Net assimilation rate, specific leaf area and leaf mass ratio: which is most closely correlated with relative growth rate? A meta-analysis

Authors


†E-mail: Bill.Shipley@USherbrooke.ca

Summary

  • 1Data were compiled consisting of 1240 observations (614 species) from 83 different experiments published in 37 different studies, in order to quantify the relative importance of net assimilation rate (NAR, g cm−2 day−1), specific leaf area (SLA, cm2 g−1) and leaf mass ratio (LMR, g g−1) in determining relative growth rate (RGR, g g−1 day−1), and how these change with respect to daily quantum input (DQI, moles m−2 day−1) and growth form (herbaceous or woody).
  • 2Each of ln(NAR), ln(SLA) and ln(LMR) were separately regressed on ln(RGR) using mixed model regressions in order to partition the between-experiment and within-experiment variation in slopes and intercepts. DQI and plant type were then added to these models to see if they could explain some of the between-experiment variation in the relative importance of each growth component.
  • 3LMR was never strongly related to RGR. In general, NAR was the best general predictor of variation in RGR. However, for determining RGR the importance of NAR decreased, and the importance of SLA increased, with decreasing daily quantum input in experiments containing herbaceous species. This did not occur in experiments involving woody species.

Introduction

Growth, survival and reproduction are the three imperatives of any organism. In plants, growth is particularly important because both survival and reproduction depend on plant size and therefore on growth rate. Relative growth rate (RGR, g g−1 day−1) is therefore a key variable in influential models in plant ecology (Grime 1979; Tilman 1988; Westoby 1998; Grime 2001), and an understanding of its comparative ecology is critical in evaluating and improving such models.

Despite its importance, RGR is a complex phenomenon that is determined by differences in physiology, morphology and biomass partitioning. The relative contribution of these three factors is usually evaluated by decomposing RGR into its classical growth components (net assimilation rate, specific leaf area and leaf mass ratio; see equation 1). These components are functions of plant mass (MP), leaf mass (ML) and leaf projected surface area (AL). In order to compare the relative contribution of each growth component, Poorter & Van der Werf (1998) defined a ‘growth-response coefficient’ (GRC) as the slope (β1) of the linear regression given in equation 2. Such GRC values are therefore scaling (allometric) slopes. The natural logarithm of each growth component is regressed on the natural logarithm of RGR rather than the contrary, so that the slope with respect to each growth component X1, GRC) is independent of the others.

image( eqn 1a)
image( eqn 1b)
image( eqn 1c)
image( eqn 2)

The first paper to decompose RGR explicitly and measure such correlations for a group of species with contrasting ecology (Poorter & Remkes 1990) found that specific leaf area (SLA) was most strongly correlated to RGR, while net assimilation rate (NAR) and leaf mass ratio (LMR) were largely independent of RGR. If this is generally true, then one can replace RGR, a difficult and time-consuming measurement, with SLA, which is easily and quickly measured. Although a number of subsequent studies have found strong correlations between RGR and SLA, other studies have reported weak correlations between RGR and SLA, and strong correlations with other growth components. The strength of the interspecific relationships between RGR and its components therefore varies between studies. Identifying the differences between studies that control such changes may point the way to a more complete understanding of the trade-offs involved in the evolution of RGR.

Given the practical difficulties involved in such comparative experiments, it is not feasible for a single researcher to study many species and many different environmental conditions simultaneously. An alternative approach is to combine studies. A few such meta-analyses have already been published: Poorter & Van der Werf (1998) compiled data for herbaceous species, while two other studies (Cornelissen et al. 1998; Veneklaas & Poorter 1998) did the same for woody species. Cornelissen et al. (1998) found SLA to be the primary determinant of RGR, while Veneklaas & Poorter (1998) found NAR to be the primary determinant of RGR. Both Poorter & Van der Werf (1998) and Shipley (2002) evaluated the possibility that differences in the light environment might affect the relative importance of the growth components in determining RGR, and came to different conclusions, with Poorter & Van der Werf (1998) concluding that the light environment had no effect.

