Extent of Occurrence calculated by JNCC

The Extent of Occurrence is one way of measuring the range of a species. It is defined by IUCN as "the area contained within the shortest continuous imaginary boundary which can be drawn to encompass all the known, inferred or projected sites of present occurrence of a species, excluding cases of vagrancy."

"Guidelines for Using the IUCN Red List Categories and Criteria" (IUCN, May 2003) note that Extent of Occurrence can be measured by drawing a polygon around occupied sites and calculating its area. The simplest approach to this is to draw a figure known as a "convex hull" (the smallest polygon in which no internal angle exceeds 180^o).

Here are examples of convex hulls applied to two species of Orthoptera from the BRC Grasshopper and Crickets recording scheme: the Common field grasshopper (Chorthippus brunneus) and Roesel's bush cricket (Metrioptera roeselii).

Convex hull fitted to the GB distribution of Common field grasshopper

Convex hull fitted to the GB distribution of Roesel's bush cricket

It is immediately apparent that there are problems with using a convex hull to represent Extent of Occurrence. In the first example of a common and widely distributed species, the convex hull includes huge areas of sea (an area of "obviously unsuitable habitat" for this terrestrial animal!) and will therefore greatly exaggerate the range area.

In the second example, the species has a much more restricted distribution, but the area of the convex hull in this case is dominated by a few outlying colonies and again greatly exaggerates the area of the range. If we were looking at change over time, then there would potentially be a huge impact if, for example, one of the outlying colonies like the one on the Welsh coast or the one in Morecambe Bay was not surveyed in one of the time periods.

The IUCN's guidelines, suggest that the way to resolve these issues is to use a more complex way of fitting a polygon known as an "alpha shape". An alpha shape fits around the points more closely and can result in more than one polygon if there are gaps in the range.

Here are examples of alpha shapes fitted to the same two species distributions:

Alpha shape fitted to the GB distribution of Common field grasshopper

Alpha shape fitted to the GB distribution of Roesel's bush cricket.

As these examples show, fitting an alpha shape gives a much more satisfying description of the range as most people looking at the map would perceive it.

The parameter α determines how closely the shape fits. If α is very large then the alpha shape tends towards the same area as a convex hull. On the other hand, if α is very small then each point will become a separate polygon and the area of the alpha shape will tend towards zero. So, the value used for α is critical when using this method to calculate the Extent of Occurrence.

A series of case studies suggested that a value of α around 1500-1800 is suitable for British distribution Atlases at 10km square resolution using this particular formulation for fitting an alpha shape (Hull software by Ken Clarkson of the Computing Science Research Centre, Bell Laboratories, USA).