Supplementary Material
An agent-based approach to modeling impacts of agricultural policy on land use, biodiversity and ecosystem services
Mark Brady, Christoph Sahrbacher, KonradKellermann and Kathrin Happe
Table of Contents
Appendix S1. Algorithm for allocating production to plots
Appendix S2. Representation of study regions
Appendix S3. Initialization of virtual landscapes
Appendix S4. Calibration of species-area relationships
Appendix S5. Calculation of biodiversity at the landscape scale
Appendix S6. Details of agricultural policy payment schemes
Appendix S7. Validation of dynamic simulation results
References Appendix
Appendix S1. Algorithm for allocating production to plots
Since production levels generated by AgriPoliS represent profit maximizing levels given a particular set of model parameters, then a dual of this problem is to allocate optimal cropping levels across plots of agricultural land in the landscape such that the costs of producing crops are minimized. Farmers minimize the costs of crop production by growing their various crops, as far as is possible given crop rotation constraints, on contiguous areas of land. Given that farmers have maximized profits, the mathematical programme described by the equations below will allocate the optimal activity levels of a farm across the plots of land managed by the farm in the abstract landscape so that the costs of production are minimized:
where is the size of field and represents a contiguous area within farm-block allocated to cropping activity by farm l, is the optimal level of activity iprovided by the solution to farm l’s profit maximization problem, and is the size of the farm-block managed by the farm (i.e., contiguous plots of a particular soil type). In the problem statement above, reflects the diagonal value of the Q-matrix of the quadratic optimization problem. The ability to freely set each allows us to assign different weights to production activities, as farmers tend to allocate the most intensive crops to the largest fields (implying high q-value) and treat set-aside as a residual () to fill up area not used in crop production.
The data required to solve this problem are optimal activity levels and the farm-blocks managed by each farm. The solution is the set of fields that maximizes the sum of the square of field size subject to the constraints that total activity levels cannot exceed optimal levels and the sum of field sizes cannot exceed the area of contiguous plots of land. The nonlinear form of the objective function implies that larger fields are preferred to smaller. The quadratic form was chosen because it is straightforward to solve and provides a convenient way to represent farmers’ preferences for field structure via the Q-matrix.
Appendix S2.Representation of study regions
The study regions are represented in AgriPoliS by the selection and weighting of farms from the Farm Accountancy Data Network (FADN 2008) which consists of accountancy data from an annual survey of farms carried out by the Member States of the EU. For details of the procedure for simultaneously selecting and up-scaling farms see Sahrbacher and Happe (2008). In this section we compare the representation (i.e. creation and calibration) of the virtual case-study regions in AgriPoliS with the real regions according to official statistics. By calibration success we mean, how well is the observed structure of agriculture in the real region, in the reference year (2001), represented by the virtual region modeled in AgriPoliS. The quality of the virtual representation of a region in AgriPoliS depends primarily on three factors; i) the quantity and quality of the regional statistics where the main structural indicators are the size distributions of farms and livestock herds, ii) consistency of the regional data, meaning whether it is from the same source, and iii) the number of farms available in the FADN sample for the region. The quantity, quality and consistency of regional statistics for Sweden are high on EU standards. However the number of farms from Jönköping and Västerbotten Counties in the FADN sample is small, but this does not seriously affect the representation of the regions. These regions are quite homogenous and are dominated by family farms. Further, the variation in farm size is not excessively large and dairying is the most important livestock activity. Given this homogeneity, the diversity among farms in the sample is large enough to represent the regions well.
The results of the calibration procedure for Jönköping County are presented in Table S1 and those for Västerbotten County in Table S2. At the top of the tables we present general characteristics such as the total number of farms, total utilized agricultural area (UAA), and total number of livestock, and after that structural characteristics such as the number of farms per farm type and legal form, amount of arable land and meadows, number of farms per size class and number of animals per livestock size class. The second column of these tables contains the regional statistical data. Some minor adjustments to the regional data were however necessary. Farms smaller than 10ha have not been considered in the virtual regions for two reasons. First, the FADN-farm sample does not include such small farms, and secondly, the behavior of small or hobby farms cannot be represented in a MIP model under the assumption that they maximize their household income. There were also small discrepancies in the total number of dairy cows and in the sum of dairy cows by herd size in the statistics. Finally, only the major agricultural production activities in the regions are considered (i.e. arable crops, grass fodder, dairying, beef and lamb). The regional data were adjusted after consultation with the Swedish Board of Agriculture. Adjusted data are in bold font in the column ‘Considered’for each region inTables S1 and S2. The fourth column shows the weighted farm characteristics, i.e. the structure of the virtual region. The fifth column shows the relative deviations between the individual characteristics of the adjusted real region and the virtual region. The last column compares data from the virtual region to the regional data.
