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Sample procurement and data analysisTo establish a diachronic dataset of Galápagos tortoise dietary stable isotope ecology, we selected samples from five sources (see Supplemental Text): the American Museum of Natural History, New York, New York, (2) the California Academy of Sciences, San Francisco, California, (3) the Natural History Museum, London, England, (4) the National Museum of Natural History, Smithsonian Institution, Washington, D.C., and (5) the Thompson’s Cove (CA-SFR-186H) archaeological site in San Francisco, California. We provide details regarding sample provenience information and date-of-death as supplemental information. From these collections, we obtained single or multiple isotope samples from a total of 57 individual tortoises representing the following subspecies (n = 10) and islands: five C. n. abingdonii (Pinta Island), one C. n. becki (Volcán Wolf, Isabela Island), five C. n. chathamensis (San Cristóbal Island), four C. n. darwini (Santiago Island), thirteen C. n. duncanensis (Pinzón Island), four C. n. guentheri (Sierra Nega, Isabela Island), six C. n. hoodensis (Española Island), one C. n. microphyes (Volcán Darwin, Isabela Island), four C. n. niger (Floreana Island), nine C. n. porteri (Western Santa Cruz Island), one C. n. vicina (Cerro Azul, Isabela Island), one unknown Isabela Island tortoise, two C. n. vicina tortoises which were transported, lived and collected on Rabida Island, and one unknown tortoise (Chelonoidis niger ssp.; unknown Island—the San Francisco Gold Rush sample). The two earliest collected tortoises in our sample date to1833 and the latest tortoise is from 1967, representing a period of 134 years.To understand tissue-specific isotopic variation and fractionation for the purposes of reconstructing long-term dietary ecology, we sampled tortoise bone collagen (n = 57), bone apatite (n = 23), scute keratin (n = 8) and skin (n = 2) for carbon (δ13Ccollagen and δ13Capatite), nitrogen (δ15N), hydrogen (δD) and oxygen (δ18Oapatite) stable isotopes. All samples were drilled or cut using a Dremel rotary tool with either a blade or diamond spherical bit attachment and were transported to the University of New Mexico, Center for Stable Isotopes (UNM-CSI), Albuquerque, NM, for preparation and analysis. All statistical and metric data analysis and visualization occurred in R (4.0.4) and RStudio (2022.02.4). We provide reproducible source code supplemental to the text35.Bone collagen δ13C, δ15N and δDAnalysis of bone collagen, skin and scute keratin for carbon, nitrogen and hydrogen stable isotopes followed standardized protocols (e.g., see36). For bone collagen, we cut and demineralized a small portion of bulk bone in 0.5 N hydrochloric acid (HCl) at 5 °C for 24 h prior to rinsing all samples to neutrality using deionized water. For lipid extraction, we immersed the samples in a solution of 2:1 chloroform:methanol (C2H5Cl3) for 24 h (repeated three times) while also sonicating samples for 15 min to ensure complete chemical saturation. Preparation of skin and scute keratin samples was only included this during the later lipid extraction step (i.e., no demineralization required). After 72 h we rinsed all samples to neutrality and lyophilized the tortoise samples for another 24 h. We then measured approximately 0.5–0.6 mg of bone collagen/skin/scute tissue into tin capsules for carbon (δ13Ccollagen) and nitrogen (δ15N) stable isotope analysis. We also measured approximately 0.2–0.3 mg of bone collagen/skin/scute tissue into silver capsules for hydrogen (δD) isotope analysis. We report isotope values in delta (δ) notation, calculated as: ((Rsample/Rstandard) − 1) × 1000, where Rsample and Rstandard are the ratios (e.g., 13C/12C, 15N/14N) of the unknown and standard material, respectively. Delta values are reported as parts per thousand (‰).Carbon and nitrogen samples were measured on a Costech 4010 elemental analyzer (Valencia, California, USA) coupled to a Scientific Delta V Plus isotope ratio mass spectrometer by a Conflo IV, and hydrogen samples were measured on a Finnigan high-temperature conversion elemental analyzer (TC/EA) coupled to a Thermo Scientific Delta V Plus mass spectrometer by a Conflo IV at UNM-CSI (see37 for details on the high temperature conversion method for hydrogen analysis). All nitrogen and carbon isotope data are reported relative to atmospheric N2 and V-PDB, respectively. The data were corrected using lab standards with values of δ15 N = 6.4‰ and δ13C =  − 26.5‰ (casein protein), and of δ15N = 13.3‰ and δ13C =  − 16.7‰ (tuna muscle) that have been calibrated relative to the universally accepted standards: IAEA-N1, USGS 24, IAEA 600, USGS 63, and USGS 40.To ensure equilibrium between the exchangeable hydrogen in tissue samples and local atmosphere38, we weighed hydrogen standards and samples into silver capsules and allowed both to sit in the laboratory for at least 2 weeks before analysis. Hydrogen data were corrected using three UNM-CSI laboratory keratin standards (δDnon-ex =  − 174‰, − 93‰, and − 54‰) of which the δDnon-ex values were previously determined through a series of atmospheric exchange experiments. These standards were also calibrated to USGS standards CBS and KHS values of − 178.8‰ and − 47.5‰, respectively (see39,40 for details and updated values). To quantitate any error imparted to our collagen data through correction with keratin standards, a UNM-CSI cow (Bos taurus) bone collagen standard was analyzed in every run over a 6-month period (July 2017–January 2018) and gave an inter-run standard deviation of 3.9‰, suggesting the difference in percent exchangeable hydrogen between collagen and keratin tissues did not significantly impact our results. All hydrogen isotope data are reported relative to Vienna-Standard Mean Ocean Water (V-SMOW). The H3 factor was between 8 and 8.5 for all runs.Collagen precision (standard deviation; SD) for within-run analyses is  More

