The contributions of host population size and maternal transmission rate to fluctuating Wolbachia frequencies

Animals form diverse relationships with microorganisms. Many insects host maternally transmitted endosymbionts such as Wolbachia that alter host fitness and reproduction. Roughly half of all insect species carry Wolbachia , but population frequencies of the endosymbiont can fluctuate across time and geography for reasons that are poorly understood. For instance, the frequencies of facultative w Mel Wolbachia in host Drosophila melanogaster , as well as related " w Mel-like" strains in D. yakuba -clade hosts, fluctuate over timescales as short as a month at a given location. Recent work suggests that Wolbachia frequencies may fluctuate under certain conditions due to temperature effects that disrupt maternal transmission. We simulated temporal Wolbachia dynamics to test whether fluctuating frequencies can be explained solely by the stochasticity of a finite host population or, alternatively, due to perturbations of the maternal transmission rate over time. We implemented a discrete generation model in the newly developed R package wlbcmodeler to evaluate how host population size, maternal transmission rates, and Wolbachia effects on host fitness (fecundity) and reproduction (cytoplasmic incompatibility; CI) contribute to Wolbachia fluctuations over time. Broadly, we find that strains like w Mel that do not cause strong CI tend to generate larger stochastic fluctuations over time, as compared to Wolbachia like w Ri in D. simulans that cause strong CI. Within a biologically plausible set of parameter values, we find that the maternal transmission rate has the strongest effect on the variance and mean of temporal Wolbachia frequencies, relative to host fitness effects and CI. Large frequency fluctuations can arise under certain specific conditions due to either stochastic or deterministic dynamics, for example, due to a decline in the maternal transmission rate of all hosts or a subpopulation of "low transmitters." While these simulated dynamics may help explain empirical examples of w Mel-like Wolbachia fluctuations over years-long periods, other factors (e.g., insect demography) likely contribute to fluctuations observed over short month-long periods.