Ecological intactness

From this part on, the series follows one region, Serra Verde, through the steps of a restoration plan. This part measures human pressure. You read a map of the human footprint, turn it into the ecological intactness of every cell (how free it and its surroundings are of human pressure), and map where restoring pasture and cropland would raise the intactness of the whole landscape the most. At the end you have the intactness map, a map of where restoration pays most for it, and a before-and-after comparison of the landscape with all its converted land restored.

The idea#

The human footprint#

The Human Footprint Index sums eight human pressures in each cell of the world's land on a scale of 0 to 50: built environments (10 where land is built), croplands (7), pasture (4), population density, night-time lights, railways, roads and navigable waterways (Sanderson et al., 2002; Venter et al., 2016). A footprint of 0 is wilderness; a footprint of 4 is the pressure of a pasture alone. Venter et al. (2016) published global maps of it at 1 km for 1993 and 2009, freely available.

From footprint to intactness#

A cell can be free of pressure and still be degraded by what surrounds it: a patch of forest in the middle of a city is not intact. Beyer et al. (2020) defined the ecological intactness of a cell from the quality of the cell and of its neighbourhood, and used it to show how much intactness the world's ecoregions have lost. Strassburg et al. (2020) used the same measure as one of the benefits of their global restoration plan, and Terraflux computes it as they did.

The quality of habitat against the human footprint: it falls to 0.2 at a footprint of 4 — The quality q = exp(-γh) of a cell with footprint h (green), with γ chosen so that a footprint of 4, a pasture's, leaves a fifth of the quality. Dashed: q to the power z = 0.5, the term each cell contributes to a pair.

Key idea

The quality of habitat of a cell with footprint \(h\) is \( q = e^{-\gamma h} \), with \(\gamma = -\ln(0.2)/4 \approx 0.40\): 1 without footprint, 0.2 at a footprint of 4. The intactness of cell \(i\) is

\[ Q_i = \frac{\sum_j (q_i\, q_j)^{z}\, w_{ij}}{\sum_j w_{ij}}, \qquad w_{ij} = e^{\beta d_{ij}} \]

over the cells \(j\) within a radius of \(i\) (itself included), where \(d_{ij}\) is their distance in km, \(\beta = -0.2\) per km makes nearer cells count more, and \(z = 0.5\). \(Q_i\) runs from 0 (the cell or its surroundings fully transformed) to 1 (the cell and all its neighbourhood free of pressure).

Where restoring helps most#

Restoring a share \(x_k\) of cell \(k\) lowers its footprint by a reduction \(a_k\) per unit: restoring a pasture removes a pressure of 4, a cropland 7. The total intactness of the landscape, \(\sum_i Q_i\), then rises, both in the cell and in every cell whose neighbourhood holds it. The intactness gradient is how fast it rises per unit restored:

\[ \frac{\partial \sum_i Q_i}{\partial x_k} \]

It is the linear benefit of intactness in a restoration plan: high where one restored cell reconnects intact surroundings, low in the middle of a city, where a restored cell stays surrounded by pressure.

When to use it#

Ranking places by human pressure in context: intactness is a better proxy for the condition of biodiversity than the footprint alone, because it accounts for the surroundings.
A benefit of restoration besides species and carbon: the sixth part adds it to a restoration plan, with the gradient as its value per cell.
Tracking change: intactness computed from footprints of two years shows where pressure grew around remaining habitat.

What it is not for: intactness is not habitat for a given species (that is the area of habitat of the next part), and it says nothing about connectivity for movement (see the corridors of the previous part, or habitat networks).

What you need#

A human footprint map in a projected CRS: the cells' size in km enters the weights. Serra Verde's footprint.tif is a footprint index on 60 × 90 cells of 1 km (SIRGAS 2000 / UTM 23S, EPSG:31983).
The reduction per unit restored, here from the land cover: land_cover.tif holds the share (0 to 1) of six classes in every cell, as six named bands: forest, savanna, mangrove, pasture, cropland and urban.