Using a targeted metabolomics approach, we showed that late copepodite stages of the keystone Arctic copepod Calanus glacialis experience important changes in several central energetic pathways following exposure to decreasing pH. These findings shed light on the physiological changes underpinning the effects of OA on fitness related traits such as ingestion rate and metabolic rate previously observed in this species17,18,20.Cellular energy metabolismCellular energy production was altered consistently in both stage CIV and CV, with concentrations of higher energy adenosine phosphates (ATP and ADP) increasing, and concentrations of the lower energy, less-phosphorylated AMP decreasing, with decreasing seawater pH. Moreover, Phospho-L-arginine, which in crustaceans functions as phosphagen in the replenishment of ATP from ADP during transient energy demands32, increased significantly in stage CV. These changes strongly suggest that exposure to low pH affects energy production and expenditure in both developmental stages, although with nuanced differences.NAD+ increased significantly in stage CIV. NAD+ is an essential redox carrier receiving electrons from oxidative processes in the glycolysis, the TCA cycle, and fatty acid oxidation to form NADH. A high NAD+/NADH ratio facilitates higher rates of these reactions and thus potentially higher rates of ATP production (unfortunately, the LC-HRMS could not detect NADH). But most importantly, the produced NADH serves as electron donors to ATP synthesis in the oxidative phosphorylation. For every ATP produced in the oxidative phosphorylation one NADH is oxidised back to NAD+. High rates of ATP production in the oxidative phosphorylation would therefore amass NAD+, as observed in stage CIV. Conversely, ATP production in the glycolysis and TCA cycle consumes NAD+ (9 NAD+ per 4 ATP) and glycolytic ATP production would decrease the NAD+ concentration with decreasing pH.Heterotrophic organisms generally face a trade-off between rate and yield of ATP production. The efficient low rate/high yield production in the TCA cycle/oxidative phosphorylation may prevail under certain circumstances, whereas under other circumstances, the less efficient high rate/low yield production in the glycolysis may predominate33. Because glycolysis and oxidative phosphorylation compete for ADP, the one dominate over the other in terms of rates depending on the substrate being metabolised. In stage CIV copepodites, the TCA cycle pathway was enriched in the MetPA, and metabolites associated with glycolysis and the TCA cycle showed significant changes in their concentrations at decreasing seawater pH. Glucose, the entry point to glycolysis, increased significantly with decreasing pH. High levels of blood glucose (hyperglycemia) have been observed as a general stress response in decapod crustaceans34. Copepods have no circulatory system (although they have a dorsal heart) but might nevertheless react similarly on the cellular level. Along with the significant increase in glucose, lactate decreased significantly with pH in stage CIV. Lactate is an inevitable end product of glycolysis, because lactate dehydrogenase has the highest Vmax of any enzymes in the glycolytic pathway and the Keq for pyruvate to lactate is far in the direction of lactate35. Accordingly, although the glycolysis was not enriched in the MetPA, conceivably because none of its intermediate metabolites were included in the analyses (the protocol did not allow for it), we hypothesise that stage CIV copepodites experience a general down-regulation of glycolysis under decreasing pH. Alternatively, the amassing of glucose and depletion of lactate could also indicate increased gluconeogenesis. Gluconeogenesis occurs during starvation to replenish glycogen stores and ingestion rates did decrease in stage CIV20. But again, we did not target any intermediates in our analyses, and thus cannot firmly conclude on this.Phosphofructokinase-1 is a key regulatory enzyme of glycolysis36. This enzyme is allosterically inhibited by ATP and activated by AMP, and interestingly this regulation is augmented by low pH37,38. Thus, phosphofructokinase-1 could be key to the down-regulation of glycolysis we hypothesise. The fact that we found increasing oxygen consumption with decreasing pH in stage CIV copepodites from the same experiment adds further momentum to this line of thought20. It seems that stage CIV copepodites might experience the so-called Pasteur effect—a decrease in glycolysis at increased levels of oxygen uptake—when exposed to decreasing pH39. Although ATP and AMP were significantly affected also in stage CV, glucose, pyruvate and lactate did not change with decreasing pH, which perhaps indicate absence of the down-regulation of glycolysis we hypothesise for stage CIV. There is, nevertheless, one indication that down-regulation may in fact occur also in this developmental stage. Alpha-glycerophosphate decreased significantly with decreasing pH in stage CV. This molecule is an intermediate in the transfer of electrons from NADH produced by glycolysis in the cytosol to the oxidative phosphorylation in the mitochondria, and decreased concentrations could result from down-regulation of the glycolysis also in stage CV copepodites.The TCA cycle was enriched for stage CIV and most of the measured TCA cycle metabolites (alpha-ketoglutarate, succinate, fumarate, and malate) showed increasing concentrations at