Re-analysis of plant CO₂ responses during the exponential growth phase: interactions with light, temperature, nutrients and water availability

Additional keywords: nutrient limitation, photosynthesis, PAR, photosynthetically active radiation, relative growth rate, RGR, water limitation.

The pre-industrial atmospheric carbon dioxide concentration [CO₂] was ~280 μmol mol^–1. It is currently increasing by ~2 μmol mol^–1 year^–1 and reached nearly 400 μmol mol^–1 by 2013 (Hartmann et al. 2013). Plants grow by absorbing CO₂ from the atmosphere, and current atmospheric concentrations are less than saturating for photosynthesis for most plants (e.g. Farquhar and von Caemmerer 1982). Plant growth is therefore likely to increase with increasing atmospheric [CO₂] (Franks et al. 2013). The important question is by how much?

For modelling studies of plant productivity under climate change (e.g. Medlyn et al. 2011; Kirschbaum et al. 2012; Peters et al. 2013; Reyer 2015), it is possible to compare growth responses to changing temperatures or rainfall with observed growth in regions that currently experience different climatic patterns. This is more difficult for responses to [CO₂] as available observations are largely restricted to a limited number of studies with experimentally altered CO₂ concentrations (Hickler et al. 2015). Therefore, CO₂ responses remain one of the most uncertain aspects of predicting future plant performance.

One can readily observe short-term photosynthetic responses to [CO₂], and studies with C₃ plants have demonstrated consistent and positive photosynthetic responses to increasing [CO₂] (Drake et al. 1997; Long et al. 2006; Kirschbaum 2011). These responses are generally in line with our understanding of the fundamental biochemical processes that govern leaves’ responses to their external environment (Farquhar and von Caemmerer 1982; Franks et al. 2013). However, photosynthetic carbon gain interacts with other plant processes. The ultimate growth response to elevated [CO₂], therefore, cannot simply be equated with the CO₂ response of photosynthesis (e.g. Poorter et al. 2013).

To better understand the response of plant growth, many experiments have been conducted over relatively short time frames under growth-chamber or glasshouse conditions, using plants grown in pots or hydroponically (e.g. Kimball 1983; Poorter 1993; Pinkard et al. 2010). Other experiments have been conducted in the field using open-top chambers or free air CO₂ enrichment (FACE) methods (Ainsworth and Long 2005; Norby and Zak 2011). The latter is generally considered to create the most realistic conditions as there are no artificial below- and aboveground barriers to modify the plants’ environment.

However, FACE experiments tend to be very resource intensive and costly (Pinkard et al. 2010), which allows only limited exploration of the response of different species or [CO₂] × environment interactions. Responses also vary from year-to-year simply because of uncontrolled climatic variability between years (e.g. Annicchiarico 2002) or inevitably-fluctuating CO₂ concentration in FACE studies (Bunce 2013). This makes it difficult to investigate CO₂ responses systematically under a variety of co-limitations, or for a range of different plant species. Short-term experiments under controlled conditions therefore retain an important role in advancing the understanding of the interaction between plant responses to elevated [CO₂] and other environmental factors.

In its simplest from, short-duration experiments can be analysed by comparing the biomass of plants grown at elevated [CO₂] for a given length of time with that of plants grown at control [CO₂]. This ratio is termed the biomass enhancement ratio (BER). Poorter and Navas (2003) compiled results from a wide range of experiments and found that BERs averaged ~1.45 for herbaceous and 1.48 for woody plants (Table 1).

Table 1.  Biomass enhancement ratios (BERs) in response to elevated [CO₂] for different plant groups, or for plants subject to different co-limitations
The data shows total dry mass stimulation for vegetative plants harvested at the end of the experimental periods. Data were summarised from a range of prior studies by Poorter and Navas (2003)

A different way to analyse CO₂ responses of young plants is by calculating their relative growth rate (RGR). Plants typically grow exponentially for some time before growth falls below that predicted by on-going exponential growth. Plant growth during and after the exponential growth phase can be described by a simple growth model (Fig. 1; Kirschbaum 2011). This allows the analysis of the interaction between time, the RGR of plants grown under low [CO₂] (RGR₃₅₀) and the ‘relative’ enhancement of RGR by elevated [CO₂] (RERC). The model by Kirschbaum (2011) assumes a constant ratio of plant size to leaf area index, a RERC of 10% (Poorter and Navas 2003), and an eventual cessation of exponential growth through increasing self-shading as is typically observed in longer-term experiments (e.g. Poorter et al. 1988; Körner 2006).

Fig. 1.  Leaf area development over time in high (solid lines; 700 μmol mol^–1) and low [CO₂] (dashed lines; 350 μmol mol^–1) based on the simple model by Kirschbaum (2011), showing leaf area index (a), the relative growth rate (b) and biomass enhancement ratio (c) under elevated and normal [CO₂] as a function of time (assuming a constant ratio of leaf area to total biomass). Simulations assume an RGR₃₅₀ of 150 g kg^–1 day^–1 and RERC of 10%, the average values reported by Poorter and Navas (2003) for experimental observations.