Here I present a more complete meta-analysis with the following properties: First, I combine both woody and herbaceous species, and compare them. Second, I explicitly model the effects of different growth conditions and species types (herbaceous/woody) in a single analysis, while taking into account the non-independence that arises from combining different studies in a single data set. Third, I determine if different growth conditions change the growth-response coefficients. Finally, I use a much larger database than other studies. Specifically, I ask three questions: (i) What is the relative importance of the three growth components in determining variation in RGR? (ii) How variable are the relationships between RGR and its growth components between experiments? (iii) Can the differences in the growth-response coefficients between experiments be related to differences in the light environment or types of species (woody/herbaceous) included in each experiment?

Materials and methods

The full data set involves 37 different publications and 614 species: 39 species of conifers, 241 species of woody dicots, 153 species of herbaceous dicots and 181 species of herbaceous monocots (primarily grasses) from Europe, the Americas and Australia. There are 1240, 1236, 1142 and 1142 observations for RGR, NAR, SLA and LMR, respectively. Because some studies grew plants in more than one light or nutrient environment, I treated each environment within a study as a separate experiment. Although most studies included only one type of species (herbaceous/woody), a few studies included both types. In such cases I separated the two types of species into different groups. There were therefore 83 different ‘experiments’[sets of species of the same type (herbaceous/woody) grown in a single environment] represented in the data set. As some studies did not report the daily quantum input (DQI, mol m−2 day−1), estimates were made following Poorter & Van der Werf (1998): for greenhouse studies conducted in the northern hemisphere, DQI = 7·5 (November to February); DQI = 15 (September, October, March or April); DQI = 25 (May to August); DQI values in the southern hemisphere were estimated the other way around. Studies conducted outside were estimated at 37·5. For publications in which data were given only graphically, values were obtained by scanning the relevant figures and extracting the data using the program DigitizeIt 1·5·7 (http://www.digitizeit.de, ShareIt! Inc., Cologne, Germany). The Appendix summarizes these data.

statistical analysis

When combining data from many experiments, there is a hierarchical data structure (within and between experiments) and therefore a hierarchical sampling structure. Consider first a single experiment (experiment j). The growth conditions are fixed and the researcher randomly chooses mj species from a larger potential pool of species. The true intercept (β0j) and slope (β1j, the GRC) of equation 2 under these growth conditions are estimated from these mj species, giving the empirical least squares estimates (b0j, b1j) for the intercept and slope. These point estimates will differ from the true values, and will have a certain degree of uncertainty which is dependent on the number of species included in the experiment (mj) and the amount of residual variation that exists under the chosen growth conditions.

Next, consider the total set of n experiments in the data set. Each experiment (its particular combination of growth conditions and species) is considered as a random draw from the set of possible combinations of growth conditions and species. The within-experiment values of the intercept and slope, averaged over all experiments, are b0. and b1.. The true values of the n intercepts, β0 = {β01, … , β0n}, and slopes β1 = {β11, … , β1n} associated with these n experiments are, themselves, random variables and assumed to be normally distributed. Thus the true values of the intercept and slope for experiment j are: β0j =β0 + δ0j and β1j =β1 + δ1j where β0 and β1 are the fixed within-experiment intercept and slope averaged over all experiments, and δ0j and δ1j are the random deviations of β0j and β1j of experiment j from the average within-experiment intercept and slope. These deviations might be related to specific growth conditions of the different experiments.

