Area accuracy
To reiterate, a ratio of the subsampled home range area over the
true-home range area was used to measure area accuracy based on equation
2.3. BRB was the most accurate home range method, regardless of
GPS-point pattern or sample size. BRB consistently had an area accuracy
of 95-99% with a standard deviation (i.e., precision) of less than
3.0% (Figure 4). T-LoCoHo also estimated area accurately, but had more
variation at different sample levels and overall had lower precision.
The precision of the other estimators varied considerably and accuracy
was most notably impacted by the shape of the GPS-point pattern; sample
size had less impact on area estimation for all home range methods. In
Figure 4, ridge density curves show the accuracy assessment for each
home range method for the GPS-point patterns and each sample size. A
taller mode near 1.0 represents greater accuracy, where the spread of
the curve indicates the variance or precision. Values > 1.0
indicates overestimation of home range area, with values < 1.0
indicating underestimation.
Figure 4: Ridge density plots of home range accuracy for area
estimation. The location of the principle mode of the curves indicates
accuracy with a taller mode near 1.0 indicating greater accuracy. The
sampling percentage is represented by the descending color gradients
(dark to light) and the different colors represent the different
methods.
Shape accuracy
The first test used to assess shape accuracy was area under the curve,
where a value closer to 1.0 indicates more accuracy. Except for
perforated patterns, each home range test maintained a mean AUC above
.85 for all GPS-point pattern shapes and sample sizes when compared to
the true-home range (Figure 5). For perforated patterns, the AUC varied
from a high of above .90 for BRB and a low below .55 for KDE, PPA, and
TDGE, with MCP only slightly more accurate. T-LoCoH maintained an AUC
above .70 for all sample levels for perforated GPS-point patterns. BRB
consistently had one of the highest or the highest AUC values.
Except for perforated patterns, TDGE was also consistently one of the
better-fit models for GPS-point pattern shape. MCP was also fairly
accurate for convex and linear shapes and had the highest AUC means for
those shapes. Excluding perforated shapes, KDE and T-LoCoH consistently
had the lowest mean AUC values.
Figure
: Mean area-under-the-curve (AUC) for estimators of home ranges for
different GPS-point patterns at samples levels of 50- 25- 10- and
05-percent of total data. A higher AUC represents a better fit for an
estimator to the GPS-point pattern.
In addition to AUC, edge density (ED) was also calculated as a ratio of
the true-home range (Hargis et al. 1998). Edge Density is a measure of
edge complexity of a home range, which indicates whether the complexity
of a home range shape was maintained when subsampled. Similar to the
analysis of area estimation, ED accuracy was evaluated via the mode,
distribution height, and spread of the ED distributions. Modes near 1.0
with higher heights and less spread represent more accurate and precise
preservation of ED in comparison to the true-home range (Figure 6). BRB
preserved edge complexity consistently across all GPS-point pattern
shapes but had less precision when sample size decreased, but was, by
far, the most accurate method for maintaining edge complexity. TDGE ED
results were most impacted by GPS-point pattern, showing considerably
different results for each pattern and having a bi-modal distribution. A
Kruskal-Wallis and Wilcoxon tests (p < 0.5) showed that for
the majority of simulations there were convincing differences for ED
values between the estimation methods and within the same method at
different sample sizes. These variations are seen in the ridge density
curves in Figure 6.
Figure
: Ridge density curves of edge density (ED) at sample levels of 05- 10-
25- and 50-percent of the data as a ratio of the ture-home range and for
the different GPS-points patterns.
In addition to assessing AUC and ED, this research calculated the
percent rate that home range estimators correctly predicted the number
of patches (i.e., distinct polygons) at the different sample levels when
compared to the true-home range (Figure 7). MCP will always estimate one
polygon for home range, so despite showing 100% accuracy for all
calculations, MCP is a very poor estimator for accurately assessing the
number of patches for GPS-point patterns that are disjoint. Of all the
estimators, T-LoCoHo was particularly inaccurate at calculating the
number of patches compared to the true-home range. The other calculation
of patches varied depending on GPS-point pattern shape and sample size.
Again, compared to the other methods, BRB was the most accurate in terms
of patch estimation.
Figure
: Bar chart showing the percentage each home ranges estimator correctly
estimated the number of home range patches when compared to the
true-home range.
Location accuracy
Location accuracy was assessed using the earth mover distance metric,
where values closer to zero indicated greater accuracy. Except for
perforated patterns, KDE and PPA consistently had the lowest EMD values.
BRB and TDGE also had relatively low EMD values. BRB had the lowest
values for perforated patterns. However, BRB was impacted by sample size
for concave, convex, and disjoint patterns. T-LoCoH and MCP had the
largest EMD values with the greatest variance (Figure 8). In general,
the precision of location estimation was low, except in the case of
perforated patterns where BRB, PPA, and TDGE all had relatively low
variance.
Figure
: Ridge density plots of earth mover distance (EMD) for each home range
estimator at the 05- 10- 25- 50-percent levels of the GPS data. Values
closer to zero indicate greater accuracy.