Loehle (1995), Gifford et al. (1996), and Kirschbaum (2011), using models like the one described above, showed that the BER during the exponential growth phase can substantially exceed the enhancement calculated on the basis of the underlying RERC. BERs depend not only on a plant’s inherent responsiveness to elevated [CO₂]_, but also on time (Fig. 1c) and on RGR₃₅₀ (Fig. 2). Over the initial growth phase, after imposition of CO₂ treatments, BERs increase with time because the positive feedback during exponential growth can amplify the initial CO₂ response (Fig. 1c; Loehle 1995; Gifford et al. 1996; Körner 2006; Kirschbaum 2011). Put simply, on the first day of a CO₂ treatment, one can compare the CO₂ response of two plants of the same size and with the same leaf area. On day 2, however, the high-CO₂ plant will benefit not only from higher CO₂, but also from its slightly higher leaf area developed during the previous day’s high-CO₂ exposure. This amplification is small at first, but increases over time to become quantitatively important (Fig. 1c).

Fig. 2.  Biomass enhancement ratios as a function of the relative growth rate at ambient [CO₂]. Model assumptions are the same as used for Fig. 1. The results shown here are for 34 days of simulations (the median length of CO₂ experiments with herbaceous plants).

However, RGRs cannot remain at peak values for very long, but begin to decrease when other growth limitations such as pot volumes or physical space that leads to self-shading, provide additional over-riding growth constraints (Gifford et al. 1996; Fig. 1b). If these effects are directly linked to plant size, they will have a greater effect on high- than low-[CO₂] grown plants (Fig. 1b) so that BERs decrease when these constraints take effect (Fig. 1c). The model also shows that for a given length of experiments, BERs correlate with RGR₃₅₀ (Fig. 2). This is because with increasing RGR₃₅₀, the positive feedback during exponential growth can more rapidly amplify the initial RERC signal into the numerically much greater BER.

Experimental observations summarised by Poorter and Navas (2003) indicated that BERs varied with changes in plant type or growing conditions, and faster-growing species had greater BERs than more-slowly growing plants (Table 1). This could mean that faster-growing species are inherently more responsive to elevated [CO₂] than slower-growing species. In contrast, Poorter and Navas (2003) also showed that the ‘absolute’ enhancement of RGR increased linearly with plants’ RGR₃₅₀. This meant that the ‘relative’ enhancement of relative growth rate by elevated [CO₂] (RERC) remained constant and was therefore independent of the RGR. If fast- and slow-growing plants had the same RERC, it implies that there are no fundamental physiological differences in their responses to elevated [CO₂]. Patterns emerging from the analyses of BERs can thus lead to different conclusions from those derived from analyses of RERCs.

Table 1 also shows that BERs of water-stressed plants and plants grown under low photosynthetically active radiation (PAR) were the same as those of plants grown without limitations (Poorter and Navas 2003). This conflicts with the theoretical understanding of the photosynthetic CO₂ response of plants that predicts greater CO₂ responsiveness for water-limited than non-limited plants (e.g. McMurtrie et al. 2008). When plants are grown with non-limiting water supply, any CO₂ response must be based on the enhancement of photosynthesis by increasing CO₂. Under water limitation, however, increasing [CO₂] also leads to partial stomatal closure (e.g. Morison 1985; Franks et al. 2013), which enhances plant water-use efficiency. As water-use efficiency is increased by increases in photosynthesis and decreases in stomatal conductance, it is numerically greater than the photosynthetic enhancement alone. This leads to the expectation of relatively greater CO₂ responses under water-limited than well-watered conditions (e.g. McMurtrie et al. 2008). However, the BER data in Table 1 imply that water-limited and well-watered plants had the same CO₂ responsiveness.

For plants grown under PAR-limited conditions, RERC might also be higher because plants operate closer to their light-compensation point where the ratio of photosynthesis to respiration is closer to one (e.g. Sims and Pearcy 1994). Any enhancement of photosynthesis could thus lead to greater relative growth enhancements under low PAR than for plants grown under high PAR where the photosynthesis to respiration ratio is already higher. Under PAR-limited conditions, plants are also more likely to be limited by carbohydrate availability than under high PAR. When plants have excess carbohydrate resources, photosynthesis may be downregulated which could reduce any beneficial effect of elevated [CO₂]. This is more likely to occur in high-PAR grown plants than in those grown under low PAR, leading to the expectation of greater CO₂ responses in low-PAR grown plants. However, this theoretical expectation also conflicts with the observation of similar BERs for plants grown under low and high PAR (Table 1).

However, explicit consideration of the positive feedback during exponential growth could reconcile these apparently conflicting findings. Plants growing under water-stressed or low-PAR conditions must have had lower RGR₃₅₀ than non-stressed plants. If their RERCs had been the same as those of non-stressed plants, it should have led to lower BERs (cf. Fig. 2). Instead, their BERs remained similar to that of unstressed plants (Table 1), which could only be possible if the RERC of water- and PAR-limited plants had actually been greater than that of unstressed plants. At a direct physiological level, stressed plants could thus have responded more strongly to elevated [CO₂] (as expressed in higher RERC) than unstressed plants, but because of the stressed plants’ lower RGR₃₅₀ that would not have led to enhanced BERs.

