Table 1 Description of the future deforestation scenarios formulated within this study

Normative models

 Historical average (HA)

Past observed yearly deforestation over 2001–2014 continues until 2050

\(CDef_{t, c}^{HA} = logN\left( {Def_{c}^{HA} + \log \left( {t + 1} \right); \sigma } \right)\) with CDef ^HA _{t, c}   the cumulated deforestation over t0−t, for country c under the HA scenario, and Def ^HA _c and σ are the model parameters. Def ^HA _c was estimated as the yearly average observed deforestation in country c during 2001–2014

 Economically rationale baseline (ERB)

All forested areas excepted integrally protected areas and indigenous territories are deforested by 2050

\(CDef_{t,c}^{ERB} = \log N\left( {Def_{c}^{ERB} + \log \left( {t + 1} \right);\sigma } \right)\) with CDef ^ERB _{t, c} the cumulated deforestation over t0−t, for country c, under the ERB scenario. Def ^ERB _c corresponds to the log of the total area assumed to be deforested in country c divided by 35 (so that all available lands would be deforested between 2015 and 2050)

 Joint Research Center Proposal (JRC)

Countries adjust their level of deforestation to half of the global average, assumed to be linearly decreasing and reach 0 in 2050 (JRC2050) or 2100 (JRC2100)

\(CDef_{t,c}^{JRC} = logN(\mathop \sum \limits_{2015}^{t} Def_{t,c}^{JRC} , \sigma )\) with \(Def_{t,c}^{JRC} = (\frac{1}{2}WDR_{0} - \alpha t) \times FC_{t,c}\) WDR₀ is the world annual initial deforestation rate. Within the present study, we chose its value according to estimates used within the Guyana-Norway agreement, corresponding to deforestation rates in developing countries only, and giving a value of 0.52% [33]. α = 0.0029 is the coefficient associated with the linear decrease in world deforestation rates (reaching zero deforestation in 2050 or 2100). FC_t,c corresponds to the forest cover of country c at time t in hectares

 Combined Incentives (CI)

Scenarios proposed within the Guyana/Norway agreement. The Business-As-Usual scenario (CI-BAU) assumes an annual deforestation rate equal to half of the deforestation rate of developing countries, or 0.275%. The most ambitious scenario, where full payments (FPS-CI for Full Payment Scenario) would be granted to Guyana assumes a yearly deforestation rate of 0.056%. Payments were assumed to decrease if deforestation increased above the FPS-CI, reaching value 0 for an annual deforestation rate above 0.1% (NPS-CI for No Payment Scenario)

\({\text{CDef}}_{{{\text{t,c}}}}^{\text{CI}} = {{\text{logN}}(\sum \limits_{2015}^{\text{t}}} {\text{Def}}_{{{\text{t,c}},}}^{\text{CI}} ;\sigma )\) with \({\text{Def}}_{{{\text{t}},{\text{c}}}}^{\text{CI}} = {\text{CI}}^{\text{S}} \times {\text{FC}}_{{{\text{t}} - 1,{\text{c}}}}\) CI^S is the rate of deforestation assumed in each scenario s (among BAU, FPS or NPS). FC_t-1,c is the forest cover in country c at time t−1 in hectares

Socio-economic models

 Gold-mining model (GM)

Yearly deforestation was explicitly modelled using population increase and gold prices as explanatory variables. Only one hypothesis was made regarding population increase within each country, while two scenarios were formulated with a low (GM-low) and high (GM-high) gold price, corresponding to the yearly average price over 2001–2014 and the double of the maximum price over the same period respectively (3077 USD/ounce)

\({\text{Def}}_{{{\text{t}},{\text{c}}}} = {\text{Def}}_{{{\text{t}},{\text{c}}}}^{\text{GM}} + {\text{def}}_{{{\text{t}},{\text{c}}}}^{\text{Dem}}\) with \({\text{Def}}_{{{\text{t}},{\text{c}}}}^{\text{GM}} = {\text{logN}}(\uptheta_{{0,{\text{c}}}}^{\text{GM}} +\uptheta_{\text{c}}^{\text{V}} \times \log \left( {{\text{GoldPrice}}_{\text{t}} } \right), \sigma^{\text{GM}} )\) and \({\text{Def}}_{{{\text{t}},{\text{c}}}}^{\text{Dem}} = {\text{logN}}(\uptheta_{0}^{\text{Dem}} +\uptheta_{1}^{\text{Dem}} \times \log \left( {{\text{PopCh}}_{\text{c}} } \right);\sigma^{\text{Dem}} )\)

[15, 30]