Defining agricultural value: derivation of break-even yields. The agricultural value of land was modeled as follows: First, we used logistic regressions (McCullagh ...
Appendix S1. Additional methodological details Defining agricultural value: derivation of break-even yields The agricultural value of land was modeled as follows: First, we used logistic regressions (McCullagh & Nelder 1989) to calculate the probability that a given area is used to farm maize or wheat. logit(θ) = β0 + β1 Y + β2 R
(1)
Where logit(θ) is the probability that an area is farmed for maize or wheat, transformed to allow a linear fit to the predictors, Y is the estimated yield for the crop (in kg ha−1 ), R is an index (expressed in meters) of topographic ruggedness (hereafter “ruggedness”) describing the elevational variation in a particular area, and β0−2 are the estimated parameters. We hypothesized that for a given ruggedness, currently farmed areas would have higher yields than unfarmed areas. Thus, for each ruggedness value, there exists a yield value that distinguishes between farmed and non-farmed areas, and this value is the “break-even” yield, above which conversion to agriculture, on average, maximizes the farmer’s welfare (Green 2012; Naidoo & Adamowicz 2005). As ruggedness increases, the break-even yield also increases. To find the break-even yield, we first found the average logit(θ) for farmed and non-farmed areas for different levels of ruggedness: (logit(θfarmed,Ri ) + (logit(θunfarmed,Ri ) (2) 2 Where BE denotes the break-even value of logit(θ), which is the mean (or midpoint) of the average farmed and non-farmed logit(θ) for a given ruggedness, the midpoint of a discrete interval of ruggedness. We used equation (2) for all intervals (i ) of ruggedness, and fit a linear function through the resulting values to find the values of logit(θ) for all possible values of ruggedness. We then solved for the break-even yield (YBE ) values by rearranging the logistic regression equation: logit(θBE,Ri ) =
YBE =
−(β0 + β2 R − logit(θBE,R )) β1
(3)
Subtracting the break-even yield from estimated yield thus indicates the potential benefits of farming a given unit of land. If the remainder is positive, then farming is likely to be profitable, whereas a negative remainder suggests that farming costs outweigh benefits. These values are expressed in units of cereal productivity (kg ha−1 ). Converting these remainders into production values (expressed in metric tonnes) and integrating over a defined area yielded the area’s agricultural value. A negative value (e.g. -1000 tonnes) means that farming the area would result in a yearly loss equivalent to what could be earned by selling 1000 tonnes of the crop. A positive value (e.g. 1000 tonnes) indicates that, by not farming, the land user is forgoing a potential annual profit equal to the value of 1000 tonnes.
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Crop modeling methods In this study, we used the wheat and maize yield simulations developed by Estes et al. (2013b) and Estes et al. (in review 2013a). The former describes the soil, historical weather data, and model development and testing procedures applied for DSSAT-CERES Maize model used to simulate baseline (i.e. present day, here represented by the years 1979-1999) maize yield and suitability. The latter provided the baseline simulations for the DSSAT-CERES Wheat model, as well as future projections for wheat and maize yields for the 2046-2065 period. We summarize here the datasets and model development approaches. Detailed descriptions of the methods can be found in the two papers mentioned. Soil and weather data The soil data necessary to run DSSAT (soil drainage rate, horizon depth, wilting point, field capacity, saturated moisture content, bulk density, and organic carbon content) were derived and mapped using pedotransfer functions applied to mapped soil units in South Africa’s Land Type database (SIRI 1987). Baseline weather data were provided by the South African Quinary Catchment database, which links climatological to 5,838 water catchments (mean area = 135 km 2 ) covering South Africa, Lesotho, and Swaziland (Schulze & Horan 2010). We used these baseline data to downscale and bias-correct an ensemble of 9 Coupled General Circulation Models (CGCMs) run under high (A2) and low (B1) emissions scenario (Nakicenovic & Swart 2000) using the self-organizing maps method of Hewitson & Crane (2006). These procedures were applied to the following CGCMs: CCCMA-CGCM3.1, CNRM-cm3, CSIRO-mk3.5, GFDL-CM2.1, GFDL-CM2.0, IPSL-CM4, MIUB-ECHO-G, MPI-ECHAM5 and MRI-CGCM-2.3.2. This procedure resulted in 18 daily weather records for the 2046-2065 period, which were used to run the DSSAT models. Model training and validation
We ran DSSAT using management parameters that represented typical South African wheat and maize management practices. These were derived from cultivar trial data and industry literature, and included parameters for planting dates, row spacing, planting density, nitrogen fertilization (32 kg ha− 1), and cultivar choice. The planting parameters were allowed to vary according to mean annual rainfall. Cultivar coefficients representing a generic short-medium season variety were used for maize, and for wheat we selected coefficients for an Australian cultivar grown in similar climates. DSSAT models were set to automatically sow when plant available water content was ≥ 70%, provided sowing occurred within a predetermined date window that fell within each crop’s typical planting season. Since planting parameters could vary according to mean rainfall and soil moisture content, our simulations incorporated some management adaptation, although this proved to have a negligible effect. We validated DSSAT using remotely sensed yield proxies, which were integrals of normalized difference vegetation index (NDVI) values recorded by the Moderate Resolution Imaging Spectrometer (MODIS; source: http://lpdaac.usgs.gov). NDVI time series were collected from known crop locations (drawn from 14,736 observations of maize and 1,355 for wheat collected by aerial crop censuses during 2006-2009; (Fourie 2009; SiQ 2007)) within defined crop field boundaries (GeoTerraImage 2008). DSSAT’s baseline simulated wheat and maize yields respectively explained 40% and 37% of variance in the NDVI yield proxies 2
aggregated to 20 km resolutions. At to the provincial scale, the maize model explained 67% of variance in reported yields for 2006-2009 (Crop Estimates Committee 2011). Potential crop production regions
