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Compilation of population life-history data
We compiled population-specific life-history data for Indo-Pacific fishes from primary literature using a combination of systematic and opportunistic searches. We obtained references primarily from Google Scholar and the web page of Fisheries and Oceans Canada (DFO, http://www.isdm-gdsi.gc.ca/csas-sccs/applications/publications/index-eng.asp), using a combination of species name and the following keywords: Pacific, temperature effects, von Bertalanffy growth, age at maturation, or natural mortality. Species names for 107 common teleosts in the Indo-Pacific Ocean were obtained from the global-capture production database of the Food and Agricultural Organization (FAO, ISSCAAP groups 31-37; available at: http://www.fao.org/fishery/statistics/global-capture-production/query/en). Although similar data are available in FishBase, a global and freely available database on fish, we opted not to use data from FishBase because temperature data associated with population records are often missing and difficult to restore due to lacking spatial coordinates in FishBase.
In total, we screened around 8000 references published in 1958–2017. We extracted data from 440 references representing peer-reviewed journal papers, stock assessment reports, governmental documents, graduate theses, and conference proceedings. Our data include 332 species, with conspecific life-history data of ≥2 records in 206 species.
We extracted available population data of seven life-history traits related to growth and maturation for each population: i.e., the von Bertalanffy growth coefficient K (yr-1) and asymptotic length L∞ (cm), age and length at 50% maturity (A50 (yrs) and L50 (cm)), allometric exponent (b) of length–weight relationship (W = aL^b), lifespan (Amax (yrs)), and natural mortality (yr-1). To make the length traits (L∞ and L50) comparable among populations, we standardized different length measures (e.g., standard length or fork length) into total length using available regression models (Supplementary Table 7). To account for between-sex differences in traits values, we coded life-history data of each population as sex-specific or combined-sexes. When data of single- and combined-sexes were both available, we primarily used combined-sexes data for our analysis. When only sex-specific data were available, we used female data.
In our selected references, the von Bertalanffy growth coefficients are primarily estimated via fitting length-at-age data (Lt, where L is length and t is age) with one of these methods: the Ford–Walford method, length-based method, and nonlinear regression fitting. As all these fitting methods involve the same model form (L_t = L_infty left( {1 – e^{ – Kleft( {t – t_0} right)}} right)) and similar optimization processes (e.g., minimizing residual errors), we consider that the growth coefficients estimated with these methods are generally comparable. However, we excluded the growth coefficient data derived from other model forms, as transforming those coefficients could introduce biases (e.g., Gompertz model or weight-based form of von Bertalanffy model). The population natural mortality data were derived from various models with distinct assumptions (Supplementary Table 8); thus, these natural mortality estimates may not be comparable. To investigate the temperature effects on natural mortality, we re-estimated natural mortality estimates for individual populations using a life-history invariant method (see Methods: Derivation of M).
We recorded additional descriptive variables for each population: e.g., ecological group (coded based on habitat types following definitions in FishBase, Supplementary Table 5), family, species, latitude, and longitude of sampling site (in decimal degrees; for the studies with multiple sampling sites, the minimum and maximum of latitudes and longitudes of sampling sites are recorded), minimum and maximum sampling depths, and sample size. Latitudes and longitudes of sampling sites were derived from available spatial coordinates, names of sampling ports, or the maps in the references.
