These data were compiled here to fit various versions of Bayesian population models and compare their performance, primarily the time required to make inferences using different softwares and versions of code. The humpback chub data were collected by US Geological Survey and US Fish and Wildlife service in the Colorado and Little Colorado Rivers from April 2009 to October 2017. Adult fish were captured using hoop nets and electro-fishing, measured for total length and given individual marks using passive integrated transponders that were scanned when fish were recaptured. The other three datasets were collected by US Forest Service. Owl data for the N-occupancy model was collected between 1990 and 2015. Owl data for the two-species example was collected between 1990 and 2011. Both owl data sets were collected in a ~1000 km2 area in the Roseburg District of the Bureau of Land Management in western Oregon, USA. Owl vocalizations (vocal lures) were used to detect barred owl or spotted owl pairs in 158 survey polygons spread throughout the study area. The avian community occupancy data were collected from 1991 to 1995 across 92 sites in the Chiricahua Mountains of southeastern Arizona, USA. 149 species were detected through repeated point counts in each year.