Philippa Kaur

The risks of open forest data exploitation are magnified by features of how forests are measured and who does the measuring. Generating long-term data on forest health and change involves physically measuring and identifying millions of trees. This means establishing, maintaining and revisiting plots, and curating records indefinitely. Trees are long-lived organisms so forests require decades of monitoring to properly infer change. Sustaining local observations for decades needs deep, long-term commitment to the unique but shifting combinations of people, institutions, regulations, interests and relationships that characterize each forest site. The challenge is enhanced by the great biodiversity of tropical forests. Measuring a single hectare of Amazon forest involves collecting and identifying up to ten times the number of tree species that are present in the UK’s entire 24 million hectares. There are very few people with the skills to do this.Long-term tropical-forest data measurements not only require effort and skill but also often carry risk and depend on some of the most disadvantaged actors in the global science community. Many forest workers (researchers, technicians, students, field assistants and local communities) lack basic job security, much less a career path, despite the long-term dedication that monitoring forests requires. In addition, many tropical forest workers may endure dangerous field conditions, with threats including kidnapping, armed insurgents, narcotraffickers, land-grabbers, infectious disease, snakebite, floods, fire, dangerous transport and gender-based violence. Besides these personal dangers, tropical scientists often lack the basic resources to measure and maintain their forest plots, let alone develop their research groups8.In contrast to the experiences of those monitoring forests on the ground, consider the context for satellite and aircraft-based measurements, which require ground-based data for validation. Space-based forest missions are expensive but are funded by public or private capital. Once in orbit, they stream data to analysts ‘for free’. This requires relatively few people to sustain, and although the analysts’ work is highly skilled, it carries little professional and physical risk and lacks commitment to place. Forest fieldwork is less capital-intensive, but needs sustained investment, is intensely human and carries substantial costs and risks. There are no automated collecting stations to help to identify and measure trees, so without the long-term dedication of many forest workers data collection simply stops.The risks and costs involved in acquiring and sustaining ground forest data are persistently overlooked, ignored or regarded as externalities to be picked up by the forest workers themselves. This is especially problematic because countries that hold the most tropical forests are among those least able to invest in science and development (Fig. 1, Supplementary Fig. 1). For example, monitoring the carbon balance of intact tropical moist forests has been estimated to cost US $7 million a year12, easily exceeding present support. By contrast, the USA alone spends over $90 million annually on its national forest inventory13. So, many tropical forest data are collected by skilled people working with minimal funding, in challenging conditions and facing other constraints, including complex layers of rules, agreements and research permits. Given such huge disparities, it is hardly reasonable to expect this output to be served on an open plate to the world.Fig. 1: Global distributions of per capita gross domestic product and tropical forest area.a,b, The 2008–2018 national average gross domestic product per capita (a) and tropical forest area per capita (b). Countries are coloured according to position from lowest (dark red) to highest (dark blue) within each global distribution.Full size imageIt is perhaps unsurprising that the most vocal proponents of making tropical and subtropical forest data open are often not those who actually measure and monitor them. Meanwhile, key beneficiaries include powerful publishers (usually with commercial interests), agencies and technology companies (often with commercial or political interests), and highly educated computer-savvy analysts wishing to integrate earth observation data with forest data (naturally with a career interest). Relatively few of these institutions and people are based in the tropics and subtropics. Fewer still are also data originators.And so, for many data originators the present meaning of making tropical forest data ‘open’ is to transfer the hard-won output of their labours to more privileged individuals and institutions, and lose more of the limited control they have over their professional lives. Power flows from the originators to public agencies, private companies and data scientists, mainly in the Global North. More

The GUTS modelFor completeness, we will prove the result for the most general GUTS model, which will also prove the result for all reduced forms.Theorem 1
For any model version within the GUTS framework, let (S(t; alpha )) denote the survival probability at time t for a given non-zero exposure profile (C_w(t)) scaled by some EMF value (alpha). For any chosen (x > 0) percentage effect (exposure-induced mortality), model end time (t_{E}) and background mortality (h_b) low enough such that (S(t_E; 0) > 0) there exists a unique EMF (alpha _*) such that$$begin{aligned} S(t_{E}; alpha _*) = left( 1 – frac{x}{100}right) S(t_E; 0), end{aligned}$$
(2)
(alpha _*) is the (hbox {LP}_{x}) for the exposure profile.
