Neutral landscapes in a study

Part 1 showed what each neutral landscape model draws. This part puts them to work in the two ways they are used in research. First as an experiment: landscapes in which the amount of habitat and its fragmentation vary independently, each combination repeated with ten seeds, to see how eight common landscape metrics respond, which is impossible with real landscapes, where the two go together. Then as a null model: is the evergreen forest of Augusta, Georgia, more aggregated than chance would make a forest of the same amount? At the end you will be able to design a neutral landscape experiment, run its replicates as a batch, and test a real pattern against a neutral expectation.

The idea#

Amount and fragmentation, untangled#

In real landscapes, the amount of habitat and its fragmentation are correlated: landscapes with little forest usually have it in many small pieces. A study of real landscapes that finds fewer species where the forest is fragmented cannot tell whether fragmentation or the loss of forest is to blame. Fahrig (2003) reviewed the evidence and concluded that the effects of habitat loss are large and consistent, while those of fragmentation per se, at a constant amount, are weaker and of either sign. To measure fragmentation at a constant amount, one needs landscapes where the two vary independently, and neutral landscapes make them to order (With & Crist, 1995; With, 1997).

The same design answers a question about the tools themselves: does a landscape metric measure fragmentation, or does it also change with the amount? A metric that changes with the amount alone confounds the two, and Neel et al. (2004) and Wang et al. (2014) found that many do.

Replicates and seeds#

A neutral landscape is one draw. Its metrics vary from seed to seed, and a conclusion about a kind of landscape needs several draws: replicates, each with its own seed. Their mean estimates the expected value; their spread, how much a single landscape can differ by chance. Ten replicates are enough to see a trend; a test at the 5% level needs at least 19 (the observed value against 19 neutral ones is one chance in 20 of being the most extreme by chance).

When to use it#

• A factorial experiment before a field study, to know which metrics will separate amount from fragmentation in your range of landscapes; or as the landscapes of a simulation (dispersal, a population model) whose response to amount and fragmentation you want.
• A null model to ask whether a pattern (aggregation, connectivity, the shape of patches) is more than chance, and how much structure a neutral model needs to reproduce it.
• A neutral copy of a real map to test whether a model that uses the map (a land change model, a prioritization) depends on its spatial structure or only on its composition.
• Not to replace real landscapes in predictions about a place.

What you need#

Only Terraflux for the experiment. For the null model, a real map: we use augusta.tif, the land cover of the landscape metrics tutorials. In the application, the template Templates > Surfaces and uncertainty > More neutral landscapes has nlm.binarize and nlm.classify on neutral surfaces.

An experiment: amount by fragmentation#

The design#

Three levels of fragmentation, made by fractal surfaces (nlm.fbm) of three smoothness values, dimension 0.5 (fragmented), 1.0 (intermediate) and 1.5 (aggregated); nine amounts of habitat, 10 to 90%, made by cutting each surface with nlm.binarize; ten replicates (seeds 1 to 10). In all, 3 × 9 × 10 = 270 landscapes of 200 × 200 cells of 30 m (6 × 6 km), each measured by eight class metrics of the habitat.

Enlarge

Build the model#

format = "terraflux/1"

[[nodes]]
id = "fragmented"
op = "nlm.fbm"
params = { rows = 200, columns = 200, resolution = 30, dimension = 0.5, seed = 1 }

[[nodes]]
id = "intermediate"
op = "nlm.fbm"
params = { rows = 200, columns = 200, resolution = 30, dimension = 1.0, seed = 1 }

[[nodes]]
id = "aggregated"
op = "nlm.fbm"
params = { rows = 200, columns = 200, resolution = 30, dimension = 1.5, seed = 1 }

[[nodes]]
id = "cut_f"
op = "nlm.binarize"
inputs = { map = "fragmented.map" }
params = { breaks = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] }
note = "Nine maps: a stack."

[[nodes]]
id = "cut_i"
op = "nlm.binarize"
inputs = { map = "intermediate.map" }
params = { breaks = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] }

[[nodes]]
id = "cut_a"
op = "nlm.binarize"
inputs = { map = "aggregated.map" }
params = { breaks = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] }

[[nodes]]
id = "metrics_f"
op = "metrics.signatures"
inputs = { maps = "cut_f.map" }
params = { class_metrics = ["pland", "np", "ed", "lpi", "ai", "cohesion", "enn_mn", "area_mn"], classes = [2] }
note = "A row per amount."

