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.