Serra Verde

Serra Verde is an imaginary coastal region of 60 × 90 km, the example data of landschaft's prioritization module: mountains in the north-west, a coastal plain with three cities, a highway and two rivers, and the ocean (no data) in the south-east. The data are synthetic, made to behave like real planning data, so that every step of a plan can be shown on one small region. Replace them with your own maps of the same kinds.

The application's template Ecological intactness (Templates menu, group Conservation and restoration) builds the same model on a footprint drawn by chance.

Build the model#

The footprint and the reduction#

Add a raster.read node for footprint.tif. For the reduction, read the two anthropic bands of the land cover with two more raster.read nodes on land_cover.tif, setting their band to pasture and cropland (a band can be chosen by its name). A raster.calc node with inputs p and c computes the footprint that restoring one unit of each cell removes, the mean of 4 (pasture) and 7 (cropland) weighted by their shares:

(4 * p + 7 * c) / (p + c) if p + c > 0 else 0

Intactness and its gradient#

restoration.intactness takes the footprint and gives the intactness map. Its settings are Beyer et al.'s: radius (3 cells), gamma (−ln(0.2)/4), beta (−0.2 per km) and z (0.5), and cell_size (the cells' size in km, read from a projected grid; give it for a grid without CRS). With a reduction and a restored map (the share of each cell restored) it gives the intactness after restoring them.

restoration.intactness_gradient takes the footprint and the reduction and gives, for every cell, the gain in total intactness per unit of the cell restored.

Intactness and where restoring raises it most: the footprint, the reduction a unit restored removes (from the shares of pasture and cropland), the intactness, its gradient, and the intactness with all converted land restored.

Model file (TOML)

format = "terraflux/1"

[[nodes]]
id = "footprint"
op = "raster.read"
params = { path = "footprint.tif" }
note = "Human footprint, 0-50, cells of 1 km."

[[nodes]]
id = "pasture"
op = "raster.read"
params = { path = "land_cover.tif", band = "pasture" }

[[nodes]]
id = "cropland"
op = "raster.read"
params = { path = "land_cover.tif", band = "cropland" }

[[nodes]]
id = "reduction"
op = "raster.calc"
inputs = { p = "pasture.raster", c = "cropland.raster" }
params = { expression = "(4 * p + 7 * c) / (p + c) if p + c > 0 else 0" }
note = "Footprint removed per unit restored: 4 pasture, 7 cropland."

[[nodes]]
id = "intactness"
op = "restoration.intactness"
inputs = { footprint = "footprint.raster" }
params = { radius = 3 }

[[nodes]]
id = "gradient"
op = "restoration.intactness_gradient"
inputs = { footprint = "footprint.raster", reduction = "reduction.map" }
params = { radius = 3 }
note = "Gain in total intactness per unit of each cell restored."

[[nodes]]
id = "all_converted"
op = "raster.calc"
inputs = { p = "pasture.raster", c = "cropland.raster" }
params = { expression = "p + c" }
note = "Every share of pasture and cropland restored."

[[nodes]]
id = "after"
op = "restoration.intactness"
inputs = { footprint = "footprint.raster", reduction = "reduction.map", restored = "all_converted.map" }
params = { radius = 3 }

Read the results#

Footprint and intactness#

The mean footprint is low (2.0) because most of the region is mountain forest, but the intactness tells a sharper story: around the highway, the rivers' farms and the cities, intactness falls below 0.3 well beyond the cells that bear the pressure, because every cell within three cells of them shares it. Over the region, 70% of the cells have an intactness above 0.5, and the mean is 0.70.

Where restoration raises it most#

The gradient is highest (up to 2.3) at the fringe of the converted land, where a restored cell is surrounded by intact land and lifts its neighbours too. It is lowest along the highway and around the cities: restoring a farm there removes its own pressure, but the cell stays next to a road or a town and its quality stays low. On average a unit of converted land restored adds 0.92 to the total intactness.

Restoration at the fringe

The gradient rewards restoring land next to intact habitat, the same advice the distance to the forest gave in the first part for natural regeneration. Both point to the edges of what remains.

