regions. SSP4 is also characterized by decreased collaborations between regions of the world with a decline of international trade flows.<sup>3</sup> SSP5, commonly labelled “Conventional development”, is characterized by much more investment in human capital and a decrease of inequalities and vulnerability to climate change. Under this scenario however, high economic growth is based on conventional technologies with high carbon and resource intensities, which increases the challenge for mitigation; international cooperation is high and characterized by strong trade relations. However, a lack of environmental consideration leads to patterns of consumption putting higher pressure on natural resources, particularly in terms of diets.<sup>4</sup> The SSP narratives aim to describe alternative futures in a comprehensive way, covering all sectors of the economy. Here, we have considered only a subset of the scenario elements, based on their relevance and compatibility with the model structure. . Table 1 summarizes the covered elements. The SSPs provide quantitative information for a handful of drivers, namely economic growth (GDP) and demographic change in terms of total population distributed by sex, age and education. The magnitude and direction of many other drivers is provided only qualitatively or semi‐quantitatively (O’Neill _et al._ , 2014). Semi‐quantitative drivers relevant for agriculture and forestry were quantified for this study mostly following the approach presented in Herrero _et al._ (2014).

Crop yield projections are estimated based on historical development over the period 1980‐2010 using an econometric relation linking the yields to GDP per capita development. The projections hence vary across SSPs and are performed for four classes of countries grouped by level of income (Herrero _et al._ , 2014). GDP per capita change has been selected as the explanatory variable because it can be considered as proxy both for resources available for investment in the necessary R&D and for the demand developments, and because it is provided quantitatively as part of the SSPs.

_Table 1. Differentiated drivers and their quantification the two SSPs used in this paper_

|**Driver**|**Method / Source**|**Scenario**|**pattern**|
|---|---|---|---|
|||**SSP4**|**SSP5**|
|**Population**|IIASA population<br>projection (Lutz_et al._,<br>2014)|High population growth<br>globally, due to high growth<br>rates in Africa and Asia|Low population growth<br>globally, due to low growth<br>rate in Africa and Asia|
|**GDP per capita**|OECD GDP projection<br>(IIASA, 2015)|Strong GDP per capita<br>growth in advanced<br>regions; moderate growth<br>in middle income countries;<br>low growth for least<br>advanced countries|Strong GDP per capita<br>growth in all regions of the<br>world|
|**Crop yield projection**|Growth rates<br>correlation with<br>patterns of GDP per|Strong yield growth for<br>advanced regions,<br>moderate yield growth in<br>middle income countries,|Strong yield growth for all<br>regions, with catching up of<br>middle income regions on<br>advanced regions.|

3 The SSP4 scenario is used as a backbone for the analysis of a “Poverty” case in the World Bank report on Climate Change and Poverty.

4 The SSP5 scenario is used as a backbone for the analysis of a “Prosperity” case in the World Bank report on Climate Change and Poverty due to the catching up patterns observed for income per capita in developing countries. In our analysis, SSPs and level of global warming are not considered correlated, making such an interpretation possible. It should be noted however that in practice, much higher cost would have to be supported by the energy sector to limit drastic increase in GHG emission levels. This question goes however beyond the scope of this paper 10