Some references were excluded to avoid ambiguity. For example, we excluded references of fish in estuary and artificial habitats (e.g., aquaculture species). To alleviate noise in the datasets, we rejected data lacking clear descriptions of study area (e.g., studies that did not define sampling sites or those that aggregated samples across a very broad range) and those lacking explicit information on fitting procedures for the growth or maturation models (e.g., lacking information on sample size, suitable range of length-at-age data, independent samples, description of the fitting methods, a plot of data with the fitted line, or other means for assessing the fit). Similarly, we excluded studies without descriptions of fitting methods for estimating natural mortality (as suggested by 14). For stock assessment reports and review papers, we scrutinized the summarized data based on original publications and rejected data lacking clear sampling or fitting information. Lastly, we removed duplicated data cited in multiple reports.
Compilation of population temperature data
We used available in situ data of mean decadal sea temperature as habitat data. These temperature data were obtained from the World Ocean Atlas 2013 (NOAA Atlas NESDIS 73; 43; hereafter referred to as WOA13; available at: https://www.nodc.noaa.gov/cgi-bin/OC5/woa13). Sources of the WOA13 temperature data include temperature profiles measured by various instruments43. The mean decadal temperature profile was calculated by averaging six decadal datasets spanning 1955–201243. For our analysis, we used the mean decadal temperature profile data in the Indo-Pacific region, with a horizontal resolution of 0.25° and depth segments of 5 m from surface to 100 m and depth segments of 25−100 m for >100 m (maximum depth = 5500 m)43. As rates of temporal changes in the ocean temperature were slow (e.g., 1.48 °C per century; 25), we did not account for the small temperature changes due to differences in time of measurements between the temperature and life-history data.
We matched the mean decadal temperature profile data with spatial coordinates for each of these populations. For populations with single sampling sites, we assumed that their potential habitats centered at the sampling sites and extended for 0.5° in the north, south, east, and west directions. Further, for populations with multiple sampling sites, we assumed that their habitats were bounded by the ranges of latitudes and longitudes of sampling sites. To account for habitat depths, we estimated the minimum and maximum depths of populations based on ranges of sampling depths or description of depths of species habitats in the references. When depth information was unavailable, we used the maximum depth of the species in FishBase as the maximum depth for a population. For each population, we derived two habitat variables: SST and BT. SST is the temperature at 0 m (WOA13 data; 43). BT is the temperature at the maximum depths of populations. Finally, we calculated the minimum, mean, maximum, and coefficients of variation of each of the habitat indices for each population.
Derivation of natural mortality (M)
Population-specific natural mortality (hereafter referred as M) provides insight into population sustainability under fishing or environmental changes (i.e., high natural mortality indicates high degree of sustainability13,15). However, because estimates of M from different models are not necessarily comparable, we re-estimated M for each population using the model II of Gislason et al.14, which builds on well-established empirical relationships44,45 and has some theoretical backing46,47. The equation is:

