# Concave Polygons

The pros & cons of different analysis techniques are discussed in detail in the review of home range analyses and for a more comprehensive recent review, see "A Manual for Wildlife Radio Tagging" (Kenward 2001) and Kenward et al. 2001.

## Contents

## Introduction

Ranges creates concave polygons by seeking least clockwise locations (i.e. the next location on the outside of the range moving in a clockwise direction) from the most southwest location, as for convex polygons. If the distance to the next convex corner is less than the selected edge restriction distance, it seeks the next least clockwise location within that restriction distance, followed by the most clockwise location from the vector back towards the previous location until reaching the next convex corner. It starts a new polygon if the separation between locations is greater than the restriction distance. Outlying locations become grid cells if a boundary strip is in use. If the restriction distance is set less than the tracking resolution, the range is estimated entirely as grid cells, with side lengths defined by the resolution of the tracking technique.

Cores at 5% intervals, which provide a utilisation distribution in other range analyses, are not available for concave polygons. This is because all the locations are included in the analyses. However, a process analogous to utilisation plotting can be obtained by progressively reducing the restriction distance.

## Selected edge restriction

The edges of concave polygons are selected either by specifying a proportion of the maximum range width (which by default is 0.5 and must be less than 1) or by giving a value greater than 1 (which defines a convex polygon) to set a restriction length in metres. The default follows Harvey & Barbour (1968). The edge length is standardised for all animals in the file if you use metres.

#### Output of grid cells

If you select a proportion (or length) that is smaller than the minimum distance between locations (your tracking resolution), the output is of single grid cells. If you set the length equal to your resolution, adjacent occupied grid cells are joined using the "Rook's" rule (i.e. adjacent horizontal and vertical cells join, but not adjacent diagonal cells).

## Incremental area analysis

Incremental area analysis is used to answer the question "how many locations do I need to estimate a home range?" Starting with the first three locations (the minimum needed to estimate a polygon area without a boundary strip), the new area is estimated as each location is added. This permits the consecutive areas, which tend to increase initially as the animal is observed using different parts of its range, to be plotted against number of locations until there is evidence of stability, which indicates that adding further locations will not improve the home range estimate. The default is to plot the edge round all the locations that have been added, but it is also possible to choose a single, smaller core. The consecutive area estimates have to be saved to an output file, so that the result can be examined using in the main window.

Note that incremental plots of concave polygons tend to require more locations to reach stability than those from convex polygons. This is because ranges can fragment.