We identified potential crop production regions using threshold values of yield and the coefficient of variation (CV) in yield. These thresholds were determined by extracting simulated yield and yield CV values from known crop locations (the aerial census points) and from randomly selected crop absence points falling beyond the outermost crop census points. The selected thresholds maximized the true positives (the number of actual crop observation points falling above the threshold value for yield and below the threshold value for yield CV) and true negatives (the number of randomly selected non-crop points falling below the threshold value for yield and above the threshold value for yield CV). We used these thresholds to create binary suitability maps for each crop in the baseline period, and from each of the future yield simulations. The accuracy of baseline suitability maps was assessed against observed suitability surfaces derived using kernel density estimates of crop fields falling within the observed maize and wheat distributions. The maize suitability model was 86% accurate, and the wheat suitability model was 95% accurate, although it had a fairly large commission error of 53% due to the small size of the wheat production region relative to the rest of the country. Crop yield projections
As described in the main text, 36 yield projections were run for each crop, 18 in which the crop models’ CO2 levels were set to projected future concentrations, and 18 in which they were set to observed ambient concentrations for the 1979-1999 period. These low CO2 treatments assumed that crops will experience no photosynthetic or water use efficiency gains under elevated CO2 , and they were run to assess how much model simulations of crop response to elevation CO2 affected projections. The differences between the median yield projections for each treatment showed 16% higher yields for maize under elevated CO2 and 28% gains for wheat. The median model projections under the high CO2 treatments showed a 7% gain in maize yields and a 27% increase for wheat. For the low CO2 treatments the median yield changes were -9% for maize and +1% for wheat. Estimating current agricultural values: Model-fitting and assessment steps To fit the logistic regression model (Appendix S1) we used geo-referenced maize (n = 11,390) and wheat (n = 1,183) observations collected during annual aerial censuses of South Africas crop growing regions (SiQ 2007, and see Appendix S1), to represent crop presences, the positive case in the binomial response variable. To represent the negative (absence) case, we selected points from unfarmed areas within the suitable crop growing regions. To define unfarmed areas, we first merged each crops modeled and observed suitability maps (Estes et al. 2013b), and then excised from these surfaces a digital map of South African crop field boundaries (Fourie 2009). The remaining areas represented potentially suitable land for growing these crops that is not currently farmed. We randomly selected subsets of the crop observations points (2000 maize, 888 wheat) and placed equal numbers of random points on the unframed land use maps. We extracted the modeled yield and ruggedness values for 3
each point, used these to fit the logistic regression model, and then calculated the breakeven yield values (Eq. 2-3), repeating this for 1000 iterations. We assessed logistic regression model fit using the area under curve (AUC) of the Receiver Operating Characteristic curve (Fielding & Bell 2002). We also used binary classification metrics to assess how effectively break-even yield values distinguished between crop and non-crop observations. We classified crop field observations as either true positives (TP) or false negatives (FN), depending on whether their estimated yield values were either greater or less than the break-even yields for their corresponding ruggedness values. Non-crop points were classed as true negatives (TN) if their yield values were below the break-even yield, or false positives (FP) if above. These four categories were used to calculate the classification accuracy of the break-even yield function: TP+TN (4) TP+FP+TN+FN We constructed 95% confidence intervals for each model parameter and accuracy measure using their 2.5th and 97.5th percentile values resulting from the 1000 iterations. We used the mean break-even yield intercept and slope to calculate the final break-even yield map for each crop from the ruggedness map, which we then subtracted from the corresponding modeled yield maps, and converted to units of production (tonnes). Accuracy = 100
Comparing agricultural values between croplands and conservation lands Since crop field values were collected from individual grid cells, and each conservation land’s potential is the integral of agricultural values from all of its agriculturally suitable cells, we first found the average agricultural value for all agriculturally suitable cells falling within each conservation land before comparing the distributions of agricultural values from conservation lands to those from crop lands. This allowed comparison on the same scale.
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Green, J., 2012. Incorporating Costs and Processes into Systematic Conservation Planning in a Biodiversity Hotspot. Ph.D. thesis, University of Cambridge, Cambridge, UK. Hewitson, B. and R. Crane, 2006. Consensus between GCM climate change projections with empirical downscaling: precipitation downscaling over South Africa. International Journal of Climatology 26(10):1315–1337. McCullagh, P. and J. A. Nelder, 1989. Generalized Linear Models. Chapman and Hall, New York. GeoTerraImage (member of National Crop Statistics Consortium), 2008. South African crop field boundaries. Technical report, http://www.geoterraimage.com. Naidoo, R. and W. Adamowicz, 2005. Economic benefits of biodiversity exceed costs of conservation at an african rainforest reserve. Proceedings of the National Academy of Sciences of the United States of America 102(46):16712–16716. Nakicenovic, N. and R. Swart, 2000. Special Report on Emissions Scenarios. Cambridge University Press, Cambridge. Schulze, R. and M. Horan, 2010. Methods 1: Delineation of South Africa, Lesotho and Swaziland into quinary catchments. In R. Schulze, B. Hewitson, K. Barichievy, M. Tadross, R. Kunz, M. Horan & T. Lumsden, editors, Methodological Approaches to Assessing EcoHydrological Responses to Climate Change in South Africa, pages 63–74. WRC Report 1562/1/10, Water Research Commission, Pretoria, South Africa. SiQ, 2007. Point frame sampling: Producer independent crop estimate system (PICES). http://www.siq.co.za. SIRI, 1987. Land type series. In Memoirs on the Agricultural Natural Resources of South Africa. Soil and Irrigation Research Institute, Department of Agriculture and Water Supply, Pretoria, South Africa.
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