Box 1. The CO₂-fertilisation hypothesis

The stimulation of photosynthesis by CO₂ has been called “CO₂ fertilisation” (Ciais et al., 2014), a term that goes back to global carbon cycle modelling in the 1970’s (Bacastow & Keeling, 1973). However, “CO₂ fertilisation” or “CO₂ fertilisation effect” have been used to refer to the [CO₂] response of any number of variables across scales. This broad usage has been a source of confusion and more commonly, “fertilisation” is a value-laden, agricultural term that means the addition of nutrients to increase crop yield. Acknowledging the precedence of the term, its multiple uses, and that CO₂ responses of some processes may be neutral or negative, we opt to refer to “CO₂ responses” of explicitly defined variables and scales.

We reserve the term “CO₂ fertilisation” solely to label the hypothesis that: **plant responses to increasing atmospheric [CO₂] lead to increasing terrestrial-ecosystem carbon storage causing negative feedback on atmospheric [CO₂] growth.** This definition of the CO₂-fertilisation hypothesis is explicit about the feedback on atmospheric [CO₂] growth, implying the potential of this process to slow climate change. The hypothesis is therefore defined at climate-change relevant scales, i.e. global in space and decadal to centennial in time.

For the CO₂-fertilisation hypothesis to be true, Eq. B1 must be positive at the global scale and over a specified time period:

$$ \Delta NEP = \Delta C_{eco} = \Delta C_{veg} + \Delta C_{soil} \qquad (\text{Eq. B1}) $$

where NEP is net ecosystem production, C<sub>veg</sub> and C<sub>soil</sub> are plant and soil (including litter and coarse woody debris) terrestrial carbon that sum to give total ecosystem carbon (C<sub>eco</sub>), and Δ represents change due to increasing [CO₂]. A change in carbon storage is the net result of inputs and outputs (Olson, 1963):

$$ \frac{dC}{dt} = I - kC \qquad (\text{Eq. B2}) $$

where C is stored carbon, I is the input, and k is the turnover rate of the pool (the inverse of mean residence time).

Net primary production (NPP) represents the net input of carbon to C<sub>veg</sub> and is calculated as gross primary production (GPP), which responds directly to iCO₂, minus autotrophic respiration (R<sub>a</sub>). In practice, NPP is often estimated from total biomass production (BP), the sum of leaf, wood, root, and reproductive tissue production over a given time period (Vicca et al., 2012). In addition to BP, NPP includes carbon used for the production of volatiles, root exudation, supply to symbionts, and
Box 1. The CO₂-fertilisation hypothesis

The stimulation of photosynthesis by CO₂ has been called “CO₂ fertilisation” (Ciais et al., 2014), a term that goes back to global carbon cycle modelling in the 1970’s (Bacastow & Keeling, 1973). However, “CO₂ fertilisation” or “CO₂ fertilisation effect” have been used to refer to the [CO₂] response of any number of variables across scales. This broad usage has been a source of confusion and more commonly, “fertilisation” is a value-laden, agricultural term that means the addition of nutrients to increase crop yield. Acknowledging the precedence of the term, its multiple uses, and that CO₂ responses of some processes may be neutral or negative, we opt to refer to “CO₂ responses” of explicitly defined variables and scales.

We reserve the term “CO₂ fertilisation” solely to label the hypothesis that: **plant responses to increasing atmospheric [CO₂] lead to increasing terrestrial-ecosystem carbon storage causing negative feedback on atmospheric [CO₂] growth.** This definition of the CO₂-fertilisation hypothesis is explicit about the feedback on atmospheric [CO₂] growth, implying the potential of this process to slow climate change. The hypothesis is therefore defined at climate-change relevant scales, i.e. global in space and decadal to centennial in time.