Nutrient-limited plants must have also had lower RGR₃₅₀ than plants grown with adequate nutrition. Their observed lower BERs (Table 1), therefore, could have also been due to their lower RGR₃₅₀ rather than indicate a lower inherent CO₂ responsiveness of nutrient-limited plants. Put differently, even if RERC had remained unaffected by nutrient limitations, the BERs of nutrient-limited plants could have still been reduced through their lowered RGR₃₅₀, leaving it uncertain whether CO₂ responsiveness interacts with nutrient limitations.

Photosynthetic theory also clearly shows a strong [CO₂] × temperature interaction, with much greater CO₂ responsiveness at higher temperatures (e.g. Farquhar and von Caemmerer 1982; Medlyn et al. 2002). This has led to the expectation of similar interactions between temperature and plant-growth responses to elevated [CO₂] (e.g. Long 1991; Kirschbaum 1994). A critical analysis of experimental observations is needed to ascertain whether that expectation based on photosynthetic observations is consistently expressed in plant growth responses.

In the present work, we have re-analysed available reports of CO₂ responses during plants’ exponential growth phase in combination with temperature, and PAR, nutrient or water limitations. We analysed each reported response pattern with respect to calculated RGR₃₅₀ and the relative enhancement of respective RGRs under elevated CO₂ (RERC). Through these analyses, we tried to obtain insights into the physiological relationships between the CO₂ responses of plants and these different co-limiting factors. This included only C₃ plants as the photosynthetic CO₂ response is very different for C₃ and C₄ plants (e.g. Ainsworth and Long 2005) and therefore likely to interact differently with other growth-limiting factors.

We obtained data from 78 experiments published in the literature. From each experiment, we extracted information on experimental conditions, such as mean daytime temperatures, high and low [CO₂], and the imposition of any PAR, nutrient or water limitations. We used observations of total plant dry weights, or the nearest equivalents (such as aboveground biomass when total biomass was not given), reading values from available graphs or tables and fitting a simple growth model to each dataset to derive RERCs under the experimental conditions. The principal criterion for inclusion in this analysis was for growth to be exponential for at least the early part of respective experimental periods so that relative growth rates could be calculated. All data presented below were derived from these experimental data obtained from the literature. Details of the data sources have been given in the Supplementary Material, which is available online.

In the model, the growth increment of biomass dB/dt was calculated at daily intervals as:

where B is biomass, t is time, and k₁ and k₂ are parameters fitted to respective datasets. In this expression, the first exponential term described the exponential growth phase and the second exponential term the down-turn in growth towards the end of the exponential growth phase.

The inclusion of this second exponential term allowed the incorporation of data obtained beyond the initial exponential growth phase, although data that deviated too strongly from exponential growth were excluded from the analysis. The asymptotic term k₂ was constrained to be the same for plants exposed to different [CO₂], but was allowed to differ between plants exposed to different co-limiting factors. This implicitly assumed that growth after the exponential phase was reduced through factors that could be linked to plant biomass per se with no difference between high- and low-[CO₂] grown plants. It meant that such size limitations affected high-[CO₂] grown plants slightly earlier than low-[CO₂] grown plants (cf. Poorter et al. 1988).

Initial biomass at time 0 was set to the same value for plants grown under different conditions and different [CO₂]. This was generally a fitted value based on observations reported for older seedlings unless the actual biomass of plants at the start of respective treatments was reported. Goodness of fit was assessed by residual sums of squares of log-transformed biomass data. For each data pair at high and low [CO₂], we thus obtained two k₁ values, k_1,low and k_1,high, which represented the fitted values at low and high [CO₂]. The observed relative CO₂ enhancement of RGR, c_enh, is the physiological relevant measure of the growth enhancement under specific experimental conditions. It was calculated as:

Many experiments used 350 for low, and 700 μmol mol^–1 for high [CO₂], but other experiments used a variety of concentrations. To improve comparability of the findings from different studies, all data were normalised by calculating the relative enhancement of relative growth rate by [CO₂], RERC, at standardised high and low [CO₂] of 350 and 700 μmol mol^–1 based on the theoretical CO₂ response of C₃ plants:

where E_{350, 700} is the theoretical enhancement of photosynthesis calculated under 350 and 700 μmol mol^–1, respectively, and E_low,high is the calculated enhancement under the actual low and high [CO₂] used in respective experiments.

The CO₂ enhancement of photosynthesis, E_low,high, was calculated as:

where c_high and c_low are photosynthetic responses at high and low [CO₂] respectively.

The theoretical photosynthetic CO₂ response, c_p, for RuBP-regeneration limited photosynthesis was calculated following Kirschbaum (1994) as:

where c_i, is the intercellular [CO₂] and Γ_* is the CO₂ compensation point in the absence of non-photorespiratory respiration.

The c_i was taken to be two-thirds of ambient [CO₂] and assumed to remain constant under changing [CO₂] (Ball et al. 1987). Γ_* was calculated following Bernacchi et al. (2001), as:

where T is the estimated mean daytime temperature.