$$ln left( M right) = 0.55 – 1.61ln left( L right) + 1.44ln left( {L_infty } right) + ln left( K right),$$
(1)

where M is natural mortality and L is the midpoint of length range (cm) of a population, respectively14. As the length range data were not available to us, we constrained L to be the length at age-at-50% maturity (A50) to estimate M, following the invariant relationship among mortality-at-age at maturation, L50, L∞ and K13,48. Further, because A50 data are available for fewer number of populations (n = 119, about 8.5% of total populations), we restored the missing values of A50 based on a theoretical linear relationship between population A50 and (frac{{L_{50}}}{{K times L_infty }})49. With the available data of A50, L50, L∞, and K for 70 populations, we fitted this linear relationship (F = 204.6, df = 1,68, R2 = 0.75, P  25 yr-1). Range of M’s for the remaining 1387 populations is 0.05–21.8 yr-1 (Supplementary Fig. 1). These Gislason M estimates were used in the subsequent regression and life-table modeling analysis.
Evaluation of the relationships between temperature and life-history traits
Because life-history variation is nested within phylogenetic levels, we used the linear mixed-effect model (LME) to explore the relationships between each life-history trait and each temperature index, simultaneously accounting for species- and family-related variance as random effects. We used the lme4 and lmetest packages in R (www.r-project.org50;) to construct these LME models. Given the eight different temperature indices (e.g., four descriptive metrics nested within two temperature variables), we constructed eight LME models for each life-history trait. For each model, a natural-log transformed life-history trait is the response variable, a species mean-centered habitat index is a single fixed-effect variable, and species and family are two random-effect variables. We considered four alternative model structures for random effects: i.e., with either family or species as random intercepts, and with either family or species as random intercepts and slopes.
We evaluated strength of each of fixed- and random-effect variables using the likelihood ratio test51. Specifically, we estimated the log likelihood between a pair of full and alternative models (with one less fixed or random variables), deriving the test statistics (i.e., 2 times the difference between log likelihood of two models) and P value. If the two models were not different significantly (e.g., P  > 0.05), we selected the more parsimonious model. Otherwise, significant difference between these two models (e.g., P ≤ 0.05) indicates pronounced variation in the response variable due to the additional fixed or random effect in the full model. Furthermore, when neither family nor species accounts for significant variance in the response variable, we reduced the model to a simple linear regression with a habitat index as the sole fixed-effect predictor. We selected the best model structure to depict the relationship between each of the eight habitat indices and a life-history trait.
We observed pronounced intra-specific variability in the empirical K and L∞ for some of our study species; e.g., ≥3-fold differences in these traits within some species. Because large variability in K and L∞ within a species may be partially due to that the estimation of these traits depends on one another, we conducted PCA with these two traits and evaluated the ratios of maximum-to-minimum scores of the first PC1 among species. We found 34 species with the absolute values of the ratios of PC1 scores ≥3, whereas 285 species had |ratios| 0 indicate positive warming effects on population growth rates). To derive (frac{{R_0}}{G}), we built an age-structured model (i.e., a life-table33;), incorporating functions for growth increment (in length and weight), maturity states, fecundity, and survivorship probability. The length-at-age data (Lt) were calculated using the von Bertalanffy growth model (Eq. (3)):

$$L_t = L_infty left( {1 – e^{ – Kleft( {t – t_0} right)}} right),$$
(3)

where t denotes age, and L∞, K, and t0 are the von Bertalanffy growth coefficients. Weight-at-age data (Wt) were estimated using an allometric function of Lt (Eq. (4)):

$$W_t = alpha L_t^beta.$$
(4)

Also, fecundity (mt) is an allometric function of Wt (Eq. (5)23:

$$m_t = delta W_t^gamma.$$
(5)

Because of lacking data on the length-weight and fecundity-weight relationships for many populations, we assumed constant intercepts and slopes for Eqs. (4) and (5) (i.e., α = 0.02, β = 3, γ = 1.18, δ = 2930). However, L∞ and K data are available for most populations in our data (n = 1,387). As a result, we used these data to derive length-at-age for each population (assuming t0 = 0). Also, we used the model-derived A50 estimates (Supplementary Fig. 7) to account for maturity state for mt for each population (i.e., mt = 0 for t  More