[[nodes]]
id = "metrics_i"
op = "metrics.signatures"
inputs = { maps = "cut_i.map" }
params = { class_metrics = ["pland", "np", "ed", "lpi", "ai", "cohesion", "enn_mn", "area_mn"], classes = [2] }

[[nodes]]
id = "metrics_a"
op = "metrics.signatures"
inputs = { maps = "cut_a.map" }
params = { class_metrics = ["pland", "np", "ed", "lpi", "ai", "cohesion", "enn_mn", "area_mn"], classes = [2] }

How the pieces connect, and why:

• Nodes 1 to 3 draw the surfaces. Only dimension differs; the seed is the replicate. resolution = 30 gives the cells a size, so that areas are in hectares and distances in metres.
• Nodes 4 to 6: nlm.binarize with a list of breaks gives a stack of nine maps, one per amount, all cut from the same surface: the arrangement is the same at every amount, only the threshold moves. Habitat is 2, the matrix 1.
• Nodes 7 to 9: metrics.signatures with a stack on maps gives a row per layer, and with class_metrics and classes = [2] a column per metric of the habitat (np_2, ed_2...). One node measures all nine amounts.

Running the model gives one replicate. For ten, run it as a batch, changing the seed of the three surfaces together:

terraflux submit factorial.toml --replicates 10 --seed-input fragmented.seed,intermediate.seed,aggregated.seed

--replicates 10 runs the model ten times with seeds 1 to 10 (--first-seed changes the start), each in a folder of its own under batch/, in parallel on this machine's cores or on the machines of a cluster (parallel computing); --seed-input names the settings that take the seed. Make the three tables outputs of the model so that each run writes them. In the application, the Many runs pane does the same.

Read the results#

The share of habitat is exactly 10, 20... 90% in every landscape: the amount is controlled. The other metrics:

How to read the four charts together:

• No metric is a pure measure of fragmentation. Every one changes with the amount of habitat, and some (number of patches, edge density) in a hump that makes the same value mean different things at different amounts.
• The aggregation index is the most faithful of the four here: it orders the levels of fragmentation the same way at every amount. Edge density does too, but with its hump. The largest patch only below the percolation threshold.
• Report the amount and model it. In a study of real landscapes, include pland as a covariate and test the configuration metric given the amount; better, choose landscapes in which the two vary independently (Pasher et al., 2013).

The spread between replicates matters too:

A null model: is the forest aggregated?#

The real pattern#

The evergreen forest covers 37.5% of Augusta's map, in 139 patches with an aggregation index of 77.4% (part 2 of the landscape metrics). Is that aggregated? Compared with what? Three neutral models give three answers, each a different hypothesis:

• Random (nlm.random): the forest's cells were placed independently. The weakest null: almost any real pattern beats it.
• Fractal, rough (nlm.fbm, dimension = 1.0): the forest follows an autocorrelated but rough environment.
• Fractal, smooth (nlm.fbm, dimension = 1.5): it follows a smooth environment, large hills and valleys.

Each is drawn on the grid of the real map, cut to the forest's exact share, and measured the same way, 19 times.

Build the model#

format = "terraflux/1"

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

[[nodes]]
id = "forest"
op = "raster.reclassify"
inputs = { map = "cover.raster" }
params = { rules = "42 -> 2\n* -> 1" }
note = "Evergreen forest (2) and the rest (1)."

[[nodes]]
id = "observed"
op = "metrics.class"
inputs = { map = "forest.map" }
params = { metrics = ["pland", "np", "ed", "ai", "lpi"], show = "ai" }

[[nodes]]
id = "neutral"
op = "nlm.fbm"
inputs = { like = "cover.raster" }
params = { dimension = 1.5, seed = 1 }
note = "On the real map's grid."

[[nodes]]
id = "cut"
op = "nlm.binarize"
inputs = { map = "neutral.map" }
params = { breaks = 0.3754 }
note = "The forest's share, 37.54%."

[[nodes]]
id = "expected"
op = "metrics.class"
inputs = { map = "cut.map" }
params = { metrics = ["pland", "np", "ed", "ai", "lpi"], show = "ai" }

Two connections make the comparison fair. Node 4 takes the real map on its input like: the neutral landscape is drawn on the same grid (rows, columns, cell size), so areas and distances are comparable. Node 5 cuts it at the forest's share, 0.3754, read from node 3's table: the amount is the same, and only the arrangement differs. The replicates are again a batch, --seed-input neutral.seed.

Read the results#

Enlarge

The real forest is much more aggregated than random, and more than a forest following a rough environment; it is less aggregated than a forest following a smooth one, but has a similar number of patches. Its structure lies between the two fractal models, nearer the smooth one. With 19 replicates the smallest possible p-value is 0.05; for a paper, run 99 or 999.

