Our study area comprises all Tropical & Subtropical coniferous forest, Tropical & Subtropical Dry Broadleaf Forests, Tropical & Subtropical Moist Broadleaf Forests, and Tropical & Subtropical Grasslands, Savannas & Shrublands (which contains some forested ecosystems) within +25 to -25 degree latitudes, excluding Australia. Using the Copernicus 2019 land cover raster (Buchhorn et al., 2020) we defined areas available for restoration as classes 121 (Open forest, evergreen needle leaf), 123 (Open forest, deciduous needle leaf), 122 (Open forest, evergreen broad leaf), 124 (Open forest, deciduous broad leaf), 125 (Open forest, mixed), 126 (Open forest, unknown), 20 (Shrubs), 30 (Herbaceous vegetation), and 40 (Cultivated and managed vegetation/agriculture (cropland)) (Buchhorn et al., 2020). This is summarised as the proportion of land available for restoration within each 1km2 resolution planning unit. All other classes were considered as unavailable for restoration.

The definition of the areas that are deemed available for restoration can have a profound impact on the spatial distribution of areas selected for forest restoration, and this issue is a key consideration for planning and policy related to large-scale forest restoration. The definition is uncontentious for the tropical and subtropical forest biomes where areas that were once forested but are no longer forced can be defined reliably, and where areas associated with land uses that are not available for forest restoration (e.g. urban areas, water, wetlands) can be excluded. However, it is more difficult to define areas available for forest restoration in other biomes. For example, the Tropical & Subtropical Grasslands, Savannas and Shrublands biome contains 58 ecoregions including woodlands, savannah, forest-savannah, pine forests, bushlands, shrublands, grasslands, and other types, and spanning montane, tropical, subtropical and xeric conditions.

There is a legitimate concern that including non-forest ecoregions such as savannahs in forest restoration planning could be perceived as promoting, or lead to, afforestation of these systems. However, there are three reasons we argue some of these ecoregions should not be unilaterally excluded from forest restoration planning. First, tree cover is an important component of several of these ecoregions and they may, therefore, represent areas that could support some level of forest restoration without compromising their ecological integrity.

Second, ecoregions and biomes are coarsely mapped and may contain a range of other ecosystem types at smaller scales. As some of the ecoregions are large (e.g. the Cerrado), excluding them may result in a substantial impact on the area considered available for forest restoration. Furthermore, transitions between ecoregions can sometimes be gradual, hence the boundaries are subjectively defined. For large ecoregions, error in the mapping of boundaries can substantially alter the area of the ecoregion and hence the area deemed available for forest restoration. For example, a ±1 km distance error in the definition of the boundary of the Cerrado translates to a potential ±38,000 km2 (3.8 M ha) variation in the ecoregion area (estimated using an inner and outer buffer of the Cerrado ecoregion polygon).

Third, there are many ecosystems that appear to be at risk of transitioning to alternative states as anthropogenic pressures have altered some of the biophysical processes (e.g. fire regimes, climate change, elephant abundance) that maintain some ecoregions in a non-forested, or partially forested, state. Climate change in particular has the potential to drive substantial changes in the distribution of some ecosystems over the coming decades. In that context, there may be some ecoregions that are currently non-forested, but fostering a transition to a forest ecosystem may be deemed appropriate if there is a high likelihood the current ecosystem would be lost anyway.

There is considerable subjectivity and uncertainty in the definition of areas deemed available for restoration. Many of the decisions are subjective, are sensitive to error in datasets, and may not be robust to climate change impacts. Ultimately, it is likely to fall to individual nations to make these decisions, though science could play an important role in informing those decisions. There is a research need to produce a high resolution (e.g. 30m-100m) estimate of the areas that could be deemed available for restoration under a variety of assumptions, based on a range of ecological and biophysical data, and that provides an assessment of risk in the context of climate change. Also needed is a spatially explicit assessment of the potential for perverse outcomes to arise from forest restoration.

We formulate the problem of where to restore forest to maximise benefits, quantified in a range of ways among the scenarios, as a linear programming problem (a formal, mathematical optimisation framework). Specifically, the objective considers biodiversity conservation and climate change mitigation, while accounting for implementation and opportunity costs. The objective function is:

where x is a vector of decision variables representing the proportion of each planning unit to restore; s is the expected change in carbon sequestration resulting from forest regeneration relative to current land cover conditions; b is the expected benefit to biodiversity conservation, summed across all species, following restoration (described in detail below); and c and e are the opportunity and establishment costs associated with restoration, respectively. Carbon sequestration, biodiversity and cost metrics are quantified as rates per unit area of restoration. The relative contribution of climate change mitigation and biodiversity conservation objectives is determined by the weights ws and wb. They are required because the equivalence of objectives with different units is a subjective decision that must be made by decision-makers.