Baudrot and Charles10 calculated (LC_{50}) values for GUTS-RED-SD and GUTS-RED-IT. Their results implied the result of Theorem 1 for the main regulatory models. Our work makes the result explicit and generalises it to the whole GUTS framework. Another result of Theorem 1 is that the (hbox {LP}_{x}) is monotonically increasing with respect to x. For example, the (hbox {LP}_{50}) will always larger than the (hbox {LP}_{10}) for the same exposure profile. This result comes directly from (S4) in the SI.DEB modelsDue to the additional complexity of the DEB model we split the result into multiple theorems and proofs, starting by showing continuity and monotonicity of the damage ODE.
Theorem 2

Let
(C_w)
be some external concentration over time. Assume an effects model where the effects of higher exposure on growth and/or reproduction are always adverse (or zero) at all points in time. Then, defining the scaled damage ODE as
$$begin{aligned} begin{aligned} frac{D(t; alpha )}{dt} =&k_d(x_u alpha C_w – x_eD) – (x_G + x_R)D. end{aligned} end{aligned}$$
(3)

Then, for any combination of feedbacks (varvec{X} = [varvec{X}_u, 0, varvec{X}_G, varvec{X}_R]), damage is monotonically increasing with respect to (alpha), and is continuous with respect to (alpha) as long as changes to L and R are continuous. Moreover, damage is strictly monotonically increasing with respect to (alpha) whenever (D(t;1) > 0).
The limitation that (varvec{X}_e = 0) will be discussed in greater detail later. However, depending on the pMoA of the stressor we can extend the result of Theorem 2 slightly.
Corollary 3.1
If the pMoA of a substance directly affects reproduction and does not affect growth, i.e. (varvec{S} = [0, 0, 0, s_{R}, s_{H}]) then the results of Theorem 2holds for any combination of feedbacks.
Finally, we can step from the results of Theorem 2 and Corollary 3.1 to show the existence and uniqueness of a critical multiplier ((hbox {EP}_{x}) or (hbox {LP}_{x})) for growth, reproduction and survival.
Theorem 3
Consider the DEB-TKTD model of Jager11 and a substance such that at least one of Theorem 2or Corollary 3.1hold. Further, let (C_w(t)) be a non-zero exposure profile where the time of first exposure is before (t_1) as defined in Table 1. Then, for any chosen percentage effect level (x > 0) there exists a unique EMF (alpha _* >0) such that$$begin{aligned} min left( frac{L(t_{E}; alpha _*)}{L_(t_{E}; 0)}, frac{R_c(t_{E}; alpha _*)}{R_c(t_{E};0)}, frac{S(t_{E}; alpha _*)}{S(t_{E}; 0)}right) = 1 – frac{x}{100} end{aligned}$$
(4)
this (alpha _*) is the (hbox {EP}_{x}) (or (hbox {LP}_{x})) for the exposure profile (C_w(t)).

