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 2 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)


FigA1

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.


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