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Table 1. Ten candidate models to describe lag time
distributions for naturalised plants in Britain. Models 1-5 specified a
truncated normal distribution with T() the upper limit for truncation.YP is the present (set to the year 2000),Yi is the year of introduction of the i th
species and Pi and Ai are
variables specifying whether the i th species was perennial
(Pi = 1) or not (Pi = 0),
and annual (Ai = 1) or not
(Ai = 0). The β are the parameters
estimated for each model. Log-transformations of the mean [e.g.,\(\mathrm{\log}\left(\mu_{Y_{i}}\right)\)] and standard deviation
[e.g., \(\mathrm{\log}\left(\sigma_{Y_{i}}\right)\)] ensured these
remained positive. Models 6-10 specified a truncated Weibull
distribution parameterised in terms of a shape (k ) and scale
(λ ) parameter, with k and λ related to the mean and
standard deviation as shown (Justus et al. 1978). ΔPSIS-LOO is
the difference in PSIS-LOO (Pareto smoothed importance sampling
leave-one-out cross-validation) between each model and the best fitting
model, which had ΔPSIS-LOO = 0 (shown in bold).