The 2-dimensional regionalisation of Bass Strait used a grid-based approach (Figure 13-1). The east-west limits of the grid boundaries were 143.511oE and 149.611oE respectively with a southern limit chosen at 41.268oS. A grid interval of 0.1o was chosen to provide a fine-scale coverage of the area however in certain areas the resolution of the coastal bathymetry was inadequate; such as the coastline off Victoria where the coastal depth drops off rapidly from the shore.
Figure 13-1 Grid structure used for the 2-dimensional Bass Strait regionalisation.
Two datasets were generated. The first set being the 'raw' transaction polygons, with geographical limits as entered by the taxonomists, and the second set taking into account bathymetric contours. In order for the data to be handled as matrices, the datasets generated were in a gridded format.
An interim grid was extracted from the previously generated bathymetry data with its size reduced to the area of interest and the cell size being 0.1 degrees. Those cells which were valid (i.e. not land) were then converted into a point coverage. The position of each point (x,y) was then added to the point coverage as attributes.
Each species polygon or region was intersected with the point coverage and the list of cell locations where the species was present written out. A location file containing the position number with longitude and latitude was also generated.
In the second dataset, where the regions themselves were used, the approach was modified to ensure that the region topology was maintained. An example of this is a 20 to 50m 'doughnut' around an island. In this case the 0 to 20m polygon is not a valid area where the species is found and must be treated differently to the 20 to 50m polygon. This was accomplished by first converting the regions into a polygon coverage ensuring that the topology was maintained in the new coverage by the use of attributes. The intersection was then done with this polygon coverage and the resulting point coverage was reduced by selecting only those points which were contained within the valid region.
This gridded matrix comprising occurrence of species in each cell was used for the 2-dimensional analysis of Bass Strait.
We were not aware of a 2-D species dissimilarity algorithm based on the Jaccard statistic so a number of approaches were trialed. One approach was to extend the 1-D approach by collecting all species in cells adjacent to a central cell into a bucket, and by collecting those species in the central cell to another bucket. The 1-D species dissimilarity algorithm was then applied to these two buckets to compute a Jaccard. A major problem with this bucket approach is that it brings into comparison, between two contiguous squares, species that are present in neither. An alternate approach is to look for edges of ranges. The number of differences - or range edges - between contiguous cells summed over the possible number of comparisons with the central cell would provide an alternate statistic. Unlike the Jaccard, such a statistic is not normalised for the possible number of species which could have range edges hence this would make it difficult to discriminate unusually high zones (in a local sense).
A third approach is to subdivide each cell into 9 subcells with each subcell holding the respective Jaccard computed between the full cell and its adjacent neighbours. Thus, each of the N, S, E and W subcell contains the Jaccards computed between the central full cell and its neighbour which shares a face of the subcell. The corner subcells contain the average of the two Jaccards from the NE-SW comparison and the NW-SE comparison. The central subcell contained the average of the values of the surrounding 8 subcells. Whilst this approach was able to identify boundaries, there were problems in the uniformity of the boundary representation when split down to the 9 subcells. For example a latitudinal boundary would be captured by the top and bottom rows of the subcells but the middle row had a chequered representation.
The final approach trialed and subsequently used was based on recognising that at each cell, the species dissimilarity was essentially a vector with components representing the dissimilarity between the central cell and its 4 immediate neighbours (i.e. not including corner neighbours). The complex components were computed by splitting the central cell into 4 subcells. The real component of the subcells was computed by assigning the dissimilarity between the central cell and the cell above to the top two subcells and similarly, the dissimilarity with the bottom cell was assigned to the bottom two sub cells. For the complex component, the difference between the central cell and the cell to the left was assigned to the two subcells to the left and similarly, the dissimilarity with the cell to the right assigned to the right two subcells. Each subcell is a complex number with components representing dissimilarity comparisons in two directions. The magnitude, or absolute value, of these complex numbers was used as the statistic describing the dissimilarity (at a subcell level). The phase information was not used in the analysis.
A probability-based threshold formulation equivalent to that for the string analysis was not developed. Instead, global threshold based on the box-and-whiskers criterion (median plus 1.5 times the interquartile range) was used; the criterion was calculated only for those cells with non-zero values.
Next Chapter: 14. Biological Regionalisation: Results