• Base rate;
  • Bayesian modelling;
  • biological invasions;
  • naturalization;
  • Tens Rule;
  • woody weeds


We present methods for estimating the base proportion of introduced alien species that will naturalize, and the distribution of time until naturalization occurs. The approach is Bayesian, incorporating prior estimates of the probability of naturalization and the time from introduction to naturalization. A worked example uses data on the introduction and time to recorded naturalization of woody perennials introduced to South Australia. Up until 2007, 188 of 2230 (8.4%) woody perennials listed in nursery catalogues between 1843 and 1985 were recorded as having naturalized. If prior information on naturalization rates from elsewhere is ignored, the available data suggest that the most likely proportion of introduced plants that will naturalize is large (0.93) though uncertain (95% CI 0.51–0.99), with the corresponding mean time to recorded naturalization being protracted (522 years) and similarly uncertain (95% CI 360–678 years). Alternatively, if informative prior estimates of both the naturalization probability and the time to recorded naturalization are incorporated, the most likely probability of naturalization is estimated to be 18.6% (95% CI 15.5–23.4%). For those plants that do naturalize, the most likely value for the mean time from importation to recorded naturalization is 149 years (95% CI 130–174 years). Our results illustrate the potentially long timescale of the naturalization process, and the challenges this presents for obtaining accurate estimates of naturalization parameters.