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.