For Jönköping, the virtual region covers only 57% of the farms in reality, but they use 94% of the total UAA (due to the elimination of small farms). The deviation between the number of farms in the virtual region and the number of farms considered for the representation is only 2%. The maximum deviation of real to virtual characteristics for Jönköping is only 4%, which occurred for arable land and meadow. For all other characteristics, the deviation is smaller. If less structural indicators are available, the data are not consistent, and it is difficult to achieve a perfect representation of a region. This is the case for Västerbotten where the small number of FADN farms (32) affected the calibration somewhat negatively due to a lack of farms with meadow, farms between 50–100ha, and dairy cows in herds of 10–24. Consequently, one can say that the agricultural structure of Jönköping is very well represented in AgriPoliS whereas that for Västerbotten is less well represented but adequate.
Table S1Results of representation of Jönköping County in AgriPoliS
General characteristics / Regional Data / Considered and adjusted data / Virtual region / Deviation to considered data[1-(4)/(3)] / Coverage of the regional data [(4)/(2)]
(1) / (2) / (3) / (4) / (5) / (6)
Number of farms / 3824 / 22161) / 2165 / -2% / 57%
Utilised agricultural area (UAA; ha) / 134216 / 1252042) / 126704 / 1% / 94%
Number of beef cattle older than 1 year / 20403 / 20403 / 20605 / 1% / 101%
Number of dairy cows / 33158 / 33158 / 33322 / 0% / 100%
Number of suckler cows / 12173 / 12173 / 12262 / 1% / 101%
Number of ewes and rams / 8548 / 8548 / 8580 / 0% / 100%
Sows after the first mating / 4826
Fattening pigs / 14325
Structural characteristics
Area (ha)
Arable land / 91369 / 823572) / 85606 / 4% / 94%
Meadows / 42847 / 42847 / 41098 / -4% / 96%
Total / 134216 / 1252042) / 126704
Number of farms specialised in4)
Field crop farms (13, 14, 60) / 1166
Grazing livestock (41, 42, 43, 44) / 2054
Pig and poultry (50) / 19
Mixed farms (71, 72, 81, 82) / 931
Total / 4170
Number of farms in different size classes
2-10 ha / 1608
10-20 ha / 779 / 779 / 758 / -3% / 97%
20-30 ha / 438 / 438 / 433 / -1% / 99%
30-50 ha / 506 / 506 / 493 / -3% / 97%
50-100 ha / 400 / 400 / 389 / -3% / 97%
More than 100 ha / 93 / 93 / 92 / -1% / 99%
Total / 3824 / 2216 / 2165
Number of dairy cows per herd size class
1-9 / 474 / 4783) / 472 / -1% / 100%
10-24 / 5332 / 53743) / 5394 / 0% / 101%
25-49 / 14717 / 148323) / 14976 / 1% / 102%
More than 50 / 12377 / 124743) / 12480 / 0% / 101%
Total / 32900 / 33158 / 32322
Notes: 1) Farms with less than 10 ha arable land are not considered;a total of 1608 farms.
2) The total UAA was reduced by 5.6 ha for each of the 1608 farms not considered (or 7% of the UAA).
3) There is a small difference in the total number of dairy cows and in the sum of dairy cows by herd size, thus the number of each herd size is adjusted to the total number of dairy cows. Sources: Statistics Sweden (SCB 2003); 4) Swedish Board of Agriculture (SJV 2002).
Table S2Results of the representation of Västerbotten County in AgriPoliS
General characteristics / Regional Data / Considered and adjusted data / Virtual region / Deviation to considered data[1-(4)/(3)] / Coverage of the regional data [(4)/(2)]
(1) / (2) / (3) / (4) / (5) / (6)
Number of farms / 2506 / 15001) / 1469 / -2% / 59%
Utilised agricultural area (UAA; ha) / 74414 / 680322) / 69740 / 3% / 94%
Number of beef cattle older than 1 year / 7297 / 7297 / 7199 / -1% / 47%
Number of dairy cows / 15526 / 15526 / 16519 / 6% / 106%
Number of suckler cows / 1130 / 1130 / 1140 / 1% / 101%
Number of ewes and rams / 3857
Sows after the first mating / 2322
Fattening pigs / 15039
Structural characteristics
Area (ha)
Arable land / 70269 / 644233) / 66950 / 4% / 95%
Meadows / 4145 / 36093) / 2790 / -23% / 67%
Total / 74414 / 680323) / 69740
Number of farms specialised in5)
Field crop farms (13, 14, 60) / 1807
Grazing livestock (41, 42, 43, 44) / 745
Pig and poultry (50) / 21
Mixed farms (71, 72, 81, 82) / 544
Total / 3117
Number of farms per size class
2-10 ha / 1006
10-20 ha / 516 / 516 / 527 / 2% / 102%
20-30 ha / 250 / 250 / 248 / -1% / 99%
30-50 ha / 283 / 283 / 289 / 2% / 102%
50-100 ha / 328 / 328 / 278 / -15% / 85%
More than 100 ha / 123 / 123 / 127 / 3% / 103%
Total / 2506 / 1500 / 1469
Number of dairy cows per herd size class
1-9 / 299 / 3324) / 329 / -1% / 110%
10-24 / 3593 / 39924) / 4640 / 16% / 129%
25-49 / 6926 / 76964) / 8049 / 5% / 116%
50-74 / 2240 / 24894) / 2500 / 0% / 112%
More than 74 / 915 / 10174) / 1001 / -2% / 109%
Total / 13973 / 15526 / 16519
Note: 1) Farms with less than 10 ha are not considered. 2) The total UAA was reduced by 6.3 ha for each of the 1006 farms not considered.3) The area of arable and meadow is reduced according to the total UAA by keeping the relative proportions of arable and meadow.