The two components of the objective function represent the returns (benefits divided by costs) of forest restoration to biodiversity conservation (b/(c + e); US$−1 km−2 ) for each species j; climate change mitigation (s/(c + e); tonnes US$−1 km−2 ), where the total cost of forest restoration is the sum of the opportunity costs (c; US$−1 km−2 ) and the establishment costs (e; US$−1 km−2 ). Np is the total number of planning units and Ns is the total number of species.

The first constraint limits the total restoration area to target T. The second constraint limits the proportion of each planning unit that can be restored, where u (range: 0-1) is determined by calculating the proportion of each planning unit containing cover types that are not available for restoration (e.g. water and urban areas).

This equation represents the cost-effectiveness scenario. For comparison a maximum-benefit formulation was also calculated in which the cost denominator is removed. Two other reference solutions were also calculated that did not involve optimisation. The random allocation solution iteratively selected planning units, restoring each one up to the total available area for restoration (u), until the total restoration area target (T) had been achieved. This was repeated 100 times and the average returns calculated. The minimum cost solution restored forest in planning units in order of ascending cost until the target was achieved. The benefits and costs associated with these two references scenarios were then calculated.

We implement this problem formulation separately for each nation, as that is the scale at which planning is translated into implementation.

Biodiversity conservation was quantified as the estimated mean reduction in extinction risk among all forest-associated species resulting from forest restoration. This estimation is based on the extinction risk model of (Thomas et al., 2004):where a is the current habitat area, or future projected habitat area following restoration, A0 refers to the original habitat area, corresponding to pre-settlement conditions, and z determines how extinction risk increases as habitat is lost (here, z = 0.25). The benefit to biodiversity conservation (B) of forest restoration among species is then estimated as:, where ec is the extinction risk based on current habitat area, er is the projected extinction based on the habitat area following restoration, and N is the number of species included in the model. Estimating the area parameters requires spatially explicit estimates of the species range and habitat within the range for each species of interest. We use the Spatial Planning for Area Conservation in Response to Climate Change (SPARC) dataset (Hannah et al., 2020; Marquet et al., 2020), which modelled the ranges of approximately 103,000 species in the Neotropics, the Afrotropics and the Indo-Malayan tropics. Benefits of the SPARC dataset over other species range collections is that a large number of species are represented including a strong representation of plants, and the ranges are modelled in a consistent manner.

The SPARC project modelled current species distributions on the basis of species location data sourced from multiple datasets (e.g. BirdLife, GBIF, VertNet, BIEN) with filtering to exclude records with missing, duplicated, or errant location data (see Hannah et al., 2020; Marquet et al., 2020, for details). Distributions were modelled for species with at least 10 occurrence records, with the domain of the predictions limited to within 500 km of occurrence records. The environmental covariates used related to bioclimatic conditions (mean annual temperature, mean diurnal temperature range, seasonality of temperature, minimum temperature of the coldest month, mean annual precipitation, seasonality of precipitation; WorldClim v1.4, www.worldclim.org), an accumulated aridity index (Marquet et al., 2020), and soil variables (depth to bedrock, pH, clay proportion, silt proportion, bulk density; all means within the top 1m) (Soilgrids; www.soilgrids.org).

The climate and soil variables used in the distribution modelling are likely to be associated with the potential distribution of habitat. While these SPARC SDM ranges are expected be less extensive than Extent of Occurrence (EOO) ranges because they may already partially reflect the distribution of habitat through the proxies of climate and soil variables, they are expected to be more extensive than Area of Habitat (AOH; also referred to as Extent of Suitable Habitat - ESH) range estimates because they do not explicitly reflect the distribution of habitat (for a discussion of EOO and AOH see Brooks et al., 2019).

Quantifying what constitutes habitat for each species is a challenging problem. Species-habitat associations have been defined for 9,932 of the SPARC species (IUCN), through a process of assessment by experts. For the remaining species we use the empirical location data for each species to estimate the habitat association using a map of the IUCN habitat types (Jung et al., 2020). Specifically, we calculate the proportion of occurrence records occurring within each of the Level 1 IUCN habitat classes, and identify the threshold that maximises the sensitivity and specificity of the predicted habitat associations for the 9,932 species with defined habitat associations. As our focus is on forest restoration we restrict our analysis to the subset of species with forest associations, which could be predicted with 81.6% accuracy.

