CRAFTY: competition for land between agent functional types

The previous part gave every parcel a farmer of its own. Large regions have millions of land managers, too many to describe one by one, and too varied to describe as one. CRAFTY groups them into agent functional types, as ecologists group plants into plant functional types: intensive farmers, extensive farmers, foresters, conservationists. Each type produces services (food, timber, recreation, carbon) from the capitals of the land it manages (soil, forest, infrastructure, people), and the types compete for land wherever the demand for their services is not met. In this part you will build the template CRAFTY: farmers and foresters node by node, run it for 20 steps while the demand for food grows, follow the supply of food and timber against their demand, and see how the settings of the competition (how much land is on offer each step, how readily a manager gives way) shape the landscape. At the end you will know what each number of a CRAFTY model means and how to read its results.

The idea#

Functional types, capitals and services#

CRAFTY (Competition for Resources between Agent Functional TYpes) was introduced by Murray-Rust et al. (2014) to model land use over large regions with agents, without describing every land manager. It was later applied to the whole of Great Britain and of Europe (Brown et al., 2018, 2019). Its vocabulary:

• Capitals: what a cell offers, each scaled from 0 to 1. In CRAFTY-EU they follow the five capitals of the sustainable livelihoods framework: natural (soil fertility, climate suitability for crops, growing stock), human, social, manufactured (roads, irrigation) and financial. Here two natural capitals: the soil's fertility and the forest's growing stock, wood.
• Services: what society demands from the land, in its own units: food, timber, meat, recreation, biodiversity. Here food and timber.
• Agent functional types (AFTs): kinds of land managers, each with how much of each service it can produce and how much it depends on each capital. Here farmer and forester.
• Demand: how much of each service is wanted at each step, from scenarios of population, diets and trade.

Production, utility and competitiveness#

The utility makes the competition follow the demand: a service whose demand is met is worth nothing more (\(u_s = 0\)), so the AFTs that produce only it lose all competitiveness; a service far from its demand is worth much, so the AFTs that produce it win cells. The supply and the utilities are updated after every change of manager, so the land settles where the supply meets the demand, if the landscape can produce it.

Giving up and giving in#

Two thresholds per AFT describe how attached its managers are to their land:

• Giving up (giving_up): a manager whose competitiveness on its own cell falls below this threshold may abandon the cell, which becomes unmanaged. At each step it leaves with probability giving_up_rate. A high threshold describes managers who need a good return to stay (commercial farmers); a low one, managers who stay whatever happens (smallholders with no alternative).
• Giving in (giving_in): a managed cell is taken over by another AFT only if that AFT's competitiveness exceeds the incumbent's by more than the incumbent's giving-in threshold. It is the resistance to being bought out.

Every step, a share search of the cells is offered, in a random order. For each offered cell, the most competitive AFT takes it if the cell is unmanaged (and the AFT's competitiveness is above 0), or if it beats the incumbent by the incumbent's giving_in. Random numbers come from a counter of the seed, the step and the cell, so the same seed always gives the same maps.

When to use it#

CRAFTY answers questions about how land use responds to the demand for what land produces: which mix of land uses meets a demand for food, timber and recreation in 2050; where farming retreats if yields rise; what happens to forests when demand for meat grows; how attachment to land (giving-up and giving-in thresholds) slows or speeds the response. Brown et al. (2018) used it to explore how land managers' behaviours change the pathways towards visions of the future of land in Great Britain; Brown et al. (2019) found that, across Europe, plausible behaviours could lead to the breakdown of the supply of some services under some scenarios.

Use it when the demand is for services rather than for areas of classes. When the demand is the area of each land use, CLUE-S (the first series) is simpler; when it is the supply of goods by land systems with intensities, see CLUMondo. CRAFTY is not a model of individual decisions: the managers of one AFT are interchangeable. For individual agents with their own state, see agents.