decreasing pH. Trigg et al.40 observed a similar increase in concentrations of TCA cycle-related metabolites in the Dungeness crab, Cancer magister (Dana, 1852), at decreased pH and concluded that TCA cycle activity is upregulated under OA. Since NAD+ is the product of the transport of electrons from the TCA cycle to the oxidative phosphorylation in the mitochondria,  the increase in NAD+ concentration we observed in stage CIV could reflect an increase in the flow of electrons from the TCA cycle to the oxidative phosphorylation, and by extension an increase in the energy production by the TCA cycle and the oxidative phosphorylation. There is negative feedback from the TCA cycle to glycolysis through inhibition of phosphofructokinase-1 by citrate, a metabolite of the TCA cycle38. Unfortunately, we did not target citrate in our targeted approach to specifically test this hypothesis, but the amassing of NAD+ do provide additional support to the idea that glycolysis is down-regulated at decreasing pH. Again, there is a less clear picture of how cellular energy metabolism is affected by decreasing pH in stage CV when compared to stage CIV. There was no clear pattern of regulation of TCA metabolites, and the TCA cycle was not enriched in the MetPA. Nevertheless, alpha-ketoglutarate concentrations did increase with decreasing pH in CVs.The glyoxylate/dicarboxylate cycle was also enriched in the pathway analysis, but this is probably also a result of the increases in concentrations of alpha-ketoglutarate, succinate, fumarate, and malate, and we are unable to distinguish it from the TCA cycle based on the set of metabolites analysed.Conclusively, lowered glycolysis due to inhibition of phosphofructokinase-1 and upregulation of the TCA cycle and oxidative phosphorylation at low pH in stage CIV appear plausible causes for the changes in ATP, ADP and AMP concentrations we observed. Alongside these effects, down-regulation of transcription of genes involved in the glycolysis were also present in nauplii of C. glacialis exposed to 35–38 days of low pH conditions16. On the other hand, studies on the acclimatisation and adaptation to OA in another calanoid copepod species, Pseudocalanus acuspes (Giesbrecht, 1881), showed no increase in expression of mitochondrial genes at pHT 7.54, which would have been expected if the TCA cycle or oxidative phosphorylation is upregulated41. Interestingly, De Wit et al.41 also showed natural selection in a large fraction of mitochondrial genes under OA conditions. Even evolutionarily conserved sequences, such as cytochrome oxidase subunit I, were under selection and it was hypothesised that the mitochondrial function of oxidative phosphorylation is a target for natural selection in copepods at low pH41.Besides its role in the transfer of energy from the mitochondria to the cell, ATP is also used to fuel cell homeostasis and active cellular acid–base regulation by activation of ATP-dependent enzymes involved in osmo-ionic- and acid–base regulation. In crustaceans, acid–base status is linked to ion regulation, and is maintained primarily through ion transport mechanisms moving acid and/or base equivalents between the extracellular fluid and the ambient water42. One prominent process in this respect is regulation by Na+/K+-ATPase42,43. While this regulation takes place in the gills of decapod crustaceans43, it is located in the maxillary glands and other specialised organs on the swimming legs of copepods44. Any extensive ATPase mediated pH regulation could have manifested itself by decreasing ATP concentrations, but this is contrary to what we report here. Interestingly, while the pCO2-sensitive isopod Cymodoce truncata (Leach, 1814) is able to maintain its cellular ATP concentration at the expense of the concentration of carbonate anhydrase (an enzyme involved in the cellular transformation of water and CO2 to bicarbonate ions and H+ prior to the ATPase mediated transport of H+ across the cell membrane), the pCO2-tolerant isopod Dynamene bifida (Torelli, 1930) upregulates ATP with no functional compromise to CA concentrations45. Finally, C. glacialis nauplii have shown upregulation of Na+/H+-antiporters independent of ATPase as a response to OA16, which one could hypothesise also may be the case in the copepodites. Arctic populations of the amphipod Gammarus setosus also do not experience increased ATPase activity during OA conditions46. It seems that C. glacialis faces OA without any ATP dependent acid/base regulation activity.Glycolysis is the first step of catabolism of carbohydrates for the production of energy. When down-regulating glycolysis the copepods may be increasingly dedicated to catabolism of amino acids e.g. through oxidative deamination of glutamate and/or catabolism of fatty acids through beta-oxidation to produce the energy they require21. Both lead to the production of molecules entering the TCA cycle and ultimately the oxidative phosphorylation for energy production in the mitochondria.Amino acid metabolismOf the free amino acids which were significantly affected by decreasing pH, the majority decreased in concentration, for both stage CIV and CV copepodites. This could be an indication of changes in protein synthesis at decreasing pH. Supporting this idea, biosynthesis of aminoacyl-tRNA was indicated as significantly enriched in the MetPA in both stage CIV and CV. Aminoacyl-tRNA partakes in the elongation of the protein amino acid chain during protein synthesis and the enrichment was most likely due to the changes in concentration of the many amino acids tested. One probable cause of protein synthesis is the increased demands of enzymes needed to handle stress at low pH, including for example enzymes