The best point estimates of β0j and β1j over the n experiments (0j and 1j) are the values that minimize the squared error loss, defined for the slopes as: inline image and analogously for the intercepts. If we have information on only a single experiment (j = 1), then this would be the least squares estimates b01 and b11 for that experiment, irrespective of the number of species involved or the degree of residual variation (the precision of the estimates). However, if one also has information from many other experiments, the best estimates on average (called ‘empirical Bayes estimates’ or ‘best linear unbiased predictors’) are a weighted average of the least squares estimates for that particular experiment (b0j and b1j) and the average within-experiment values (b0. and b1.) over all experiments (Candel 2004 and references therein): 1j = λjb1j + (1 − λj)b1. and analogously for the intercepts for each experiment. The weighting (λj) depends on the precision of the estimate of b0j or b1j in experiment j, thus on the number of species and the residual within-experiment variation, and on the variation of b0j or b1j across experiments. The larger the number of species in the experiment, and the smaller the residual variation in the experiment, the more the estimate is weighted towards the least squares estimates unique for that experiment (λj → 1). Thus the best estimates (b̂0j and 1j) will differ most from the least squares values estimated on a single experiment when the slope and intercept from that experiment has least square estimates that are both imprecise, and that are unusually large or small relative to the between-experiment variation; intuitively this states that one should discount estimates that are poorly estimated and also unlikely to occur by chance. See chapter 3 of Bryk & Raudenbush (1992) for details.

These statistical models are fitted using a linear mixed model via the lme function in s-plus (SPLUS 1999) estimated using restricted maximum likelihood and assuming normality of the random components (the between-experiment and within-experiment covariance matrices of slopes, intercepts and residuals). Normality of the random components was determined graphically following Pinheiro & Bates (2000).

The full mixed model is given in equation 3. The intercept (β0j) and slope (β1j, GRCX) of growth component X for a given experiment were allowed to vary randomly between the j experiments, and also allowed to be a function of ln(DQIj). The intercepts, normally defined, are the expected values of ln(Xij) when ln(RGRij) = 0, that is when RGR = 1; such values never occur in practice. Instead the values of ln(RGRij) were centred around the mean of the full data set (RGR = 0·04 g g−1 day−1) so that the intercepts represent the values ln(Xij) at this typical value of RGR. Finally, as preliminary analyses showed strong effects of plant type (herbaceous or woody), separate analyses were conducted for each group of experiments.

ln(Xij) = β0j + β1j ln(RGRij) + ɛij

β0j = β0 + δj

β1j = β0 + β3 ln(DQIj) + γj

image
image( eqn 3)

Other mixed model regressions follow a similar logic and structure.

Results

general trends

Table 1 summarizes the values of RGR and its components over all experiments. Also shown are the between-experiment and within-experiment random variation (variance components) of the ln-transformed values. Variation between experiments was greater than variation between species within an experiment for every variable and for experiments involving both types of species (herbaceous/woody). The RGR and NAR were always more variable than SLA and LMR, and more of the variation in RGR and NAR was due to differences between experiments.

Table 1.  Average values (± 2 SD) of relative growth rate (RGR, g g−1 day−1), net assimilation rate (NAR, g m−2 day−1), specific leaf area (SLA, cm2 g−1) and leaf mass ratio (LMR, g g−1), back-transformed from ln-scale, and between- and within-study random variation of ln-transformed values (percentage of total variance)
AttributeAverage (± 1 SD), back-transformedVariance*
Between-studyWithin-study
  • *

    Percentage in parentheses.

  • NAR is expressed in units different from the figures.

All experiments
ln(RGR)  0·08 (0·01, 0·53)1·05 (86)0·18 (14)
ln(NAR)  6·58 (0·9, 36·11)0·85 (86)0·14 (14)
ln(SLA)250 (127, 493)0·12 (56)0·09 (44)
ln(LMR)  0·49 (0·31, 0·79)0·06 (57)0·04 (43)
Experiments involving woody species
ln(RGR)  0·04 (0·005, 0·35)0·93 (76)0·29 (24)
ln(NAR)  3·7 (0·54, 25·0)0·84 (82)0·19 (18)
ln(SLA)234 (89, 614)0·13 (52)0·12 (48)
ln(LMR)  0·48 (0·24, 0·94)0·07 (57)0·06 (43)
Experiments involving herbaceous species
ln(RGR)  0·15 (0·06, 0·37)0·12 (61)0·08 (39)
ln(NAR) 11·1 (0·39, 31·6)0·18 (64)0·10 (36)
ln(SLA)283 (137, 586)0·07 (53)0·06 (47)
ln(LMR)  0·50 (0·30, 0·83)0·03 (51)0·03 (49)

