Figure 2

Frequency plot of the number of individual Non Indigenous Species found in 134,265 inspections with 1411 border detections (blue) and 141 post-border detections (red) between 2009 and 2015. Black line indicates fitted mixture distributions comprising a log-normal (LN) density for detections of less than an extreme number of organisms, and point probability masses for detections of zero organisms (I _i=0 ), single organisms (I _i=0 ) (for post-border surveillance) and extreme numbers of organisms (thresholds l of 100 and 50 for border and post-border surveillance, respectively). This last mixture component (for extreme numbers of organisms) is depicted as a uniform U(l,u) (0 < l < u) probability bounded by the threshold l to the modelled potential maximum number of organisms u, estimated as u = ((k + 1)/k)(m − 1), where k is the sample size and m is the sample maximum. Note that these estimates are indicative only, given sensitivity to the choice of threshold and the assumption of uniform, independent large detections. The third inset is a close-up of the fitted mixture distribution for the post-border detections of less extreme numbers of organisms. The corresponding model is given by \({y}_{i}={w}_{1}{I}_{i=0}+{w}_{1}{I}_{i=1}+{w}_{3}\,\mathrm{LN}(\mu ,{\sigma }^{2})+{w}_{4}U(l,u)\) where w _j denote the weights for the four components of the mixture, \(j=1,\mathrm{..},4,{w}_{j} > 0,\,\sum {w}_{j}=1\). Note that for a three-component mixture, w₃ = 0.