The landscape level, diversity and contagion

A class metric looks at one land cover; a landscape metric looks at all of them together. How many kinds of land cover are there, and how evenly do they share the map? Are the classes in large blocks or finely mixed? Does every class meet every other, or only some? This part answers these questions with metrics.landscape, first on four landscapes built to have exactly the same composition, so that only the arrangement differs, then on the land cover of Augusta with two legends, its 15 classes and the same map grouped into 8. At the end you will know which landscape metrics measure composition and which configuration, and why a landscape metric is only as meaningful as the legend it is computed on.

The idea#

Diversity: how many classes, and how even#

Diversity indices come from information theory and community ecology. A landscape's classes are treated like the species of a community, their shares of the map like the species' relative abundances.

Contagion and interspersion: how mixed#

Contagion (O'Neill et al., 1988; Li & Reynolds, 1993) measures how clumped the classes are, from the adjacencies of cells: if you stand on a cell of class \(i\), how likely is the neighbouring cell to be of class \(k\)? A landscape of large blocks has mostly like adjacencies (forest beside forest) and a high contagion; a finely mixed one has many unlike adjacencies and a contagion near 0. It mixes two things, how dispersed the cells of each class are and how interspersed the classes are with each other (Riitters et al., 1996), which is why FRAGSTATS also gives the interspersion and juxtaposition index (IJI), which measures only the second: from the edges between patches, how evenly every class meets every other class. 100% when every pair of classes shares the same length of edge; low when some classes meet only some others.

Information theory: a consistent frame#

Nowosad and Stepinski (2019) showed that two numbers from information theory, computed on the pairs of neighbouring cells, place any categorical map in a space that separates composition from configuration:

• the marginal entropy (ent): the diversity of the classes (Shannon's diversity in bits, \(\log_2\));
• the conditional entropy (condent): how uncertain the class of a cell's neighbour is when the cell's class is known: high when the classes are finely mixed, low when they are in blocks;
• the mutual information (mutinf = ent − condent): how much a cell's class tells about its neighbour's, the aggregation; and its relative version relmutinf (mutual information over marginal entropy).

They are landscapemetrics' complexity metrics (type = "complexity").

When to use it#

• Diversity (pr, shdi, sidi, shei) to compare the heterogeneity of landscapes: a habitat-heterogeneity hypothesis (more kinds of land cover, more species), the diversity of farming landscapes, the variety of habitats available around a site.
• Contagion, IJI, AI to say whether the mosaic is coarse or fine-grained; landscape-level ed for the amount of edge of all kinds.
• The information-theory metrics when you want two numbers that are clearly composition and configuration, for example to classify many landscapes (part 6).
• Not to describe one habitat: landscape metrics treat all classes alike, the forest and the parking lot. For one habitat use the class level (part 2).

What you need#

A categorical map in a projected system, as in parts 1 and 2: augusta.tif. The four landscapes of the first section are drawn by Terraflux's neutral landscape models, so those models run as they are. In the application, the template Templates > Landscape metrics > Landscape metrics has a metrics.landscape node set to the diversity metrics (type = "diversity").

Four landscapes, one composition#

Build them#

format = "terraflux/1"

[[nodes]]
id = "cover"
op = "nlm.random_cluster"
params = { rows = 150, columns = 150, resolution = 30, p = 0.5, weights = [0.25, 0.25, 0.25, 0.25], seed = 5 }
note = "Four classes, 25% each, in clusters."

[[nodes]]
id = "landscape"
op = "metrics.landscape"
inputs = { map = "cover.map" }
params = { metrics = ["pr", "shdi", "shei", "sidi", "siei", "ed", "lpi", "contag", "iji", "ai", "ent", "condent", "mutinf", "relmutinf"] }

nlm.random_cluster draws clusters of cells and gives each a class, roughly in the proportions of weights; p sets how large the clusters grow. Its map goes to the map input of metrics.landscape, whose table has one row with every metric listed. The other three landscapes change only node 1:

• One dominant class: the same model with weights = [0.82, 0.06, 0.06, 0.06];
• Salt and pepper: nlm.random (a value at random in every cell) cut into four equal classes by nlm.classify (weights = [0.25, 0.25, 0.25, 0.25]);
• Smooth bands: nlm.gaussian_field with range = 25 (a smooth surface) cut the same way. Because nlm.classify cuts the surface by its values, class 1 is the lowest ground and class 4 the highest, so class 1 meets only class 2, and so on.

format = "terraflux/1"

[[nodes]]
id = "s"
op = "nlm.random"
params = { rows = 150, columns = 150, resolution = 30, seed = 5 }

[[nodes]]
id = "cover"
op = "nlm.classify"
inputs = { map = "s.map" }
params = { weights = [0.25, 0.25, 0.25, 0.25] }

[[nodes]]
id = "landscape"
op = "metrics.landscape"
inputs = { map = "cover.classes" }
params = { metrics = ["pr", "shdi", "contag", "iji", "condent", "mutinf"] }

Note the port: nlm.classify's output is classes, not map.