Figures 1–3 present the patterns of variation between ln-transformed RGR and each of its determinants. In each figure the first graph (a) shows the trend when species from all experiments are combined. The second graph (b) shows the trends under a constant environmental context (within-experiment trends); this is done by centring each variable about its mean for each experiment. The third graph (c) shows how the average values of ln(RGR) vary with the average values of each growth component, calculated for each experiment.

Figure 1.

Relationships between net assimilation rate and relative growth rate [ln(NAR, g cm−2 day−1) and ln(RGR, g g−1 day−1)]. ○, Woody species; •, herbaceous species. (a) Each point represents a single species measured in one of 83 experiments. (b) Each point represents the deviation inline image of a single species j in experiment i from the mean of experiment i; this shows only within-experiment variation. (c) Each point represents the mean values of ln(NAR)ij and ln(RGR)ij in experiment j. (d) Histograms of the growth-response coefficients (GRCNAR), the slope of ln(NAR) regressed on ln(RGR) of each experiment, including the effects of daily quantum input (DQI).

Figure 2.

Relationships between specific leaf area and relative growth rate [ln(SLA, cm2 g−1) and ln(RGR, g g−1 day−1)]. See Fig. 1 for details.

Figure 3.

Relationships between leaf mass ratio and relative growth rate [ln(LMR, g g−1) and ln(RGR, g g−1 day−1)]. See Fig. 1 for details.

Table 2 summarizes the correlations associated with these graphs. NAR always had the highest correlation to RGR, either when comparing species within a single experiment; comparing species both within and between experiments; or comparing average values per experiment across experiments. The relative importance of SLA vs LMR depended on the type of species (herbaceous/woody) and on whether the comparison was done within or between experiments.

Table 2.  Pearson's correlation coefficients between ln(RGR) and each of its components, calculated for all experiments together, and for experiments involving herbaceous and woody species
Parameter ln(NAR)ln(SLA)ln(LMR)
  1. RGR, relative growth rate; NAR, net assimilation rate; SLA, specific leaf area; LMR, leaf mass ratio.

  2. Correlations based on (i) species means over all experiments; (ii) deviations of each species from the mean of its own experiment; or (iii) means per experiment compared across experiments.

Species means across all experimentsAll0·86 0·29 0·36
Herbs0·54 0·24 0·17
Woody0·85 0·19 0·48
Species means within experimentsAll0·59 0·49 0·19
Herbs0·48 0·28 0·10
Woody0·64 0·59 0·23
Experiment means across all experimentsAll0·92 0·16 0·51
Herbs0·61 0·29−0·03
Woody0·91−0·16 0·70

relationships between rgr or growth components and dqi

Combining all experiments and including the type of species (herbaceous/woody), a mixed model ancova showed that both the slope and intercept of ln(RGR) with respect to ln(DQI) differed between the two types of species. ln(DQI) had no effect on ln(RGR) (slope = 0·03, t33 = 0·25, P = 0·80) within the experiments involving herbaceous species, but was associated with an increased ln(RGR) in experiments involving woody species (slope = 0·48, tν=46 = 4·88, P < 10−3). However, there was still substantial residual variation (Fig. 4a), and 70% of this residual variation was due to between-experiment variation that was not related to DQI.

Figure 4.

Relationships between relative growth rate (RGR, g g−1 day−1), net assimilation rate (NAR, g cm−2 day−1), specific leaf area (SLA, cm−2 g−1) and leaf mass ratio (LMR, g g−1) plotted against the total daily input of photosynthetically active radiation (DQI, mol m−2 day−1).

