# **2.4 Methods and assumptions**

Our analysis is based on several key assumptions. First, we assume that any urbanization that occurs on current land used for crop and livestock (i.e., as of 2010) will result in a significant impact on the agricultural production there. Specifically, such an overlap could culminate in either a loss of crop or livestock previously produced on the piece of land, or it could lead to a proximity of urban and agricultural functions, which may alter agricultural production cycles and scales.

Second, for the baseline condition, since the urban expansion data use 2015 as the starting year, any crop or livestock that overlap with the 2015 urban extent are _not_ counted toward the initial agricultural production (see Table 2). Consequently, only crop and livestock outside of the 2015 urban extent are aggregated for the baseline quantity of crop and livestock production. This would lead to eliminating about 2- 6 percent of crop or livestock production in the data (see Table A1.6).<sup>9</sup> Third, we assume no further expansion of land used for crop and livestock beyond its footprint in 2010. To clarify, the potential impact on crop and livestock production is calculated based on how much future urban expansion is projected to extend into current land used for crop and livestock production. This assumption is made despite acknowledging that a growing global population would entail increasing crop and livestock demands in the future. While such intricate dynamics would affect impacts on crop and livestock production, it is beyond the scope of this paper to devise robust models for future land uses.

Fourth, we assume that receding urban frontiers does _not_ replenish land used for crop and livestock production. To elaborate, while the data from Chen et al. (2020) shows that across different SSP scenarios, urban extents could in fact decrease in some parts of the world, in part due to declining urban populations, we assume that these urban contractions will not result in land being reclaimed for agricultural use. Urban contractions may have implications for crop and livestock production. This assumption is based on historical trends, while shrinking cities often leads to vacant land and deteriorating infrastructure, rather than reconversion to land uses prior to urbanization (Florentin 2019). Therefore, once an area for crop and livestock production becomes urbanized, the production there is assumed to be part of the estimated production loss permanently. The urban expansion projection data, available in 10-year intervals, are used as proxies to estimate the cumulative urban extent around the world.

Based on the above assumptions, we adopt the following method for our analysis: First, raster calculations are performed to derive the areas of urban expansion for 2040 and 2100 for all five SSP scenarios. Since we assume that the potential impact on crop and livestock production due to urbanization is irreversible, we use cumulative urban extents for each time period. For example, to calculate the urban expansion for 2040, we overlay urban projections for all previous decades (2020, 2030, and 2040). Any area that has ever been marked as urban is considered part of the cumulative urban extent, regardless of whether the area subsequently deurbanizes or not.<sup>10</sup> Following this, we calculate the percentage of the urban extent that is _newly urban_ compared to

> 9 Table A1 in the Annex displays the overlap percentages between food production and urban extent in grid cells. 10 This assumption holds true for any of the years preceding the 10-year interval from 2010 to 2100. Only 3 years of dataset are extracted to analysis for this working paper; 2010, 2040 and 2100.

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