# Location Analysis

This panel provides a number of analyses of location data, which are used either to provide simple inter-location measures, including dispersal detection, or to estimate home ranges. A wide variety of different methods of range analysis have been published. Ranges implements those that have been used to produce refereed publications beyond a first description, including convex polygons (sometimes called minimum convex polygons, MCPs), concave polygons (with restricted edges), polygons in clusters, ellipses and contouring from harmonic means and other density kernels. Grid cells may be plotted by selecting options within concave polygons.

The pros and cons of these different techniques are discussed in more 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).

Below you will find a brief outline of each technique and a link to a description of how it is implemented in Ranges.

## Contents

## Inter-location Measures

These are useful for providing plots and summary statistics from continuous recording sessions or from tags that regularly record GPS locations. Other applications include the estimation of indices of daily distances and speeds for animals tracked intermittently, and the investigation of dispersal, including a dispersal detector.

More on this topic can be found here: Inter-location Measures.

## Convex Polygons

Convex polygons have external angles which are all greater than 180º. Minimum convex polygons (MCPs) are the smallest of such polygons which can be drawn around a set of locations. The outermost of these, which includes 100% of the locations, has been widely used to define ranges. It is therefore useful for comparisons, even though its area and shape are heavily influenced by outlying locations.

More on this topic can be found here: Convex Polygons.

## Concave Polygons

Concave polygons (or "restricted edge polygons"), can be used to eliminate large areas that are not visited, such as lakes at the edges of areas used by terrestrial animals. Lines are only drawn between edge locations if they are shorter than a selected fraction of the range width. This makes the range concave where linkages between edge fixes are long.

More on this topic can be found here: Concave Polygons.

## Ellipses

Ellipses, usually estimated to include 95% of the location density distribution, are another long-standing technique. They do not define range shape well but require few locations to reach a maximum area estimate and are therefore useful for identifying habitat available to animals that cannot be tracked frequently.

More on this topic can be found here: Ellipses.

## Neighbour Linkage (Cluster analysis, OREPs)

Neighbour linkage or cluster analysis is particularly good for eliminating outliers and separating range cores. This can identify patchiness in range use, for instance where the study animal forages in several separate areas. Convex polygons are used to provide an outline around these cores, that are calculated by looking at the distances between all locations rather than the distances from one centre.

More on this topic can be found here: Neighbour Linkage.

## Harmonic Mean Contours

The harmonic mean model (Dixon & Chapman 1980) estimates the location density distribution (equivalent to the probability of encountering the animal) at intersections of an estimation matrix. The density function used is the reciprocal of the mean inverse distances of all the locations from each intersection. Contours containing a specified percentage of actual locations or estimated location density are then interpolated across the matrix. Harmonic mean contours are sensitive to intersection spacing unless the analysis centres locations between intersections or has at least two intersections per unit of tracking resolution, but provide contours that are least sensitive to outlying locations and most precise in fitting core locations.

More on this topic can be found here: Harmonic Mean Contours.

## Kernel Contours

Strictly speaking, kernel analyses include the harmonic mean approach. Worton (1989) introduced the concept of using a function with a negative exponential term for distances of locations from intersections of the estimation matrix. This is a mathematically robust kernel that produces more consistent results than harmonic mean contouring, but is more sensitive to outlying locations

Location densities at matrix intersections are derived using a bivariate normal kernel estimator. This is less matrix-dependent than the harmonic mean function, so there is no need to centre locations between intersections or have very large matrices: the result is very similar for 20x20 and 100x100 grids. With relatively low smoothing, stable size estimates can be obtained with 15-20 locations.

More on this topic can be found here: Kernel Contours.

## Midline Analyses (Interlocation, Linear Ranges and Clusters)

Midline analyses assess the distance between locations using the route along a user-defined line, rather than the shortest route between them as in all other analyses. This was developed principally for fish in rivers but could be useful for riparian species or other situations where movements are restricted to a simple network. The analyses require a midline file along which all distances will be measured, this needs to be a Ranges vector line file formatted correctly. Midline inter-location measures distances and speeds along the line. Midline linear ranges finds the maximum linear extents from all of the locations in a range, and produces a linear range which is a subsection of the input midline file. Midline clusters was developed as a potential means of estimating the home range areas of fish in rivers using the same methodology as for cluster analysis, but with all distances calculated along the midline rather than the shortest route between locations. Publications using midline techniques include Hodder et al. (2007) and Knight et al. (2009).

More on this topic can be found here: Midline Analysis.