With respect to ln(NAR), a mixed model ancova showed that the intercept differed between the two types of species (t79 = −2·97, P = 0·004) and that ln(NAR) increased with ln(DQI) (slope = 0·37, t79 = 2·22, P = 0·03). There was no significant difference in the effect of ln(DQI) on ln(NAR) between the two types of species (interaction: t79 = 1·40, P = 0·17). Removing the interaction term and refitting the model gave the following allometric relationships: NAR = 2 × 10−4DQI0·58 (herbaceous species), NAR = 8 × 10−5DQI0·58 (woody species). On average, a herbaceous species had an NAR that was 2·5 times that of a woody species at an equivalent DQI. There was substantial residual variation (Fig. 4b), and 65% of this residual variation was due to between-experiment variation that was not related to DQI.

Considering ln(SLA), a mixed model ancova found no significant interaction between ln(DQI) and plant type (t77 = −0·14, P = 0·89). Removing this interaction term and refitting showed that average SLA decreased with increasing DQI with a scaling exponent of −0·20 (±0·03), but that the average SLA at a common daily quantum input was higher in the herbaceous species (t78 = −4·95, P < 10−4). The allometric relationships were SLA = 518DQI−0·20 (herbaceous species) and SLA = 379DQI−0·20 (woody species). On average, a herbaceous species had an SLA that was 1·4 times that of a woody species at an equivalent DQI. There was substantial residual variation (Fig. 4c), and a majority (66%) of this residual variation was due to within-experiment variation associated with differences between species at a constant DQI.

For ln(LMR), the mixed model ancova detected a significant interaction term between ln(DQI) and plant type (t77 = 2·45, P = 0·02), meaning that the relationship between ln(LMR) and ln(DQI) varied with the type of species. Re-analysing these data separately for each type of species showed that ln(LMR) decreased significantly with increasing ln(DQI) in the herbaceous species (t33 =−2·52, P = 0·02) but not in the woody species (t44 = 1·65, P = 0·11). Within the herbaceous species, the allometric relationship was LMR = −0·25DQI−0·14. There was substantial residual variation (Fig. 4d), and 55% of this residual variation was due to within-experiment variation associated with differences between species at a constant DQI.

variability of the growth-response coefficients and their relationship to daily quantum input (dqi)

GRC for NAR

Ignoring the effect of differing DQI between experiments (Table 3), the average within-experiment GRCNAR was 0·54 (±0·08) for herbaceous species and 0·55 (±0·03) for woody species. However, the GRCNAR values differed substantially between experiments, as shown by the large standard deviations of the between-experiment slopes. Including the ln(DQI) of each experiment explained 26% (experiments involving herbaceous species; Table 4) and 19% (experiments involving woody species; Table 5) of the between-experiment variation in GRCNAR.

Table 3.  Parameters (± SD) of mixed-model regressions of each ln-transformed growth determinant on ln(RGR), centred about its grand mean; the intercept is therefore the mean at RGR = 0·08 g g−1 day−1
Parameterln(NAR)ln(SLA)ln(LMR)
  1. RGR, relative growth rate; NAR, net assimilation rate; SLA, specific leaf area; LMR, leaf mass ratio, GRC, growth-response coefficient.

