Index Of Patchiness for Stations 1.0

(c) 2005. Dietrich Radel & Jennifer Brown

- Updated September 1, 2005

As the name implies, this programs calculates an index of patchiness for measures from stations. Details of the index can be found in Brown, J.A., McAuliffe, R.J., and Hickling, G.H. (2004). A new trap-catch index of patchiness in animal distributions. Wildlife Research 31:433-436.

The index is based on work by Professor Joe Perry, on spatial analysis by distance indices (SADIE) (Perry, J. N. 1995. Spatial analysis by distance indices. Journal of Animal Ecology 64, 303-314). More details of SADIE can be found on http://www.rothamsted.bbsrc.ac.uk/pie/sadie/.

The input file format is a simple text file. The first line of the file should be the number of stations, and should be an integer value. For example, if there were twenty stations the first line of the text file will be 20. The next lines are the counts of each station, in order from the first station to the last station. These counts maybe integers (e.g., the number of animal tracks at the station) or maybe decimals (e.g., the proportion of nights that the station was visited). Each station's value needs to be on a new line. As an example, if there were twenty stations and the counts of animal tracks at each station were 2, 2, 3, 1, 1, 2, 0, 2, 1, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 1 the input file would look like this.

To start, open the program and click on OPEN FILE. This will bring up a window that will allow you to browse your computer and select the input text file. The program output the results to the screen immediately.

The observed distance is the distance the observed station values have to move to give a regular pattern over all the stations. For the example data the observed distance is 38.2. The observed mean is the value each station would need to be to achieve a regular pattern. In the example it is 1.2.

The station values are then randomly permuted among the stations, and the distance the randomly permuted values have to move to give the regular pattern is calculated. In total the random permutation is conducted 999 times. The average shuffle distance is the average of the distances the permuted station values would have to move to achieve the regular pattern, over the 999 permutations. The average shuffle distance, index of patchiness and the probabilty will all vary somewhat every time the program is run on a data set. This is because the 999 permutations are randomly generated. When we ran the program on the example data set, the average shuffle distance was 23.4.

The index of patchiness is the ratio of the observed distance to the average of the distances from the permuted station values. The index of patchiness for the example data was 1.636.

The probability is calculated as the proportion of distances from permuted station values that were at least as large as the value of the observed distance. This is used to estimate if the observed arrangement of station values is significantly different from a random arrangement. For the example data P = 0.074.

Contact Information

Biomathematics Research Centre
Mathematics and Statistics
University of Canterbury
Private Bag 4800
CHRISTCHURCH 1
New Zealand

Email: j.brown@math.canterbury.ac.nz