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Soil organic matter is essential for maintaining soil health and sustaining plant growth. Loss of soil organic matter often leads to degradation of soil quality1. It also constitutes the largest terrestrial organic carbon (C) pool (~ 2,400 Pg C in top 2 m soil). This soil organic C (SOC) pool is three times greater than the amount of C in the atmosphere2. An increase or decrease of C in soils by only a small percent represents a substantial C sink or source for atmospheric CO2. Studies have been conducted to predict SOC of croplands under climate change3,4,5. However, crop management changes with adaptation to future climate6,7,8,9 (such as changes in varieties and planting dates) were ignored in most studies. Thus, we carried out a regional study to assess the impact of projected climate change and elevated CO2 on SOC in agricultural systems with management adaptation.
A change in SOC is a result of the net effect of the changes in SOC decomposition rates (the main C outflow) and C inputs from plants10 (main C inflow). In a warmer climate, the higher temperature could increase the decomposition rate in both the short and long term11. Decomposition will also be sensitive to increases or decreases in precipitation10 predicted by climate models8. Carbon input is mainly from root and surface residue litter that is not removed from the system through harvest, grazing or burning. Changes in temperature, precipitation, and atmospheric CO2 all affect this input through plant growth and production6. These climatic changes are also likely to affect management practices in the future7. Although systemic management changes are possible that can limit the impact of climate change, such as moving from dryland to irrigated systems, smaller adjustments including changes in varieties and planting dates have less barriers for adoption. These adjustments to management have been found to affect both crop production (C input) and decomposition7,12, with potentially larger effects on crop production7. These interactions are complex, and the overall change to SOC pools in agricultural lands remains uncertain.
Here we present the results from a simulation of SOC dynamics for more than 54,000 locations, covering 34,600,000 ha of cropland in the U.S. Corn Belt (Supplementary Fig. 1a). These locations have historically been managed with a corn (Zea mays L.) and soybean (Glycine max L.) rotation, which is the most common crop rotation in this region. Corn and soybean yields in this region account for about 85% of US crop production13. In our simulation, the widely used biogeochemical model DayCent14,15 was driven by weather data from the Representative Concentration Pathway 4.5 (RCP 4.5) climate change scenario8. Predictions from three General Circulation Models (GCMs; GFDL-CM3, MIROC-ESM, and MRI-CGCM3) were downscaled to generate daily weather (32 km grid) and used to assess the uncertainty. The main goal was to quantify the change in surface soil C (0–20 cm) under management adaptation with the selection of alternative crop varieties and planting dates to maintain high levels of crop production in future climate scenarios from 2041 to 2071. Alternative crop varieties were based on those currently available in the United States without consideration of additional crop breeding or genetic modifications that could further enhance production in the future. A no climate change scenario (historical weather with current CO2 level) was used as the baseline for comparisons.
Crop production trends
We found that, without adaptation, the average corn yield during the 2041–2071 period in the Corn Belt would drop in all three GCM climate scenarios in comparison with the baseline with no climate change (Fig. 1). Yield decreased by 17% (GFDL-CM3), 34% (MIROC-ESM), and 2% (MRI-CGCM3) under the respective scenarios. The difference between GCMs can be attributed to differences in the projected temperature and precipitation (Supplementary Fig. 2). Similar yield decreases were seen for soybean as found for corn if there is no adaptation (decreased by 13% for GFDL-CM3, 28% for MIROC-ESM, and increased by 8% for MRI-CGCM3).
Figure 1

Predicted grain yield of (a) corn and (b) soybean in the 2041 to 2070 period.