  2. Random components of model not significantly different from zero (5% significance level) are shown in bold type.

Herbaceous species
Average within-experiment intercept (α)−7·12 (±0·06) 5·45 (±0·05)−0·74 (±0·04)
Average within-experiment slope (β, GRC) 0·54 (±0·08) 0·28 (±0·06) 0·09 (±0·03)
SD of between-experiment intercepts (σλ) 0·31 0·24 0·20
SD of between-experiment slopes (σδ) 0·40 0·28 0·12
Between-experiment correlation of slopes and intercepts (rα,β)−0·28−0·30−0·31
Within-experiment SD (ɛ) 0·26 0·23 0·17
Woody species
Average within-experiment intercept (α)−7·48 (±0·07) 5·61 (±0·07)−0·61 (±0·03)
Average within-experiment slope (β, GRC) 0·55 (±0·03) 0·38 (±0·03) 0·12 (±0·02)
SD of between-experiment intercepts (σλ) 0·42 0·46 0·15
SD of between-experiment slopes (σδ) 0·10 0·16 0·11
Between-experiment correlation of slopes and intercepts (rα,β)−0·30−0·49−0·32
Within-experiment SD (ɛ) 0·33 0·26 0·22
Table 4.  Parameters (± SD) of mixed-model regressions of each ln-transformed growth determinant on ln(RGR), centred about its grand mean, and ln(daily quantum input); the intercept is therefore the mean at RGR = 0·08 g g−1 day−1 and DQI = 1 mol m−2 day−1
Parameterln(NAR)ln(SLA)ln(LMR)ln(LMR)
  1. RGR, relative growth rate; NAR, net assimilation rate; SLA, specific leaf area; LMR, leaf mass ratio, GRC, growth-response coefficient; DQI, daily quantum input.

  2. Random components of model not significantly different from zero (5% significance level) are shown in bold type. Analyses done only on experiments using herbaceous species.

Average within-experiment intercept (α)−7·40 (t612 = −19·3, P < 0·001) 5·46 (t614 = 18·19, P < 0·001)−0·51 (t614 = −2·09, P = 0·04) −0·26 (t615 = 1·44, P = 0·15)
Average within-experiment slope for ln(growth component) (β1, GRC)−0·62 (t612 = −1·38, P = 0·17) 1·06 (t614 = 3·05, P = 0·002) 0·42 (t614 = 1·98, P = 0·05)  0·09 (t615 = 2·59, P = 0·01)
Average between-experiment slope for ln(DQI) (β2) 0·09 (t33 = 0·75, P = 0·46)−0·002 (t33 = −0·02, P = 0·98)−0·08 (t33 = −1·01, P = 0·32) −0·16 (t33 = −2·74, P = 0·01)
Average within-experiment interaction of ln(growth component) × ln(DQI) 0·38 (t612 = 2·62, P = 0·009)−0·26 (t614 = −2·28, P = 0.02)−0·11 (t614 = −1·57, P = 0·12) 
SD of between-experiment intercepts (σλ) 0·32 0·24 0·21 0·21
SD of between-experiment slopes of β1δ) 0·34 0·24 0·12 0·13
Between-experiment correlation of slopes (β1) and intercepts (rα,β)−0·46−0·36−0·56−0·55
Within-experiment SD (ɛ) 0·26 0·23 0·17 0·17
Average within-experiment GRC−0·62 + 0·38 ln(DQI) 1·06 − 0·26 ln(DQI)   0·09
Table 5.  Parameters (± SD) of mixed model regressions of each ln-transformed growth determinant on ln(RGR), centred about its grand mean, and ln(daily quantum input); the intercept is therefore the mean at RGR = 0·08 g g−1 day−1 and DQI = 1 mol m−2 day−1
Parameterln(NAR)ln(NAR)ln(SLA)ln(SLA)ln(LMR)ln(LMR)ln(LMR)
  1. RGR, relative growth rate; NAR, net assimilation rate; SLA, specific leaf area; LMR, leaf mass ratio, GRC, growth-response coefficient; DQI, daily quantum input. Random components of model not significantly different from zero (5% significance level) are shown in bold type. Analyses done only on experiments using woody species.

