What landscape metrics are

A landscape metric is a number that describes the pattern of a map: how much of each land cover there is, how many pieces it is broken into, how large and how convoluted they are, how mixed the classes are. Ecologists use them to compare landscapes, to follow one landscape through time, and to relate pattern to what lives in it. This first part of the series explains what the metrics measure and the choices that every one of them depends on, then runs a first model on a real land cover map: the 133 metrics of landscapemetrics (and 123 more of FRAGSTATS) at the three levels of patch, class and landscape. At the end you will be able to read a table of landscape metrics and know which settings to report with it.

The idea#

Pattern and process#

Landscape ecology starts from one claim: the spatial pattern of a landscape affects ecological processes, and the processes in turn shape the pattern (Turner, 1989). A forest bird's chance of breeding depends on how far its nest is from an edge; a beetle's chance of reaching the next wood depends on how far it is and what lies between; a fire spreads further through a continuous fuel than through a patchwork. To test such ideas we need to measure pattern, and to measure it the same way in every study. Quantitative indices appeared in the 1980s (O'Neill et al., 1988); the program FRAGSTATS gathered them into one library with standard definitions (McGarigal & Marks, 1995), and the R package landscapemetrics reimplemented them in open source (Hesselbarth et al., 2019). Terraflux computes the metrics of landscapemetrics with the same definitions (through the library landschaft), so its numbers can be compared with the literature.

Composition and configuration#

Every metric describes one of two aspects of a map (McGarigal & Marks, 1995; Gustafson, 1998):

• Composition: what is in the landscape and in which amounts, without reference to where. The share of each class, the number of classes, their diversity. Composition does not change if you shuffle the cells.
• Configuration: how it is arranged. The size and shape of patches, their isolation, how aggregated or interspersed the classes are. Configuration changes when you shuffle the cells.

Clumped

Random

The distinction matters ecologically. The amount of habitat (composition) and its fragmentation (configuration) have different effects on species, and many configuration metrics change with the amount alone (Neel et al., 2004): with less forest, there are usually more and smaller patches. Measure both, and read configuration in the light of composition. The fragmentation tutorials come back to this.

Patches, and the neighbour rule#

Most metrics are built on patches: groups of cells of the same class connected to each other. "Connected" needs a rule. With 4 neighbours (the rook's rule) two cells belong to the same patch only if they share a side; with 8 neighbours (the queen's rule) touching at a corner is enough.

Enlarge

The rule is a statement about the organism: can it cross where two patches touch only at a corner? For a forest bird, probably; for a ground beetle in a hedgerow network, perhaps not. FRAGSTATS and landscapemetrics use 8 neighbours by default, and so does Terraflux (directions = 8). Every metric that counts or measures patches depends on it: say which you used.

Three levels#

The metrics are computed at three levels (McGarigal & Marks, 1995):

Class and landscape metrics are often summaries of the patch metrics: the mean patch area of the forest (area_mn), its standard deviation (area_sd), its coefficient of variation (area_cv). Others exist only at their level: diversity needs several classes, contagion the adjacencies of the whole map.

Grain and extent#

Every metric depends on two properties of the map that have nothing to do with the landscape itself:

• the grain: the size of a cell (and the smallest patch the mappers drew, the minimum mapping unit);
• the extent: the area the map covers.

A finer grain shows more small patches and more edge; a larger extent takes in more classes and larger patches. This was shown early (Turner et al., 1989) and studied systematically since: some metrics change predictably with the grain, others erratically (Wu, 2004). The slider shows the same land cover at five grains, from its own 30 m to 240 m, each coarser map made by the most common class of the cells it covers.

Enlarge

PlayCell size (m)

None of these maps is wrong; they answer questions at different scales. The lesson is practical: compare metrics only between maps of the same grain, extent and legend, and choose the grain for the organism and the process, not because a map happens to exist at it.

When to use it#

Landscape metrics answer questions of the form "how does this landscape differ from that one", "how did it change", and "does the pattern around a site explain what we observe there":

• comparing the fragmentation of the forest of several regions, or of one region at two dates;
• describing the landscape around sampling sites (bird counts, pollinator traps, camera traps) and using the metrics as predictors (part 5);
• mapping where a landscape is diverse or fragmented with a moving window (part 4);
• classifying many landscapes into kinds by their metrics (part 6).

