Differences to FRAGSTATS

Comparison with FRAGSTATS

landscapemetrics re-implements landscape metrics as they are mostly described in the FRAGSTATS software (McGarigal et al. 2023). Therefore, we compare our results with the results of FRAGSTATS. On patch-level we use a correlation approach testing values calculated by landscapemetrics and FRAGSTATS have at least a correlation of p>=0.975 because we are not able to exactly match patches. On class- and landscape-level we can match individual values and test if no deviation is larger than 5%. In the process, we recognized a few differences between the results. Some metrics in FRAGSTATS are interdependent across scales. Thus, if there is a deviation at the patch level, it propagates through the class- and landscape-level. In this document, we list the metrics with deviations at the lowest level only. Unfortunately, we do not have access to the source code of FRAGSTATS. Therefore, we are not able to finally explain all present differences of results.

General differences

Firstly, the patch ID is ordered in a different way, due to technical reasons (how connected patches are specified). Therefore, one has to pay attention comparing the results on patch level for FRAGSTATS and landscapemetrics.

All double precision floating point numbers are rounded in FRAGSTATS. Contrastingly, we do not round the numbers. Naturally, this can lead to small deviations between the results. However, these small differences should have no influence on any interpretation of the results.

There are quite a few metrics on class- and landscape-level that summarize patch level metrics (e.g., the mean, standard deviation (sd) or coefficient of variation (cv) of all values belonging to class i). While the results are identical for single patches and the mean of all patches, there are some slight differences between lanscapemetrics and FRAGSTATS for the sd and the cv. landscapemetrics uses base R functions and standard statistical definitions to summarize the patch level metrics. Again, difference are only very minor and should not affect interpretation of the results. In the following, we are comparing the cv and sd for the patch area.

We are including the cv calculated from all patch areas and the actual output of FRAGSTATS as well as the output of landscapemetrics. Interestingly, the cv calculated from all patches of FRAGSTATS is identical to the cv of landscapemetrics, but the already summarized result of FRAGSTATS is slightly different.

# function to calculate coefficient of variation
cv <- function(x) {
    (sd(x) / mean(x)) * 100
}

Click for details

class	fs_output	fs_calc	lsm_calc	lsm_fun
1	147.1030	156.02630	156.02630	156.02630
3	77.2108	84.58015	84.58015	84.58015
2	124.4360	129.51715	129.51715	129.51715

As for the cv, there are also minor differences for the sd. The result calculated from all patch areas of FRAGSTATS is identical to the result of landscapemetrics, but not the summarized result of FRAGSTATS.

Click for details

class	fs_output	fs_calculated	lsm_calculated	lsm_output
1	0.0030	0.0031899	0.0031899	0.0031899
3	0.0062	0.0067946	0.0067946	0.0067946
2	0.0022	0.0023313	0.0023313	0.0023313

Specific differences

Different definitions of the core area of a patch result in differences for all metrics that somehow related on the core area or number of disjunct core areas. landscapemetrics uses a cell-centered definition of the core area, namely “a cell is defined as core area if the cell has no neighbour with a different value than itself (rook’s case).” Contrastingly, FRAGSTATS uses “[…] a method involving the use of a variably-sized masked placed on cells on the perimeter of a patch […]”. Especially for patches with rather complicated shapes this seem to result in different core-metric values.

GYRATE metric

According to FRAGSTATS the radius of gyration for a patch consisting of only a single cell should equal GYRATE = 0.

[…] GYRATE = 0 when the patch consists of a single cell […]

However, for patches containing a single cell FRAGSTATS returns a value of GYRATE = 0.5. In the following table, patches with an area of area = 0.0001 consist of only one cell.

Click for details

fs_id	fs_area	fs_gyrate	lsm_id	lsm_area
1	1e-04	0.5	1	1e-04
24	1e-04	0.5	4	1e-04
28	1e-04	0.5	5	1e-04
13	1e-04	0.5	11	1e-04
15	1e-04	0.5	13	1e-04
18	1e-04	0.5	16	1e-04
20	1e-04	0.5	17	1e-04

Additionally, we recognized small differences for all other patches as well. However, we could not find an explanation for this difference, yet.