For the CO₂-fertilisation hypothesis to be true, Eq. B1 must be positive at the global scale and over a specified time period:

$$ \Delta NEP = \Delta C_{eco} = \Delta C_{veg} + \Delta C_{soil} \qquad (\text{Eq. B1}) $$

where NEP is net ecosystem production, C<sub>veg</sub> and C<sub>soil</sub> are plant and soil (including litter and coarse woody debris) terrestrial carbon that sum to give total ecosystem carbon (C<sub>eco</sub>), and Δ represents change due to increasing [CO₂]. A change in carbon storage is the net result of inputs and outputs (Olson, 1963):

$$ \frac{dC}{dt} = I - kC \qquad (\text{Eq. B2}) $$

where C is stored carbon, I is the input, and k is the turnover rate of the pool (the inverse of mean residence time).

Net primary production (NPP) represents the net input of carbon to C<sub>veg</sub> and is calculated as gross primary production (GPP), which responds directly to iCO₂, minus autotrophic respiration (R<sub>a</sub>). In practice, NPP is often estimated from total biomass production (BP), the sum of leaf, wood, root, and reproductive tissue production over a given time period (Vicca et al., 2012). In addition to BP, NPP includes carbon used for the production of volatiles, root exudation, supply to symbionts, and
changes in non-structural carbohydrates (NSCs). However, these carbon fluxes are difficult to measure and often have very short residence times, somewhat akin to respiratory carbon. Therefore, to align with measurements and residence time we use BP to decompose changes in C<sub>veg</sub>:

$$ \frac{dC_{\text{veg}}}{dt} = BP - k_{\text{veg}}C_{\text{veg}} \qquad (\text{Eq. B3}) $$

where k<sub>veg</sub> is the turnover (litterfall and mortality) rate of vegetation biomass. For soils, the inputs to C<sub>soil</sub> are vegetation litter production and mortality, as well as non-biomass NPP fluxes (S) that include exudation and carbon supply to symbionts:

$$ \frac{dC_{\text{soil}}}{dt} = k_{\text{veg}}C_{\text{veg}} + S - k_{\text{soil}}C_{\text{soil}} \qquad (\text{Eq. B4}) $$

where k<sub>soil</sub> represents the turnover rate of soil carbon caused by microbial decomposition.
changes in non-structural carbohydrates (NSCs). However, these carbon fluxes are difficult to measure and often have very short residence times, somewhat akin to respiratory carbon. Therefore, to align with measurements and residence time we use BP to decompose changes in C<sub>veg</sub>:

$$ \frac{dC_{\text{veg}}}{dt} = BP - k_{\text{veg}}C_{\text{veg}} \qquad (\text{Eq. B3}) $$

where k<sub>veg</sub> is the turnover (litterfall and mortality) rate of vegetation biomass. For soils, the inputs to C<sub>soil</sub> are vegetation litter production and mortality, as well as non-biomass NPP fluxes (S) that include exudation and carbon supply to symbionts:

$$ \frac{dC_{\text{soil}}}{dt} = k_{\text{veg}}C_{\text{veg}} + S - k_{\text{soil}}C_{\text{soil}} \qquad (\text{Eq. B4}) $$

where k<sub>soil</sub> represents the turnover rate of soil carbon caused by microbial decomposition.
Box 2. Evidence themes

**Theme 1—Direct exposure to elevated CO₂:** Experiments in which plants are grown in CO₂-enriched air and observations of plants growing close to geological CO₂ sources provide the only direct evidence of plant and soil responses to future [CO₂]. The first eCO₂ experiments were typically at the scales of hours or days and of leaves or small, individual plants. Ecosystem-scale open-top chambers (OTC) and larger free-air CO₂ enrichment (FACE) experiments have since been implemented over decades in more natural settings. All of these experiments provide evidence for the direct CO₂-effect on photosynthesis and stomatal conductance. These experiments also provide valuable data on biomass production, allocation to organs, and transpiration. The time scale of most experiments (<10 years), however, is generally much shorter than many ecosystem processes, and evidence for CO₂-effects on mortality, plant community dynamics, or changes in soil carbon stocks is limited.

