Comparison of Fractal Realizations Using Landscape Metrics

Representative landscape metrics for size actual 129 × 129 cell landscapes each compared with 25 synthetic landscapes generated by the Fractal Landscape Realizer. The two actual landscapes for which experts most frequently selected the synthetic map as real, chose the two maps equally, and most frequently selected the actual map as real in a pairwise presentation are indicated. Related metrics are grouped together. Map resolution is 1 km².

* indicates metrics for which the actual map was more than one standard deviation and more than 5% different from the mean.

** indicates metrics for which the actual map was more than two standard deviations and more than 5% different from the mean.

Synthetic Chosen Over Actual

Map 3
Landscape Metric^a	Actual Map	Realized		Percent Difference^b
Landscape Metric^a	Actual Map	Mean	Standard Deviation	Percent Difference^b
Total Area (km²)	16407	16407.00	0.00	0.00
Largest Patch Index (%)	73.79	74.33	0.84	0.73
Number of patches	192	193.24	26.27	0.65
Patch Density (#/km²)	0.012	0.012	0.002	-1.33
Mean Patch Size (km²)	85.45	86.74	14.46	1.50
Patch Size Coeff of Variation (%)	1023.36	1034.09	73.99	1.05

Total Edge (km)	3811	3454.64	334.16	-9.35	*
Edge Density (km/km²)	0.23	0.21	0.02	-9.36	*
Landscape Shape Index	9.61	8.91	0.65	-7.25	*
Mean Shape Index	1.52	1.38	0.03	-9.24	**
Area-Weighted Mean Shape Index	7.08	6.83	0.81	-3.54

Double Log Fractal Dimension	1.469	1.461	0.012	-0.56
Mean Patch Fractal Dimension	1.039	1.027	0.001	-1.11
Area-Weighted Mean Fractal Dimension	1.165	1.163	0.009	-0.13

Total Core Area (km²)	4622	4811.96	972.08	4.11
Number of Core Areas	16	15.64	4.56	-2.25
Mean Core Area per Patch (km²)	24.07	25.94	9.11	7.74
C.V. Mean Core Area per Patch (%)	1341.85	1358.57	102.50	1.25
Mean Area per Core (km²)	288.87	339.05	133.23	17.37
C.V. Mean Area per Core (%)	4504.07	4711.08	727.74	4.60
Total Core Area Index (%)	28.17	29.33	5.92	4.11
Mean Core Area Index (%)	0.31	0.29	0.13	-8.27

Mean Nearest Neighbor Distance (km)	1.71	2.34	0.46	36.68	*
C.V. Nearest Neighbor Distance (%)	161.28	226.00	101.52	40.12
Mean Proximity Index	995.98	1543.40	567.78	54.96

Shannon's Diversity Index	0.819	0.819	0.000	0.00
Simpson's Diversity Index	0.402	0.402	0.000	0.00
Modified Simpson's Diversity Index	0.515	0.514	0.000	-0.19
Patch Richness	7	7.00	0.00	0.00

Map 10
Landscape Metric^a	Actual Map	Realized		Percent Difference^b
Landscape Metric^a	Actual Map	Mean	Standard Deviation	Percent Difference^b
Total Area (km²)	15500	15500.00	0.00	0.00
Largest Patch Index (%)	23.15	42.24	5.28	82.49	**
Number of patches	156	243.12	23.11	55.85	**
Patch Density (#/km²)	0.010	0.016	0.001	56.00	**
Mean Patch Size (km²)	99.36	64.32	6.19	-35.27	**
Patch Size Coeff of Variation (%)	359.29	705.07	72.05	96.24	**

Total Edge (km)	4902	3636.16	340.02	-25.82	**
Edge Density (km/km²)	0.32	0.23	0.02	-25.83	**
Landscape Shape Index	12.21	9.67	0.68	-20.81	**
Mean Shape Index	1.76	1.40	0.02	-20.62	**
Area-Weighted Mean Shape Index	4.75	4.07	0.49	-14.17	*