involved in acid–base- and osmo-regulation or regulation of energy production. Increased protein synthesis caused by OA conditions has been observed in larvae of the purple sea urchin Strongylocentrotus purpuratus (O.F. Müller, 1776), where in vivo rates of protein synthesis and ion transport increased ∼50%47. Costs of protein synthesis are high and have shown to constitute a major part of copepod metabolic demand48 and we did observe significant increases in metabolic rate in copepodite stage CIV from the same experiment20 giving further credit to the idea that protein synthesis was upregulated.An alternate but not mutually exclusive explanation is that the copepods experience increased amino acid catabolism under OA. Glutamate increased in stage CIV accompanied by a significant increase in alpha-ketoglutarate in both stage CIV and CV. Alpha-ketoglutarate is part of the metabolic pathway of glutamine, glutamate and arginine in which glutamate acts as an intermediate in catabolism of these amino acids when it is deaminated to alpha-ketoglutarate to enter the TCA cycle49. Glutamate metabolism (in conjunction with alanine and aspartate metabolism) was significantly enriched in the MetPA in both stage CIV and CV, and these changes could be taken as an indication of a shift towards amino acid catabolism with decreasing pH. The key enzyme catalysing the oxidative deamination of glutamate is glutamate dehydrogenase (GDH), which functions in both directions: deamination of glutamate to form alpha-ketoglutarate or formation of glutamate from alpha-ketoglutarate. Studies on the ribbed mussel, Modiolus dernissus (Dillwyn, 1817), have shown that the balance of this action is strongly pushed towards deamination when pH decreases from 8.0 to 7.550. GDH is activated by ADP, and one could argue that the increase in ADP we observed would work against this shift, but ADP activates GDH mainly in the glutamate forming direction51. The other measured amino acids enter the TCA cycle at different positions we unfortunately could not target in our analyses. Glutamate also partakes in the arginine biosynthesis pathway in which it is transformed to ornithine to enter the urea cycle. Arginine biosynthesis was enriched in the MetPA and it is therefore possible that decreasing pH also changes amino acid catabolism to increase urea excretion. Decreasing pH has a similar depressing effect on amino acid concentration in the gills of the shore crab Carcinus maenas (Linnaeus, 1758) which also has been interpreted as a sign of increased protein catabolism52. Hammer and colleagues52 argued that this increase in catabolism served to buffer H+ by supplying nitrogen to NH4 formation in the cells. All in all, we hypothesise that increased amino acid catabolism, possibly driven by changes in GDH activity, and the down-regulation of glycolysis by inhibition of phosphofructokinase-1 may be major drivers of a shift from carbohydrate metabolism towards catabolism of amino acids.D-glutamine/D-glutamate metabolism was highly enriched in the MetPA in both developmental stages. Several studies show enriched D-glutamine/D-glutamate metabolism in crustaceans [e.g. 53], but they offer no explanation of its function or the reason why it is enriched. While D-glutamate act in neurotransmission, this action is evolutionarily restricted to ctenophores, and biochemical measurements of D-amino acid concentrations have shown absence of D-glutamate in crustaceans54,55.We observed no changes in concentrations of 8-oxy-2-deoxyguanosine, a product of DNA oxidation. Furthermore, regulation of cellular response to oxidative stress is down-regulated in C. glacialis nauplii16, and OA may not induce oxidative stress in C. glacialis.Fatty acid metabolismBesides their importance in energy storage as wax esters, fatty acids are involved in many central processes in cells, most prominently through their function as cell membrane building blocks. Many fatty acids are obtained from the diet but some longer chain fatty acids, such as 20:1n-9 are synthesised de novo in copepods56. Stage CV copepodites experienced increases in most of the targeted free fatty acids (18 of 21) with decreasing pH. Only one of those 18 increased significantly, but since the direction of change were the same in all, we argue that the pattern of change does merit consideration. Conspicuous exceptions were eicosapentaenoic acid (EPA) 20:5n-3 and docosahexaenoic acid (DHA) 22:6n-3, which both decreased significantly. The only other study (to our knowledge) of metabolomic effects of environmental changes in copepods showed the exact same response to starvation in a mix of C. finmarchicus and C. helgolandicus stage CV copepodites, with most fatty acids increasing while EPA and DHA decreased in concentration57. EPA and DHA are key marine polyunsaturated fatty acids (PUFAs) exclusively produced by marine algae. They contribute a major fraction of the fatty acids of cell membrane phospholipids58, and zooplankton reproductive production is highly dependent on especially EPA59. EPA and DHA are key for cell membrane fluidity, which for calanoid copepods is especially important during diapause in the deep during copepodite stage CV60. They have also been linked to diapause buoyancy control, and are selectively metabolized in diapausing copepodites61. The importance of EPA and DHA for cell membrane integrity may be central for the changes we observed. Glycerol-3-phosphate, the precursor for the glycerol backbone of cell membrane phospholipids also decreased significantly and it seems decreasing pH could affect cell membrane turnover.Changing fatty acid concentration could be due to either a change in lipid intake from feeding or increased