4) There is a small difference in the total number of dairy cows and in the sum of dairy cows by herd size, thus the number of each herd size is adjusted to the total number of dairy cows.Sources: Statistics Sweden (SCB 2003); 5) Swedish Board of Agriculture (SJV 2002).
Appendix S3. Initialization of virtual landscapes
The values of the landscape initialization parameters used to create the virtual landscapes for Jönköping and Västerbotten Counties are specified in Table S3 (explanations provided in text associated with Table 1 in the main article). Two different types of arable land are initialized in Västerbotten to reflect the larger variation in yields in this region. Average and median block size are considerably smaller in Jönköping than Västerbotten (Table S4), hence the choice of smaller pixel size for Jönköping. The OVERSIZE is similar in both regions and creates more plots of each land type than are actually found in the region according to the formula The higher the OVERSIZE the greater the chance of a farm-agent being allocated contiguous plots close to the farm centre. The parameter NON_AG_LAND is set higher in Jönköping to achieve the greater fragmentation of blocks in this landscape (see Fig. 3). The overall size of the virtual landscape created by AgriPoliS is
After the allocation of agricultural land to farm-agents according to their resource endowments the area of non-agricultural land finally initialized in the virtual landscape will be the residual area, i.e., The landscape initialization procedure is exemplified in pseudo code in Fig. S1.
Table S3Landscape initialization parameters used to create virtual case-study regions
Parameter / Description / Jönköping / VästerbottenNO_OF_SOILS / Different soil types defined / 2a / 3b
PLOT_SIZE / Standard pixel size / 0.5 ha / 1.0 ha
OVERSIZE / Additional land initialized in region / 1.15 / 1.12
NON_AG_LAND / Share of non-agricultural land / 0.90 / 0.7
Notes: This table follows from Table 1 in the main article. a) The two soil types initialized for Jönköping are Arable_Land and Meadow_Land; b) The three soil types initialized forVästerbotten are Arable_Land_low, Arable_Land_high and Meadow_Land.
Fig. S1Initialization of the virtual landscape in AgriPoliS in pseudo code
To provide an indication of the accuracy of the landscape initialization procedure we compare the distributions of arable land blocks (contiguous areas of arable land type that are separated from other arable plots by either non-agricultural land or land type meadow) in the real landscapes with those of the virtual landscapes. In Table S4 we compare descriptive statistics of the distributions of block size for the real and virtual landscapes. As can be seen the mean and standard deviation of block size are almost identical for the real and virtual landscapes in both regions. Median block size is significantly lower in the virtual landscapes due to the minimum pixel size in the model landscape being set lower than the median block size in the real landscapes. Here a trade-off must be made and our landscape initialization then creates too many blocks comprising a single pixel.
Table S4Comparison of real and modelled landscapes based on size distribution of arable land blocks
Jönköping / VästerbottenStatistic / Reala
2001 / Modelb
2001 / Diffc / Reala
2001 / Modelb
2001 / Diffc
Total arable area / ha / 89 239 / 89 331 / <1% / 66 900 / 66 805 / <1%
Blocks / nr / 48 383 / 48 460 / <1% / 28 235 / 28 425 / <1%
- number > 2 ha / % / 25% / 22% / -12% / 39% / 27% / -30%
- total area > 2 had / % / 64% / 66% / <1% / 74% / 62% / -16%
Block size - mean / ha / 1.84 / 1.84 / <1% / 2.37 / 2.35 / -1%
- median / ha / 1.04 / 0.50 / -52% / 1.60 / 1.00 / -38%
- standard dev. / ha / 2.53 / 2.79 / 10% / 2.51 / 2.53 / 1%
- minimum / ha / 0.30 / 0.50 / 67% / 0.30 / 1.00 / 233%
- maximum / ha / 69.51 / 37.50 / -46% / 34.30 / 36.00 / 5%
a Real landscape statistics for blocks ≥ 0.3ha in calibration year, i.e. 2001 (SJV 2003). b Model landscape generated by AgriPoliS for 2001. c Percentage difference between real and modeled characteristic. d Total area of blocks greater than 2 ha in size.