What you need#

• Capitals: maps from 0 to 1, a layer each, named. Rescale real variables (yield potential, growing stock, distance to markets inverted) to 0 to 1, where 1 is the best for the AFTs that use them.
• The land at the start: who manages each cell, as 1, 2... in the order of the AFTs, 0 for unmanaged cells, missing outside the region. From a land cover map, reclassify each class to the AFT that manages it.
• The AFTs: for each, its production of each service, its sensitivity to each capital, its giving-up and giving-in thresholds, and optionally a land cover class for the output map.
• A demand: a table with a column per service and a row per step. If it has fewer rows than steps, the last row holds for the steps after it.

The template CRAFTY: farmers and foresters (in the application, Templates) draws its capitals and its starting land by chance, so it runs as it is.

Build the model#

Step 1: the capitals and the land at the start#

format = "terraflux/1"

[[nodes]]
id = "fertility"
op = "nlm.gaussian_field"
params = { rows = 100, columns = 100, range = 15, seed = 101 }

[[nodes]]
id = "wood"
op = "nlm.gaussian_field"
params = { rows = 100, columns = 100, range = 25, seed = 102 }

[[nodes]]
id = "capitals"
op = "stack.of"
inputs = { fertility = "fertility.map", wood = "wood.map" }

[[nodes]]
id = "start"
op = "nlm.random_cluster"
params = { rows = 100, columns = 100, p = 0.5, weights = [0.5, 0.5], seed = 103 }

1. fertility (nlm.gaussian_field) draws the soil's fertility, 0 to 1, in patches about 15 cells across. With real data, a raster.read of a capital already scaled to 0 to 1.
2. wood draws the forest's growing stock, in larger patches, independent of the soil.
3. capitals (stack.of) puts them in one stack whose layers take the names of the node's inputs: fertility and wood. These are the names the AFTs' sensitivities use.
4. start (nlm.random_cluster) draws clusters of two classes, half each: 1 farmers, 2 foresters. The numbers must be the positions of the AFTs in the list given to the allocation (1 the first, 2 the second).

Step 2: the demand and the loop#

format = "terraflux/1"

[[nodes]]
id = "fertility"
op = "nlm.gaussian_field"
params = { rows = 100, columns = 100, range = 15, seed = 101 }

[[nodes]]
id = "wood"
op = "nlm.gaussian_field"
params = { rows = 100, columns = 100, range = 25, seed = 102 }

[[nodes]]
id = "capitals"
op = "stack.of"
inputs = { fertility = "fertility.map", wood = "wood.map" }

[[nodes]]
id = "start"
op = "nlm.random_cluster"
params = { rows = 100, columns = 100, p = 0.5, weights = [0.5, 0.5], seed = 103 }

[[nodes]]
id = "demand"
op = "table.of"
params = { columns = ["food", "timber"], rows = [[1500, 1500], [1600, 1500], [1700, 1500], [1800, 1500], [1900, 1500], [2000, 1500], [2100, 1500], [2200, 1500], [2300, 1500], [2400, 1500], [2500, 1500], [2600, 1500], [2700, 1500], [2800, 1500], [2900, 1500], [3000, 1500], [3100, 1500], [3200, 1500], [3300, 1500], [3400, 1500]] }

[[nodes]]
id = "simulation"
op = "control.repeat"
inputs = { times = 20, land = "start.map" }

[nodes.body]
carry = { land = "compete.land" }
collect = { cover = "compete.cover", info = "compete.info" }

[[nodes.body.nodes]]
id = "compete"
op = "crafty.allocate"
inputs = { land = "@land", capitals = "capitals.stack", demand = "demand.table", step = "@step", seed = 7 }
params = { search = 0.2, giving_up_rate = 0.2, afts = [
  { name = "farmer", class = 1, production = { food = 1.0 }, sensitivity = { fertility = 2.0 }, giving_up = 0.05, giving_in = 0.1 },
  { name = "forester", class = 2, production = { timber = 1.0 }, sensitivity = { wood = 1.0 }, giving_up = 0.05, giving_in = 0.1 },
] }