What does that tell an ecologist? That the forest's aggregation is not chance, which few would doubt, and, more usefully, how much structure a model of it needs. A simulation of this landscape (a land change model, a species spreading through it) run on rough fractal forests would make the forest too scattered; on smooth ones, slightly too compact.

A neutral copy of a real map#

nlm.classify with a real map on its input real cuts a neutral surface into the classes of the real map with their exact shares. The copy has the real composition and a neutral configuration: a reference to test what a model's result owes to the real arrangement.

format = "terraflux/1"

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

[[nodes]]
id = "field"
op = "nlm.gaussian_field"
inputs = { like = "cover.raster" }
params = { range = 8, seed = 7 }

[[nodes]]
id = "neutral"
op = "nlm.classify"
inputs = { map = "field.map", real = "cover.raster" }
note = "The real map's classes and shares."

[[nodes]]
id = "real_metrics"
op = "metrics.landscape"
inputs = { map = "cover.raster" }
params = { metrics = ["np", "ed", "shdi", "contag"] }

[[nodes]]
id = "neutral_metrics"
op = "metrics.landscape"
inputs = { map = "neutral.classes" }
params = { metrics = ["np", "ed", "shdi", "contag"] }

Real

Neutral copy

Diversity is identical (the composition is), and every configuration metric differs: the real landscape has three times fewer patches and much less edge. A copy cut from a smoother field (a larger range) would come closer; trying ranges until the copy matches one metric is a simple way to fit a neutral model to a real landscape.

Settings that change the answer#

• The neutral model, above: it is the hypothesis. Report which, with its settings, and prefer more than one.
• The number of replicates: 10 to see a trend, 19 for a test at 5%, 99 or 999 for a paper.
• The grid: draw on the real map's grid (like) so that areas, distances and the map's border are the same.
• The amount: cut at the real share with nlm.binarize, exactly.
• The neighbour rule of the metrics, the same for the real and neutral maps.

Common pitfalls#

• A null model that is too weak. Beating the random model is easy and says little. Test against models with structure.
• One replicate. See the spread of the 270 landscapes above.
• The same seed for every replicate (a batch without --seed-input on the right settings): ten copies of one landscape.
• Neutral maps on a different grid from the real one: metrics in hectares or metres no longer compare.
• Ignoring the map's border. A real map is cut from a larger landscape; a neutral one is not. Large patches cut by the border look smaller; measure both the same way, or on an inner area.

Going further#

• Landscape metrics: every metric used here.
• Fragmentation: habitat loss and fragmentation per se, measured around every cell.
• Parallel computing: batches of replicates on many cores and machines.
• The operator reference: nlm.fbm, nlm.binarize, nlm.classify, metrics.signatures.

References#

• Fahrig, L. (2003). Effects of habitat fragmentation on biodiversity. Annual Review of Ecology, Evolution, and Systematics, 34, 487–515. https://doi.org/10.1146/annurev.ecolsys.34.011802.132419
• Gardner, R. H., Milne, B. T., Turner, M. G., & O'Neill, R. V. (1987). Neutral models for the analysis of broad-scale landscape pattern. Landscape Ecology, 1(1), 19–28. https://doi.org/10.1007/BF02275262
• 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
• Pasher, J., Mitchell, S. W., King, D. J., Fahrig, L., Smith, A. C., & Lindsay, K. E. (2013). Optimizing landscape selection for estimating relative effects of landscape variables on ecological responses. Landscape Ecology, 28(3), 371–383. https://doi.org/10.1007/s10980-013-9852-6
• Remmel, T. K., & Fortin, M.-J. (2013). Categorical, class-focused map patterns: characterization and comparison. Landscape Ecology, 28(8), 1587–1599. https://doi.org/10.1007/s10980-013-9905-x
• Wang, X., Blanchet, F. G., & Koper, N. (2014). Measuring habitat fragmentation: an evaluation of landscape pattern metrics. Methods in Ecology and Evolution, 5(7), 634–646. https://doi.org/10.1111/2041-210X.12198
• With, K. A. (1997). The application of neutral landscape models in conservation biology. Conservation Biology, 11(5), 1069–1080. https://doi.org/10.1046/j.1523-1739.1997.96210.x
• With, K. A., & Crist, T. O. (1995). Critical thresholds in species' responses to landscape structure. Ecology, 76(8), 2446–2459. https://doi.org/10.2307/2265819