fatty acid catabolism. While ingestion rates decreased in stage CIV, they were unchanged in stage CV with decreasing pH20. Also, Thalassiosira weissflogii (Grunow) G.Fryxell & Hasle, 1977, the diatom we fed to the copepods, is rich in 16:0, 16:1n-7 and EPA59. The concentrations of 16:0 and 16:1n-7 increased, whereas EPA concentration decreased. If fatty acid concentrations reflected feeding, we would have seen increased concentrations of all three. We therefore believe that the general increases in concentrations of free fatty acids were caused by increasing catabolism of the wax esters stored in stage CV. It may be that due to the metabolic reconfiguration to enter hibernation, stage CV copepodites are already committed to the catabolism of fatty acids through beta-oxidation, and stored wax esters are being hydrolysed to increase the availability of free fatty acids for energy production. Mayor and colleagues57 arrived at the same conclusion. We hypothesise that stress due to low pH increases the organism’s energetic demands, but carbohydrates are not used to accommodate these demands due to the down-regulation of the glycolysis, rather demands are met by hydrolysing and metabolising wax esters in stage CV. The further ramifications of future OA could therefore be a less efficient build-up of wax esters so important for hibernation in this species.Finally, besides their importance for cell membrane fluidity, EPA and DHA are important precursors for eicosanoid endocrine hormones. These hormones are important regulators of, among other processes, ion flux62. As mentioned above, acid base regulation is coupled to osmoregulation in crustaceans42, and the decrease in concentrations of these two specific fatty acids, when all other fatty acid concentrations increased might represent an indication for changing endocrine hormone production to counter adverse whole-organism effects of OA.Changes in metabolite concentrations cannot be directly translated into changes in the rate of the processes they are involved in. However, they do pin-point processes which are affected by the imposed environmental changes. Also, in our analyses we targeted a limited range of molecules. In that respect OA could inflict changes in other important metabolic pathways we did not investigate. The absence of specific biochemical pathways in our analyses and discussion should therefore not be taken as indication that these are not implicated in this species responses to OA.From our previously published study on copepodites from the same incubations, we know that high pCO2/low pH conditions have detrimental effects on the balance between energy input (ingestion) and energy expenditure (metabolism) in stage CIV copepodites but not in stage CV copepodites20. The effects we report here help in this sense to shed light on the metabolic origin of the rather severe effects on energy balance we observed in stage CIV copepodites and the difference in response between stage CIV and CV20. Copepods develop through six nauplii and five copepodite stages before maturation, and while previous studies show negligible effects in stage CV and adults17,18,20, any effects in any developmental stage along the way will affect the fitness of the individual and the recruitment to the population as a whole. In addition, the enhanced fatty acid metabolism observed in stage CV needs further investigation, to determine the magnitude of the fitness implications of the energy diverted away from energy storage for hibernation. More

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Aerial imagesWe use publicly available aerial images of Rwanda at 0.25 × 0.25 m2 resolution, collected in June–August of 2008 and 2009. The images were acquired from 3,000 m altitude above ground level, originally with a mean ground resolution of 0.22 × 0.22 m2 pixel size then resampled to 0.25 × 0.25 m2, using a Vexcel UltraCam-X aerial digital photography camera34. The images exhibit a red, green and blue band stored under 8 bit unsigned integer format. The aerial images cover 96% of the country and the remaining 4% was filled with satellite images from WorldView-2, Ikonos, Spot and QuickBird satellite sensors which are part of the publicly available dataset.Environmental dataWe use locally available climate data: mean annual rainfall, mean annual temperature and elevation data (10 × 10 m2 resolution) to assess relationships between tree density, crown cover and environmental gradients. We also use land cover data to extract the spatial extent of plantations, forest, farmland, and urban and built-up areas for our landscape stratification. Climate data were obtained from the Rwanda Meteorological Agency as daily records from 1971 to 2017. The national forest map was manually created in 2012 using on-screen digitizing techniques over the 2008 aerial images35. A forest was defined as ‘a group of trees higher than 7 m and a tree cover of more than 10% or trees able to reach these thresholds in situ on a land of about 0.25 ha or more’51. A shrub was defined as ‘a group of perennial trees smaller than 7 m at maturity and a canopy cover of more than 10% on a land of about 0.25 ha or more’. The forest dataset was composed of 105,690 forest polygons, classified as either natural forest (closed natural forest, degraded natural forest, bamboo stand, wooded savanna and shrubland) or ‘forest plantations’ (Eucalyptus spp., eucalyptus; Pinus spp., pine; Callitris spp., callitris; Cupressus spp., cypress; Acacia mearnsii, black wattle; Acacia melanoxylon, melanoxylon; Grevillea robusta, grevillea; Maesopsis eminii, maesopsis; Alnus acuminata, alnus; Jacaranda mimosifolia, jacaranda; mixed species, mixed; and others) (Extended