**Theme 2—Tree growth measurements:** Tree rings and forest inventories provide long-term estimates of wood BP in forest ecosystems across the globe (e.g. Hember et al., 2019; Hubau et al., 2020). Tree ring data are annually resolved estimates of individual stem growth over the past decades to millennia (e.g. Babst et al., 2014). These data provide insight into individual growth variability in relation to environmental changes including soil moisture, temperature and potentially also iCO₂. Repeated inventories of forest ecosystems offer an assessment of forest-scale dynamics and the demographic processes of recruitment, growth, and mortality over the past decades and in some cases around century length (Pretzsch et al., 2014). Inventories tend to have a coarser temporal resolution (5-10 year resurveys) but represent forest-stand spatial scales, albeit that plot scale varies widely: 0.067 ha forest inventory analysis, c. 1-2 ha (e.g. Brienen et al., 2015; Hubau et al., 2020), 50 ha ForestGEO network (e.g. Chave et al., 2008).

**Theme 3—Ecosystem monitoring:** Ecosystem eddy-covariance and global remote-sensing may detect effects of iCO₂ on carbon, water, and energy fluxes over the recent decades. Tower-based sensors are used to calculate ecosystem-scale (c. 1 km) carbon, water, and energy fluxes from the covariance of gas concentrations and vertical wind velocity (Baldocchi, 2003). A global network of continental networks (http://fluxnet.fluxdata.org), synthesises flux-tower data from 916 sites, some in operation for over two decades, while the majority have run for a decade or less and are located in temperate ecosystems (Chu et al., 2017). Satellite and other aircraft-borne Earth observing systems
Box 2. Evidence themes

**Theme 1—Direct exposure to elevated CO₂:** Experiments in which plants are grown in CO₂-enriched air and observations of plants growing close to geological CO₂ sources provide the only direct evidence of plant and soil responses to future [CO₂]. The first eCO₂ experiments were typically at the scales of hours or days and of leaves or small, individual plants. Ecosystem-scale open-top chambers (OTC) and larger free-air CO₂ enrichment (FACE) experiments have since been implemented over decades in more natural settings. All of these experiments provide evidence for the direct CO₂-effect on photosynthesis and stomatal conductance. These experiments also provide valuable data on biomass production, allocation to organs, and transpiration. The time scale of most experiments (<10 years), however, is generally much shorter than many ecosystem processes, and evidence for CO₂-effects on mortality, plant community dynamics, or changes in soil carbon stocks is limited.

**Theme 2—Tree growth measurements:** Tree rings and forest inventories provide long-term estimates of wood BP in forest ecosystems across the globe (e.g. Hember et al., 2019; Hubau et al., 2020). Tree ring data are annually resolved estimates of individual stem growth over the past decades to millennia (e.g. Babst et al., 2014). These data provide insight into individual growth variability in relation to environmental changes including soil moisture, temperature and potentially also iCO₂. Repeated inventories of forest ecosystems offer an assessment of forest-scale dynamics and the demographic processes of recruitment, growth, and mortality over the past decades and in some cases around century length (Pretzsch et al., 2014). Inventories tend to have a coarser temporal resolution (5-10 year resurveys) but represent forest-stand spatial scales, albeit that plot scale varies widely: 0.067 ha forest inventory analysis, c. 1-2 ha (e.g. Brienen et al., 2015; Hubau et al., 2020), 50 ha ForestGEO network (e.g. Chave et al., 2008).

**Theme 3—Ecosystem monitoring:** Ecosystem eddy-covariance and global remote-sensing may detect effects of iCO₂ on carbon, water, and energy fluxes over the recent decades. Tower-based sensors are used to calculate ecosystem-scale (c. 1 km) carbon, water, and energy fluxes from the covariance of gas concentrations and vertical wind velocity (Baldocchi, 2003). A global network of continental networks (http://fluxnet.fluxdata.org), synthesises flux-tower data from 916 sites, some in operation for over two decades, while the majority have run for a decade or less and are located in temperate ecosystems (Chu et al., 2017). Satellite and other aircraft-borne Earth observing systems
have been measuring the reflectance of electromagnetic radiation from Earth's surface, used to infer
changes in vegetation cover, leaf area, and biomass at the global scale (Fensholt et al., 2004; Smith
et al., 2020). Reflected wavelengths from Landsat (first launched in 1972), MODIS, and other
instruments can be used to measure the fraction of absorbed photosynthetically active radiation
(fAPAR) and greenness indices, which are further used to infer LAI, GPP, and NPP with the help of
simple models (Myneni et al., 1997; Field et al., 1998). Microwave wavelengths are used to measure
vegetation optical depth (VOD, first available in the early 1980s) which can be used to infer
vegetation water content and, by extension, vegetation biomass (Liu et al., 2015).

