SORTIE-ND
Software for spatially-explicit simulation of forest dynamics

# Ripley's K Calculator

This behavior calculates the Ripley's K function for all trees in the plot as well as for the members of each species.

### Parameters for this behavior

Parameter nameDescription
Ripley's K - Maximum Distance (m)The maximum distance out to which to calculate K values.
Ripley's K - Distance Increment (m)The distance increments at which K will be calculated. Smaller increments mean a smoother curve but also more processing time.

### How it works

The Ripley's K function is a measure of the way trees are spatially distributed across the plot. K values are calculated repeatedly for a succession of distances out to a maximum, giving a curve. The Ripley's K statistic for a given distance t is calculated as:

where:

• K(t) is the K value at distance t
• A is the plot area in square meters
• X is the number of pairs of trees in the plot less than t meters apart
• n is the total number of trees in the plot

The size of the distance increment is given in the Ripley's K - Distance Increment (m) parameter. The maximum distance out to which to calculate K is given in the Ripley's K - Maximum Distance (m) parameter. Most Ripley's K formulas come with a term for edge correction, which is not needed in SORTIE-ND as the plot has no edges. (See the SORTIE-ND Plot topic for more on the plot's shape.)

Only saplings and adult trees are included in K calculations.

The K values are calculated for all trees in the plot as well as for individual species. In the case of an individual species, X is the number of pairs of trees of that species, and n is the total number of trees of that species.

The resulting K values are stored in the Ripley's K grid.

### How to apply it

Add this behavior to your run. There is no need to apply it to specific tree species or types. Indeed, any such specifications will be ignored. This behavior does not automatically create output. Once you have added this behavior to your run, the Detailed output grid setup window will list the Ripley's K grid. Save all the data members of this grid. You can then view the K values as a line graph and use the graph to save the K values as a text file.