1. The annual rate of increase of a wildlife population is the change in abundance or density from one year to the next. This paper compares the expected and observed means and frequency distributions of annual instantaneous rates of increase (r) for unmanipulated field populations of the European rabbit Oryctolagus cuniculus, red fox Vulpes vulpes and house mouse Mus domesticus in Australia.
2. The observed mean r was not significantly different from zero, the expected value, for each species, and the observed frequency distributions were not significantly different from the expected normal distributions.
3. The observed distributions were used to estimate the threshold proportions of pests that need to be killed, harvested or sterilized to stop population growth. To stop maximum population growth, as can occur after large population reductions, the proportion to kill, harvest or sterilize ranged from 0·65 year–1 for foxes to 0·97 year–1 for house mice. It is recommended that the estimates are tested experimentally.
4. The estimated proportions of pests to control were compared with extensive field data detailing attempts to control the pests. Estimated required levels of fox control were often less than observed levels of control. The required levels of rabbit and house mouse control could be higher than observed levels.