• demand (table.of) writes the demand as a table: columns food and timber, a row per step. Food grows by 100 every step, from 1500 to 3400; timber stays at 1500. The units are those of the production: a cell of full fertility managed by a farmer produces 1 of food. With real data, a table read from a file of scenarios, or a demand computed by agents (see a coupled model).
• simulation (control.repeat) runs 20 steps. It carries one value, land: @land is the starting map at step 1 and, after it, the map the previous step gave (carry = { land = "compete.land" }). It collects cover (the land cover of each step) and info (the supply and demand of each step).
• compete (crafty.allocate), in the body, runs one step of the competition. Its inputs: land the managers at the start of the step (@land); capitals the stack, by name; demand the table; step the row of the demand to use (@step); seed the seed of its random numbers. Its settings:
  • afts, the list of AFTs, in order (1 farmer, 2 forester). For each, production (here one service each, at most 1 per cell), sensitivity (the farmer depends on fertility with an exponent of 2, the forester on wood with 1), giving_up = 0.05 and giving_in = 0.1, and class, the land cover class written in the cover output for its cells.
  • search = 0.2: a fifth of the cells offered each step.
  • giving_up_rate = 0.2: a manager below its giving-up threshold leaves with a chance of one in five each step.
  • services (not set here): which column of the demand each service reads; by default every column, by its name.

Its outputs: land (1, 2, or 0 for unmanaged cells) for the next step, cover (the class of each cell's AFT, 0 unmanaged), and info, a table with a row per service (service 0 is the first in alphabetical order, here food, 1 timber): its demand, the supply_before the step and the supply after it.

From the command line, add outputs for what you want written:

[outputs.cover]
from = "simulation.cover"      # cover.tif, a band per step

[outputs.info]
from = "simulation.info"       # info.csv, two rows (food, timber) per step

terraflux run crafty.toml --out crafty

The 20 steps over 10,000 cells take a few hundredths of a second.

Read the results#

Supply and demand, step by step#

Enlarge

PlayStep

Three phases can be read in the chart and the maps:

1. Too much timber. At the start half the cells are foresters, whose timber (2,950 before the first step) is twice the demand of 1500. The utility of timber is 0, so the foresters' competitiveness is 0, below their giving-up threshold, and a fifth of them leave at each step. Within three steps the supply of timber falls to the demand, and almost 30 % of the land is unmanaged.
2. Timber balanced, food short. From step 4 the timber supply stays close to 1500, a little below it: as soon as it rises above the demand, foresters become uncompetitive and some leave; as soon as it falls below, foresters take cells back. Food is short from the start, so farmers take the unmanaged cells and some of the foresters' cells where fertility is high.
3. A demand the landscape cannot meet. The food demand grows by 100 a step, the supply by about 50. If every one of the 10,000 cells were farmed, the landscape would produce 2,953 of food (the sum of fertility²): from step 15 the demand exceeds what the land could ever give. At step 20, 63 % of the land is farmed and produces 2,317 for a demand of 3,400.

Enlarge

Why do 13 % of the cells stay unmanaged while food is short? The farmers' competitiveness on a cell is \(u_{food} \times \text{fertility}^2\). At step 20, \(u_{food} = (3400 - 2317)/3400 \approx 0.32\); on a cell of fertility 0.4 that is \(0.32 \times 0.16 = 0.05\), exactly the giving-up threshold. Farmers take such cells and leave them again; the unmanaged cells have a mean fertility of 0.41, against 0.59 on the farmed ones. They are marginal land, not worth farming at the value food has.

How to report it#

Report the AFTs with their production, sensitivities and thresholds (a table), the capitals and how they were scaled, the demand scenario, the search and giving-up rate, the number of steps and the seeds. Show the supply against the demand of each service over time (the chart above), the land cover at the end, and the share of unmanaged land. Compare scenarios of demand, and of behaviour (the thresholds), rather than presenting one run as a forecast.