**Theme 4—Large-scale constraints:** At regional-to-global scales, several long-term data-streams provide constraints on the global carbon budget and its change over time. These data streams include near-surface and vertical profiles of atmospheric CO₂ concentration and δ13C, global water-cycle measurements, and atmospheric composition from ice cores. Atmospheric CO₂ measurements can be combined with other data and models to infer the global carbon budget and spatial details of land carbon uptake (Friedlingstein et al., 2019; Peylin et al., 2013). The impact of vegetation responses to iCO₂ on the hydrological cycle measured by stream gauges can also act as further indirect evidence (Ukkola et al., 2016; Trancoso et al., 2017). Carbonyl sulphide (OCS) can be used to infer global carbon assimilation because it is taken up by plants through stomata and is transformed by carbonic anhydrase (Wohlfahrt et al., 2012; Whelan et al., 2018).
have been measuring the reflectance of electromagnetic radiation from Earth's surface, used to infer changes in vegetation cover, leaf area, and biomass at the global scale (Fensholt et al., 2004; Smith et al., 2020). Reflected wavelengths from Landsat (first launched in 1972), MODIS, and other instruments can be used to measure the fraction of absorbed photosynthetically active radiation (fAPAR) and greenness indices, which are further used to infer LAI, GPP, and NPP with the help of simple models (Myneni et al., 1997; Field et al., 1998). Microwave wavelengths are used to measure vegetation optical depth (VOD, first available in the early 1980s) which can be used to infer vegetation water content and, by extension, vegetation biomass (Liu et al., 2015).

**Theme 4—Large-scale constraints:** At regional-to-global scales, several long-term data-streams provide constraints on the global carbon budget and its change over time. These data streams include near-surface and vertical profiles of atmospheric CO₂ concentration and δ13C, global water-cycle measurements, and atmospheric composition from ice cores. Atmospheric CO₂ measurements can be combined with other data and models to infer the global carbon budget and spatial details of land carbon uptake (Friedlingstein et al., 2019; Peylin et al., 2013). The impact of vegetation responses to iCO₂ on the hydrological cycle measured by stream gauges can also act as further indirect evidence (Ukkola et al., 2016; Trancoso et al., 2017). Carbonyl sulphide (OCS) can be used to infer global carbon assimilation because it is taken up by plants through stomata and is transformed by carbonic anhydrase (Wohlfahrt et al., 2012; Whelan et al., 2018).
Box 3. Consideration of methods and bias

**eCO2 experiments.** Confinement of roots in pots can limit below-ground resources. While eCO2 can accelerate leaf area gain in open-grown plants leading to compound interest that does not occur with closed canopies (Norby *et al.*, 1999). These experiments represent early post-disturbance "reorganising", and possibly open-canopy, ecosystems but are not representative of closed-canopy ecosystems. Oscillating [CO₂] may lessen physiological responses (Allen *et al.*, 2020). The step-change in [CO₂] results in a large shift in the ecosystem resource balance (Walker *et al.*, 2015), while soil disturbance can increase nutrient availability (Körner 2006). Many experiments (and evidence themes more broadly) do not quantify total BP, especially root BP. Even the longest-running experiments are short-lived relative to the lifespan of trees. Landscape-scale atmospheric feedbacks (e.g. increased VPD that could mitigate reductions in transpiration) cannot be accounted for (Leuzinger *et al.*, 2015).

