Patch and class metrics

Part 1 introduced the three levels of metrics. This part works at the first two. At the patch level, every wood, field and pond of a map gets its own numbers: how large it is, how convoluted its outline, how much of it is far from an edge, how far it is from the next patch of its kind. At the class level, those numbers are summarised for each land cover and joined by metrics of the class as a whole: how much of the map it covers, how many pieces it is broken into, how much edge it has, how aggregated it is. We run them on the land cover of Augusta, Georgia (the map of part 1), compute a few by hand on three toy patches, and move the two things that change them most: the depth of the edge, and the aggregation of the habitat. At the end you will be able to choose a small set of patch and class metrics for a question and explain what each one says.

The idea#

A patch is the unit an ecologist often thinks in: a wood, a wetland, a meadow. Its size matters for the species that need large areas; its shape for those that avoid edges; its isolation for those that must move between patches. The patch metrics measure these three things, each in several ways, and the class metrics summarise them over all the patches of a class (McGarigal & Marks, 1995).

The metrics fall into families, which landscapemetrics and Terraflux follow (type):

Three patches of the same area#

The clearest way to see what shape and core metrics do is three patches of exactly the same area.

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Isolation and aggregation#

Isolation is measured at the patch level by the Euclidean distance to the nearest patch of the same class (enn), from cell centre to cell centre. With 8 neighbours, two separate patches are at least one cell apart, so enn is never less than two cells.

Aggregation is a property of a class: are its cells together or scattered? Several metrics measure it, each differently:

Means, and area-weighted means#

A class metric is often a patch metric summarised: the mean area of the forest's patches (area_mn), its standard deviation (area_sd), its coefficient of variation (area_cv). The mean over patches is dominated by the many small patches. FRAGSTATS also offers the area-weighted mean (area_am, shape_am, cai_am...), in which every patch weighs by its area: the value of the patch that a random cell of the class belongs to. It is usually closer to how the habitat is experienced. Area-weighted means come from FRAGSTATS, not landscapemetrics; ask for them by name, or with extras = true.

When to use it#

• Patch metrics when patches are the unit of the study: occupancy surveys of ponds or woodlots, where patch area and isolation are the predictors of island biogeography and metapopulation theory; or to find the patches with the most interior, the most edge, the most isolated.
• Class metrics to compare the habitat of several landscapes or dates: is there less forest, and is it more fragmented? A small set covers most questions: pland (amount), np or mesh (subdivision), ed (edge), ai or cohesion (aggregation), enn_mn (isolation), shape_am (shape) and cai_am (interior, with a justified edge depth).
• Not for the structural role of each cell (use MSPA), nor for connectivity for a species with a dispersal distance (use habitat networks).

What you need#

A categorical map in a projected system with metres, as in part 1. We use augusta.tif (160 × 120 cells of 30 m). In the application, Templates > Landscape metrics > Patches and their shapes starts a model with the patch metrics, GuidosToolbox's parcellation and the contortion of the forest on a land cover drawn by chance.

Build the model#

format = "terraflux/1"

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

[[nodes]]
id = "patches"
op = "metrics.patch"
inputs = { map = "cover.raster" }
params = { metrics = ["area", "perim", "shape", "frac", "core", "cai", "enn", "gyrate"], show = "shape" }
note = "A row per patch; map: the shape index of each."

[[nodes]]
id = "classes"
op = "metrics.class"
inputs = { map = "cover.raster" }
params = { metrics = ["ca", "pland", "np", "lpi", "area_mn", "area_am", "shape_mn", "shape_am", "ed", "ai", "cohesion", "enn_mn", "cai_mn"], show = "ai" }
note = "A row per class; map: the aggregation of each."

Both take node 1's map and are independent. The metrics lists are the choices that matter: every metric you list is a column of the table. show names the one painted on the output map: for the patches, every patch takes its own value; for the classes, every cell takes the value of its class. Change show and run again to see another metric as a map (Ctrl+Enter on the node).

The edge depth of the core metrics is edge_depth, in cells (default 1). It belongs to the question, not to the map: how far into a forest do edge effects reach for the species or process you study? Choose it from the literature, as for MSPA's edge width.