Differences in CO₂ stimulation under different co-limitations (low PAR, nutrient or water stress), ΔRERC, were simply calculated as:

where RERC_s and RERC_o are the respective CO₂ stimulations under stressed and optimal conditions.

The extent of growth-limitation by the co-limitations, g_lim, was calculated as:

where k_1,low(s) and k_1,low(o) are the calculated RGR₃₅₀ for stressed and optimal growth conditions, respectively. The closer this ratio is to 0, the stronger is the environmental limitation, while the ratio becomes 1 for optimal growth.

Initial parameter fitting was done using a customised Excel spreadsheet, using Excel’s ‘Solver’ add-in to find parameter sets with minimised residual sums of squares. A copy of the spreadsheet is available from the authors upon request. Subsequent statistical analyses were undertaken using Genstat 12 (VSN International, Hemel Hempstead, UK). Regression analysis was used to assess correlations between RERC and photosynthetic CO₂ enhancement, and between ΔRERC and various co-limiting factors. Two-sample, two-tailed, t-tests were used to assess for differences between woody and herbaceous plants. Differences were considered to be significant if P < 0.05.

Use of the fitting and analysis routine is demonstrated in Fig. 3 with a dataset (for well-watered plants) obtained from Townend (1995). Over the initial growth phase to about day 70, data followed an exponential growth pattern, shown by the near-linear relationships on the logarithmic plots in Fig. 3c, d.

Fig. 3.  Illustration of the data analysis method used here, demonstrated with fertilised (a, c) and nutrient-limited data (b, d) from Townend (1995). Symbols show the observations and solid lines the fitted model (Eqn 1). Open symbols refer to plants grown at 350 and closed symbols to plants grown at 700 μmol mol^–1. Data in (c, d) are shown on a logarithmic scale. The lines were calculated with k_1,high(o) = 0.044 day^–1, k_1,low(o) = 0.037 day^–1, k_1,high(s) = 0.039 day^–1, and k_1,low(s) = 0.035 day^–1, leading to RERC_o = 0.19, RERC_s = 0.11 and g_lim = 0.95.

Growth then increasingly fell below exponential growth after day 70, with data points after this time falling below an implicit straight line fitted to the early points that indicated exponential growth. The second exponential term in Eqn 1 allowed the reduced growth to be described adequately as well. Townend (1995) also reported some data beyond day 180, but observations at those later stages deviated so strongly from exponential growth that those data were excluded from the analysis.

The key derived parameters for the present work were the initial slopes of the fitted curves over the exponential growth phase (equivalent to k₁). However, it was often difficult to confidently describe parameters for the exponential phase alone because most experiments provided few data points over that period, and the duration of the exponential growth period was also often uncertain. These problems were lessened by use of Eqn 1 that allowed data from the early post-exponential phase to be included as well.

The initial slopes of the curves fitted to these data gave the RGRs under different conditions. The relative difference between RGRs at high and low [CO₂] (ΔRERC) was taken as the appropriate measure of the plants’ CO₂ response as it was independent of the duration of experiments and thus unconfounded by time or other factors. This CO₂ response could then be related to interactions with other co-limiting factors. In this particular example (Fig. 3), increasing [CO₂] increased RGR by 19% (RERC = 0.19) for plants with adequate nutrition, and by 11% for nutrient-limited plants.

Different experiments used different combinations of low and high [CO₂], with only ~12% of experiments using the ‘standard’ combination of 350 and 700 μmol mol^–1. This provided an opportunity to assess the response of the relative growth enhancements of RGR, c_enh, to differences in the combination of low and high [CO₂]. RERC differs from c_enh through its normalisation to a standard combination of low and high [CO₂].

Photosynthetic enhancements were calculated from mean daytime temperature and the experimental low and high [CO₂] but used no actual measurements from those experiments whereas c_enh was calculated from observed growth measurements. Although individual c_enh observations showed considerable scatter, mean c_enh, calculated over defined ranges of photosynthetic enhancement, were tightly and linearly correlated (r² = 0.94, P < 0.001) with photosynthetic enhancements (Fig. 4). We also compared the response of woody and herbaceous plants, but found no significant difference in the deviation of individual data from the line of best fit between woody and herbaceous plants (P = 0.070).

Fig. 4.  Observed CO₂ enhancement of RGR, c_enh, plotted against calculated photosynthetic CO₂ enhancement. Shown are all observations (small symbols; n = 238) for herbaceous (circles) and woody species (triangles), and mean growth enhancement (large symbols) averaged over 0.05 intervals of photosynthetic enhancement. Error bars show 95% confidence intervals. The solid line was forced through the origin and fitted to the means, given by c_enh = 0.495 E_low,high (r² = 0.94; P < 0.001). This figure combines all data obtained for unstressed plants. A few individual data points were located outside the defined axis limits, but all data were included in the calculated averages.

This linear correlation between c_enh and calculated photosynthetic enhancement (in the averaged data) was surprisingly tight across a wide range of calculated photosynthetic CO₂ enhancements, with no indication for c_enh to have deviated from a linear relationship over the whole range of experimental conditions. However, the observed c_enh was only about half (0.495) of the calculated photosynthetic enhancement (Fig. 4), indicating that some other plant factors (i.e. changes in specific leaf area) or negative feedback factors (e.g. in response to excess carbohydrate) caused the ultimate growth response to be only half of the initial photosynthetic enhancement.