**Many 'measurements' rely on models in their calculation,** thus have the potential to omit or pre-suppose a CO₂ effect. For example, satellite GPP (e.g. Sun *et al.*, 2018) and NPP (e.g. Kolby-Smith *et al.*, 2016) are calculated from fAPAR using an LUE model (Monteith, 1972) that often does not include the CO₂ effect on photosynthesis (De Kauwe *et al.*, 2016). Thus, changes in GPP result only from changes in LAI (fAPAR) or climate. Conversely, measurement-models that include a CO₂ effect are thus not independent of iCO₂, e.g. iWUE from δ¹³C, OCS, or isotopomers, and thus have the potential to pre-suppose a CO₂-related trend.

**Carbon isotope discrimination during photosynthesis** reduces the ¹³C:¹²C ratio (δ¹³C) in plant material and is used to calculate iWUE from δ¹³C (Farquhar *et al.*, 1982; Farquhar & Cernusak, 2012). The commonly used model neglects mesophyll and photorespiration discrimination (Farquhar *et al.*, 1982; Farquhar & Cernusak, 2012), and accounting for these effects can increase iWUE trends by around 50 % (Keeling *et al.*, 2017).

**Tree-ring trends are subject to sampling and survivorship biases** (Brienen *et al.*, 2012; Peters *et al.*, 2015) that can affect growth trends by up to 400 % (Hember *et al.*, 2009; Nehrbass-Ahles *et al.*, 2014), leading some to question whether tree-rings should be used for trend detection at all (Brienen *et al.*, 2012). However, tree-rings are the only data that give insight into tree BP since the industrial revolution.
Box 3. Consideration of methods and bias

**eCO2 experiments.** Confinement of roots in pots can limit below-ground resources. While eCO2 can accelerate leaf area gain in open-grown plants leading to compound interest that does not occur with closed canopies (Norby *et al.*, 1999). These experiments represent early post-disturbance "reorganising", and possibly open-canopy, ecosystems but are not representative of closed-canopy ecosystems. Oscillating [CO₂] may lessen physiological responses (Allen *et al.*, 2020). The step-change in [CO₂] results in a large shift in the ecosystem resource balance (Walker *et al.*, 2015), while soil disturbance can increase nutrient availability (Körner 2006). Many experiments (and evidence themes more broadly) do not quantify total BP, especially root BP. Even the longest-running experiments are short-lived relative to the lifespan of trees. Landscape-scale atmospheric feedbacks (e.g. increased VPD that could mitigate reductions in transpiration) cannot be accounted for (Leuzinger *et al.*, 2015).

**Many 'measurements' rely on models in their calculation**, thus have the potential to omit or pre-suppose a CO₂ effect. For example, satellite GPP (e.g. Sun *et al.*, 2018) and NPP (e.g. Kolby-Smith *et al.*, 2016) are calculated from fAPAR using an LUE model (Monteith, 1972) that often does not include the CO₂ effect on photosynthesis (De Kauwe *et al.*, 2016). Thus, changes in GPP result only from changes in LAI (fAPAR) or climate. Conversely, measurement-models that include a CO₂ effect are thus not independent of iCO₂, e.g. iWUE from δ¹³C, OCS, or isotopomers, and thus have the potential to pre-suppose a CO₂-related trend.

**Carbon isotope discrimination during photosynthesis** reduces the ¹³C:¹²C ratio (δ¹³C) in plant material and is used to calculate iWUE from δ¹³C (Farquhar *et al.*, 1982; Farquhar & Cernusak, 2012). The commonly used model neglects mesophyll and photorespiration discrimination (Farquhar *et al.*, 1982; Farquhar & Cernusak, 2012), and accounting for these effects can increase iWUE trends by around 50 % (Keeling *et al.*, 2017).