Following Strassburg et al. (2020), we simplify the IUCN habitat categories into six general habitat types (forest, savannah, shrubland, natural grassland, wetland, desert) for which the presettlement distributions were estimated. The area of original habitat (A0) is derived by identifying area of the intersection between the species distribution models and the presettlement habitat distributions for each species. Current habitat area was determined by intersecting the species distribution models with an estimate of the current distribution of these five habitat types derived by reclassifying a contemporary 100 m resolution map of the IUCN habitat types (Jung et al., 2020). The contribution of forest restoration in each cell to the reduction in extinction risk among all species is calculated using a weighted sum of the expected rates of change in extinction risk. Specifically, for each planning unit the set of species that would benefit from forest restoration at that location is identified using the SDM. The expected reduction in extinction risk arising from forest restoration is the tangent to the extinction risk function at the current level of habitat throughout the range, and is calculated numerically. Forest restoration in any cell changes the benefit of restoration in other cells. We therefore solve the optimisation problem in increments, updating the extinction risk benefit calculation after each increment.

The contribution of each species to the extinction risk reduction benefit is determined by a species weighting scheme that assigns equal total weights between plants and animals (0.5 to each) and for animals then assigns equal weights among mammals, birds, reptiles and amphibians (0.125 total weight to each). Within each of those taxonomic groups the total weight is divided equally among all species in that group. The weights sum to unity among all species. Without a weighting scheme plants would have a disproportionately large influence on the solution due to their disproportionately high representation among the set of species included in SPARC.

Climate change mitigation, measured here as potential carbon sequestration (PCS) in aboveground biomass (AGB), is one of the benefits that can inform spatial restoration planning for tropical forest ecosystems. Restored tropical forests contribute to the reduction of CO2 in the atmosphere through carbon sequestration and, thus, to mitigate global climate change (Brancalion et al., 2019b; Strassburg et al., 2019). A map of predicted old-growth forest aboveground biomass (OGF-AGB) was created at 100m resolution using an iterative Random Forest model in Google Earth Engine. To do so, a large number of potential predictor variables, including topographic, edaphic, and bioclimatic, were tested, and predictor variables that did not add to the power of the model were removed. The final model estimated OGS-AGB to within 20 Mg/ha for a global validation sample of several thousand points. We then calculated the difference between the year 2017 AGB at 100m resolution and then excluded pixels having more than 50% OGF-AGB as those would be less suitable for restoration. The remaining restoration suitable pixels provided 100m resolution PCS-AGB, which were then summed to create a 1x1 km estimate of PCS-AGB for each pixel. Our approach provides a minimum and maximum bounded uncertainty for PCS-AGB through the incorporation of the standard error AGB uncertainty maps available in our input 100m AGB maps (CCI AGB 100m). The workflow and maps were developed by Dr. Eben Broadbent and Almeyda Zambrano of the Spatial Ecology and Conservation Lab (www.speclab.org) at the University of Florida (publication in preparation).

WePlan–Forests accounts for both opportunity costs and restoration implementation costs. Accounting for opportunity costs is important to reduce conflict between agricultural productivity and forest restoration as it increases the likelihood that forest restoration will be concentrated into areas of marginal agricultural productivity. Opportunity cost may also be linked to the probability of long-term success of forest restoration (Brancalion et al., 2019a). Accounting for establishment costs is important in order to maximise the return on investment from restoration activities.

Establishment costs were estimated using a statistical model that was based on forest restoration project data (n = 234 observations) extracted from 50 World Bank project reports spanning 24 countries (Vincent, Kaczan, et al., in prep.). The criteria for inclusion were that the area and costs, or the cost per unit area, of restoration must have been explicitly reported. The dataset excluded observations from Eastern Europe as they are not relevant to the context of tropical forest restoration, and excluded unusual special-purpose activities (e.g. mangrove restoration, tree-planting along highways, planting bamboo, etc) as they are not representative of the type of activities most relevant to tropical forest restoration. A distinction was made between afforestation, referring to forest regeneration on land where the most recent use was not forest (typically agriculture), and reforestation, referring to regeneration of forest land that recently lost its tree cover due to harvesting, wildfire, or some other source of damage. Costs included all expenditures associated with regeneration until the new stand was ‘free to grow’ (approx. 3-5 years, depending on project and site).

