de Oliveira Silva et al. reply —

Goulart et al. make some interesting observations about the context of our study, its modelling assumptions and data. We clarify these issues but refute that our study is unrealistic or misleading. Indeed, we have been conservative with some assumptions and it would be possible and plausible to accentuate the counterintuitive result we present.

In our reference to sustainable agricultural intensification (SAI) we note the contested nature of the concept and do not imply a comprehensive characterization of the term. This includes the equity and governance trade-offs undoubtedly encountered in more granular research on mitigation. Our contribution provides one mathematical example of a plausible SAI scenario developed at a meaningful scale. We hope it partly fills a conspicuous gap in the literature, largely populated by normative conceptual papers rather than 'empirically based mechanisms' that might form policy evidence.

We suggest that the scenarios are based on sound empirical evidence, referenced in our supplementary information. This includes the recently observed decoupled livestock deforestation (DLD) scenario that resulted from more rigorous deforestation control and a changing market environment1,2. The DLD contrasts with the coupled livestock deforestation scenarios, which encompass worst case assumptions about how deforestation responds to demand. We suggest these are likely to accommodate potential Jevons paradox effects.

The profit maximization assumption is contestable, but we note that alternative assumptions are no less subjective. Furthermore, deviations from profit maximization will not significantly affect the results or main conclusions. This is because the level of intensification is not based on profit maximization, as land availability and demand are exogenous to our model. In unreported analysis other objective functions were tested (for example, minimization of land use change) with similar results.

While important, the heterogeneity of local ecosystem dynamics and gamma diversity are largely beyond the resolution of the model we employed. Nevertheless, we can draw some conclusions in relation to the impacts of intensification on biodiversity. We contest the characterization of large intensive farms versus smallholdings suggested by Goulart and co-authors: recent monitoring suggests the opposite3,4,5. Due to legal enforcement, large ranchers are reducing deforestation to avoid prosecution, while significant deforestation is attributable to smallholders1.

There is considerable experimental and practical evidence showing that pasture recovery can be accomplished with fertilization in much of the Cerrado6. Moreover our scenarios account for all related greenhouse gases using a life cycle approach. Since little nitrogen is applied in the Cerrado7, the issue of water pollution is negligible. Water consumption for intensification measures is also small, demand being mostly for livestock. On deforestation emissions, we suggest that it is impossible to know in advance where deforestation is going to happen in the biome for the period of study. We are confident that alternative assumptions on which physiognomies would be converted to grasslands would be at least as open to being contested.

The study proposes recovery of degraded areas already planted with exotic grasses. We stated that recovery strategies are based on existing Brachiaria spp. pastures as the preferred species for pasture recovery, productivity and costs (see supplementary information). We also note evidence that degraded pastures have worse effects on ecosystem function than productive pastures8. The use of native Cerrado species for cattle production is of minor importance9.

Finally, there is no reason to believe that land would be abandoned or taken out of production within the demand range we studied. Note that the scenarios were based on projections to 2030. Even in the demand scenario of 30% below baseline (DBAU–30%) productivity would remain approximately at the current level.