**Tree-ring trends are subject to sampling and survivorship biases** (Brienen *et al.*, 2012; Peters *et al.*, 2015) that can affect growth trends by up to 400 % (Hember *et al.*, 2009; Nehrbass-Ahles *et al.*, 2014), leading some to question whether tree-rings should be used for trend detection at all (Brienen *et al.*, 2012). However, tree-rings are the only data that give insight into tree BP since the industrial revolution.
Many studies use tree-ring width as a proxy for wood BP because it is a direct measurement. However, trees grow in three dimensions and change in the one-dimensional ring-width does not directly scale with wood volume growth and thus BP in different sized trees. Conversion to the two-dimensional basal area increment (BAI) helps unify this size mismatch, but again does not account for non-linear change in wood BP with tree size (Anderson-Teixeira et al., 2015). Allometric scaling should be applied to ring-width and BAI to attempt a best possible estimate of wood BP (e.g. Dye et al., 2014). Static allometric relationships over time can introduce bias where environmental changes have altered resource allocation. For example, shifting allocation from wood to leaves in Russian forests reconciled apparently conflicting inventory data that suggested BP declines while remote sensing suggested increases (Lapenis et al. 2005). Furthermore, wood volume growth does not always scale with BP as wood density can also change (Pretzsch et al., 2018).

Forest inventory plots (c. 1 ha and less) can under-sample mortality, resulting in over-estimates of biomass accumulation (Chambers et al. 2013). Generally, statistical power for detecting and attributing change in mortality and SOM is often low (Hungate et al., 2009; Sulman et al., 2018; McMahon et al., 2019). Statistical power for detection is low due to measurement uncertainty, low signal-to-noise, heterogeneity, and potential pre-treatment differences. Low statistical power presents a real challenge for attribution when using commonly used binary mortality assessments or bulk SOM measurements (Sulman et al., 2018; McMahon et al., 2019). Furthermore, satellite data, flux-towers, and experiments all suffer from short time-periods, often with much background variability that can obscure or amplify trends.

Quantification of global 'natural' NBP is confounded with quantification of land-use change-related NBP which is uncertain (95 % CI is 92 % of the mean flux; Friedlingstein et al., 2019). Land-use change-related NBP is calculated using bookkeeping models that account for complex legacy effects and many elements of land-use change, which adds to the uncertainty (Pongratz et al., 2014). Furthermore, potentially substantial interactions of land-use change-related NBP and iCO2 are not considered by these methods. C<sub>veg</sub> and C<sub>soil</sub> changes, loss of storage/sink capacity, and potential CO<sub>2</sub> interactions with secondary succession all convolve land-use change and 'natural' NBP fluxes suggesting a false dichotomy in these flux calculations.

Calculating and interpreting β, or any relative response, is challenging for carbon stocks in which pre-change values can be large, change is the product of two opposing fluxes cumulative over
Many studies use tree-ring width as a proxy for wood BP because it is a direct measurement. However, trees grow in three dimensions and change in the one-dimensional ring-width does not directly scale with wood volume growth and thus BP in different sized trees. Conversion to the two-dimensional basal area increment (BAI) helps unify this size mismatch, but again does not account for non-linear change in wood BP with tree size (Anderson-Teixeira et al., 2015). Allometric scaling should be applied to ring-width and BAI to attempt a best possible estimate of wood BP (e.g. Dye et al., 2014). Static allometric relationships over time can introduce bias where environmental changes have altered resource allocation. For example, shifting allocation from wood to leaves in Russian forests reconciled apparently conflicting inventory data that suggested BP declines while remote sensing suggested increases (Lapenis et al. 2005). Furthermore, wood volume growth does not always scale with BP as wood density can also change (Pretzsch et al., 2018).

Forest inventory plots (c. 1 ha and less) can under-sample mortality, resulting in over-estimates of biomass accumulation (Chambers et al. 2013). Generally, statistical power for detecting and attributing change in mortality and SOM is often low (Hungate et al., 2009; Sulman et al., 2018; McMahon et al., 2019). Statistical power for detection is low due to measurement uncertainty, low signal-to-noise, heterogeneity, and potential pre-treatment differences. Low statistical power presents a real challenge for attribution when using commonly used binary mortality assessments or bulk SOM measurements (Sulman et al., 2018; McMahon et al., 2019). Furthermore, satellite data, flux-towers, and experiments all suffer from short time-periods, often with much background variability that can obscure or amplify trends.