Read them#

Read the table by rows:

• The diversity rows (PR to SIDI, and ENT) cannot tell the last three apart. They have the same composition, and diversity is composition. SHDI = 1.386 = ln 4 is the most four classes can have, SHEI = 1. Only the dominated landscape differs.
• The configuration rows (ED to AI, CONDENT, MUTINF) separate them. Salt and pepper has the most edge, no contagion, no mutual information: knowing a cell's class tells you nothing about its neighbour's. Clusters have a quarter of that edge, a contagion of 25% and a mutual information of 1 bit.
• IJI tells the smooth bands apart. Its classes are as clumped as the clusters (similar contagion), but class 1 meets only class 2 and class 4 only class 3: interspersion falls to 66%, while in the two random arrangements every class meets every other (IJI near 100).
• The dominant landscape has a high contagion (72.5%) mostly because one class covers 82% of it: contagion mixes composition into configuration. Its IJI is lower because the three small classes rarely meet each other.

Contagion and AI disagree on the smooth bands (contagion below the clusters', AI above): they weigh different things, the distribution of adjacencies among classes and the like adjacencies of each class.

Diversity as one class takes over#

The curve is not linear: a landscape can lose much of its evenness before the indices notice, and a landscape that is 90% one class still scores SHDI 0.45. Compare diversity between landscapes with the same number of classes, or use the evenness indices.

A real map with two legends#

The same land cover can be described with many legends. The NLCD of Augusta has 15 classes; its first level groups them into 8 (water, developed, barren, forest, shrub, grassland, agriculture, wetlands). raster.reclassify does it with a rule per line.

format = "terraflux/1"

[[nodes]]
id = "cover"
op = "raster.read"
params = { path = "augusta.tif" }

[[nodes]]
id = "level1"
op = "raster.reclassify"
inputs = { map = "cover.raster" }
params = { rules = "11 -> 1\n21 22 23 24 -> 2\n31 -> 3\n41 42 43 -> 4\n52 -> 5\n71 -> 6\n81 82 -> 7\n90 95 -> 8" }
note = "15 classes into 8."

[[nodes]]
id = "m15"
op = "metrics.landscape"
inputs = { map = "cover.raster" }
params = { metrics = ["np", "ed", "lpi", "pr", "shdi", "shei", "contag", "iji", "ai", "mesh"] }

[[nodes]]
id = "m8"
op = "metrics.landscape"
inputs = { map = "level1.map" }
params = { metrics = ["np", "ed", "lpi", "pr", "shdi", "shei", "contag", "iji", "ai", "mesh"] }

In the Node pane of node 2, the rules are typed one per line: 21 22 23 24 -> 2 puts the four developed classes in class 2. Nodes 3 and 4 are the same metrics on the two maps, side by side.

15 classes

8 classes

Enlarge

Nothing on the ground changed, yet the number of patches fell by 60%, edge density by half, diversity by 40%, and contagion rose by 13 points. Only IJI barely moved. The legend is as much a choice of scale as the cell size: the map's thematic resolution (Castilla et al., 2009). Two studies of the "same" landscape with different legends will report different landscapes. Choose the legend for the question (what does the species distinguish?) and keep it the same for every map you compare.

Settings that change the answer#

• The legend, above.
• directions for the patch-based metrics (np, lpi, iji, mesh); contagion and AI use adjacencies of cells and do not depend on it.
• For the complexity metrics, neighbourhood (4 or 8 neighbours for the pairs of cells, default 4), ordered (ordered pairs, default true) and base (the logarithm, default log2, in bits). Report them with the values.
• classes_max for the relative richness rpr (richness over the most classes there could be).

Common pitfalls#

• Reading diversity as configuration. A landscape of four classes in fine salt and pepper and one in four large blocks have the same SHDI. If the question is about fragmentation, diversity is the wrong metric.
• Contagion with one dominant class. Contagion rises with dominance as well as with clumping; read it with an evenness index.
• Contagion with one class. With a single class, contagion and the evenness indices are undefined (NA): a zone of a map that is all forest has no contagion. Tables of many zones then have NA values (part 5).
• Comparing landscapes with different numbers of classes. Richness drives SHDI. Use evenness, or the same legend.
• No data as a class. As in part 1: a value meaning "no data" counted as a class raises richness and diversity.

Going further#

• Part 4: the landscape metrics of the window around every cell, as maps.
• Part 6: many landscapes compared and classified by their metrics.
• Neutral landscapes: the generators used above, and how to use them as null models.
• The operator reference: metrics.landscape, raster.reclassify, nlm.random_cluster, nlm.classify.

References#

• Castilla, G., Larkin, K., Linke, J., & Hay, G. J. (2009). The impact of thematic resolution on the patch-mosaic model of natural landscapes. Landscape Ecology, 24(1), 15–23. https://doi.org/10.1007/s10980-008-9310-z
• Li, H., & Reynolds, J. F. (1993). A new contagion index to quantify spatial patterns of landscapes. Landscape Ecology, 8(3), 155–162. https://doi.org/10.1007/BF00125347
• 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
• Nowosad, J., & Stepinski, T. F. (2019). Information theory as a consistent framework for quantification and classification of landscape patterns. Landscape Ecology, 34(9), 2091–2101. https://doi.org/10.1007/s10980-019-00830-x
• 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., Wickham, J. D., & Jones, K. B. (1996). A note on contagion indices for landscape analysis. Landscape Ecology, 11(4), 197–202. https://doi.org/10.1007/BF02071810
• Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
• Simpson, E. H. (1949). Measurement of diversity. Nature, 163, 688. https://doi.org/10.1038/163688a0