## 2 Experimental Section
### Change in the Land Cover Nesting Structure  
The GTAP-BIO model divides the managed land cover of each region into three broad land categories of cropland, forest, and pasture by AEZ. Cropland denotes existing cultivated land. Managed forest represents all types of forests, and pastureland covers all types of range, grassland, and pasture. Pasture does not include shrubland, which cannot be converted to cropland in GTAP. In this model land can move from one type to another type subject to economic and biophysical constraints. For example, a low productivity pasture will not be converted to cropland when a more suitable land is available for conversion. The supply of and demand for land are modeled at the AEZ level. The derived demands for cropland, forest and pasture are determined from the production functions of crop, forest, and livestock sectors. The land supply side of the model represents a land allocation CET process. The implemented land supply structure of the earlier versions of the GTAP-BIO model put forest, pasture, and cropland in one nest and assumed that forest and pasture land can be converted to crop land with identical rates of land transformation elasticities. This implies that land can be converted from forest and pasture to cropland with equal ease and/or economic opportunity cost. In the real world often it is not as easy or inexpensive to convert forest to cropland as pasture. For example, farmers frequently switch back and forth from pasture and grassland to crop production and _vice versa_ in the Northern Plains regions of the USA (including parts of Iowa, Minnesota, North Dakota, South Dakota and Montana) [20] where converting grasslands to crop production and _vice versa_ is not costly. However, transforming managed forests to cropland is not a common practice. In general, per hectare cost of converting one type of land to another type is equal to the difference in their present values per hectare [21], the value of each type of land is equal to the net present value of its future annual net return/rent, and the net present value of land can evaluated by its annual rent over a discount rate. [PERSON] _et al._[21] have shown that in general pasture land rent is higher than forest land rent, and both of these land rents are smaller than cropland rent across the world except in a few places. This means that the net costs of converting pasture land to crop production should be less than the net costs of converting forest to cropland. Putting forest, pasture, and cropland in the same nest ignores this important fact. To remove this deficiency, we created a new land supply nesting structure, shown in the bottom panel of Figure 1, which has cropland and pasture in one nest and the substitution between forest and the combined \"_pasture-cropland_\" in the second nest. In this paper we use the notation \"_pasture-cropland_\" for the combination of pasture and cropland in the land supply tree. We continue to use the notation \"cropland pasture\" for low productivity cropland which has been cultivated in past but is not under crop production at present. In the new nesting structure parameter \(\rm{ETL1_{F}}\) shows the land transformation rate between forest and combined pasture-cropland, parameter \(\rm{ETL1_{P}}\) indicates the land transformation rate between cropland and pasture land, and parameter \(\rm{ETL2}\) represents the rate of land transformation among cropping activities as usual. To take into account the fact that converting pasture land to cropland is easier and/or less costly than converting forest to cropland, it is assumed that in each region the value of \(\rm{ETL1_{P}}\) is \(\rm{\alpha}\) percent larger than the value of \(\rm{ETL1_{F}}\). Note that, in the absolute term, the higher the value of land transformation elasticity the lower the economic cost of land transformation.