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With adaptation, both corn and soybean yields increased compared with no adaptation: an increase of 5% for corn and 19% for soybean (average of the three GCMs) compared with the baseline. The larger increase in soybean yield was due to the C3 crop being more responsive to the CO2 fertilization than C4 crops16. The standard deviation of yields across the three GCMs in the adaptation scenarios was lower than that of the no adaptation scenarios (15% and 39% lower for corn and soybean respectively). Simulated crop yields were more stable under climate change with adaptation management compared to without adaptation. The stability in yields is because, without crop adaptation associated with the selection of alternative crop varieties, an increase in temperature shortens the growing period of the crop17,18. Each GCM predicts a longer growing season with warmer temperatures. When a longer-season maturity variety was simulated as an adaptation pathway, the extended growing period allows the crop to use the full window of optimal solar radiation. This leads to similar amounts of production from year to year between GCM climate scenarios. The spatial pattern of the yield changes was very different for the two crops (Supplementary Fig. 3) due to the difference in crop response to temperature, day length (photoperiod), and elevated CO2. Our overall predictions of crop yield change were generally in agreement with other studies9,17,19,20.
Carbon input trends
Crop yields are good indicators of total net primary production and are found to be proportional to the total C input to soils in the U.S. Corn Belt21 (i.e., crop yield to total biomass does not vary much geographically). Our simulations predicted the average input to be 3.7 Mg C ha−1 year−1 under the no climate change scenario for the 2041–2070 period (Supplementary Fig. 4). With climate change but no adaptation, all counties (an administrative subdivision of a state in the U.S.) had lower C input (GCMs ensemble mean) compared with the baseline. However, with adaptation, more than half of the counties (most counties in the northern part of the region) had higher C input than those of the baseline. Compared with the no adaptation scenario, all counties in the Corn Belt maintained higher C input with adaptation. The average C input across climate scenarios in the Corn Belt region was predicted to be 3.0 and 3.9 Mg C ha−1 (a change of − 19% and 5% from the baseline) with no adaptation and adaptation scenarios, respectively. The standard deviation of the adaptation scenarios across the three GCMs was 47% lower than without adaptation, suggesting a counteracting effect of adaptation to climate change.
Decomposition factor trend
In contrast to C input, the decomposition factor, which reflected the relative change in decomposition rate due to temperature and moisture effect (ranges from 0 to 1, with higher rates associated with values closer to 1), increased in all counties regardless of the adaptation (Supplementary Fig. 4). Larger decomposition factors can be explained by an increase in soil temperature and wetter soil conditions associated with climate change projections. Wetter soil conditions were a result of a reduced transpiration rate under high levels of atmospheric CO2 and increased precipitation projected by the three GCMs. The average decomposition factor (across three GCMs) was predicted to be 0.41, 0.49, and 0.47 for baseline, without adaptation, and with adaptation scenarios. The standard deviations were 27% lower with adaptation for the decomposition factor across the three GCMs than without adaptation. If adaptation does not occur under the GCM scenarios, the growing period of the crops was reduced due to global warming and resulted in less total transpiration and wetter soil conditions, which increased decomposition. With adaptation, the longer-season maturity variety continued to grow over a longer period and consumed more water, reducing soil moisture to lower levels, thus lowering decomposition (average annual evapotranspiration was 2.0–5.1% higher in the adaptation scenario compared with no adaptation). The soil moisture differences among GCMs were lower with crop adaptation.
Soil organic C trends
Without climate change (baseline scenario), the predicted sub-region SOC in the top soil ranged from less than 30 Mg C ha−1 to more than 80 Mg C ha−1(Fig. 2a). The highest levels of SOC were found in the western part of the region where soil clay content is high (Supplementary Fig. 1). The low levels of SOC found in Michigan and northern Indiana can be attributed to the soils with high sand content. In addition, tillage intensity varies among the counties22, contributing to differences in SOC levels among counties. With climate change, there were losses of SOC in almost all counties if there was no adaptation (Fig. 2b). This was the net result of decreased C inputs and increased decomposition rates (Supplementary Fig. 4). With adaptation, the northern part of the Corn Belt tended to gain SOC (Fig. 2c) due to increased C inputs (Supplementary Fig. 4), while the other areas tended to lose SOC. Compared with no adaptation, the adaptation scenario resulted in higher SOC stocks in all counties of the Corn Belt, which was also found in a modeling study of a site in Michigan9.
Figure 2

Predicted soil organic carbon (SOC) in the top soil (0–20 cm) averaged for the three GCMs in the U.S. Corn Belt, including (a) the baseline scenario and (b) the difference between the no adaptation scenario and baseline, and (c) the difference between the adaptation scenario and baseline. Maps were generated using the R “ggmap” package39 (Version 2.6.1; https://journal.r-project.org/archive/2013-1/kahle-wickham.pdf).

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Over the period from 2041 to 2070, the average SOC in the Corn Belt reached a new equilibrium state in the baseline scenario with no climate change (Fig. 3). Without adaptation in the climate change scenarios, SOC decreased over time. Rapid loss of C was predicted for the 2041–2050 period with the rate decreasing gradually over the 2051–2070 period. With adaptation, two GCMs (GFDL-CM3 and MRI-CGCM3) predicted similar changes over time as the baseline, while the SOC values for the other GCM (MIROC-ESM) were slightly lower than the baseline.
Figure 3

Area-weighted average soil organic carbon stocks for simulations with and without adaptation for corn/soybean rotations between 2041 and 2070. These projections are based on the same historical data and initial values for SOC pools.

