Stochastic Fluctuations of the Facultative Endosymbiont <i>Wolbachia</i> due to Finite Host Population Size

Many insects and other animals host heritable endosymbionts that alter host fitness and reproduction. The prevalence of facultative endosymbionts can fluctuate in host populations across time and geography for reasons that are poorly understood. This is particularly true for maternally transmitted <i>Wolbachia</i> bacteria, which infect roughly half of all insect species. For instance, the frequencies of several <i>w</i>Mel-like <i>Wolbachia</i>, including <i>w</i>Mel in host <i>Drosophila melanogaster</i>, fluctuate over time in certain host populations, but the specific conditions that generate temporal variation in <i>Wolbachia</i> prevalence are unresolved. We implemented a discrete generation model in the new R package <i>symbiontmodeler</i> to evaluate how finite-population stochasticity contributes to <i>Wolbachia</i> fluctuations over time in simulated host populations under a variety of conditions. Using empirical estimates from natural <i>Wolbachia</i>-<i>Drosophila</i> systems, we explored how stochasticity is determined by a broad range of factors, including host population size, maternal transmission rates, and <i>Wolbachia</i> effects on host fitness (modeled as fecundity) and reproduction (cytoplasmic incompatibility; CI). While stochasticity generally increases when host fitness benefits and CI are relaxed, we found that a decline in the maternal transmission rate had the strongest relative impact on increasing the size of fluctuations. We infer that non- or weak-CI-causing strains like <i>w</i>Mel, which often show evidence of imperfect maternal transmission, tend to generate larger stochastic fluctuations compared to strains that cause strong CI, like <i>w</i>Ri in <i>D. simulans</i>. Additional factors, such as fluctuating host fitness effects, are required to explain the largest examples of temporal variation in <i>Wolbachia</i>. The conditions we simulate here using <i>symbiontmodeler</i> serve as a jumping-off point for understanding drivers of temporal and spatial variation in the prevalence of <i>Wolbachia</i>, the most common endosymbionts found in nature.