Ecological Archives A023-026-A1
Beth E. Bukowski, William L. Baker. 2013. Historical fire regimes, reconstructed from land-survey data, led to complexity and fluctuation in sagebrush landscapes. Ecological Applications 23:546–564. http://dx.doi.org/10.1890/12-0844.1
Appendix A. Minimum line and polygon trials.
A minimum line-segment length was chosen because conversion of raw surveyor data to polygons produced unnatural patchiness (Fig. A1b). I refined the polygon creation procedure using ReGAP data for a 16-township test area in the Nevada study area (Fig. A1a). Using the ArcGIS Identify tool, section lines for the test area were assigned to ReGAP vegetation classes, creating a grid of vegetation data similar to the GLO section-line data. Line segments were converted to single-part features, and segments shorter than the specified minimum were deleted. Segments longer than the minimum were converted to midpoints and then used to generate Thiessen polygons. Because the procedure was based on midpoints, areas occupied by deleted line segments were automatically assigned to adjacent vegetation types. Trials were run using minimum line-segment lengths of 0 m, 160 m, 320 m, and 480 m (Fig. A1b-e). For trials using a minimum line segment, generated polygons were compared to a modified ReGAP dataset where polygons below a corresponding minimum area had been removed (Table A2). Resulting patch sizes were compared to the original ReGAP polygon patch size using a two sample t-test of the geometric means and a χ2 goodness-of-fit test of patch-size distributions (Table A3). The minimum polygon area corresponding to the minimum line length was determined by multiplying 259 ha (the size of the largest polygon that could be generated from a single midpoint) by the fraction of the line length represented by the minimum line segment (0.1, 0.2, and 0.3 respectively). This gave minimum polygon sizes of 25.9 ha, 51.8 ha, and 77.7 ha, respectively. Visually, the 160-m minimum line segment (Fig. A1c) resulted in a much more meaningful representation than using no minimum segment length (Fig. A1b). Although larger line segments created less blocky representations, they also sacrificed considerable detail (Fig. A1d-e). The 160-m minimum also gave the best statistical results for both a two-group t-test of the geometric mean patch size and the χ2 goodness-of-fit test for patch-size distribution (Table A3).
Table A1. Minimum line segments and total line length for categories of interest.
Study area | Number of entries | Total length | ||||
All line segments (n) |
Line segments < 160 m (n) |
Segments < 160 m as a percentage of all entries |
All line segments (km) |
Line segments < 160 m (km) |
Segments < 160 m as a percentage of all line segments |
|
ID | 5,573 | 250 | 4.49% | 7,587 | 22.1 | 2.91% |
NV | 5,607 | 246 | 4.39% | 6,901 | 22.1 | 0.32% |
OR | 6,605 | 311 | 4.71% | 8,711 | 26.7 | 0.31% |
WY | 3,353 | 14 | 0.42% | 5,210 | 1.3 | 0.03% |
Totals | 21,138 | 821 | 3.88% | 28,408 | 72.2 | 0.25% |
Table A2. Comparison of ReGAP Polygons to Generated Thiessen Polygons.
Count | Minimum area (ha) |
Maximum area (ha) |
Geometric mean of area |
Mean area (ha) |
Standard deviation |
|
Original ReGAP polygons | 11,776 | 0.00 | 45,438 | 1 | 13 | 470 |
Thiessen polygons No min. length |
2,238 | 0.00 | 15,007 | 15 | 67 | 457 |
ReGAP polygons Min. area 25.9 ha |
206 | 27 | 52,132 | 101 | 726 | 4,002 |
Thiessen polygons Min. length 160 m |
203 | 10 | 50,601 | 113 | 757 | 3,917 |
ReGAP polygons Min. area 38.9 ha |
142 | 42 | 52,931 | 183 | 1.053 | 4,857 |
Thiessen polygons Min. length 240 m |
127 | 16 | 51,540 | 170 | 1,178 | 5,028 |
ReGAP polygons Min. area 51.8 ha |
112 | 52 | 45,437 | 108 | 1,119 | 4,690 |
Thiessen polygons Min. length 320 m |
92 | 42 | 72,787 | 418 | 2,410 | 8,178 |
ReGAP polygons Min. area 77 ha |
83 | 93 | 53,926 | 40 | 1,802 | 6,375 |
Thiessen polygons Min. length 480 m |
63 | 25 | 52,123 | 473 | 2,374 | 7,092 |
Table A3. Comparison of ReGAP Polygons to generated Thiessen polygons.
No difference in means (two sample t-test) |
No difference in geometric means (two sample t-test) |
No difference in patch-size distribution (χ2 goodness-of-fit test, using classa counts) |
|
Pair 1 (original ReGAP and Thiessen polygons) |
t = -4.95 p = 0.000 df = 3,127 |
t = -86.66 p = 0.000 df = 2,864 |
n = 2238 df = 7 χ2 = 14,368.5 p = 0.000 |
Pair 2 (min. area 25.9 ha and min. line length 160 m) |
t = 0.06 p = 0.950 df = 410 |
t = 0.79 p = 0.431 df = 410 |
n = 203 df = 6 χ2 = 2.47 p = 0.872 |
Pair 3 (min. area 38.9 ha and min. line length 240 m) |
t = 0.21 p = 0.838 df = 261 |
t = -0.39 p = 0.695 df = 251 |
n = 127 df = 6 χ2 = 30.01 p = 0.000 |
Pair 4 (min. area 51.8 ha and min. line length 320 m) |
t = 1.48 p = 0.142 df = 130 |
t = 4.92 p = 0.000 df = 213 |
n = 92 df = 5 χ2 = 40.87 p = 0.000 |
Pair 5 (min. area 77.7 ha and min. line length 480 m) |
t = 0.50 p = 0.618 df = 125 |
t = 0.65 p = 0.516 df = 119 |
n = 63 df = 5 χ2 = 20.43 p = 0.001 |
a Classes used include
For Pair 1: 0–25, 25–50, 50–100, 100–200, 200–500, 500–1000, 1000–5000, 5000–100,000 (N = 8)
For Pairs 2 and 3: 0–50, 50–100, 100–200, 200–500, 500–1000, 1000–5000, 5000–100,000 (N = 7)
For Pairs 4 and 5: 0–100, 100–200, 200–500, 500–1000, 1000–5000, 5000–100000 (N = 6)
Fig. A1. Comparison of Thiessen polygon reconstructions of test landscape using differing minimum line segment lengths; (a) Original ReGAP data for the test area, (b) Thiessen polygon reconstruction of ReGAP data using 0-m minimum, (c) Thiessen polygon reconstruction of ReGAP data using 160-m minimum, (d) Thiessen polygon reconstruction of ReGAP data using 320-m minimum, (e) Thiessen polygon reconstruction of ReGAP data using 480-m minimum.