PARA metric

The documentation of FRAGSTATS defines the perimeter-area ratio the following:

[…] PARA equals the ratio of the patch perimeter (m) to area (m2). […]

Contrastingly, the output of FRAGSTATS gives the result as the ratio of the patch perimeter in meters to area in hectares.

We implemented PARA as documented in the FRAGSTATS manual using square meters. Nevertheless, the differences between the softwares are only based on different units, as shown by converting the FRAGSTATS output to meters per square meters.

Click for details

fs_id	fs_area	fs_perim	fs_para	lsm_id	lsm_area	lsm_perim	lsm_para	lsm_para_ha
1	0.0001	4	40000.000	1	0.0001	4	4.0000000	40000.000
24	0.0001	4	40000.000	4	0.0001	4	4.0000000	40000.000
28	0.0001	4	40000.000	5	0.0001	4	4.0000000	40000.000
13	0.0001	4	40000.000	11	0.0001	4	4.0000000	40000.000
15	0.0001	4	40000.000	13	0.0001	4	4.0000000	40000.000
18	0.0001	4	40000.000	16	0.0001	4	4.0000000	40000.000
20	0.0001	4	40000.000	17	0.0001	4	4.0000000	40000.000
11	0.0002	6	30000.000	14	0.0002	6	3.0000000	30000.000
21	0.0002	6	30000.000	18	0.0002	6	3.0000000	30000.000
27	0.0003	10	33333.333	8	0.0003	10	3.3333333	33333.333
16	0.0003	8	26666.667	22	0.0003	8	2.6666667	26666.667
9	0.0005	12	24000.000	2	0.0005	12	2.4000000	24000.000
25	0.0005	10	20000.000	9	0.0005	10	2.0000000	20000.000
26	0.0006	10	16666.667	21	0.0006	10	1.6666667	16666.667
2	0.0009	16	17777.778	25	0.0009	16	1.7777778	17777.778
22	0.0013	22	16923.077	28	0.0013	22	1.6923077	16923.077
19	0.0016	22	13750.000	7	0.0016	22	1.3750000	13750.000
8	0.0024	32	13333.333	15	0.0024	32	1.3333333	13333.333
3	0.0034	38	11176.471	10	0.0034	38	1.1176471	11176.471
23	0.0036	34	9444.444	12	0.0036	34	0.9444444	9444.444
6	0.0040	34	8500.000	27	0.0040	34	0.8500000	8500.000
7	0.0055	38	6909.091	20	0.0055	38	0.6909091	6909.091
17	0.0068	52	7647.059	19	0.0068	52	0.7647059	7647.059
12	0.0072	60	8333.333	3	0.0072	60	0.8333333	8333.333
5	0.0080	68	8500.000	6	0.0080	68	0.8500000	8500.000
14	0.0113	100	8849.558	24	0.0113	100	0.8849558	8849.558
10	0.0148	104	7027.027	26	0.0148	104	0.7027027	7027.027
4	0.0159	90	5660.377	23	0.0159	90	0.5660377	5660.377

SHAPE metric

We are following the definition provided in the latest version of the FRAGSTATS manual, in which the shape index is defined as the perimeter (m) divided by the square root of the area (m2) of patch ij, adjusted by a constant to adjust for a square standard. Yet, for some patches there are minor differences between landscapemetrics and FRAGSTATS.

CIRCLE metric

According to FRAGSTATS, for patches with only one cell CIRCLE = 0.

[…] CIRCLE = 0 for one cell patches. […]

Nevertheless, because also patches with only one cell have a dimension in the raster context, we decided to calculate the CIRCLE metric for such patches.

Click for details

fs_id	fs_area	lsm_id	lsm_area	lsm_circle
1	1e-04	1	1e-04	0.3633802
24	1e-04	4	1e-04	0.3633802
28	1e-04	5	1e-04	0.3633802
13	1e-04	11	1e-04	0.3633802
15	1e-04	13	1e-04	0.3633802
18	1e-04	16	1e-04	0.3633802
20	1e-04	17	1e-04	0.3633802

It seems like FRAGSTATS uses the largest distance between the corner points of the cells to calculate the diameter of the circumscribing circle. However, this does not necessarily result in the correct circumscribing circle. While this approach works well for more compact patch shapes, there are some cases in which the approach fails. One example are T-shaped patches. Contrastingly to FRAGSTATS, our algorithm calculates the true circumscribing circle also for such patches.

