Assessing model fit and estimating the invasion debt
I used the best-performing model based on the LOO criteria to model the full lag time distribution and used simulation to assess how well the modelled lag time distribution matched the data. To do this, I simulated a lag time for each species given its actual year of introduction by drawing a random value from the lag time distribution specified by the best-performing model. I carried out 10000 simulated draws for each species, binned the simulated lag times into 20 year intervals, calculated the mean and 95% quantiles for the number of species in each bin, and compared these simulated outcomes with the actual distribution of lag times in 20 year bins.
For a species introduced in year Yi , the modelled lag time distribution for that year allows us to calculate the probability that the species will naturalise in yearYt , where Yt> Yi . The total number of species expected to naturalise in year Yt can be calculated as the sum of the probabilities that each previously introduced species will naturalise in year Yt . We can therefore use this approach to estimate the number of species expected to naturalise in each year beyond the present and sum those estimates to calculate the invasion debt (Fig. 2). The difficulty is that we do not know the total number of species introduced each year that are going to naturalise because we only observe species that have naturalised. In Appendix S3, I show how the fitted lag time distribution coupled with the introduction dates can be used to estimate the total number of species introduced each year that will naturalise, and hence estimate the invasion debt. For each life-form group, I used the methods in Appendix S3 to model the average number of species introduced per year between 1500 and 1960 that have or will naturalise in the foreseeable future, and thus calculate the invasion debt.