Quantification of global 'natural' NBP is confounded with quantification of land-use change-related NBP which is uncertain (95 % CI is 92 % of the mean flux; Friedlingstein et al., 2019). Land-use change-related NBP is calculated using bookkeeping models that account for complex legacy effects and many elements of land-use change, which adds to the uncertainty (Pongratz et al., 2014). Furthermore, potentially substantial interactions of land-use change-related NBP and iCO2 are not considered by these methods. C<sub>veg</sub> and C<sub>soil</sub> changes, loss of storage/sink capacity, and potential CO<sub>2</sub> interactions with secondary succession all convolve land-use change and 'natural' NBP fluxes suggesting a false dichotomy in these flux calculations.

Calculating and interpreting β, or any relative response, is challenging for carbon stocks in which pre-change values can be large, change is the product of two opposing fluxes cumulative over
multiple years, and concepts of steady-state and non-steady state apply. Ideally we would like to
know β from pre-change steady-state to post-change steady-state. However, an ecosystem may not
be in steady-state prior to change and post-change ecosystems enter a transient phase and can take
a long time to reach steady-state. Calculated during the transient phase, β will be a function of initial
stocks and the developmental stage explored (seedling, sapling, mature tree) and signals will
accumulate over time. For ecosystems not in steady-state pre-change, β of the changes in the stock
increment is not sensitive to initial stocks, but could be large where pre-change increments are small
(i.e. when pre-change the system is close to steady-state). For steady-state ecosystems pre-change,
acknowledgment that β is non-steady-state is needed and a β that explicitly includes temporal scale
would be ideal.
multiple years, and concepts of steady-state and non-steady state apply. Ideally we would like to
know β from pre-change steady-state to post-change steady-state. However, an ecosystem may not
be in steady-state prior to change and post-change ecosystems enter a transient phase and can take
a long time to reach steady-state. Calculated during the transient phase, β will be a function of initial
stocks and the developmental stage explored (seedling, sapling, mature tree) and signals will
accumulate over time. For ecosystems not in steady-state pre-change, β of the changes in the stock
increment is not sensitive to initial stocks, but could be large where pre-change increments are small
(i.e. when pre-change the system is close to steady-state). For steady-state ecosystems pre-change,
acknowledgment that β is non-steady-state is needed and a β that explicitly includes temporal scale
would be ideal.
References

**Ainsworth EA, Long SP. 2005.** What have we learned from 15 years of free-air CO2 enrichment (FACE)? A meta-analytic review of the responses of photosynthesis, canopy. *New Phytologist* **165**: 351–371.

**Ainsworth EA, Rogers A. 2007.** The response of photosynthesis and stomatal conductance to rising [CO2]: mechanisms and environmental interactions. *Plant Cell and Environment* **30**: 258–270.

**Allen LH, Kimball BA, Bunce JA, Yoshimoto M, Harazono Y, Baker JT, Boote KJ, White JW. 2020.** Fluctuations of CO2 in Free-Air CO2 Enrichment (FACE) depress plant photosynthesis, growth, and yield. *Agricultural and Forest Meteorology* **284**: 107899.

**Anderson-Teixeira KJ, McGarvey JC, Muller-Landau HC, Park JY, Gonzalez-Akre EB, Herrmann V, Bennett AC, So CV, Bourg NA, Thompson JR, et al. 2015.** Size-related scaling of tree form and function in a mixed-age forest (E Sayer, Ed.). *Functional Ecology* **29**: 1587-1602.

**Anderson-Teixeira KJ, Wang MMH, McGarvey JC, LeBauer DS. 2016.** Carbon dynamics of mature and regrowth tropical forests derived from a pantropical database (TropForC-db). *Global Change Biology* **22**: 1690–1709.

**Arora VK, Katavouta A, Williams RG, Jones CD, Brovkin V, Friedlingstein P, Schwinger J, Bopp L, Boucher O, Cadule P, et al. 2019.** Carbon-concentration and carbon-climate feedbacks in CMIP6 models, and their comparison to CMIP5 models. *Biogeosciences Discussions*: 1–124.

