FIGURE CAPTIONS
Figure 1 . Hazard functions (inset boxes) and the associated
probability density distributions (main panels) where lag times follow a
Weibull distribution (see Appendix S1). Parameter k determines
the shape of the hazard function: A if k = 1, the hazard
is constant over time and the lag time distribution is negative
exponential; B if 1 < k < 2 the
hazard function is downward accelerating and the lag time distribution
shifts to unimodal for all k > 1; C ifk = 2 the hazard function is linear; D if k> 2 the hazard function is upward accelerating. Each panel
shows three hazard functions and associated lag time distributions given
the shape parameter k , with distributions having a mean lag time
of approximately 100 (red lines), 200 (blue lines) or 300 (black lines)
years. In each of B-D , a steeper hazard function results in the
lag time distribution having a smaller mean and variance (see Appendix
S1 for details).
Figure 2 . Lag time (the lag between introduction and
naturalisation in years) plotted against year of first introduction for
708 plant species naturalised in Britain, with marginal histograms for
lag time and year of first introduction (shaded grey). The lag times for
each introduction year are truncated at the sloping line because we can
only observe species that have naturalised up to the present (set to the
year 2000). The two inset histograms (shaded blue) show the distribution
of lag times for species introduced in the periods 1620-1640 and
1890-1910 (shown by the blue vertical lines). These lag time
distributions are truncated at the dotted lines on the histograms. The
black curves are normal distributions fitted to the truncated lag time
data with the area under the curve beyond the year of truncation (shaded
red) estimating the invasion debt (the number of species introduced in
each period that are yet to naturalise based on the truncated lag time
distribution for species that have naturalised).
Figure 3 . A-C Parameter estimates for model 4 (the
best-performing model, see Table 1). Filled circles are the means of the
posterior distributions and vertical lines show the 95% credible
intervals. A shows the estimated mean and standard deviation of
the expected lag times for trees and shrubs introduced in 1500 AD;B shows the rate at which the mean and standard deviation of
the lag time distribution changed per year after 1500 AD; Cshows the mean lag times of perennial herbs and annual/biennial species
relative to trees/shrubs, which were set as the reference class. All
parameter estimates are on the loge scale. D-FHazard functions by life-form for model 4 for the years 1650, 1750, 1850
and 1950, showing the increase in the hazard (a number proportional to
the probability a species will naturalise in the next small time step
given it has not yet naturalised) over time following introduction.
Figure 4 . The observed distribution of lag times (grey
histograms) for: A all species and B-F species
introduced in different centuries (starting in 1500 through to 1900).
For each century, the observed lag times are truncated at a maximum
value shown as dashed lines on each histogram. The black lines show the
mean predicted distribution of lag times based on the actual dates of
introduction and 10000 simulations of each species lag time derived from
model 4 (see text), with the red shading showing the 95% quantiles from
the simulations.
Figure 5 . Histograms with 20 year bins for year of introduction
and year of naturalisation for 708 naturalised plant species in Britain
grouped by life-form (A, D = trees/shrubs; B, E =
perennial herbs; C, F = annual/biennial species). The most
recent year of introduction for naturalised species in the data (1960)
is shown as a dashed line in A-C , and the most recent year of
recorded naturalisation (2000) is shown as a dashed line inD-F . The black curves in D-F show the expected number
of species naturalising in each 20 year interval based on the actual
dates of introduction (A-C ) and the expected lag times
estimated using model 4. For each life-form, the area under the curve
beyond the year 2000 (shaded red in D-F ) estimates the invasion
debt for that life-form (the number of species introduced before 1960
that are yet to naturalise based on the truncated lag time distribution
of the species that have naturalised). The black curves in A ,C and E show the trend in the number of species
introduced in each 20 year period that will naturalise in the
foreseeable future (see Appendix S3 for details).
Figure 1 .