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These results show that adaptation with the selection of longer-season varieties can lead to a similar SOC level as the baseline and GCM scenarios under a moderate climate change projection (RCP 4.5). Although the predicted climate was very different for the three GCMs, the SOC levels with adaptation were similar and not very different from the baseline with no climate change. In contrast, without adaptation, SOC storage levels were farther apart from each other and the baseline. This indicates a strong resistance to the effects of climate change in agricultural systems in the Corn Belt region if there is the selection for alternative varieties and planting dates that are better adapted to the changing climatic conditions.
We found the variation (CV 2.89%) of the predicted total SOC stock across the GCMs in the adaptation scenarios was much smaller than the variation (CV 5.88%) in the no adaptation scenarios. This corresponds to reduced variation in C input and decomposition factors. Because the increased decomposition rate was compensated by the higher overall C input, the SOC stock maintained similar levels as the baseline without climate change.
Limitations
In this study, we did not evaluate the possibility of new technologies that could be developed in the future and influence production, decomposition and other variables influencing SOC levels, as these changes are difficult to predict. For example, new technologies associated with crop breeding and other genetic improvements, pest control, and other developments could increase C input and result in higher SOC stocks than our predictions. Management practices such as adding cover crops, which increases C input, may also further enhance SOC stocks23. In contrast, large areas of removal of corn stover for biofuel production (not considered in our simulation) could reduce the total SOC stock24. Although most SOC is concentrated in the surface soil, subsoil C has been found to respond to warming climates and affects SOC stocks25. Future research should also address subsoil C dynamics. More

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Our method was implemented in the Google Earth Engine (GEE) platform19. We divided it into four steps. Figure 2 summarizes our approach, including the input of the raw data (land-use and land-cover from 1985 to 2018 and the water surface), and the output data (from 1986 to 2018), which included maps of the annual secondary forest increment (Product 1), annual secondary forest extent (Product 2), annual secondary forest loss (Product 3; from 1987 to 2018), and annual secondary forest age maps (Product 4).
Fig. 2

Workflow of the proposed method.