Table 1 Table of the state variables and pMoAs (including combinations of pMoAs) in the DEB-TKTD model11.Full size table
The monotonicity of effects on all state variables in the DEB model means that, for the conditions described in Theorem 3, the (hbox {EP}_{x}) (or (hbox {LP}_{x})) is also monotonically increasing with respect to x.We should note here that one can either setup an algorithm to find the critical multiplier value for growth, reproduction and survival individually and then select the minimum or setup the algorithm to directly find the minimum critical multiplier as in (4). Both will produce the same result, but the second approach is likely to be faster.One could argue that ERA should consider the combined effects of lethal and sublethal stress on the individual’s fitness. This is possible using the continuous form of the Euler–Lotka equation24$$begin{aligned} B(t) = int _0^t B(t-a) l(a)b(a) da, end{aligned}$$
(5)
where B(t) is the number of births at time t, l(a) is the fraction of females which survive to age a and b(a) is the birth rate for mothers of age a. For the offspring of a test population which all have the same age (as is the standard in long-term toxicity experiments) this integral collapses to a single point, (B(t-a) = 1) when (t=a) and zero elsewhere. The DEB model provides exactly the values which we need to calculate B(t). Namely$$begin{aligned} l(a) = S(a), quad b(a) = frac{d}{dt}R_c(a). end{aligned}$$One can now find the births per individual per time predicted by the DEB model as$$begin{aligned} B(t) = S(t)frac{d}{dt}R_c(t). end{aligned}$$
(6)
Integrating (6) over the duration of the experiment gives the expected number of offspring produced per female alive at the start of the test.There are two clear options for how to proceed. Firstly, one could calculate (int _0^{t_E} B(t) dt) for each EMF and compare it to the control, similar to finding (hbox {EP}_{x}) values for individual endpoints. Alternatively, one can use B(t) as the basis to estimate the intrinsic population growth rate25. This quantity provides an estimation of population growth based on the survival and fecundity over time of individuals. Indeed, it is listed as a potential output value in the experimental guidelines for standard Daphnia magna reproduction tests26. For the first of these options we offer an extension to Theorem 3.
Corollary 3.2
Consider a DEB-TKTD model and exposure profile such that Theorem 3holds. The number of expected offspring per female, given by$$begin{aligned} mathrm {B}(t_E; alpha ) = int _0^{t_E} S(t; alpha )frac{d}{dt}R_c(t; alpha ) dt end{aligned}$$has a unique (hbox {EP}_{x}) (alpha _*) such that$$begin{aligned}frac{mathrm {B}(t_E; alpha _*)}{mathrm {B}(t_E; 0)} = 1 – frac{x}{100}end{aligned}$$
Our results provide a rigid boundary to the applicability domain of the EMF approach both in terms of existence and uniqueness. Existence relies on the initial time in the profile when external concentration is non-zero, as described in Table 1. While it is important to know about these conditions, they will rarely inhibit an ERA, since long initial periods with zero exposure are uncommon.Cases where uniqueness cannot be guaranteed require more caution and it is unwise to use root-finding algorithms. In the next subsection we explore what can happen outside of this domain and provide suggestions for how to still produce a single reliable (hbox {EP}_{x}) value.Surface:volume scaling of eliminationThere is a reason that in Theorem 2, (varvec{X}_e = 0) was specified. In some cases when (varvec{X}_e = 1) a higher multiplier is no guarantee of higher damage for all time. Consider a substance which acts on assimilation and has surface area:volume scaled elimination (i.e. (varvec{X} = [0, 1, 0, 0])). The damage ODE under some EMF (alpha) is then$$begin{aligned} frac{dD}{dt} = k_d left( alpha C_w – frac{L_m}{L} D right) , end{aligned}$$where (L_m) is the maximum length the organism can reach. The EMF has a positive direct effect on damage, but also an opposing indirect effect. Increasing damage decreases the size of the organism which, due to the surface area:volume elimination of damage, enables faster elimination of damage. As a result, not only does Theorem 2 no longer hold but in fact a larger multiplier value can cause lower damage at some points in an exposure profile. In other words, we observe a paradoxical result whereby more exposure translates to less effect some time after exposure.Figure 3 illustrates what we will refer to as the “more is less” scenario. The exposure consists of a single pulse early in the animal’s life, modelled for two multiplier values, (alpha _2 > alpha _1). During the exposure phase the direct effect of the higher exposure causes higher damage and greater effects on size. After the pulse, external exposure is zero, and therefore the external concentration and uptake remain zero regardless of (alpha). Regardless of the EMF, scaled