The dependent variable in the statistical model was the natural log of establishment costs per hectare expressed in 2011 US$. The independent variables included GDP per capita (natural log transformed), a binary variable distinguishing between afforestation and reforestation, a binary variable distinguishing between natural and active regeneration, a binary variable indicating whether the project was initiated pre- or post-2010, a continuous variable representing the proportion of the country associated with temperate/boreal biomes, a binary variable indicating whether the cost accounted for overhead costs or not, and the total area of forest regeneration (natural log transformed). The model explained approximately half of the variation in the data (R2 = 0.46; Vincent, Kaczan, et al., in prep.), which is reasonable performance given the wide range of countries, years and restoration contexts represented by these reports. A strength of this model is that it is based on empirical evidence in contrast to alternative approaches to estimating establishment costs that are based on expert opinion. The model indicates that establishment costs are positively associated with per-capita GDP, that reforestation is more expensive than afforestation (this appears to arise as a result of the increased difficulty and expense of accessing and preparing partially forested sites compared to marginal agricultural lands), and that there are scales of economy associated with the total area of forest restored.

Establishment costs were estimated spatially using gridded GDP estimates for 2011 (Kummu et al., 2018) and a model of the potential for natural regeneration (Beyer et al., in prep.). The latter was used to determine the value of the binary active/natural regeneration variable for each cell. All of the other binary variables were set to 0, and we use the mean restoration area among all projects (9604 ha) to estimate establishment costs. Establishment costs were transformed from 2011 to 2017 US$ using annual inflation rates (2012-2017: 1.019, 1.037, 1.056, 1.067, 1.078, 1.099, respectively).

Opportunity costs were based on estimates of annual land rent (a measure of net income generated by land) for cropland and pastureland (2017 USD values) at a resolution of approximately 10km (Vincent & Yi, in prep.). As an initial step, gross annual revenue was determined separately for cropland and pastureland using existing gridded data sources (cropland: MapSPAM, www.mapspam.info; pastureland, Gridded Livestock of the World, https://dataverse.harvard.edu/dataverse/glw), augmented by national data from FAOSTAT (http://www.fao.org/faostat/en/#data/QC; http://www.fao.org/faostat/en/#data/QL). In the final step, detailed farm budget data from large-scale household surveys conducted by the World Bank and FAO in several dozen developing countries were used to convert gross annual revenue to annual land rent. The cropland opportunity cost layer took precedence over the pastureland opportunity cost in areas where the two overlap. Establishment costs are short-term but opportunity costs are ongoing. We therefore calculate the total cost of restoration in each cell as the establishment cost plus the in perpetuity opportunity cost (the opportunity cost divided by a discount rate of 5%).

The difficulties of defining the areas available for restoration are described above. This analysis makes several other assumptions and judgments that are likely to influence the analysis.

The analysis assumes that the climate mitigation and biodiversity conservation benefits arising from active and natural regeneration do not differ. However, active regeneration may sometimes be associated with planting non-native tree species that have commercial value (e.g. eucalypts for timber production, or species with food-production value). For example, Brazil’s Forest Code allows up to 50% of non-native species to be used in forest restoration. Depending on how these species are planted and maintained, they may still have substantial value for carbon sequestration, but they are likely to have diminished value for biodiversity conservation. The link between the proportion of non-native species planted and the value to biodiversity conservation has not been well established, but it could mean that this analysis has overestimated the extinction-reduction benefits arising from active regeneration.

This analysis also ignores any variation in the temporal rates at which benefits arise spatially, or as a function of the regeneration method. There may be substantial differences in these rates as a result of differences in seedling establishment and survival, competition, succession, and growth rates. Accounting for some of these effects and their implications for the rates at which benefits are achieved is a goal for the future refinement of the WePlan–Forests decision support platform.

This analysis enforces no assumptions about the maximum level of forest cover that might be permitted in an area, which typically results in a substantial spatial concentration of fully-restored forested areas (see solution maps). Large, contiguous blocks of forest may provide additional benefits to biodiversity (e.g. reduction in edge effects, reduced accessibility to people) but may have detrimental impacts on local communities. It would be straightforward to limit the maximum area of forest cover at a planning unit or jurisdictional level if nations wish to identify forest restoration solutions that are more aligned with the land sharing perspective than the land sparing perspective.

This analysis focuses on the benefits and costs at the societal level, and does not account for land tenure and livelihoods at local levels. A major challenge for policy is to identify ways of funding forest restoration and compensating affected landowners such that there is no net negative impact. Ideally, both society and individuals achieve net benefits from forest restoration (so called win-win solutions).

All of these assumptions could be addressed within the WePlan–Forests framework through collaboration with individual nations.

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