Double Log Fractal Dimension	1.436	1.403	0.011	-2.29
Mean Patch Fractal Dimension	1.051	1.030	0.001	-1.95
Area-Weighted Mean Fractal Dimension	1.139	1.123	0.008	-1.37

Total Core Area (km²)	1153	3533.36	739.82	206.45	**
Number of Core Areas	25	21.72	3.45	-13.12
Mean Core Area per Patch (km²)	7.39	14.75	3.70	99.60	*
C.V. Mean Core Area per Patch (%)	711.26	1139.48	160.51	60.21	**
Mean Area per Core (km²)	46.12	169.25	54.03	266.98	**
C.V. Mean Area per Core (%)	1682.20	3706.01	803.84	120.31	**
Total Core Area Index (%)	7.44	22.80	4.77	206.44	**
Mean Core Area Index (%)	0.55	0.55	0.11	1.76

Mean Nearest Neighbor Distance (km)	2.09	2.81	0.38	34.50	*
C.V. Nearest Neighbor Distance (%)	121.29	186.09	41.89	53.42	*
Mean Proximity Index	569.49	458.22	100.65	-19.54	*

Shannon's Diversity Index	1.546	1.502	0.000	-2.83
Simpson's Diversity Index	0.732	0.708	0.000	-3.28
Modified Simpson's Diversity Index	1.317	1.232	0.000	-6.48	**
Patch Richness	7	7.00	0.00	0.00

Maps Chosen Equally

Map 17
Landscape Metric^a	Actual Map	Realized		Percent Difference^b
Landscape Metric^a	Actual Map	Mean	Standard Deviation	Percent Difference^b
Total Area (km²)	15623	15623.00	0.00	0.00
Largest Patch Index (%)	15.35	20.98	5.42	36.71	*
Number of patches	239	412.32	51.74	72.52	**
Patch Density (#/km²)	0.015	0.026	0.003	75.47	**
Mean Patch Size (km²)	65.37	38.55	5.63	-41.02	**
Patch Size Coeff of Variation (%)	394.99	588.73	76.32	49.05	**

Total Edge (km)	6251	5868.68	495.54	-6.12
Edge Density (km/km²)	0.40	0.38	0.03	-6.11
Landscape Shape Index	14.34	13.57	0.99	-5.33
Mean Shape Index	1.69	1.38	0.02	-18.46	**
Area-Weighted Mean Shape Index	4.82	4.64	0.40	-3.81

Double Log Fractal Dimension	1.492	1.444	0.012	-3.24
Mean Patch Fractal Dimension	1.044	1.028	0.001	-1.57
Area-Weighted Mean Fractal Dimension	1.147	1.136	0.005	-1.00

Total Core Area (km²)	1083	1506.84	523.92	39.14
Number of Core Areas	22	22.56	4.92	2.55
Mean Core Area per Patch (km²)	4.53	3.84	1.79	-15.25
C.V. Mean Core Area per Patch (%)	856.60	1097.37	153.16	28.11	*
Mean Area per Core (km²)	49.23	71.77	34.98	45.80
C.V. Mean Area per Core (%)	2626.73	4405.30	1009.33	67.71	*
Total Core Area Index (%)	6.93	9.64	3.35	39.14
Mean Core Area Index (%)	0.27	0.26	0.09	-4.46

Mean Nearest Neighbor Distance (km)	2.24	2.00	0.21	-10.59	*
C.V. Nearest Neighbor Distance (%)	358.87	181.85	57.91	-49.33	**
Mean Proximity Index	342.81	344.90	99.20	0.61

Shannon's Diversity Index	1.893	1.884	0.000	-0.47
Simpson's Diversity Index	0.822	0.818	0.000	-0.49
Modified Simpson's Diversity Index	1.724	1.703	0.000	-1.22
Patch Richness	10	10.00	0.00	0.00