damage can only decrease during this phase. However, the effects of the higher multiplier are still relevant. As Fig. 2 shows, the feedback processes still influence damage dynamics. The model organism exposed to (alpha _2C_w) is smaller and therefore able to eliminate damage more rapidly because (varvec{X}_e = 1). This eventually leads to lower damage for the model organism exposed to (alpha _2C_w) (i.e. (D(t; alpha _1) > D(t; alpha _2))). The more is less phenomenon can also impact growth and cumulative reproduction, as seen in Fig. 3b,c. Sometime after exposure (L(t;alpha _2) > L(t; alpha _1)) and (R(t;alpha _2) > R(t; alpha _1)). For survival, and any additional endpoints without recovery, this “crossover” is unlikely, mortality during the exposure phase (where (D(t; alpha _2) > D(t; alpha _1))) will almost certainly dominate any mortality during the recovery phase. Figure 3d shows that for certain (x%) effect levels (vertical axis) multiple (hbox {EP}_{x}) values exist.Figure 3An illustration of the issues which can occur using the EMF approach for substances with surface area:volume scaled elimination (i.e. (varvec{X} = [0, 1, 0, 0])). The (non-multiplied) exposure is a constant (1 mu g/L) for the first 14 days and zero thereafter and effects assimilation only ((varvec{S} = [1, 0,0, 0, 0])). (a) Scaled damage, (b) length over time, (c) cumulative reproduction. (d) Endpoint value as a proportion of control after 40 days. The shape of these curves show that certain effect levels can be caused by two distinct multiplier values. Parameter values are (L_0 = 0.1), (f = 1), (r_B = 0.1), (L_p = 0.6), (L_m = 1), (R_m = 15), (kappa = 0.8), (y_P = 0.64) (z_b = 0.1), (b_b = 1), (k_d = 0.05), (varvec{X} = [0, 1, 0, 0]). See the SI for the definitions of these parameter values.Full size imageIn practice, instances of non-uniqueness such as Fig. 3 will be rare since they rely on a sudden and significant decrease in external exposure. Moreover, EMF methods for DEB-TKTD models will include a moving time window method18 consisting of many exposures constructed sequentially and assessed. Each window will produce an (hbox {EP}_{x}) value, but only the lowest will be relevant for the ERA. A time window which starts slightly earlier in the broader exposure profile would feature the same pulse later in the model organism’s lifespan and thus not allow organism recovery. Depending on the exact endpoint used, one would expect those windows to have a lower (and unique) (hbox {EP}_{x}). However, the potential for multiple (hbox {EP}_{x}) values raises concerns across all areas which impose a multiplicative margin of safety. We cannot guarantee that a multiplier resulting in (x%) effects exists nor that any value found by the algorithm is unique.Although not pictured here, maintenance and growth pMoAs and combinations of feedbacks which include (varvec{X}_e = 1) can also produce the “crossover” in the damage values and the “more is less” phenomenon seen in Fig. 3. It can also arise for scenarios which do not feature a deviation from the standard rules for growth (e.g. a starvation phase) and for other DEB based models. The SI features a similar plot to Fig. 3 showing damage crossover for a standard DEB model.Knowing this, the obvious question is how to proceed? Certainly with caution when (varvec{X}_e = 1) is necessary in model calibration and validation. Under such circumstances algorithms must ensure that the (hbox {EP}_{x}) value found is the lowest multiplier which gives (x%) effects when there is a risk of non-uniqueness. The brute force approach, incrementing from zero until the desired effect level is met or exceeded, is one example. Whether it is realistic for higher EMF values to cause reduced effects in vivo then does not alter the conservatism of the approach for ERA.Table 2 summarises the domain where the margin of safety approach can be used in conjunction with a root-finding algorithm without concern in the DEB-TKTD model of Jager11. For model configurations where non-uniqueness could emerge using another method to find the (hbox {EP}_{x}) is advisable. For example, a brute-force approach starting from an EMF of 0 in small increments (e.g. by 0.1). Without good reason, calibration should first be attempted with no feedbacks. Under this guiding philosophy of pursuing model simplicity we expect that the problem cases will be rare.Table 2 A table to mark under which scenarios the EMF approach is and is not guaranteed to produce a unique (hbox {EP}_{x}).Full size tableOther issuesThe damage crossover illustrated in the previous subsection occurs more commonly, and to a greater extent, when the pMoA is assimilation effects. This is because, at least in this standard implementation, stress can cause (100%) effect and completely cease assimilation when (s_A ge 1) (see SI for details). When this is the case, higher exposure (even from an increased multiplier) does not translate to