This effect can be seen more clearly in the histograms in Fig. S1 which show the frequency of occurrence of blocks in different size classes in the real and virtual landscapes. Both the real and modeled distributions are heavily skewed to the left with a concentration of blocks about the mean and larger fields being represented by a flat tail (note the similarity of the frequency of large blocks in the real and virtual landscapes). Although AgriPoliS hasn’t been able to reproduce the exact distribution of blocks by size class it does represent the overall structure of the landscape in terms of large and small blocks well (which is important because of potential size economies in production). To demonstrate this we compare also in Table S4 the proportion of the arable area comprising blocks ≥ 2 ha (i.e. the size category 3 and above). As can be seen these are well represented for Jönköping with only a minor deviation between the real and virtual landscapes (i.e. <1%). A larger deviation occurs for Västerbotten with the number and total area of larger blocks being underrepresented. What is important in the context of this study is that the model landscapes provide an adequate representation of the real landscape for the purpose of analyzing the regional impacts of changes in agricultural policy. Overall the comparison of descriptive statistics and histograms indicate that the model landscapes are representative of the real landscapes, since they capture the general characteristics of each landscape.
Fig. S2Frequency of arable blocks by size in ha for the real and virtual landscapes a) Jönköping b) Västerbotten
Finally in Table S5 we list the land use categories used in the evaluation of landscape mosaic and calculations of mosaic indices for the baseline year 2004 according to the Shannon-Weiner Index, Eq. 2, (whereis the proportion of land use i in the virtual landscape in 2004).
Table S5Shannon-Wiener Index in 2004
Jönköping / VästerbottenLand use / / / /
Silage - intensive / 0.02 / 0.08 / 0.14 / 0.28
Silage - extensive / 0.16 / 0.29 / 0.11 / 0.24
Arable Pasture / 0.06 / 0.16 / 0.12 / 0.26
Arable Crops / 0.06 / 0.17 / 0.07 / 0.19
Meadow / 0.15 / 0.28 / 0.02 / 0.08
Forest / 0.55 / 0.33 / 0.53 / 0.34
Baseline Shannon-Weiner Index / 1.00 / 1.32a / 1.00 / 1.39a
Source: Calculations according to habitat areas in 2004. a Maximum possible index value 1.79
Appendix S4. Calibration of species-area relationships
The indicator used to evaluate the impact of policy reform on biodiversity is based on the number of unique species associated with particular agricultural habitat. Threatened species are by definition “unique” in some way. The Swedish Species Information Centre’s species database(ArtDataBanken 2005) contains information about the state of almost 20000 multi-cellular organisms found in Sweden. The status of each species has been assessed using the internationally accepted criteria for red listing established by the IUCN (2001). Of the species analyzed in Sweden some 3771 have been red-listed and 1735 classified as threatened; of these 488 reproduce in Jönköping and 505 in Västerbotten. Clearly a large number of threatened species are supported in these regions.
The red list is of course incomplete since it only considers species that have been studied in some detail. There are thousands of insects, beetles, etc. that have never been studied and hence lack the information required to red-list them. The red list has therefore been formulated in a fairly arbitrary manner but this is quickly changing thanks to the work of the Swedish Species Information Centre. Despite these limitations this is the best knowledge we have and is based on a systematic categorization that ensures lists for different habitats and regions are comparable. An important criterion is the geographic extent of the species which considers its occurrence in other regions or countries and hence its risk of extinction. Another criterion is a quantitative analysis of the risk of extinction within a specific timeframe. Overall the red-list not only provides an indication of a species local uniqueness but also, to a certain extent, on a global scale. Assuming that the red listdespite its incompletenessprovides a measure of the relative importance of various habitat for biodiversity value then our biodiversity indicator (Eq. 2) should provide a reliable measure of the relative change in biodiversity value, because the species-area relationshipis based on a homothetic production function.
Almost 46% of threatened species in Sweden reproduce in agricultural landscapes and 50% in forest landscapes. Generally speaking, biodiversity in Sweden increases from north to south. However, the competition for land is higher in the South and the proportion of protected land is lower, which partly explains why local extinction has been greater in the South. Jönköping, in the South, is one of the counties where local extinction has been highest (21%) and Västerbotten, in the North, lowest (9%) (ArtDataBanken, 2005). Tables S6 and S7 provide an overview of threatened species by group and agricultural habitat in each county. As can be seen meadow is the single most important habitat for conservation of biodiversity in these landscapes (which is also the case for Swedish agricultural landscapes generally). Unfortunately it was not possible for us to evaluate the impact of changes in the length of arable field edges explicitly (but represents potential for future development of AgriPoliS).