Map 14
Landscape Metric^a	Actual Map	Realized		Percent Difference^b
Landscape Metric^a	Actual Map	Mean	Standard Deviation	Percent Difference^b
Total Area (km²)	16057	16057.00	0.00	0.00
Largest Patch Index (%)	69.32	74.11	0.52	6.92	**
Number of patches	150	190.40	13.95	26.93	**
Patch Density (#/km²)	0.009	0.012	0.001	32.00	**
Mean Patch Size (km²)	107.05	84.77	6.21	-20.81	**
Patch Size Coeff of Variation (%)	851.88	1020.61	38.61	19.81	**

Total Edge (km)	3163	2657.84	152.60	-15.97	**
Edge Density (km/km²)	0.20	0.17	0.01	-15.98	**
Landscape Shape Index	8.92	7.92	0.30	-11.18	**
Mean Shape Index	1.65	1.40	0.02	-14.80	**
Area-Weighted Mean Shape Index	5.37	4.46	0.40	-16.96	**

Double Log Fractal Dimension	1.454	1.403	0.009	-3.50
Mean Patch Fractal Dimension	1.048	1.032	0.001	-1.57
Area-Weighted Mean Fractal Dimension	1.143	1.129	0.007	-1.25

Total Core Area (km²)	4553	6173.28	477.45	35.59	**
Number of Core Areas	14	8.52	2.18	-39.14	**
Mean Core Area per Patch (km²)	30.35	32.69	4.28	7.69
C.V. Mean Core Area per Patch (%)	1119.14	1357.12	53.03	21.26	**
Mean Area per Core (km²)	325.21	795.09	317.22	144.48	*
C.V. Mean Area per Core (%)	3518.31	6154.55	927.60	74.93	**
Total Core Area Index (%)	28.36	38.45	2.97	35.59	**
Mean Core Area Index (%)	0.51	0.37	0.06	-26.28	**

Mean Nearest Neighbor Distance (km)	1.87	2.85	0.59	52.70	*
C.V. Nearest Neighbor Distance (%)	208.18	211.33	65.42	1.51
Mean Proximity Index	406.51	693.72	188.30	70.65	*

Shannon's Diversity Index	0.760	0.758	0.000	-0.26
Simpson's Diversity Index	0.386	0.384	0.000	-0.52
Modified Simpson's Diversity Index	0.487	0.485	0.000	-0.41
Patch Richness	6	6.00	0.00	0.00

Actual Chosen Over Synthetic

Map 16
Landscape Metric^a	Actual Map	Realized		Percent Difference^b
Landscape Metric^a	Actual Map	Mean	Standard Deviation	Percent Difference^b
Total Area (km²)	16435	16435.00	0.00	0.00
Largest Patch Index (%)	32.31	30.68	2.49	-5.07
Number of patches	306	514.76	41.34	68.22	**
Patch Density (#/km²)	0.019	0.031	0.002	64.84	**
Mean Patch Size (km²)	53.71	32.11	2.37	-40.22	**
Patch Size Coeff of Variation (%)	800.59	931.80	87.44	16.39	*

Total Edge (km)	5100	6651.40	470.15	30.42	**
Edge Density (km/km²)	0.31	0.40	0.03	30.42	**
Landscape Shape Index	11.68	14.70	0.92	25.91	**
Mean Shape Index	1.46	1.36	0.02	-7.00	**
Area-Weighted Mean Shape Index	5.48	6.45	0.71	17.70	*

Double Log Fractal Dimension	1.522	1.529	0.008	0.48
Mean Patch Fractal Dimension	1.032	1.026	0.002	-0.60
Area-Weighted Mean Fractal Dimension	1.152	1.161	0.009	0.74

