Testing for significant variation in presence data case study 2 P brassicae

Because the presence points identified to represent the aestivating population of P. brassicae were a small percentage (1.5%) compared with the total number of presences, the method proposed for the D. v. virgifera case was not appropriate to assess any variation within the P. brassicae presence dataset according to aestivating and non-aestivating presences. A different approach that considers the difference in variables selected when using the two classes of P. brassicae presence dataset was employed. This approach was appropriate as it was less density dependent and the values inferred from the presence points and their position in the feature space of the selected variables was important rather than the number of presences in each class.

The relative positions of the aestivating and non-aestivating class presence points with regard to the newly invaded locations in New Zealand were compared in the PCA transformed feature space of four different variable combinations (Figure 5.5).

The first plot (A) where all variables are indiscriminately used did not provide a very good discrimination between the background (the rest of the world) and the presence points. Plot (D) shows the feature space constructed out of variables selected for aestivating presences, here there was a distinct clustering of presence points in the aestivating and non-aestivating classes that is not captured in Plot (B) and Plot (C).

149

Figure 5.5: Comparison of the relative positions of aestivating and non-aestivating presence points in feature space of four different bioclimatic variables combinations.

(A) P. brassicae global occurrences in PCA transformed feature space of 39 predictors. (B) P. brassicae global occurrences in PCA transformed feature space of 15 variables selected according to the complete P. brassicae presence dataset (n=2,241). (C) P. brassicae global occurrences in PCA transformed feature space of 11 variables selected according to presences in the non-aestivating class (n=2,206). (D) P. brassicae global occurrences in PCA transformed feature space of four variables selected according to presences in the aestivating class (n=35).

A more systematic analysis was undertaken to check if the effect of the low prevalence aestivating class of presence points, could have been masked when prediction was performed using all presence points. Figure 5.6 shows the one standard deviation (SD) and two standard deviation (2SD) ellipses drawn with the mean centres for the aestivating, non- aestivating and unclassed presences as the respective centre of the directional ellipses.

150

Figure 5.6: Distribution directional 1SD and 2SD standard deviational ellipses (SDE) derived from the centre means of aestivating, non-aestivating and combined presences of P. brassicae on the feature space of variables selected according to (A) non-aestivating presences (B) aestivating presences. Green stars show P. brassicae locations in New Zealand.

Only the feature spaces constructed out of the variables selected based on the aestivating and non-aestivating class of P. brassicae presence points were used for the SDE analysis. The feature space constructed out of the variables selected based on the combined presence dataset (Figure 5.6-B) is not considered as it is very similar with the non-aestivating feature space. The long axes of the ellipses indicate the direction of the respective distributions.

151

The configuration of the different presence points on the feature space from variables selected based on the non-aestivating presences (Figure 5.6-A) show no proximity between the newly invaded New Zealand locations and P. brassicae presence points. The New Zealand locations were outside the 1SD and 2SD ellipses of the aestivating, non-aestivating and combined presence clusters in Figure 5.6-A. The second feature space (Figure 5.6-B) however, shows that the New Zealand locations were partially contained in the 1SD ellipse derived from the mean centre of the aestivating clusters and wholly contained in the 2SD ellipses of all three clusters. The 1SD ellipses of the combined presence points and the non- aestivating points did not include any New Zealand points and was distinctly further from the 1SD ellipse based on the aestivating presences.

Evidently, the feature space according to the aestivating presence points explained the environmental similarity between the invaded New Zealand locations and all P. brassicae points better than when all presences or just non-aestivating presences were used to select variables. Moreover, the direction of the distribution of both presence classes was aligned with the newly invaded locations in New Zealand in the second feature space constructed with variables selected for aestivating presence points.

Table 5.2. Circularity index of the directional standard deviational ellipses computed for the three types of presence data classes on two types of environmental variable feature spaces.

Presence data

class

Feature

space* mean x mean y

σx (2SD) σy (2SD) rotation (θ) Ci aestivating 1 15.12 3.44 31.39 143.94 87.36 0.22 non-aestivating 1 62.96 -51.19 190.85 89.74 95.12 0.47 all presences 1 62.20 -50.32 191.10 90.88 95.71 0.48 aestivating 2 52.14 83.97 53.57 73.87 49.03 0.73 non-aestivating 2 -84.65 18.21 65.14 118.28 50.03 0.55 all presences 2 -82.46 19.25 66.02 128.87 53.27 0.51

*The Feature spaces one and two are made up of the 1st _{and 2}nd _{principal components of the PCA} transformed data of variables selected based on non-aestivating and aestivating presence points respectively. The shaded rows show ellipses that have higher directional (oblong) distribution, hence the low circularity index (Ci) index. Theσx and σy are given as 2xSD divide the values by two for the

152

The circularity index for the ellipses of the presence dataset clusters tested is given in Table 5.2. The direction of the different presence distributions on the two feature spaces shown in Figure 5.6 are indicated by the straight line drawn through the mean centre of the respective presence distributions inclined at the angle of rotation of the directional ellipse, this line is also the long axis of the respective ellipses.