Data Fig. 7i). We separate shrubland from natural forest and merged it with savanna into the class ‘savannas and shrublands’. We further separated tree plantations and grouped them into Eucalyptus and non-Eucalyptus plantations. Then, a farmland map was acquired from the Rwanda Land Management and Use Authority (RLMUA)52 and overlaid with the 2012 forest cover map as a reference to clean the overlapping parts, under an assumption that the overlap is due to land use dynamics. Finally, a layer marking urban and built-up areas was acquired from RLMUA as well and the same preprocessing step as done for farmlands was applied. The combination of the land cover datasets resulted in our stratification scheme with six classes: natural forests, savannas and shrublands, Eucalyptus plantations, non-Eucalyptus plantations, farmland and urban and built-up.Mapping of individual trees using deep learningWe used the open-source framework developed by ref. 17 to map individual tree crowns. The framework uses a deep neural network based on the U-Net architecture53,54. We trained the network using 97,574 manually delineated tree crowns spread over 103 areas/bounding boxes representing the full range of biogeographical conditions found across Rwanda. To cope with the challenge of separating touching tree crowns, we used a higher weight for boundary areas between crowns, as suggested in refs. 17,53. Crown sizes in the predictions were found to be 27% smaller as compared to the manual delineations within the 103 training areas, due to the applied boundary weight that emphasizes gaps between tree crowns. Therefore, to calculate the real canopy cover, we extended each predicted tree crown by 27% and dissolved the touching crowns into continuous features. We counted single tree crowns for each hectare presented here as tree density and the percentage of each hectare covered by the extended tree crowns as canopy cover.We developed a postprocessing method that separates clumped tree crowns and fills any gap inside a single crown (Extended Data Fig. 2). Our postprocessing method, which we refer to as detect centre and relabel (DCR), determines the crown centres in the model predictions assuming that tree crowns have a round shape and then relabels the model predictions on the basis of weighted distances to the identified crown centres. First, DCR performs a distance transform, computing for each pixel the Euclidean distance to the nearest pixel predicted as background. Let the transformed image be distance-transformed (DT). Then an m × m maximum filter is applied to DT, where m depends on the size of the smallest object to be separated. We store all pixels for which the original DT value is the same before and after max-filtering. These pixels are the instance centres as they are furthest away from the boundary and have the highest distance values within the area defined by m. In the case of several connected instance centres in regions where multiple connected pixels have the same distance from the background, only a single instance centre is kept. Finally, each pixel x predicted as a crown in the original image is assigned to its nearest instance centre, where the distance function penalizes background pixels on the connecting line between the instance centre and x.Allometry for biomass and carbon stock estimationGenerally, allometric equations define a statistical relationship between structural properties of a tree and its biomass55,56. In our case, we assume a relationship between the crown area and aboveground biomass (AGB), which varies between biomes36. Since destructive AGB measurements are rare, we established biome-specific relationships between crown diameter (CD) derived from the crown area (CD = 2√(crown area/π)) and stem diameter at breast height (DBH) (equations (3) and (6)). DBH has been shown to be highly correlated with AGB36,37,38,39,40. We then used established relationships from literature to derive AGB from DBH for savannas and shrublands (equation (4)), tree plantations (equation (5)) and natural forests (equation (7)). AGB was predicted for each tree and summed for 1 ha grids to derive AGB in the unit Mg per ha. Values were multiplied by 0.47 (refs. 57,58) to derive aboveground carbon (AGC). Summed numbers over land cover classes are considered as carbon stocks. The bias as reported here was calculated following the approach from ref. 36 reporting the relative systematic error in per cent:$$mathrm {bias} = frac{1}{N}mathop {sum}limits_{i = 1}^N {frac{{(Y_{mathrm {obs}} – Y_{mathrm {pred}})}}{{Y_{mathrm {obs}}}}}times 100$$
(1)
The error for the evaluation with NFI data was defined by:$$mathrm{bias} = frac{{left| {mathop {sum}nolimits_N {(Y_{mathrm{obs}} – Y_{mathrm{pred}})} } right|}}{{left| {mathop {sum}nolimits_N {Y_{mathrm{obs}}} } right|}}$$
(2)
For trees outside natural forests, we used the database from ref. 36 including 10,591 field-measured trees from woodlands and savanna plus 952 samples from agroforestry landscapes in Kenya37 to establish a linear relationship between CD and DBH (Extended Data Fig. 3a). The Kenyan dataset is compatible with the trees in Rwanda. To ensure compatibility, the Kenya data contained open-grown trees most of which are of the same families or genus as in Rwanda grown under the same conditions, the latter factor shown to be important for generalizing37.A major axis regression (average of four runs each 50% of the data) led to equation (3):$${{{mathrm{DBH}}}}_{{{{mathrm{predicted}}}}},{{{mathrm{in}}}},{{{mathrm{cm}}}} = – 4.665 + 5.102 times {{{mathrm{CD}}}}$$
(3)
