“The effects of overdispersion and zero inflation (e.g., poor model fits) can result in misinterpretation in studies using count data. These effects have not been evaluated in paleoecological studies of predation and are further complicated by preservational bias and time averaging. We develop a hierarchical Bayesian framework to account for uncertainty from overdispersion and zero inflation in estimates of specimen and predation trace counts. We demonstrate its application using published data on drilling predators and their prey in time-averaged death assemblages from the Great Barrier Reef, Australia. Our results indicate that estimates of predation frequencies are underestimated when zero inflation is not considered, and this effect is likely compounded by removal of individuals and predation traces via preservational bias. Time averaging likely reduces zero inflation via accumulation of rare taxa and events; however, it increases the uncertainty in comparisons between assemblages by introducing variability in sampling effort. That is, there is an analytical cost with time-averaged count data, manifesting as broader confidence regions. Ecological inferences in paleoecology can be strengthened by accounting for the uncertainty inherent to paleoecological count data and the sampling processes by which they are generated.” >> see more in Paleobiology