We then investigated the interactions between CO₂ enhancement and other physiological variables after normalising observed CO₂ enhancements to a standard combination of low and high [CO₂], designated as RERC.

Fig. 5a shows RERCs observed at different temperatures in individual studies. There was no indication of any systematic differences between woody and herbaceous plants (P = 0.058). Fig. 5b analyses these data further by calculating means and confidence intervals over 5°C temperature intervals. The overall mean RERC was 0.14 ± 0.02, with no significant change over temperatures from 12 to 40°C. It is readily apparent that the observed data did not conform to the theoretical relationship, with observations exceeding the expected CO₂ enhancement at cold temperatures and falling below it at higher temperatures.

Fig. 5.  (a) Relative enhancement of relative growth rate, RERC, (b) mean enhancement over different temperature intervals shown with 95% confidence intervals, and (c) RGR₃₅₀, the recorded relative growth rate under low [CO₂], all expressed against mean daytime temperature. Data from herbaceous species are shown as circles and data from woody species as triangles in (a) and (c). Data in (b) and the larger symbols in (c) were calculated over 5° temperature intervals. The blue line in (b) shows the theoretically expected RERC, based on the theoretical enhancement of photosynthesis (Eqn 4) and the empirical term of 0.495 obtained from the slope of the line in Fig. 4. The pink straight line in (b) is given by RERC = 0.10 + 0.0019 T (r² = 0.24; P = 0.32). The line in (c) is a polynomial fitted to the observations for better illustration of the trend. Mean RERC was 0.144 ± 0.021 for all data, with 0.136 ± 0.018 for herbs and 0.168 ± 0.062 for woody species.

Observed RGR₃₅₀ had an optimum between 25 and 30°C (Fig. 5c), but the below-optimum reductions in RGR₃₅₀ were not extreme at either high or low temperatures. The observations thus covered a range of physiologically meaningful conditions. It discounted the possibility of high-temperature grown plants having failed to display the expected CO₂ responsiveness because of growth under biologically damaging conditions. This was further confirmed by plotting RERC against RGR₃₅₀ (Fig. 6). RERC was independent of RGR₃₅₀, with no statistically significant correlation between them. The key observation here is that there was no positive correlation between RGR₃₅₀ and RERC. Had plants with low RGR₃₅₀ also shown low RERCs, it might have indicated that plants experiencing physiologically extreme conditions might not have shown a normal CO₂ response. However, the absence of a positive correlation meant that it was unlikely for physiological dysfunction at extreme temperatures to have accounted for the lack of stronger CO₂ enhancement.

Fig. 6.  Relative enhancement of relative growth rate by [CO₂], RERC, expressed as a function of RGR₃₅₀ in different experiments. Symbols as for Fig. 5. The solid line has been fitted to the data, given by: RERC = 0.16 – 0.15 × 10⁻³ RGR₃₅₀ (r² = 0.008; n = 140; P = 0.31).

Fig. 7 shows RERC differences (ΔRERC) between plants grown at limiting and adequate PAR. Values on the x-axis show the extent to which RGR₃₅₀ was reduced under low PAR, and values on the y-axis show ΔRERC between plants grown under low and high PAR in the same experiment. If CO₂ responsiveness had been independent of the extent of PAR limitation, the data should have simply scattered around the x-axis without any trends with changing PAR limitations.

Fig. 7.  ΔRERC plotted against the relative PAR limitation of RGR₃₅₀ in different experiments. Data for each individual experiment were represented by the large black symbol at (1,0) to represent the normalised observation at high PAR, and one or more normalised points (smaller coloured symbols) at lower PAR characterised by a reduced RGR₃₅₀ and a ΔRERC between that observed in low and high PAR. Symbols as for Fig. 5. The solid line was fitted to the data, forced through 0 at 1. ΔRERC = 0.28 – 0.28 g_lim (r² = 0.38; n = 19; P < 0.001), where g_lim is the relative PAR limitation of RGR₃₅₀ (Eqn 8).

However, plants grown under severely limiting PAR displayed stronger CO₂ responsiveness than that observed under higher PAR levels. The difference in responsiveness was only slight for minor PAR limitations, with g_lim > 0.8, but for lower ratios, the effect became stronger and clearly apparent. For g_lim < 0.8, eight out of 10 observations showed higher CO₂ responsiveness under limiting than adequate PAR (Fig. 7).

There was little fertility effect on ΔRERC for relative nutrient limitations >0.6, but the most severely stressed plants showed markedly reduced CO₂ responsiveness (Fig. 8). Three of the five experiments with g_lim < 0.5 even had calculated negative RERCs (data not shown), which meant that their growth was actually reduced by exposure to elevated [CO₂].

