cytoplasmic incompatibility, male killing, feminization, and parthenogenesis). The scale of infection among species has been a major subject of investigation, but quantification has been difficult because various approaches have yielded different estimates. One under-appreciated aspect of this problem arises when multiple--yet independent--samples are taken within a taxon. When independent samples within a taxon are treated as levels of a hierarchy, the problem is greatly simplified because data are partially pooled according to taxon. Here, we present a hierarchical Bayesian approach to estimate infection frequency where multiple independent samples were collected across several taxonomic levels. We apply this model to estimate the rates of infection for Wolbachia in the Lepidoptera, and then extend the model to account for phylogenetic non-independence. In addition, we highlight the current knowledge regarding Wolbachia and its effects within Lepidoptera. Our model estimates that the rate of endosymbiont infection for the Lepidoptera is approximately 12%. Given our limited knowledge regarding the phenotypes induced by these endosymbionts and the low infection rate, we urge caution when extrapolating the results of positive assays.