# LoCoH (Local Convex Hull)Homerange Generator

 NEWS A new version of LoCoH in the R open-source statistical programming language is now available. New features include: options for adaptively dealing with outlying areas based on local point density web interface - upload your own data in shapefile or text format toolbox for ArcGIS 9.x See http://locoh.cnr.berkeley.edu for details. Version 2.1 of LoCoH for ArcView 3.x is now available for downloading. Main new feature: save nearest neighbor associations to diskto speed processing of large datasets

## Introduction and method

LoCoH is an ArcView 3.x extension for estimating home range or a habitat utilization distribution of animals based on point data representing individual observations. This type of analysis is typically used to see which part of a habitat an individual animal, or group of individuals, use most often, based on observational sightings, radio telemtry, or data from GPS collars.

LoCoH is based on the k-NNCH (nearest-neighbor convex hull) method described in Getz and Wilmers (2004). The method creates a home range distribution by first looking at each point and identifying a user-specified number of nearest neighbors. Next, minimum-convex polygons (local hulls) are created for each point and its k nearest neighbors, where k is specified by the user. (Note: the paper by Getz and Wilmers creates local hulls from k-1 nearest neighbors, but the LoCoH software constructs hulls from each point and its k nearest neighbors.) These hulls are then sorted smallest to largest, and then added up (or merged together) one by one. When enough of the merged local hulls enclose 10% of the original points, the resulting polygon is saved as the "10th percentile isopleth". Because the hulls are merged smallest to largest, the 10th percentile isopleth also represents the 'densest' or most heavily used part of the habitat. Additional local hulls are then added until 20% of the original points are enclosed, which then becomes the 20th percentile isopleth. This continues until all of the points are enclosed. The last isopleth encloses all of the original points.

Compared to other methods for constructing home ranges (such as Minimum Convex Polygon and kernel methods), the k-NNCH method has several advantages that make it particularly well-suited for landscapes with 'sharp' features such as lakes, fences, or steep terrain. These type of landscape features often result in spatial distributions containing holes, sharp boundaries, corners, or corridors. In these cases, k-NNCH density isopleths have been shown to better approximate the true area represented by the data than kernel or alpha-hull methods. k-NNCH isopleth also have the property of converging to the true area represented by the data as the number of data points increases (Getz and Wilmers 2004), thus the method is particularly well suited when there is a lot of observational data (e.g., from a GPS collar).

## Using the method

The k-NNCH method is computationally simple which minimizes the number of parameters to set and makes it easy to use. The general sequence of steps for using the method is as follows:

1. Select an appropriate value of k (number of nearest neighbors) based on the distribution of points.
2. Decide how to handle duplicate points and cap isopleths.
3. Create isopleths.
4. Analyze results.

### Selection of K

The number of points to use for constructing local hulls must be between three (the smallest number of points needed to create a polygon) and the total number of points being analyzed. In practice, low values such as k=3 tend to result in a number of 'holes' or areas where the animal was not seen but is most likely to use. Larger values of k increase the total area of the isopleths, but values which are too large can result in local hulls that cut across areas where the animal was not observed and is unlikely to use.

There is no optimum value for k that will work for every dataset, because it depends on the spatial distribution of the points and the number of observations. Getz and Wilmers (2004) propose a "minimum covering of spurious holes" (MCSH) rule for selecting a value of k which results in local hulls that cover most areas that the animal is known to exist, but minimizes the number of areas where the animal is unlikely to be. This is illustrated in Figures 1-3.

Figure 1. Radio collar observations of wolves against hill shade background. Clearly the individuals are avoiding steep slopes.

Figure 2. Local hulls when k=6 shows a lot of 'holes'

Figure 3. Local hulls when k=14 shows most areas covered

Figure 4. 90% isopleths enclosing 90% of all points for k=13

### ArcView 3.x

LoCoH is available as an extension for ArcView 3.x. See the help file for instructions on installation and use.

LoCoH 2.1 for ArcView 3.x (534 Kb), Help file

### ArcGIS 9.x

ArcGIS 9.x users are encouraged to download and install the R version of LoCoH, which includes a toolbox that can be added to your ArcToolbox pane in ArcMap. See http://locoh.cnr.berkeley.edu/arctutorial for details.

If you have problems getting the ArcToolbox for the R version of LoCoH working, please see these trouble-shooting tips.

Archived below are ArcMap templates which contain VBA scripts to generate isopleths use the LoCoH method. But note:

• The LoCoH ArcMap templates can be downloaded below but are no longer being developed or supported
• Users have reported problems with ArcMap crashing when using these templates under ArcGIS 9.3.1

LoCoH for ArcGIS 8 (ArcObjects version). For installation instructions, see the help file for the ArcGIS 9 version.

## References

Getz, W. and C. Wilmers. 2004. A local nearest-neighbor convex-hull construction of home ranges and utilization distributions. Ecography 27: 489-505. View PDF (1.13 Mb).

Development of LoCoH was made possible by support from the National Science Foundation (NSF/NIH EID Grant DEB-0090323).