higher stress. This differs from other pMoAs, whose stress values are unbounded. Indeed, replacing (1 – s_A) with (1/(1 + s_A)) in the model ((S5) in the SI) reduces the occurrence and scale of “crossovers” such as Fig. 3. However, the formulation of the pMoA should not be based on how it might affect the algorithm or the EMF.Certain species require further deviations from the standard model. For instance, different life-stages, growth and/or reproduction rules might be introduced to explain observed phenomena. Before models featuring these deviations are used in an EMF approach one should consider the potential issues as we have done in this section. While a proof of existence and uniqueness of the (hbox {EP}_{x}) for each model variant is ideal it is also infeasible. However, modellers should ensure that their approach is robust enough to deal with issues around existence and uniqueness. Checking that the model endpoint is reduced by (x%) when the (hbox {EP}_{x}) is applied to the exposure profile is an easy way to check accuracy and existence. An argument (if not a full, formal proof) for uniqueness should also be considered. In cases where that is not possible, the algorithm must be set up to identify the lowest (hbox {EP}_{x}), or check that no lower values exist.One common addition is to DEB-TKTD models which feature starvation is to assume that there is some maximum amount of starvation/shrinking which an animal can survive. Once that point is met or exceeded death is instantaneous27. Such death mechanisms cause problems. They can introduce a discontinuity in the response versus multiplier value for a given time window (i.e. a “jump” in plots such as Fig. 3). For instance, if in the example given in Fig. 3 the animal was not allowed to shrink, and instead died, then the multiplier of 6 would result in (100%) effects on survival (and significant growth effects). In contrast, the exposure when the multiplier is 2 is survivable and the animal can recover. Presumably, for some critical (alpha _c in (2, 6)) the exact threshold for death is reached. This (alpha _c) is a discontinuity between partial and (100%) effects relative to control. Under some circumstances this will prohibit finding a multiplier which results in exactly (x%) effects, regardless of the method used.There are two readily apparent solutions to this at the individual level. One is to set (alpha _c) as the multiplier for the window, the second is to replace such discrete responses with graded responses. In this example for instance, shrinking could add to the lethal hazard h. It is not possible to universally recommend one approach over the other as it will depend on the species’ behaviour. Once that decision has been made these issues must be recognised and reported by the modellers. More

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In this study we analysed how tree and arborescent palm species richness was related to aboveground carbon stock, commercially relevant timber stock, and commercially relevant NTFP abundance in tropical forests, and how these relationships were influenced by environmental stratification at different spatial scales. We found that species richness showed significant relationships with all three ecosystem services stock components, but its relationships were strongly influenced by variation across forest types and biogeographical strata. This is further explained below.Across the Guiana Shield, species richness showed a positive relationship with carbon stock and timber, but not with NTFP abundance. Although relationships only differed in significance among the biogeographical subregions, they differed in direction between terra firme forests and white sand forests. Species richness was positively related to carbon stock and timber stock in terra firme forests, whereas it was negatively related to NTFP abundance in white sand forests. The positive species-carbon relationship across forests of the Guiana Shield is in line with the effects described by hypotheses such as the ‘niche complementarity’ and ‘selection effect’10 and is in line with previous findings at regional spatial scales6,21. To our knowledge, the relationship between species richness and timber stock has not been previously analysed for tropical forests. Interestingly, the observed positive species-timber relationship in terra firme forests of the Guiana Shield contrasts with the negative species-timber relationship found for subtropical forests in both the U.S.A. and Spain20, although this may be explained by the difference in ecosystems. The non-significant species-NTFP abundance relationship across the Guiana Shield and the negative relationship within white sand forests seems to contradict previous findings. Steur et al.24 found a negative species-NTFP abundance relationship for tropical forests in Suriname. However, this negative relationship was found across multiple forest types, including flooded