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Input data
We used the land-use and land-cover data from the Brazilian Annual Land-Use and Land-Cover Mapping Project (MapBiomas Collection 4.1; https://mapbiomas.org/en/colecoes-mapbiomas-1)1 as input data. This dataset was obtained through the classification of images from the Landsat satellite series (30-m spatial resolution) using a theoretical algorithm implemented in the GEE platform19. Details about the processing of the dataset can be found in the Algorithm Theoretical Basis Document20. More detail about the land-use and land-cover classes can be found in the MapBiomas website (https://mapbiomas.org/en/codigos-de-legenda?cama_set_language=en).
Moreover, we used the maximum water surface extent data (from 1984 to 2018) developed by Pekel et al.21 (https://global-surface-water.appspot.com) to avoid the inclusion of false detection within wetland areas in our products. This dataset contains a map of the spatial distribution of the water surface cover from 1984 to 2018, globally21. These data were obtained from 3,865,618 Landsat 5, 7, and 8 scenes acquired between 16 March 1984 and 31 December 2018. Each pixel was individually classified into water or non-water cover using an expert system21 implemented in the GEE platform19.
Step 1 – Reclassifying MapBiomas data
All MapBiomas land-use and land-cover maps from 1985 to 2018 (34 maps) were reclassified into binary maps. We assigned the value “1” for all pixels in the Forest formation class of the MapBiomas product (Legend ID: 3) and “0” for the other land-use and land-cover classes. In our reclassified maps, pixels with value of “1” were, then, associated to the class “Forest”, which includes only forests classified as old-growth and secondary (before 1985). Mangrove and forest plantation classes were excluded from our secondary forest map.
Step 2 – Mapping the Annual Increment of Secondary Forests
We mapped the annual increment of secondary forests using the forest maps produced in Step 1. This process was carried out pixel-by-pixel, where every pixel classified as Forest (value 1) in the analysed year (yi; between 1986 to 2018) and classified as non-forest (value 0) in the previous year (yi-1; i = 1985, 1986… 2017) was mapped as secondary forest. As forest cover maps before 1985 were not available in the MapBiomas product, maps of secondary forest increment start in 1986, when it was possible to detect the first transition (1985 to 1986). Thus, 33 binary maps were obtained, where the secondary forest increments (non-forest to forest) have a value of 1 and the other transitions a value of 0 (forest to forest, non-forest to non-forest, and forest to non-forest). Here, we only considered secondary forest growth in pixels that had previously an anthropic cover (forest plantation, pasture, agriculture, mosaic of agriculture and pasture, urban infrastructure, and mining) and did not overlap wetland areas.
Step 3 – Mapping the Annual Extent of Secondary Forests
We generated 33 maps of the annual extent of secondary forests. To produce the map of secondary forest extent in 1987, we summed the map of the total secondary forest extent in 1986, which is the same map as the secondary forest increment in 1986 from step 2, with the 1987 increment map, resulting in a map containing all secondary forest pixels from 1986 and 1987. Knowing that the sequential sum of these maps results in pixels with values higher than 1, to create annual binary maps of secondary forest extent, we reclassified the map produced for each year by assigning the value 1 to pixels with values between 2 and 33 (secondary forest extent) and pixels with a value 0 were kept unchanged. Finally, to remove all secondary forest pixels that were deforested in 1987, keeping in the map only pixels with the extent of stand secondary forests, we multiplied the resulting map by the annual forest cover map of 1987, produced in step 1 (Fig. 3). This procedure was applied year-by-year from 1986 to 2018 to produce the maps of annual secondary forest extent. The removal of deforested pixels provides a product depicting the extent of secondary forest deforested in each specific year and they were also included as complimentary maps (from 1987 to 2018) in our dataset.
Fig. 3

Conceptual model of the approach used to calculate the age of secondary forests throughout the Brazilian territory.

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Step 4 – Calculating the Age of Secondary Forest
Finally, we calculated the age of the secondary forests (Fig. 3). First, we summed the 1986 map of annual secondary forest extent (from Step 3) with the 1987 map to obtain the age of secondary forests in 1987 (Fig. 4). We continued this summation year-by-year until the secondary forest age map of 2018 was obtained (Fig. 4). The values of each pixel in 2018 correspond to the age of the secondary forest. To ensure the elimination of deforested secondary forests from each age map, we executed a similar procedure as described in step 3 by removing all forest pixels overlaying non-forest areas (Fig. 4). As our analyses started in 1986, it was not possible to identify secondary forests before this year. The 1986 age map, therefore, only shows one-year old secondary forests, and the 2018 map shows ages of secondary forest varying between 1 and 33 years (Fig. 4). If a secondary forest pixel with any age is cleared in a given year, it is then removed and a value of zero is attributed to the pixel. The age of this pixel, subsequently, will only be computed again if the algorithm detects a new non-forest to forest transition in the forest cover map (Step 1), which depends on the MapBiomas project classification method.
Fig. 4

(a) Scatter-plot for the relationship between the proportion of the secondary forest within the 10 by 10 km cells in the two datasets. The dashed blue line is the 1:1 line; the red line is the average regression from the bootstrap approach with 10,000 interactions; the dashed red lines are regressions using the standard deviation values of the equation parameters. All p-values from the 10,000 bootstrap interactions were lower than 0.001. (b) Jitter-plot for the proportion of the secondary forest within the 10 by 10 km cells. The red dot is the mean, and the red vertical line the standard deviation.

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