Equation (3) showed a reasonable performance with a very low bias (average of four runs on the 50% not used to establish the equation (3)): r² = 0.71; slope = 0.95; root mean square error (RMSE) = 6.2 cm; relative RMSE (rRMSE) = 42%; bias = 1%). We tested equation (3) on an independent dataset from Kenya consisting of 93 trees where AGB was destructively measured (Fig. 3b). The Kenyan database provides an uncommon opportunity to use destructive samples in which the carbon mass is not estimated indirectly and the relationship between crown area and carbon is direct: we do not need to invoke a second allometry to derive the dependent variable. All trees were open-grown trees in the same growing conditions as the agricultural areas of Rwanda. On these 93 trees, DBH can be predicted reasonably well from CD using equation (3) (r² = 0.84; slope = 0.86; RMSE = 8 cm; rRMSE = 25%; bias = 6%). We then applied an allometric equation from literature37 established for non-forest trees in East Africa to estimate AGB from DBHpredicted and compared the predicted AGB with the destructively measured AGB (r² = 0.81; RMSE = 511 kg; rRMSE = 55%; bias = 25%) showing an acceptable performance (Extended Data Fig. 3c) but indicating a systematic bias, which will be further tested with biome-specific field data (next section). We apply equation (4) to estimate AGB for trees outside forests in Rwanda in savannas and shrublands:$${{{mathrm{AGB}}}}_{{{{mathrm{predicted}}}}},{{{mathrm{in}}}},{{{mathrm{kg}}}} = 0.091 times {{mathrm{DBH}}_{{mathrm{predicted}}}}^{2.472}$$
(4)
Given the different structure of trees in farmlands, urban and built-up areas and plantations as compared to trees in natural forests and in natural non-forest areas, we used a different equation for trees in these areas. It was established in Rwanda using destructive samples from tree plantations39:$${{{mathrm{AGB}}}}_{{{{mathrm{predicted}}}}},{{{mathrm{in}}}},{{{mathrm{kg}}}} = 0.202 times {{mathrm{DBH}}_{{mathrm{predicted}}}}^{2.447}$$
(5)
A different CD–DBH relationship was established for natural forests. Here, we conducted a field campaign in December 2021 sampling 793 overstory trees in Rwanda’s protected natural forest. We measured both CD and DBH and established a logarithmic major axis regression model with a Baskerville correction59 between the two variables to predict DBH from CD (Extended Data Fig. 3d). We did four runs each using 50% of the data to establish equation (6) (average of the four runs) and the other 50% to test the performance also averaged over the four runs (r² = 0.71; slope = 0.99; RMSE = 13 cm; rRMSE = 45%; bias = 19%). Note that CD is extended by 27% to account for underestimations of touching crowns in dense forests (see previous section):$$begin{array}{l}{mathrm{DBH}}_{{mathrm{predicted}}},{mathrm{in}},{mathrm{cm}} = left({mathrm{exp}}left(1.154 + 1.248 times {mathrm{ln}}({mathrm{CD}} times 1.27) right)right.\left. times left({mathrm{exp}}(0.3315^2/2) right) right)end{array}$$
(6)
We then used a state-of-the-art allometric equation established for tropical forests38 to predict AGB from DBH for natural forests in Rwanda:$$begin{array}{l}{{{mathrm{AGB}}}}_{{{{mathrm{predicted}}}}},{{{mathrm{in}}}},{{{mathrm{kg}}}} = {{{mathrm{exp}}}}Big[ {1.803 – 0.976{{{E}}} + 0.976,{{{mathrm{ln}}}}left( rho right)}\+ 2.673;{{{mathrm{ln}}}}left( {{{{mathrm{DBH}}}}} right) – 0.0299left[ {{{{mathrm{ln}}}}left( {{{mathrm{DBH}}}} right)} right]^2 Big]end{array}$$
(7)
where E measures the environmental stress38 (a gridded layer is accessible via https://chave.ups-tlse.fr/pantropical_allometry.htm) and ρ is the wood density. Here, we used a fixed number (0.54), which is the average wood density for 6,161 trees from ref. 40, weighted according to the abundance of the species in the plots. The relative error was calculated by the quadratic mean of the intraplot and interplot variations, which is 18.2% (Extended Data Table 1b). No destructive AGB measurements were found that showed a similar CD–DBH relationship as we measured during the field trip in Rwanda’s forest. We could thus not evaluate the performance for natural forests at tree level but had to rely on plot-level comparisons (next section).Evaluation and uncertainties of the allometryBiomass estimations without direct measurements of height or DBH inevitably include a relatively high level of uncertainty at tree level38,60. Uncertainty does not only originate from the CD to DBH conversion but also the equation converting DBH to AGB. As shown in the previous section, no strong systematic bias could be detected for the CD to DBH conversion but the evaluation of the CD-based AGB prediction with an independent dataset from destructively measured AGB revealed a bias of 25%. However, this comparison (Extended Data Fig. 3c) may not be representative for an entire country having a variety of landscapes and tree species, so a systematic propagation is unlikely. We also did not have sufficient field data to evaluate the conversions in natural forests. Here, we used data from 15 natural forest plots with 6,161 trees published by ref. 40 and ref. 41 and directly compared the summed biomass of the trees we predicted over their plots. The median measured biomass for the plots is 121 MgC ha−1 and we predict a median biomass of 81 MgC ha−1 (plot-based rRMSE = 54%; bias = 11%; bias on summed plots = 26%). The overall underestimation by our prediction is not necessarily a model bias but may be partly explained by the contribution of the understory trees, which cannot be captured by aerial images. Interestingly, our C stock estimates are in the same range of magnitude as global biomass products43,44,45,61 (Extended Data Fig. 4), indicating that overstory tree-level carbon stock assessments are possible from optical very high resolution images, even in tropical forests. Several