forests that had low species richness and high NTFP abundance. These flooded forests most likely influenced the species-NTFP abundance relationship across all forest types.In contrast to the relationship between species richness and carbon stock, no mechanism has been proposed for how species richness would influence commercial timber stock and NTFP abundance. Although our results suggest that species richness had a positive relationship with timber, the relationship was not found within multiple biogeographical subregions. For NTFP abundance, species richness did not contribute to explaining variation when variation across biogeographical subregions was accounted for (i.e. was included as an explanatory variable). We here tentatively propose that both commercial relevant timber stock and NTFP abundance are driven by variation in species floristic composition, rather than by species richness. For services such as commercial timber and NTFP provisioning, only a subset of all species is relevant (in this study, 9.4% of all morphospecies for timber and 3.8% for NTFPs), and such subsets are likely not random selections. For example, for Suriname, it was found that variation in commercially relevant NTFP abundance was driven by a particularly small selection of NTFP producing species with high abundances (referred to as ‘NTFP oligarchs’)24, and for commercial relevant timber stock, it is commonly known that selections tend to include more abundant than rare species. Additionally, as the relative abundance of species tends to vary across floristic regions in Amazonia, where, for example, certain species are dominant in particular forest types and biogeographical regions31,32, it can be expected that commercial timber stock and NTFP abundance are determined by floristic composition. In support, for NTFP abundance in Suriname tropical forests, Steur et al.24 found that floristic composition was a stronger predictor of NTFP abundance than species richness.Across all of Amazonia, species richness had a positive relationship with carbon stock, but only when variation among biogeographical regions was accounted for. The positive species-carbon relationship across Amazonia partly contrasts with previous findings at continental spatial scales11,13. When variation across climatic and/or edaphic variables was accounted for, Sullivan et al.13 found no significant species-carbon relationship across South-America, while Poorter et al.33 did find a positive relationship across Meso- and South-America. Here, we propose that accounting for differences among biogeographical regions can explain the previously found contrasts at continental spatial scales. In our dataset, for individual regions, we found either a positive relationship or a non-significant, but weakly positive, relationship between carbon stock and species richness (Fig. 2). However, when the data were aggregated across all regions, this resulted in a non-significant, and weakly negative, relationship. This reflects a known statistical phenomenon referred to as a ‘Simpson’s paradox’34, in which a relationship appears in multiple distinct groups but disappears or reverses when the groups are combined. Additional post-hoc tests of leaving one region out at a time showed that this pattern was not dependent of any particular biogeographical region. This is the first time that an analysis based on empirical data provides evidence for a Simpson’s paradox in species-ecosystem service relationships.It is likely that the observed differences in carbon stock across the biogeographical regions of Amazonia are influenced by multiple factors. For example, the biogeographical regions used in our analyses were recognised according to differences in substrate history, geological age and floristic composition, which could all contribute to variation in carbon stock. The substrate history and geological age of the biogeographical regions have been related to differences in soil fertility35, while multiple spatial gradients in floristic composition identified across the Amazon coincide with a spatial gradient in wood density28. However, further analysis is needed to obtain better insight into the relative contributions of these and other variables to explain the observed variation in carbon stock across the biogeographical regions. This requires data on multiple environmental variables, including floristic composition, climatic variables such as the length of the dry period, soil conditions, and intensity of disturbance.In our analyses, terra firme forests determined the relationship of species richness with the carbon stock, timber stock, and NTFP abundance across the datasets. Although this is most likely the effect of unequal sample sizes, with terra firme forests being the dominant forest type in terms of sample size (n = 130 vs. n = 21 for the Guiana Shield dataset; n = 257 vs. n = 26 for the Amazonia dataset), we expect that the observed