On-line Appendix 1
We describe the usage of the FEARLUS model (Polhill et al. 2010; Polhill et al. 2001) here using Grimm et al.’s (2010) ODD protocol, but omitting the Design Concepts section.
Purpose
The purpose of the model is to compare the choices made by land managers in stylised climate change scenarios in which farmers are or are not given subsidies for grass that make the financial return equivalent to cereals.
Entities, state variables and scales
The agents in the model are farmers, divided into two subpopulations: farm businesses and hobby farmers. Each farmer owns one or more land parcels, for each of which they choose between land uses grass and cereals using a decision-making algorithm. Hobby farmers simply choose grass, whilst farm businesses use a case base to make the decision if their profit does not meet their individual aspiration or their tolerance for higher profit made by neighbours. The land parcels have biophysical characteristics that affect the yield of the choice their owner makes. An economic return is computed for each decision, which allows farmers to gain or lose wealth into their account. There are two scenarios, one in which a Government offers a subsidy for grass effectively giving it the same economic return as cereals (scenario A), another in which no such subsidy operates (scenario B). Farmers with negative account go bankrupt, and their land parcels sold to neighbours or to a single in-migrant land manager. Hobby farmers have off-farm income, but may sell their land without going bankrupt (probability 0.1 each year). A UML class diagram is shown in figure 1.
Figure 1. UML class diagram for this set-up of FEARLUS. The grass and cereals objects are shown for the sake of clarity, and the Government class in grey as it operates only in scenario A.
Process overview and scheduling
The following cycle is repeated for the duration of the simulation:
1. Land managers choose between grass and cereals
2. Computation of economic return
3. Sale of land parcels belonging to bankrupt land managers
Initialisation
Farm businesses start with an initial account of 2000, hobby farmers with an initial account of 0. The landscape is initialised with the land uses and biophysical characteristics shown in figure 2. All land managers are initially farm businesses.
Figure 2. Initial land uses (left: beige = cereals; green = grass) and biophysical characteristics (right – see scale for values) of land parcels.
Input
The climate and economy time series are inputs to the model. The climate affects the yield, and the economy the price per unit yield. After a burn-in period of 150 time steps, the climate increases linearly from 0 to 2. The economy always offers a higher price for cereals than for grass, again with a 150-step burn-in period. In scenario A, however, a subsidy operates such that the price for grass is the same as that for cereals.
Figure 3. Time series for climate (left) and economy (right: beige line = cereals; green line = grass). Note that the price for grass is effectively the same as that for cereals in scenario A.
Submodels
1. Land managers choose between grass and cereals
Hobby farmers always choose grass. Farm businesses first decide whether to review land use. If they are not happy with the profit they make, then they review the land uses they apply to their parcels using case-based reasoning, otherwise they make no change. Two tests are used to determine this ‘happiness’: first, whether they have made sufficient profit to meet their own aspirations; second, whether they have made sufficient profit in comparison to that made by their neighbours. Each farm business’s case base stores their experience of using cereal and/or grass on the parcels they own in the economic and climatic conditions they have experienced. As shown in figure 4, a decision is made by generating an expected state assuming the climate and price will not change, and then using the case base to construct an estimated utility for applying each of the two land uses based on the economic return obtained in their best-matching experience for the expected state. If they do not have a relevant case, they will ask their neighbours in descending order of profit made; if this fails to provide a case to use to estimate utility, then the utility is estimated by assuming the land use will meet their individual profit aspirations.
Figure 4. UML activity diagram of the decision making process for farm business agents.
2. Computation of economic return
Economic return is computed as the product of yield and price per unit yield, minus a break-even threshold (630 per land parcel). In scenario A, the government pays the farmer the difference in price between cereals and grass, such that effectively the two land uses have the same price per unit yield. In scenario B, the prices are different, as shown in figure 2. The yield for grass is the sum of the biophysical characteristics of the parcel and the climate in the current time step. The yield for cereals is the same as that for grass, except that it is zero if the sum of biophysical characteristics and climate is less than 9. In addition to the economic return from the land use choice, hobby farmers get an off-farm income of 800.
3. Sale of land parcels belonging to bankrupt land managers
A farmer with negative wealth must sell all their land parcels. Hobby farmers will on occasion also choose to sell all their land parcels. Each parcel will be sold to one of the farm business neighbours who has sufficient wealth (4000) to buy it (hobby farmers do not buy parcels from their neighbours), or an in-migrant farmer. There is a uniform probability of selecting each of the potential buyers of the parcel: the neighbours and the in-migrant. The in-migrant farmer has a probability of 0.05 of being a hobby farmer rather than a farm business. If two or more of a bankrupt farmer’s parcels are sold to an in-migrant, then they will be sold to the same in-migrant. The buying agent has their account debited by 4000 units of wealth. In-migrant farmers start with an initial wealth of 0 after this debit has been made.
References for On-line Appendix 1
Grimm, V., Berger, U., DeAngelis, D. K., Polhill, J. G., Giske, J. and Railsback, S. F. (2010) The ODD protocol: A review and first update. Ecological Modelling 221 (23), 2760-2768.
Polhill, J. G., Sutherland, L.-A. and Gotts, N. M. (2010) Using qualitative evidence to enhance an agent-based modelling system for studying land use change. Journal of Artificial Societies and Social Simulation 13 (2), 10
Polhill, J. G., Gotts, N. M. and Law, A. N. R. (2001) Imitative versus nonimitative strategies in a land-use simulation. Cybernetics and Systems 32 (1-2), 285-307.