global products overestimated biomass for non-forest areas like savannas or croplands, which is probably because they are calibrated in denser forests. The most recent products of ref. 42 and ref. 61 are much closer to the estimates from our results and the NFI. This is also seen in the grid-based correlation matrix where ref. 42 correlates best with our map, followed by ref. 61.We further use NFI data from 2014 to measure the uncertainty of the final carbon stock estimates and evaluate if systematic differences between AGB predictions and field assessments can be found for different land cover classes (Extended Data Table 1). For the NFI data, a total of 373 plots with 2,415 trees were measured and species-specific allometric equations applied62. To identify systematic errors at landscape scale, we extracted averaged values for areas around the plots from our predictions and calculated statistics on averages over all plots. Interestingly, our predictions for farmlands only show a bias of 5.9%: we estimate on average 2.46 MgC ha−1 and the inventories measure 2.37 MgC ha−1 on their 150 plots. For savanna and shrublands, we estimate 4.16 MgC ha−1 while inventories measure 3.31 MgC ha−1 (bias = 18.9%). For plantations, we estimate lower values (8.16 compared to 16.79 MgC ha−1; bias = 52.6%). To calculate the total uncertainty on country-wide C stock estimates, we weighted the bias from the different classes according to their relative area. We estimate a total uncertainty on the carbon stock predictions of 16.9% at the national scale (Extended Data Table 1).We found a very low bias for estimated C density in farmlands (5.9% bias) which make up most of the areas outside natural forests in Rwanda (Extended Data Table 1, Extended Data Fig. 6). The high bias for plantations can be explained by three factors: large bare areas considered part of plantations by the manual delineation of plantation areas (Extended Data Fig. 1); regular harvesting and continual thinning which keep many plantation trees young and small; and the fact that our aerial images are from 2008 while plantation trees have grown until 2014 with a few new NFI plots initiated after 2008. The bias in savannas and shrublands can be explained by the following factors: the presence of multistemed trees with large crowns such as Acacia spp. and Ficus spp. among others; the fact that a crown-based method overestimates C stocks of shrubs with a small height; and presence of shrub trees with both small height and small (multiple) stems. If tree-level based carbon stock assessments derived from crown diameter as presented here should become standard to complement national inventories, a database with sufficient samples to evaluate for systematic errors needs to be established for each biome and inventory and satellite/aerial image-based methods need to be further harmonized.To further quantify the error propagation of the CD to DBH conversion for our application, we established four equations each randomly using 50% of the dataset and predicted the carbon stock for each tree in Rwanda with each equation. We did this separately for natural forests and trees outside natural forests. We calculated the rRMSE between the aggregated carbon stocks for each hectare. We averaged the rRMSE for each land cover class and show that the uncertainty for all classes does not exceed 5% (Extended Data Table 2a).Evaluation and uncertainties of tree crown mappingWe created an independent test dataset, which was never seen during training and was also not used to optimize hyperparameters. The test set consists of 6,591 manually labelled trees located in 15 random 1 ha plots (Extended Data Fig. 5). Thanks to the size of the country, the plots represent all rainfall zones and three major landscapes of the country. The plot-level comparison yielded very high correlations between the predictions and the labels and is shown in Extended Data Fig. 5. We also calculated a confusion matrix showing an overall per pixel accuracy of 96.2%, a true positive rate of 79.6% and a false positive rate of 6.8% (Extended Data Table 2b). Trees outside natural forests are easy to spot and count for the human eye, so we have confidence in the plot-based evaluation. However, it is often challenging in natural forests. Here, we used again the field measurements from 15 plots with 6,161 trees40,41. We find that we underestimate the total tree count by 22.6%, which may, at least partly, be explained by understory trees hidden by overstory trees and which are, therefore, not visible in our images. New field campaigns are needed to better understand and calibrate our results and possibly correct for systematic bias.Application and evaluation beyond RwandaWe acquired 83 Skysat scenes at 80 cm for Tanzania, Burundi, Uganda, Rwanda and Kenya. The model trained on the 25 cm resolution aerial images of Rwanda from 2008 was directly applied on the Skysat images. Forest and non-forest areas were manually delineated to decide which allometric equation to use for the carbon stock conversion. We randomly selected 150 1 × 1 km2 patches and aggregated the predicted carbon density per patch and compared the results with previously published maps42,43,44,45. Results show that the model can directly be applied to comparable landscapes on different datasets. Note, however, that accurate carbon stock predictions need local adjustments with field data. We then tested the tree crown model transferability on aerial images from California (NAIP; 60 cm) and France (20 cm) and found that the model delivers realistic results without any local training or calibration (Extended Data Figure 8).Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article. More