Comparison with SDMTools

SDMTools (VanDerWal et al. 2014) (still available, but apparently not longer maintained) offers landscape metrics on patch and class level. However, it does not return the same results as FRAGSTATS. The main reason for this are different standard defaults (e.g., SDMTools always considers the global landscape boundary) and that SDMTools returns results in map units and not in m^2/hectar, as FRAGSTATS/landscapemetrics. This also explains differences between our package and SDMTools.

Jemma Stachelek was so nice to remind us of these issues and provided the comparison.

Patch metrics

To get all available metrics on, e.g., patch level with SDMTools, you have to make a binary landscape for every class in your landscape, perform connected components labelling on it and then calculate the patch metrics.

# binarize every class in the landscape and calculate patch metrics
sdmtools_result <- lapply(terra::unique(landscape), FUN = function(x){
  tmp_land <- landscape
  terra::values(tmp_land)[terra::values(tmp_land) != x] <- NA
  terra::values(tmp_land)[terra::values(tmp_land) == x] <- 1
  ccl <- SDMTools::ConnCompLabel(raster::raster(tmp_land))
  PatchStat(ccl)
})

# combine to one data frame
sdmtools_result <- dplyr::bind_rows(sdmtools_result, .id = "Class")

landscapemetrics offers for such tasks the function get_patches() and for the metrics itself all of that is done internally. To get all metrics on patch level with landscapemetrics you could for example do:

patch_metrics <- calculate_lsm(landscape, what = "patch")

Click for details

Class	patchID	n.cell	n.edges.perimeter	n.edges.internal	area	perimeter	perim.area.ratio	shape.index	frac.dim.index
clumps	1	3	8	4	3	8	2.666667	1.000000	1.261859
clumps	2	17	32	36	17	32	1.882353	1.777778	1.467903
clumps	3	21	46	38	21	46	2.190476	2.300000	1.604421
clumps	4	6	16	8	6	16	2.666667	1.600000	1.547411
clumps	5	21	34	50	21	34	1.619048	1.700000	1.405847
clumps	6	4	10	6	4	10	2.500000	1.250000	1.321928
clumps	7	3	8	4	3	8	2.666667	1.000000	1.261859
clumps	8	3	8	4	3	8	2.666667	1.000000	1.261859
clumps	9	22	48	40	22	48	2.181818	2.400000	1.607811
clumps	10	21	50	34	21	50	2.380952	2.500000	1.659195
clumps	11	14	32	24	14	32	2.285714	2.000000	1.575897
clumps	12	16	34	30	16	34	2.125000	2.125000	1.543731
clumps	13	22	48	40	22	48	2.181818	2.400000	1.607811
clumps	14	3	8	4	3	8	2.666667	1.000000	1.261859
clumps	15	13	32	20	13	32	2.461539	2.000000	1.621429
clumps	16	15	36	24	15	36	2.400000	2.250000	1.622736
clumps	17	11	24	20	11	24	2.181818	1.714286	1.494444
clumps	18	34	74	62	34	74	2.176471	3.083333	1.654834
clumps	19	2	6	2	2	6	3.000000	1.000000	1.169925
clumps	20	4	12	4	4	12	3.000000	1.500000	1.584963
clumps	21	27	62	46	27	62	2.296296	2.818182	1.663213
clumps	22	1	4	0	1	4	4.000000	1.000000	NaN
clumps	23	9	26	10	9	26	2.888889	2.166667	1.703788
clumps	24	18	42	30	18	42	2.333333	2.333333	1.627040

References

McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org
Jeremy VanDerWal, Lorena Falconi, Stephanie Januchowski, Luke Shoo and Collin Storlie (2014). SDMTools: Species Distribution Modelling Tools: Tools for processing data associated with species distribution modelling exercises. R package version 1.1-221. https://CRAN.R-project.org/package=SDMTools

2024-04-02

Comparison with FRAGSTATS

General differences

Specific differences

All core-related metrics

GYRATE metric

PARA metric

SHAPE metric

CIRCLE metric

Comparison with SDMTools

Patch metrics

References