Settings that change the answer#

The share of cells offered each step#

search sets how fast the land can respond: only the offered cells can change hands. Move the slider to see the land after 20 steps with 5 %, 10 %, 20 % and 40 % of the cells offered each step; the chart shows the food supply over the steps for each.

Enlarge

Playsearch

With 5 % of the cells offered, the land lags far behind the demand and almost a quarter is still unmanaged after 20 steps; with 40 %, it follows the demand closely until it reaches what the landscape can give. In CRAFTY, the share of land that changes hands each year is a property of a region (how active its land market is), and with yearly steps a few per cent is realistic. A model whose steps are years and whose search is 0.4 describes a land market far more fluid than any real one.

Giving in#

With a giving-in threshold of 0, a manager gives way to any AFT even slightly more competitive, and cells change hands a third more often: the land reorganises faster and meets more of the food demand. From 0.3 on, nothing changes: competitiveness here never exceeds about 0.3 (a utility of at most 1 times a production of at most 1, and much less in practice), so no AFT can ever beat an incumbent by that much, and only cells that were abandoned change hands. A threshold above the range of competitiveness switches take-overs off: check the range of \(C_a(i)\) in your model before choosing thresholds.

Giving up#

The giving-up threshold and rate decide how much land is abandoned when a service is oversupplied, as timber is at the start here. A high threshold with a high rate empties land quickly (the 30 % unmanaged of step 6); a threshold of 0 keeps every manager in place, whatever the demand. Try giving_up = 0 for the foresters in the template: timber stays oversupplied for the whole run.

Common pitfalls#

Capitals outside 0 to 1. Production uses \(k^e\) with \(k\) clipped to 1; a capital in raw units (a growing stock in m³/ha) is clipped to 1 almost everywhere, and the AFT sees a uniform landscape. Rescale every capital to 0 to 1 first, with raster.calc or nlm.rescale.

Capital names that do not match. Sensitivities name layers of the capitals stack. A sensitivity to a capital that is not in the stack stops the run with an error naming it; a capital the AFTs do not name is ignored. Name the layers with stack.of inputs (or stack.set).

Land codes that do not match the AFT list. The land map holds 1, 2... in the order of afts, 0 for unmanaged. A land cover map with its own codes (say 2 cropland, 5 forest) must be reclassified first; cells with codes beyond the number of AFTs are treated as unmanaged.

A demand in other units than the production. If a farmer on full capitals produces 1 and the demand is in tonnes, the utilities are always near 1 (the supply is tiny) or always 0. Express production per cell in the units of the demand (tonnes per cell per year), or scale the demand.

A demand beyond the landscape. Compute the most the landscape could produce of each service (the sum over cells of the best AFT's production) and compare it with the demand. Here the food demand passes it at step 15: the model can only show the shortfall.

Reading one run. The giving up and the order of the offered cells are random. Run several seeds (terraflux submit --replicates) and report the range.

Going further#

• A coupled model makes the demand come from a population of agents and lets parcel managers change the capitals.
• Agents builds individual agents with their own state.
• CLUMondo meets a demand for goods and services with land systems of different intensities.
• The operator: crafty.allocate.

References#

• Brown, C., Holzhauer, S., Metzger, M. J., Paterson, J. S., & Rounsevell, M. (2018). Land managers' behaviours modulate pathways to visions of future land systems. Regional Environmental Change, 18(3), 831–845. https://doi.org/10.1007/s10113-016-0999-y
• Brown, C., Seo, B., & Rounsevell, M. (2019). Societal breakdown as an emergent property of large-scale behavioural models of land use change. Earth System Dynamics, 10(4), 809–845. https://doi.org/10.5194/esd-10-809-2019
• Murray-Rust, D., Brown, C., van Vliet, J., Alam, S. J., Robinson, D. T., Verburg, P. H., & Rounsevell, M. (2014). Combining agent functional types, capitals and services to model land use dynamics. Environmental Modelling & Software, 59, 187–201. https://doi.org/10.1016/j.envsoft.2014.05.019