Average within-experiment intercept (α)−8·37 (t537 = −70·45, P < 0·0001)−8·38 (t538 = −76·54, P < 0·0001) 6·54 (t531 = −56·77, P < 0·0001) 6·55 (t532 = 56·23, P < 0·0001)−0·59 (t531 = −6·88, P < 0·0001)−0·61 (t532 = −7·48, P < 0·0001)−0·61 (t532 = −21·77, P < 0·0001)
Average within-experiment slope for ln(growth component) (β1, GRC) 0·55 (t532 = 5·15, P < 0·0001) 0·53 (t538 = 19·84, P < 0·0001) 0·32 (t531 = 4·55, P < 0·0001) 0·38 (t532 = 12·29, P < 0·0001) 0·18 (t531 = 3·31, P = 0·001) 0·12 (t537 = 9·31, P < 0·0001) 0·12 (t532 = 5·05, P < 0·0001)
Average between-experiment slope for ln(DQI) (β2) 0·34 (t46 = 8·40, P < 0·0001) 0·34 (t46 = 9·14, P < 0·0001)−0·35 (t531 = −9·07, P < 0·0001)−0·35 (t44 = −8·96, P < 0·0001)−0·01 (t44 = −0·24, P = 0·81) 0·00 (t44 = 0·02, P = 0·99) 
Average within-experiment interaction of ln(growth component) × ln(DQI) −0·006 (t537 = −0·28, P = 0·78) 0·03 (t531 = 1·06, P = 0·29)−0·02 (t531 = −1·18, P = 0·24)    
SD of between-experiment intercepts (σλ) 0·22 0·22 0·24 0·24 0·16 0·15 0·15
SD of between-experiment slopes of β1δ)  0·09 0·08 0·15 0·15 0·11 0·11 0·11
Between-experiment correlation of slopes (β1) and intercepts (rα,β)−0·38−0·39−0·63−0·61−0·36−0·32−0·32
Within-experiment SD (ɛ) 0·33 0·33 0·26 0·26 0·22 0·22 0·22
Average within-experiment GRC  0·53  0·38   0·12

Experiments involving herbaceous species that had a higher DQI also had a higher GRCNAR; the quantitative relationship was GRCNAR = −0·62 + 0·39 ln(DQI). Thus the predicted GRCNAR is zero at a DQI of 5; 0·5 at a DQI of 18; and 1 at a DQI of 67 mol m−2 day−1. Experiments involving woody species showed a different pattern: in these experiments the variation in ln(DQI) did not significantly affect the between-experiment differences in GRCNAR (interaction term; Table 5) although ln(DQI) did explain some of the between-experiment differences in the intercepts. Figure 5(a) plots the GRCNAR against DQI.

Figure 5.

Growth-response coefficients (GRC) for net assimilation rate (NAR), specific leaf area (SLA) and leaf mass ratio (LMR) plotted against daily quantum input (DQI, mol m2 day−1). See Fig. 1 for symbols. Solid lines are predicted values for experiments containing herbaceous species; dotted lines are predicted values for experiments containing woody species.

GRC for SLA

Ignoring the effect of differing DQI between experiments (Table 3), the average within-experiment GRCSLA was 0·28 (±0·06) for herbaceous species and 0·38 (±0·03) for woody species. The GRCSLA values differed less than GRCNAR between experiments involving herbaceous species, but were equally variable among experiments involving woody species. Including the ln(DQI) of each experiment explained 26% (experiments involving herbaceous species; Table 4) and 12% (experiments involving woody species; Table 5) of the between-experiment variation in GRCNAR.

Those experiments involving herbaceous species that had a higher DQI also had a lower GRCSLA as shown by the significant interaction term in Table 4; the quantitative relationship was GRCSLA = 1·06 – 0·26 ln(DQI). Thus the predicted GRCSLA was zero at a DQI of 61; 0·5 at a DQI of 8·7; and 1 at a DQI of 1·3 mol m−2 day−1. Experiments involving woody species showed a different pattern: in these experiments the variation in ln(DQI) did not significantly affect the between-experiment differences in GRCSLA (interaction term; Table 5) although ln(DQI) did explain some of the between-experiment differences in the intercepts. Figure 5(b) plots the GRCNAR against DQI.