Before and after#

Drag the handle to compare the intactness today with the intactness if every share of pasture and cropland were restored (the after node: the footprint lowered by the reduction times the share restored):

Now — Ecological intactness now (left) and with all 916 km² of pasture and cropland restored (right), on the same colour scale (0 dark blue, 1 yellow). The mean rises from 0.70 to 0.86, and the cells above 0.5 from 70% to 87%. The highway and the cities, which restoration does not remove, stay.

All converted land restored — Ecological intactness now (left) and with all 916 km² of pasture and cropland restored (right), on the same colour scale (0 dark blue, 1 yellow). The mean rises from 0.70 to 0.86, and the cells above 0.5 from 70% to 87%. The highway and the cities, which restoration does not remove, stay.

How to report it#

Give the footprint data and year, the cell size, the parameters (radius, γ, β, z; say if you used the defaults of Beyer et al.), the mean intactness and the share of the area above a threshold, before and after a plan. A map of the gradient shows where restoration pays most for intactness.

Settings that change the answer#

The radius sets the neighbourhood whose pressure a cell shares: a larger radius spreads the effect of a road or a town further. Each frame is a real run:

Radius (cells of 1 km) 1 — Ecological intactness with a radius of 1 to 8 cells. As the radius grows, the low intactness around the highway and the cities widens, and the mean falls slightly. The last value counts how many of the 100 cells of the highest gradient are also among the 100 highest with a radius of 3.

Radius (cells of 1 km) 2 — Ecological intactness with a radius of 1 to 8 cells. As the radius grows, the low intactness around the highway and the cities widens, and the mean falls slightly. The last value counts how many of the 100 cells of the highest gradient are also among the 100 highest with a radius of 3.

The mean barely changes, but the priorities do: with a radius of 8 cells only 59 of the 100 cells where restoring helps most are the same as with 3. Choose the radius from the distance over which pressure degrades habitat for the species you care about, and say which you used; Strassburg et al. (2020) used 3 cells.

The other parameters matter too. gamma sets how fast quality falls with the footprint (a larger value makes a pasture more damaging), beta how fast the neighbours' weight falls with distance (closer to 0 makes the far neighbours count as much as the near ones), and z how much a single bad neighbour lowers a pair.

Common pitfalls#

Degrees. The weights need distances in km: the footprint must be in a projected CRS, or cell_size given in km. Terraflux stops with a message on a map in degrees.
The reduction is per unit of the cell. A reduction of 7 and a share restored of 0.5 lower the footprint by 3.5. Restoring more than the converted share would remove pressures (roads, lights) restoration cannot remove; keep restored within the share of anthropic land.
The edge of the map. Cells near the edge have a smaller neighbourhood (only the part inside the map), so their intactness ignores pressures just outside. Include a margin around the study area.
Old footprints. The global footprint maps lag behind the land; check the year against your land cover.

Going further#

What converted land was before, and how much habitat each species has lost: Original vegetation and area of habitat, the next part.
Intactness as a benefit of a restoration plan, weighed against species and carbon: Several benefits.
The operators: restoration.intactness, restoration.intactness_gradient, and the hfi, reduction and intactness_* settings of restoration.plan.

References#

Beyer, H. L., Venter, O., Grantham, H. S., & Watson, J. E. M. (2020). Substantial losses in ecoregion intactness highlight urgency of globally coordinated action. Conservation Letters, 13(2), e12692. https://doi.org/10.1111/conl.12692
Sanderson, E. W., Jaiteh, M., Levy, M. A., Redford, K. H., Wannebo, A. V., & Woolmer, G. (2002). The human footprint and the last of the wild. BioScience, 52(10), 891–904. https://doi.org/10.1641/0006-3568(2002)052[0891:THFATL]2.0.CO;2
Strassburg, B. B. N., Iribarrem, A., Beyer, H. L., Cordeiro, C. L., Crouzeilles, R., Jakovac, C. C., et al. (2020). Global priority areas for ecosystem restoration. Nature, 586(7831), 724–729. https://doi.org/10.1038/s41586-020-2784-9
Venter, O., Sanderson, E. W., Magrach, A., Allan, J. R., Beher, J., Jones, K. R., et al. (2016). Sixteen years of change in the global terrestrial human footprint and implications for biodiversity conservation. Nature Communications, 7, 12558. https://doi.org/10.1038/ncomms12558