**Babst F, Alexander MR, Szejner P, Bouriaud O, Klesse S, Roden J, Ciais P, Poulter B, Frank D, Moore DJP, et al. 2014.** A tree-ring perspective on the terrestrial carbon cycle. *Oecologia* **176**: 307–322.

**Bacastow R, Keeling CK. 1973.** Atmospheric carbon dioxide and radiocarbon in the natural carbon cycle: II. Changes from A. D. 1700 to 2070 as deduced from a geochemical model. *Brookhaven Symposia in Biology* **30**: 86–135.

**Bachofen C, Moser B, Hoch G, Ghazoul J, Wohlgemuth T. 2018.** No carbon “bet hedging” in pine
References

**Ainsworth EA, Long SP. 2005.** What have we learned from 15 years of free-air CO2 enrichment (FACE)? A meta-analytic review of the responses of photosynthesis, canopy. *New Phytologist* **165**: 351–371.

**Ainsworth EA, Rogers A. 2007.** The response of photosynthesis and stomatal conductance to rising [CO2]: mechanisms and environmental interactions. *Plant Cell and Environment* **30**: 258–270.

**Allen LH, Kimball BA, Bunce JA, Yoshimoto M, Harazono Y, Baker JT, Boote KJ, White JW. 2020.** Fluctuations of CO2 in Free-Air CO2 Enrichment (FACE) depress plant photosynthesis, growth, and yield. *Agricultural and Forest Meteorology* **284**: 107899.

**Anderson-Teixeira KJ, McGarvey JC, Muller-Landau HC, Park JY, Gonzalez-Akre EB, Herrmann V, Bennett AC, So CV, Bourg NA, Thompson JR, et al. 2015.** Size-related scaling of tree form and function in a mixed-age forest (E Sayer, Ed.). *Functional Ecology* **29**: 1587-1602.

**Anderson-Teixeira KJ, Wang MMH, McGarvey JC, LeBauer DS. 2016.** Carbon dynamics of mature and regrowth tropical forests derived from a pantropical database (TropForC-db). *Global Change Biology* **22**: 1690–1709.

**Arora VK, Katavouta A, Williams RG, Jones CD, Brovkin V, Friedlingstein P, Schwinger J, Bopp L, Boucher O, Cadule P, et al. 2019.** Carbon-concentration and carbon-climate feedbacks in CMIP6 models, and their comparison to CMIP5 models. *Biogeosciences Discussions*: 1–124.

**Babst F, Alexander MR, Szejner P, Bouriaud O, Klesse S, Roden J, Ciais P, Poulter B, Frank D, Moore DJP, et al. 2014.** A tree-ring perspective on the terrestrial carbon cycle. *Oecologia* **176**: 307–322.

**Bacastow R, Keeling CK. 1973.** Atmospheric carbon dioxide and radiocarbon in the natural carbon cycle: II. Changes from A. D. 1700 to 2070 as deduced from a geochemical model. *Brookhaven Symposia in Biology* **30**: 86–135.

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## Supporting Information

**Notes S1.** Standardising CO2 responses with a β factor.

**Notes S2.** Calculation of β from different data types.

**Notes S3.** Modelling leaf and canopy physiology.

**Table S1.** Theoretical β's for photosynthesis.

**Figure S1.** Comparison of alternatives methods to calculate β.

**Figure S2.** Evidence β's for GPP, WUE, and BP.

**Figure S3.** Evidence β's for kveg, ksoil, NEP, and Cveg,increment.

**Figure S4.** Evidence β's for Cveg, Csoil, and Ceco.
## Supporting Information

**Notes S1.** Standardising CO2 responses with a β factor.

**Notes S2.** Calculation of β from different data types.

**Notes S3.** Modelling leaf and canopy physiology.

**Table S1.** Theoretical β's for photosynthesis.

**Figure S1.** Comparison of alternatives methods to calculate β.

**Figure S2.** Evidence β's for GPP, WUE, and BP.

**Figure S3.** Evidence β's for kveg, ksoil, NEP, and Cveg,increment.

**Figure S4.** Evidence β's for Cveg, Csoil, and Ceco.
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