Fig. 8.  ΔRERC plotted against relative nutrient limitation of RGR₃₅₀ in different experiments. Data were calculated as outlined as for Fig. 7. Symbols as for Fig. 5. ΔRERC = –0.31 + 0.31 g_lim (r² = 0.30; n = 67; P < 0.001), where g_lim is the relative nutrient limitation of RGR₃₅₀.

ΔRERC increased strongly under water stress, especially with g_lim < 0.8 (Fig. 9). The extent of ΔRERC was also quite pronounced. Under well watered conditions, RERC was only ~0.14 (cf. Fig. 5b), yet that was increased up to 3-fold when plants were water stressed (with g_lim <0.6).

Fig. 9.  ΔRERC plotted against relative water-stress limitation of RGR₃₅₀ in different experiments. Data were calculated as outlined as for Fig. 7. ΔRERC = 0.74 – 0.74 g_lim (r² = 0.59; n = 24; P < 0.001), where g_lim is the relative water-stress limitation of RGR₃₅₀.

The present work focussed on analysing plant responses to elevated [CO₂] over the initial phase of exponential growth, but how relevant is the response over that short growth phase? Although the growth response of young plants is of some importance in itself, its greater relevance lies in providing an indication of likely plant responses during their longer and more relevant later linear growth phase. As a first approximation, one can quantitatively equate the relative enhancement of RGR (RERC) with an expected relative growth enhancement of linear growth. If that extrapolation can be made, these short-term experiments can provide valuable insights into the interactions between CO₂ responsiveness and other growth-limiting factors.

Although conditions in FACE experiments are such that plant responses can manifest themselves in the most natural way without artificial confounding factors (e.g. Ainsworth and Long 2005; Norby and Zak 2011), their costs and logistic challenges limit the extent to which interactions with other growth-limiting factors can be investigated (e.g. Pinkard et al. 2010). It is simply not feasible to conduct enough FACE experiments to gain sufficient insights either into species differences, or into all the possible interactions between plants’ CO₂ responses and other growth-limiting factors.

Short-term and low-cost experiments in growth chambers and glasshouses can thus cost effectively add valuable insights to the overall understanding of the interactions between the key interacting factors. In the analysis of such experiments it is critically important, however, to be mindful of the positive feedback on growth during the exponential growth phase (Loehle 1995; Gifford et al. 1996; Körner 2006; Kirschbaum 2011). Biomass enhancement ratios (BERs) are inappropriate for expressing research results as the observed relative CO₂ enhancement is confounded by time so that a constant enhancement of RGR turns into an increasing BER with the length of experiments (Gifford et al. 1996; Fig. 1c). It is similarly confounded with the RGR of plants under normal [CO₂], RGR₃₅₀ (Fig. 2). Instead, a more generic measure of plant growth response to elevated [CO₂] is the relative enhancement of RGR by elevated [CO₂] (RERC). If needed, BERs can be easily calculated for specified combinations of RERC, RGR₃₅₀ and time.

Quantifying differences in RERC made it possible to study interactions between the CO₂ response of young plants and temperature, PAR, fertility, and water stress without being confounded by the length of experiments or RGR₃₅₀. In plants grown under optimal conditions, RERC was independent of plants’ RGR₃₅₀ (Fig. 6), which is consistent with the findings by Poorter and Navas (2003), who had primarily compared species with different inherent growth potential. Fig. 6 showed that the same pattern also holds when differences in RGR₃₅₀ were further increased by differences in experimental temperatures. As a first conclusion, fast- and slow-growing plants thus had the same RERC (Fig. 6), indicating a similar photosynthetic response and similar interaction with feedback processes. The reported differences in BERs between fast- and slow-growing plants reported in Table 1 resulted simply from differential amplification of the same underlying CO₂ response during the exponential growth phase (cf. Fig. 2).

Fig. 4 shows that it was possible to predict the growth response of plants to elevated [CO₂] directly from the calculated enhancement of photosynthesis. Photosynthetic theory can be used to calculate the enhancement of photosynthesis for any combination of temperature and low and high [CO₂] (e.g. Farquhar and von Caemmerer 1982; Kirschbaum 1994). This could be linked to the experimentally observed relative growth enhancement through the empirical constant 0.495 obtained from the slope of the straight line in Fig. 4. This tight correlation between calculated photosynthetic enhancement and observed growth enhancement thus provided an extremely useful approach for predicting the growth response of plants during their exponential growth phase.

The slope of 0.495 accounted for any changes in carbon use efficiency, specific leaf area, leaf mass fraction, or any possible reduction in photosynthesis in response to carbohydrate saturation under specific circumstances (Poorter and Navas 2003; Ainsworth and Long 2005). The correlation between photosynthesis and growth appeared to hold over a wide range of [CO₂], with no indication of saturation at high [CO₂] beyond that represented in the relevant photosynthetic equations. This provided an objective and quantitative way of accounting for the various feedbacks and secondary physiological and morphological responses that together determined the CO₂ response of plants.

At the same time, while there was a tight linear correlation between the average calculated photosynthetic enhancements and the observed growth enhancements, individual observations scattered widely around the mean response. Much of that scatter was simple random variation, given that it was often difficult to deduce the relevant parameters from sparse or noisy datasets. Additional deviation would have been related to temperature, which differed from the expected dependence (Fig. 5 and see below).