relationships reflect the general pattern. Terra firme forests are the most dominant forest type in terms of geographical area32 and were representatively sampled. Regardless, the analyses per forest type had added value. The significant relationship between species richness and NTFP abundance in white sand forests across the Guiana Shield would otherwise have been overlooked.Due to the known scarcity of reliable and adequate information on which timber and NTFP species are being commercially traded36,37,38,39, we used a fixed set of timber and NTFP species to apply across the Guiana Shield plots. However, in reality, timber and NTFP species can be expected to vary according to socio-economic factors, such as culture, access, and harvest costs, which may change over space and time. Therefore, estimates of timber stock and NTFP abundance can be expected to differ across spatial gradients, and thus, their possible relationships with species richness cannot be easily generalised. To circumvent this, timber stock and NTFP abundance would have to be estimated on the basis of ‘flexible’ species selections that can change according to local socio-economic contexts. To this end, detailed information on both commercially relevant timber and NTFP species is urgently needed. Yet, for our study area, we did not observe major differences in selected species, and we included broad selections of species, which should make timber stock and NTFP abundance robust against small deviations in species selection. It must be noted that our approach of quantifying commercial relevant timber stock and NTFP abundance does not consider the value of timber and NTFPs for subsistence use. In addition, NTFPs can also be derived from other growth forms, such as lianas, shrubs and herbs. Last, because NTFP production data was not available we used NTFP abundance as a proxy for NTFP stock, following similar assessments of NTFP stock 24,40. A limitation of this approach is that each NTFP species individual has an equal contribution to NTFP stock, whereas it can be expected that large individuals may have a larger contribution than smaller individuals and that production volumes can differ for different types of NTFPs, for example barks vs. seeds.Our findings illustrate the importance of considering environmental stratification and spatial scale when analysing relationships between biodiversity and ecosystem services. First, environmental stratification can help detect relationships that are otherwise obscured by environmental heterogeneity. For example, although the association between species richness and carbon stock across Amazonia was relatively weak (explaining ~ 3% of total variation vs. ~ 15% in the Guiana Shield) and was obscured by variation in carbon stock across biogeographical strata, by using environmental stratification the positive relationship remained detectable. Second, environmental heterogeneity tends to vary with spatial scale; therefore, its importance needs to be checked according to spatial scale. For example, at the regional scale of the Guiana Shield, biogeographical subregions explained a moderate amount of variation in carbon stock (~ 20%), while at the spatial scale of Amazonia, biogeographical regions explained more than half of total variation in carbon stock (~ 55%). Such an increase and ultimate importance of variation across biogeographical strata might also explain the absence of a significant relationship between species richness and carbon stock across African and/or Asian tropical forests as reported by Sullivan et al.13.In our analyses, we found evidence of a positive relationship between species richness and carbon stock across and within Amazonia. This supports the notion that win–win scenarios are possible in conservation approaches, where, for example, REDD+ can be expected to help conserve tropical forests that contain large amounts of carbon stock and high concentrations of species9. However, we conclude that species richness is not always a strong predictor of biomass-based ecosystem services. In our analyses, NTFP abundance was not driven by species richness, and we ultimately expect the same for timber stock. We expect that differences in floristic composition, linked to differences across forest types and biogeographical strata, will be more relevant than species richness in explaining variation in timber stock and NTFP abundance. This would mean that conserving timber and NTFP related ecosystem services requires the development of additional region-specific strategies that account for differences in floristic composition. For example, areas with high concentrations of timber or NTFPs could be considered in the designation of multiple use protected areas41, such as the extractive reserves in Brazil, or be included as ‘high conservation value areas’ (HCVAs) in sustainable forest management certification42. More

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