Total Core Area (km²)	4888	2274.76	708.90	-53.46	**
Number of Core Areas	10	16.48	2.79	64.80	**
Mean Core Area per Patch (km²)	15.97	4.49	1.59	-71.87	**
C.V. Mean Core Area per Patch (%)	1205.38	1530.70	139.90	26.99	**
Mean Area per Core (km²)	488.80	145.93	63.63	-70.14	**
C.V. Mean Area per Core (%)	5950.02	8046.98	1153.61	35.24	*
Total Core Area Index (%)	29.74	13.84	4.31	-53.46	**
Mean Core Area Index (%)	0.34	0.14	0.04	-59.79	**

Mean Nearest Neighbor Distance (km)	1.88	1.82	0.27	-3.37
C.V. Nearest Neighbor Distance (%)	264.47	184.51	86.21	-30.23
Mean Proximity Index	580.28	519.64	87.90	-10.45

Shannon's Diversity Index	1.533	1.530	0.000	-0.20
Simpson's Diversity Index	0.737	0.736	0.000	-0.14
Modified Simpson's Diversity Index	1.336	1.332	0.000	-0.30
Patch Richness	10	10.00	0.00	0.00

Map 8
Landscape Metric^a	Actual Map	Realized		Percent Difference^b
Landscape Metric^a	Actual Map	Mean	Standard Deviation	Percent Difference^b
Total Area (km²)	16553	16553.00	0.00	0.00
Largest Patch Index (%)	17.16	21.01	3.90	22.43
Number of patches	365	369.56	30.68	1.25
Patch Density (#/km²)	0.022	0.022	0.002	1.82
Mean Patch Size (km²)	45.35	45.07	3.57	-0.61
Patch Size Coeff of Variation (%)	479.97	587.91	53.71	22.49	**

Total Edge (km)	6790	6030.24	358.26	-11.19	**
Edge Density (km/km²)	0.41	0.36	0.02	-11.19	**
Landscape Shape Index	14.71	13.23	0.70	-10.03	**
Mean Shape Index	1.54	1.39	0.02	-9.88	**
Area-Weighted Mean Shape Index	4.42	5.24	0.40	18.62	**

Double Log Fractal Dimension	1.471	1.452	0.012	-1.30
Mean Patch Fractal Dimension	1.038	1.028	0.001	-0.96
Area-Weighted Mean Fractal Dimension	1.136	1.146	0.005	0.90

Total Core Area (km²)	1469	1778.88	377.40	21.09
Number of Core Areas	23	22.32	4.78	-2.96
Mean Core Area per Patch (km²)	4.02	4.86	1.15	20.73
C.V. Mean Core Area per Patch (%)	1052.92	944.30	146.70	-10.32
Mean Area per Core (km²)	63.87	84.97	35.23	33.04
C.V. Mean Area per Core (%)	3903.08	3552.59	944.67	-8.98
Total Core Area Index (%)	8.88	10.75	2.28	21.09
Mean Core Area Index (%)	0.26	0.29	0.07	13.80

Mean Nearest Neighbor Distance (km)	1.90	2.05	0.24	7.46
C.V. Nearest Neighbor Distance (%)	144.13	203.80	73.02	41.40
Mean Proximity Index	190.69	477.27	94.80	150.29	**

Shannon's Diversity Index	1.796	1.794	0.000	-0.11
Simpson's Diversity Index	0.798	0.797	0.000	-0.13
Modified Simpson's Diversity Index	1.598	1.595	0.000	-0.19
Patch Richness	10	10.00	0.00	0.00

^a Landscape metrics calculated using FRAGSTATS 2.0 (McGarigal and Marks)
^b Percent Difference equals ((mean - actual)/actual) × 100.

For additional information contact:

William W. Hargrove

Oak Ridge National Laboratory

Environmental Sciences Division

P.O. Box 2008, M.S. 6407

Oak Ridge, TN 37831-6407

(865) 241-2748

hnw@geobabble.org

The Fractal Realizer
Last Modified: Thursday, 17-May-2007 11:59:44 EDT
Warnings and Disclaimers