Differences between woody and herbaceous species, however, did not appear to add to the variability (Figs 4–6). However, there could have been other systematic differences in the response of different plants, such as between N-fixing and non-fixing plants, or other unspecified differences between species. Future data analyses to calculate differences in RERC could provide an effective way to search for further differences between species or functional groups.

We found that on average, RERC was increased by 14 ± 2% when [CO₂] was doubled, with the relative CO₂ responsiveness of plants being almost completely independent of temperature (Fig. 5). This contrasts with the findings by Poorter and Navas (2003; Table 1), who reported that BERs were lower for low-temperature grown plants. However, low temperatures are usually associated with reduced RGRs (Fig. 5c). The low BERs of low temperature-grown plants may have been a consequence of their lower RGRs that transformed invariant RERCs to lower BERs (Fig. 2).

However, it is difficult to reconcile the observed temperature-invariant RERC with the well-established interaction between temperature and photosynthetic CO₂ responses (e.g. Farquhar and von Caemmerer 1982). Photosynthesis in C₃ plants responds to [CO₂] primarily because oxygen and CO₂ compete for the primary binding site on Rubisco, with increasing temperature favouring oxygenations. Hence, with increasing temperature, photosynthesis becomes increasingly limited by [CO₂] at normal atmospheric concentrations (e.g. Farquhar and von Caemmerer 1982; Kirschbaum 1994; Medlyn et al. 2002). On the basis of that strong and universally observed photosynthetic relationship, a similar interaction was assumed to exist between temperature and the growth response to elevated [CO₂] (e.g. Idso et al. 1987; Long 1991; Rawson 1992; Kirschbaum 1994; Polley 2002).

However, studies of growth responses to [CO₂] under contrasting temperatures have provided ambiguous results. The early work reported by Idso et al. (1987), working with four different species, reported a strong [CO₂] × temperature interaction, but subsequent experiments produced more variable results. Rawson (1992) compared the strength of the [CO₂] × temperature interaction observed in various studies and concluded that, while there was greater CO₂ responsiveness at higher temperatures, it was only weakly and inconsistently expressed. Similarly, Morison and Lawlor (1999) summarised data from 106 different observations, covering 18 different species, and found only a weak [CO₂] × temperature interaction. A recent meta-analysis of experiments with increased temperatures and [CO₂] also found little support for a [CO₂] × temperature interaction in whole-plant growth responses (Wang et al. 2012).

These earlier studies, together with the very weak [CO₂] × temperature interaction observed here, indicate that the [CO₂] × temperature interaction that is clearly apparent in photosynthetic responses does not carry over into whole-plant growth responses. However, there are no obvious reasons for the absence of greater growth enhancements at higher temperatures. It could have been possible that plants experiencing extremely high or low temperatures might not have functioned normally and therefore been unable to utilise the extra carbohydrate made available through elevated [CO₂]. However, there were only moderate reductions in RGR₃₅₀ at even extreme temperatures (Fig. 5c), and there was no indication of reduced CO₂ responsiveness for the slowest-growing plants (Fig. 6). Thus, there was no evidence of physiological dysfunction to have prevented plants from utilising an enhanced carbohydrate supply.

An uncoupling of photosynthesis and growth is often associated with the assumption that plants might be sink- rather than source-limited (e.g. Millard et al. 2007; Kirschbaum 2011). If plants already have excess carbohydrate resources under normal [CO₂], it would be unlikely for their growth to be enhanced by elevated [CO₂], even if short-term photosynthetic rates could be increased. However, plants are more likely to be sink-limited under cooler conditions (Poorter et al. 2013) when maintenance respiration and growth processes might be slowed by low temperatures. This could lead to sink limitation that could hypothetically prevent a CO₂ response. In contrast, higher temperatures should stimulate respiration and growth processes (e.g. Atkin and Tjoelker 2003; Way and Yamori 2014), deplete carbohydrate reserves, and shift plants from sink to source limitation. High temperatures should create conditions favourable for full utilisation of increased photosynthetic carbon gain, and carbohydrate feedbacks should have further enhanced the [CO₂] × temperature interaction, rather than negated it. These considerations thus can provide no explanation for the absence of the expected [CO₂] × temperature interaction.

It is difficult to think of other possible explanations for this intriguing absence of the expected response pattern. However, whatever the cause for the absence of a [CO₂] × temperature interaction, it has profound implications for the modelling of plant responses to changes in future [CO₂].

The analysis showed that low PAR-grown plants were more responsive to elevated [CO₂] than plants grown under high PAR (Fig. 7). Plant growth could be more responsive to [CO₂] under PAR limitation because plants operate closer to their light-compensation point, and because PAR-limited plants are likely to be carbohydrate limited so that enhanced photosynthesis would convey greater advantages than for plants grown under higher PAR. In contrast, an analysis based on BERs had shown low- and high PAR-grown plants to be similarly responsive to elevated [CO₂] (Table 1; Poorter and Navas 2003). So, as for other interactions presented here, it is likely that the actual greater RERC under low PAR was masked by the reduction of BERs through lower RGR₃₅₀ in the plants grown under limiting PAR (cf. Fig. 2).