They are not a measure of connectivity for a given species: a metric of aggregation or isolation describes the map, not the movement of an animal through it. For that, use the habitat networks or circuit connectivity tutorials. For the structural roles of habitat cells (core, edge, corridor) use MSPA; for fragmentation measured around every cell at several scales, the fragmentation tutorials. And metrics need a question: computing all 256 and looking for something that correlates is the most common misuse (Li & Wu, 2004; Kupfer, 2012).

What you need#

A categorical map: a raster whose values are classes (land cover, habitat types, vegetation), in a projected coordinate system whose unit is the metre, so that areas come out in hectares and lengths in metres. The metrics read the cell size from the map. On a map in degrees, areas and distances are wrong: project it first (coordinate systems). Cells without a value (no data) are left out: they are not a class.

This series uses two real maps:

• augusta.tif: an excerpt of 160 × 120 cells of 30 m (1,728 ha) of the US National Land Cover Database around Augusta, Georgia, the sample map of landscapemetrics, with its 15 classes (open water, four kinds of developed land, three of forest, wetlands...);
• clc.tif: CORINE Land Cover around Hannover, Germany, 2,000 × 2,000 cells of 25 m, used in parts 4 to 7.

In the application, Templates > Landscape metrics > Landscape metrics starts a model with class, landscape and moving-window metrics on a land cover drawn by chance; replace its first node with a raster.read of your map.

Build the model#

format = "terraflux/1"

[[nodes]]
id = "cover"
op = "raster.read"
params = { path = "augusta.tif" }
note = "15 classes of land cover, 30 m."

[[nodes]]
id = "patches"
op = "metrics.patch"
inputs = { map = "cover.raster" }
params = { metrics = ["area"], show = "area" }
note = "A row per patch; a map of each patch's area."

[[nodes]]
id = "classes"
op = "metrics.class"
inputs = { map = "cover.raster" }
params = { metrics = ["ca", "pland", "np"], show = "pland" }
note = "A row per class."

[[nodes]]
id = "landscape"
op = "metrics.landscape"
inputs = { map = "cover.raster" }
params = { metrics = ["ta", "np", "pr", "shdi"] }
note = "One row for the map."

All three take the same input and do not depend on each other, so they run in parallel. Each gives a table; the patch node also gives patches, the map of the patches numbered (useful to find a patch of the table on the map), and the patch and class nodes a map of the metric named in show. Instead of listing metrics, type picks a family (area and edge, shape, core area, aggregation, diversity, complexity), and extras = true adds FRAGSTATS' metrics that landscapemetrics lacks (area-weighted means, _am, and others).

From the command line, the same model runs with terraflux run model.toml; tables that you make outputs of the model are written as CSV:

[outputs.class_metrics]
from = "classes.table"

Read the results#

Enlarge

The landscape (landscape.table): 1,728 ha, 1,144 patches, 15 classes, a Shannon diversity of 1.90. With 15 classes, the most SHDI could be is \(\ln 15 = 2.71\): the classes are far from equally common.

The classes (classes.table), the five largest:

Already the table tells a story. Woody wetlands cover 8% of the map in only 10 patches: a few large, continuous blocks along the river. Mixed forest covers 10% in 173 patches: many small pieces, often transitions between the evergreen and deciduous forests. Developed open space (lawns, road verges) covers only 4.1% but in 241 patches, the most of any class: thin, scattered strips.

The patches (patches.table): 1,144 rows. The largest is 127.9 ha; 352 are single cells of 0.09 ha. Half of the patches are smaller than 0.27 ha, while the ten largest hold 35% of the map. That is typical: a few large patches hold most of the area, and very many small ones most of the count. A mean over patches (area_mn, 1.5 ha) describes neither; part 2 shows the better summaries.

Settings that change the answer#

The same settings exist on every metrics operator, because they change the patches or the edges that all the metrics are built on:

• directions: 8 (default) or 4 neighbours. With 4, diagonal strips (roads, streams, hedgerows drawn as a staircase of cells) break into many patches: the number of patches and every per-patch mean change.
• count_boundary: whether the map's border counts as edge (default no). With it, a landscape cut by its border has more edge.
• consider_boundary: whether cells at the map's border can be core (default no).
• edge_depth: the depth of the edge, in cells, for the core-area metrics (part 2).
• convention: landscapemetrics (default) or fragstats, where the two programs differ (FRAGSTATS counts edges in physical lengths and the sizes of disjunct cores differently).

