We used the package adehabitatHR (Calenge, 2006) in the statistics program R (R Core Team, 2012) to estimate 100% minimum

convex polygon (MCP) home ranges (Mohr, 1947) for all badgers with [greater than or equal to] 8 locations.

In the first step we rejected all the specimens for which we obtained less than 30 locations, because this is the lowest number of locations required for the accurate calculation of a minimum

convex polygon (Kenward 1987) and Kernel home range (Seaman et al.

We constructed 100% minimum

convex polygon home ranges for each deer to determine geographic extent of annual use areas (Hoenes, 2008).

The rectangle is also the only example of a

convex polygon, while the other shapes are examples of concave dodecagons.

Chen, "A generating approach of random

convex polygon aggregate model," Journal of China Institute of Water Resources and Hydropower Research, vol.

Furthermore, the calculation of the home range size by two different methods demonstrated that the commonly used minimum

convex polygon method overestimated the home range compared to the less biased Brownian bridge movement model.

The line of sight checking algorithm considers an obstacle as a convex polyhedron [OMEGA] consisting a set of

convex polygon faces [F.sub.i] where i is a polygon face.

Because our aim is not a comparison of the several available home range calculation methods, we show the most commonly used (Minimum

Convex Polygon, Kernel and Brownian Bridges), without making inferences about which method is the best; but evaluating the effects that result from using different data gathering techniques (origin-different data sets) for the same individual.

For the

convex polygon window of line clipping, a well-known algorithm is proposed by Cyrus and Beck.

Then the vertex link L([upsilon]) := P [intersection] [SIGMA] of [upsilon] in P is a Euclidean

convex polygon in the horosphere [SIGMA].

P = P'\[??] for some simple polygon P' and a

convex polygon H [subset] P).

The most common preprocessing approach is to first form a

convex polygon or polyhedron using several determined extreme points, and then discard those points falling into the

convex polygon or polyhedron; see such applications in [8, 9, 16].