Kernel Home Range Estimation for ArcGIS, using VBA - Fish and ...

a b c
Figure 6.2.1. Core area determination following Powell (2000) and Horner and Powell (1990),
with random (a), even (b) and clumped (c) use of space (Adapted from Powell, 2000).
In reality things are not this simple. Random use of space may result in small clumps in the data
(Powell, 2000). At very high probabilities of use, there may be a concave shape in the graph. In
addition to this, the distribution with random use, will not be everywhere random, since the
location estimates fall-off at the periphery. So, at the edges of the distribution, the probability of
use will be significantly lower than everywhere else within the middle of the distribution. Thus, a
core area will be indicated for every distribution that has truly ‘random’ or ‘even’ use, only
because the probability of use increases significantly just inside the edge of the distribution.
Figure 6.2.2.a., is a cross section of a kernel density estimate for random use, where A and B are
two points at the edge of the distribution. Plotted using Powell’s (2000) method, the area
contoured for a low probability of use will be large (high value on y-axis, but low value on the x-
axis) while that contoured for a large probability of use will be much greater (Figure 6.2.2.b.). In
Figure 6.2.2.b., the kernel density cross section is inverted and rotated so that the axes of the
probability plot and that of the kernel plot will roughly match up. In theory, an even distribution
should produce a graph that is flat (equal area value) for all probability of use values. There
should only be one value for probability of use, since it is everywhere equal. In reality, at the
edge of the distribution probability of use will be lower than the middle but will increase slightly
before remaining constant, moving inwards from the edge (Figure 6.2.3.a.). The result of this
kernel density cross section can be seen in Figure 6.2.3.b., where there will be a core estimated
at a very low probability of use (near the boundary of the used area). Finally, in a clumped
distribution, as with normally distributed locations (Figure 6.2.4.a.), a true concave pattern is
evident in the probability plot (Figure 6.2.4.b.). Here the point where the core should be
contoured is where the probability of use increases significantly (indicated by a slope m = -1).
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