And three choices outside the operators: the grain (the slider above), the extent, and the legend: the same map with its 15 classes grouped into 8 has fewer, larger patches and a lower diversity (part 3).

Common pitfalls#

• A map in degrees. Areas in "hectares" and edges in "metres" are then meaningless. Project to an equal-area system first.
• No data coded as a class. A value of 0 or 255 that means "outside the study area" becomes a class with patches and edges unless it is set as no data (raster.read's nodata, or reclassify it to no data).
• Too many metrics. Metrics are strongly correlated: a handful of independent dimensions (amount, subdivision, edge, shape, aggregation, isolation, diversity) explain most of their variation across landscapes (Riitters et al., 1995; Cushman et al., 2008). Choose one per dimension that matters for your question (part 5 shows the correlations).
• Comparing across grains, extents or legends. See above.
• Treating a difference as significant. A metric is one value of one map. Whether two values differ beyond what chance would give needs replicates or a model of the pattern: the neutral landscapes tutorials show how.
• Map error. Misclassified cells make spurious small patches and edges; patch counts and edge metrics suffer most. Know the map's accuracy.

Going further#

• Part 2: patch and class metrics, area, shape, core, isolation and aggregation.
• Part 3: the landscape level, diversity and contagion.
• Part 4: metrics in a moving window.
• Part 5: metrics around sites, through time, and their redundancy.
• Part 6: kinds of landscapes from their metrics.
• Part 7: maps larger than memory.
• The operator reference: metrics.patch, metrics.class, metrics.landscape.

References#

• Cushman, S. A., McGarigal, K., & Neel, M. C. (2008). Parsimony in landscape metrics: strength, universality, and consistency. Ecological Indicators, 8(5), 691–703. https://doi.org/10.1016/j.ecolind.2007.12.002
• Gustafson, E. J. (1998). Quantifying landscape spatial pattern: what is the state of the art? Ecosystems, 1(2), 143–156. https://doi.org/10.1007/s100219900011
• Hesselbarth, M. H. K., Sciaini, M., With, K. A., Wiegand, K., & Nowosad, J. (2019). landscapemetrics: an open-source R tool to calculate landscape metrics. Ecography, 42(10), 1648–1657. https://doi.org/10.1111/ecog.04617
• Kupfer, J. A. (2012). Landscape ecology and biogeography: rethinking landscape metrics in a post-FRAGSTATS landscape. Progress in Physical Geography, 36(3), 400–420. https://doi.org/10.1177/0309133312439594
• Li, H., & Wu, J. (2004). Use and misuse of landscape indices. Landscape Ecology, 19(4), 389–399. https://doi.org/10.1023/B:LAND.0000030441.15628.d6
• McGarigal, K., & Marks, B. J. (1995). FRAGSTATS: spatial pattern analysis program for quantifying landscape structure (General Technical Report PNW-GTR-351). USDA Forest Service, Pacific Northwest Research Station. https://doi.org/10.2737/PNW-GTR-351
• Neel, M. C., McGarigal, K., & Cushman, S. A. (2004). Behavior of class-level landscape metrics across gradients of class aggregation and area. Landscape Ecology, 19(4), 435–455. https://doi.org/10.1023/B:LAND.0000030521.19856.cb
• O'Neill, R. V., Krummel, J. R., Gardner, R. H., Sugihara, G., Jackson, B., DeAngelis, D. L., et al. (1988). Indices of landscape pattern. Landscape Ecology, 1(3), 153–162. https://doi.org/10.1007/BF00162741
• Riitters, K. H., O'Neill, R. V., Hunsaker, C. T., Wickham, J. D., Yankee, D. H., Timmins, S. P., et al. (1995). A factor analysis of landscape pattern and structure metrics. Landscape Ecology, 10(1), 23–39. https://doi.org/10.1007/BF00158551
• Turner, M. G. (1989). Landscape ecology: the effect of pattern on process. Annual Review of Ecology and Systematics, 20, 171–197. https://doi.org/10.1146/annurev.es.20.110189.001131
• Turner, M. G., O'Neill, R. V., Gardner, R. H., & Milne, B. T. (1989). Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecology, 3(3–4), 153–162. https://doi.org/10.1007/BF00131534
• Wu, J. (2004). Effects of changing scale on landscape pattern analysis: scaling relations. Landscape Ecology, 19(2), 125–138. https://doi.org/10.1023/B:LAND.0000021711.40074.ae