Greater CO₂ responsiveness of PAR-limited plants might be a factor contributing to the increasing density of rainforest lianas that has been observed over recent decades (e.g. Phillips et al. 2002; van der Heijden et al. 2013). Lianas typically start their growth under PAR-limited conditions in the forest understorey. Greater CO₂ responsiveness would thus allow them to take greater advantage of increasing [CO₂] than the over-storey trees with which they compete. This could give lianas a competitive boost that might contribute to their increasing abundance.

CO₂ responsiveness was reduced under nutrient-limited conditions, but the trend was weak and only readily apparent in studies with severe nutrient limitations (Fig. 8). However, it was difficult to analyse CO₂ responses under nutrient-limited conditions with the approach adopted here because different nutrient levels were commonly set by applying different amounts of fertiliser at the start of experiments. For the youngest plants, those amounts could have been adequate for growth (cf. Ingestad and Lund 1986; Poorter et al. 2012) so that initial RGRs did not differ markedly between high- and low fertility-grown plants, which led to the majority of observations being bunched together with relative growth limitations ≥0.8 and similar CO₂ responsiveness. More substantial growth responses often developed at later growth stages, but those downturns had little effect on the inferred initial relative growth rates. The present findings therefore relied on only a very small number of observations where the fertility constraints were imposed in such a way that RGRs were affected from the earliest growth stages.

However, although our study provides a less certain answer as to how far nutrient limitations curtailed CO₂ responses at the plant-physiological level, it is likely that under long-term conditions in the field, feedbacks through whole-system nutrient availability strongly interact with the CO₂ response of plant growth. Plants and soils have confined C : N ranges, and any increased carbon gain through elevated [CO₂] is ultimately curtailed by the need to also obtain nitrogen so that C:N ratios can be maintained within their allowable ranges. This should reduce the CO₂ responsiveness under nutrient-limitations compared with that of well fertilised plants. This feedback effect has been observed experimentally (e.g. Norby et al. 2010; McCarthy et al. 2010) and in modelling studies (e.g. Comins and McMurtrie 1993; Kirschbaum et al. 1998). While these constraints have been investigated primarily with respect to C : N ratios, similar, although more complex, relationships also hold for phosphorus and sulfur (Kirschbaum et al. 1998).

CO₂ responsiveness strongly increased in water-stressed plants (Fig. 9). This response was consistent and apparent in all plants with a water-stress limitation of 0.9 or lower. The response was also numerically strong, giving an approximate 3-fold increase in CO₂ responsiveness from unstressed to the most severely stressed plants. When plants are water-stressed, growth limitations shift from photosynthesis that shows only moderate CO₂ sensitivity to limitation by water-use efficiency, for which greater CO₂ responsiveness can be expected (e.g. McMurtrie et al. 2008). However, just as for fertility experiments, water stress in most experiments was imposed in such a way that it only marginally affected early plant growth so that the analysis had to rely on few usable observations, but those data showed strongly increased CO₂ responsiveness under water limitation.

On the other hand, the pattern of increasing CO₂ responsiveness under water-limited conditions is not consistently observed in FACE experiments (Kimball et al. 2002; Nowak et al. 2004; McCarthy et al. 2010), not even in desert environments, where one might expect a strong and consistently enhanced CO₂ response (e.g. Newingham et al. 2013). It is thus not certain to what extent the findings from the short-term studies reported here are consistently expressed under field conditions, or, if they are not, what higher-order interactions prevent their expression under field situations.

Despite much research over many years, there is still uncertainty about the growth response of plants to elevated [CO₂] (e.g. Reddy et al. 2010; Wang et al. 2012). This is partly due to the complex interactions between the photosynthetic CO₂ response and the numerous other factors that together control plant growth. Plant growth not only provides the ultimate sink for photosynthetically fixed carbon, but can also exert a strong feedback control on photosynthetic carbon gain to ensure a balance between photosynthetic carbon gain and its use in growth (e.g. Paul and Foyer 2001). The photosynthetic response to changing [CO₂] can therefore only be fully understood if growth processes are simultaneously considered as well.

Understanding these interactions is challenging and demands experimental work in which different co-limitations can be varied together with changes in [CO₂]. Short-term experiments conducted in growth chambers or glasshouses provide a cost-effective and feasible approach to generating the data for a better understanding of these important interactions. However, studies during the plants’ exponential growth phase need to be analysed in such a way to generate generic and unconfounded growth indices that are comparable between different growth conditions and between different experiments. The present work used a novel approach by calculating the relative enhancement of plants’ relative growth rate during the initial growth phase. As a first approximation, that relative enhancement of RGR can also be used for predicting growth responses during the plants’ subsequent linear growth phase.

Overall, the present work illustrated that useful information can be obtained from short-term growth-chamber or glasshouse-based studies. However, the key is that the analysis must separate the inherent CO₂ response of plants from its amplification during the exponential growth phase. This made it possible to obtain the range of observations needed for better quantification of the CO₂ response of plants, and disentangle the direct CO₂ response from its various important co-limiting factors.