Read the results#

The patches#

The table has a row per patch. The six largest patches of evergreen forest:

(All the evergreen patches are in evergreen_patches.csv.) Patches 658 and 677 are of similar size, but 658 has half again as much outline: a shape index of 7.0 against 5.1, and less core (59 ha against 64). For an interior species, 677 is the better forest. Patch 630, smaller but compact, keeps 64% of itself as core. And every one of them is 60 m, two cells, from the next evergreen patch: in this landscape the evergreen forest is one fabric cut by roads and streams one cell wide. Its median enn is 60 m.

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The classes#

The class table (the full table in augusta_classes.csv), for six classes:

How to read it:

• The mean and the area-weighted mean of the evergreen forest's patches are 4.7 and 48 ha. The first says most patches are small; the second that a random evergreen cell lies in a patch of about 48 ha. The second is the one that matters to a forest animal.
• Woody wetlands are the most aggregated class (AI 89%, cohesion 97) in 10 patches with little edge for their area (14.5 m/ha): the river's floodplain forest is a few large, continuous blocks. But their patches are far apart (324 m on average): what little there is outside the floodplain is isolated.
• Mixed forest covers 10% in 173 small patches with an AI of 49%: it is scattered, mostly thin transitions between the other two forests, not a habitat of its own.
• Developed open space has 241 patches of 0.3 ha on average and the lowest aggregation: strips along roads.

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Settings that change the answer#

The depth of the edge#

The core area depends entirely on edge_depth. Move the slider to deepen the edge from 30 to 180 m.

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PlayEdge depth (m)

The evergreen forest covers 37.5% of the map; with an edge of 30 m, 16.9% of the map is its core; with 90 m, 3.1%. The deciduous and mixed forests lose their core much faster: they are narrower. If edge effects on your species reach 100 m, this landscape has almost no interior forest, whatever its forest cover says. Report the edge depth with every core metric, and when it is uncertain, report the curve.

The aggregation of habitat#

The class metrics of configuration are meant to measure arrangement, but they also respond to the amount of habitat. To see them respond to arrangement alone, we hold the amount fixed: four maps of exactly 35% habitat cut from fractal surfaces (nlm.fbm) of growing smoothness.

Two lessons. First, metrics of aggregation are not interchangeable: cohesion saturates at amounts where AI still discriminates, and the opposite happens when habitat is rare. Second, enn_mn rises as the habitat aggregates: with fewer patches, the nearest one is further away. A higher mean isolation does not mean a worse landscape for a species; read isolation together with patch size and number. Neel et al. (2004) mapped such behaviours over full gradients of amount and aggregation, and their figures are worth a look before choosing a metric.

Common pitfalls#

• Comparing shapes of patches of different sizes. Shape grows with area on a grid (the chart above).
• Using area_mn to say the habitat is fragmented. A falling mean patch area can mean large patches broke, or that many new small ones appeared while the large ones stayed intact. Look at np, lpi and area_am together.
• Ignoring the amount. Edge density, patch number, isolation and aggregation all change with pland. Report pland beside them, and test configuration at a fixed amount (part 5 and the neutral landscapes tutorials).
• Core metrics without an edge depth. A core area "of 17%" means nothing without "with an edge of 30 m".
• Single-cell patches. A patch of one cell has no defined aggregation (ai is NA) and a shape of 1; rare classes of a few cells (here, cultivated crops, one cell) give unstable class metrics. Drop or merge them.
• The border. Patches cut by the map's border look smaller and simpler than they are; the largest patches are the most likely to be cut.

Going further#

• Part 3: the landscape level, diversity and contagion.
• Habitat patterns: GuidosToolbox's objects by size, parcellation and the effective mesh size, the contortion of outlines.
• The operator reference: metrics.patch, metrics.class.

References#

• He, H. S., DeZonia, B. E., & Mladenoff, D. J. (2000). An aggregation index (AI) to quantify spatial patterns of landscapes. Landscape Ecology, 15(7), 591–601. https://doi.org/10.1023/A:1008102521322
• 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
• 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
• Schumaker, N. H. (1996). Using landscape indices to predict habitat connectivity. Ecology, 77(4), 1210–1225. https://doi.org/10.2307/2265590