GRC for LMR

Ignoring the effect of differing DQI between experiments (Table 3), the average within-experiment GRCLMR was 0·09 (±0·03) for herbaceous species and 0·12 (±0·02) for woody species. The GRCLMR values differed less than either GRCNAR or GRCSLA between experiments involving both herbaceous and woody species. ln(DQI) did not have a significant effect on GRCLMR (interaction term; Tables 4 and 5) and including the ln(DQI) explained none of the between-experiment variation in the GRCNAR in experiments involving either herbaceous or woody species. Figure 5(c) plots the GRCNAR against DQI.

Graph (d) of Figs 1–3 shows the distribution of GRC values across experiments: these GRC values take into account differences in DQI, so the variation is due to experiment-specific attributes other than DQI. Those experiments involving herbaceous species had greater variability in GRCNAR and GRCSLA than did the experiments involving woody species; this was especially true for GRCNAR. Figure 6 plots the relationship between the three types of GRC value. There was a trade-off between GRCNAR and GRCSLA in experiments involving both herbaceous species (r = −0·89, P < 0·0001) and woody species (r = −0·40, P = 0·0006). Experiments involving herbaceous species showed a weak positive relationship between GRCSLA and GRCLMR (r = 0·35, P = 0·04), but a negative relationship between these two growth-response coefficients in experiments involving woody species (r = −0·51, P = 0·0003). Experiments involving herbaceous species also showed a trade-off between GRCNAR and GRCLMR (r = −0·51, P = 0·002) but this did not occur in experiments involving woody species (r = 0·10, P = 0·52).

Figure 6.

Between-experiment relationships in the growth-response coefficients (GRC) of net assimilation rate (NAR), specific leaf area (SLA) and leaf mass ratio (LMR).

Discussion

Models in plant community ecology involving RGR and its components are meant to apply across different types of species and across wide environmental gradients. Empirical data sets in this field never have this level of generality. Practical constraints result in single data sets that consist of only a small number of species, usually limited to a single plant type, and constant environmental conditions. The only practical way of comparing empirical patterns with theoretical models is in combining multiple data sets and then statistically modelling this two-level sampling process.

Tilman's (1988) model of plant community structure and dynamics is predicated on the assumption that interspecific variation in RGR is determined mostly by biomass partitioning to leaves vs non-photosynthetic structures; it therefore hypothesizes that the GRCLMR be close to 1·0 irrespective of plant type or environment. In fact, the average GRCLMR was close to 0·1 and did not vary greatly between experiments with plant types. LMR was never strongly correlated to RGR either within a single plant type, within a single environmental context, or across different environments in the collection of experiments used in this study.

Westoby's (1998) model assumes that SLA is a good indicator of interspecific variation in RGR between species and across environmental gradients; it therefore hypothesizes a strong positive correlation between RGR and SLA and a GRCSLA of close to 1·0. Westoby et al. (2002) have more recently reduced the importance of the RGR–SLA link. A recent text in plant ecophysiology (Lambers et al. 1998) also describes SLA as the most important determinant of RGR. Although SLA was moderately correlated with RGR when comparing species within a single experiment (a single environmental context), there was only a very weak correlation when comparing both across species and across environments (r = 0·29). In other words, if one were to randomly sample different species along a wide environmental gradient, the correlation between ln(SLA) and ln(RGR) would be only about 0·29. If one were to randomly sample both herbaceous and woody species growing at a single point along an environmental gradient, then the correlation would be higher at r = 0·49; but if one restricted one's sampling to only herbaceous species, the correlation would be only 0·28. From this I conclude that SLA is not a very good general indicator of interspecific variation in RGR, although it can be in certain environmental contexts.

In fact, if one had to choose a single growth component then the best indicator of RGR would be NAR, irrespective of plant type or whether the comparison was made in a constant environment or across environments. If one randomly samples both between species and between environments, the correlation is 0·86. Even within a single environment, the correlation is still moderately high at 0·59. The poorest correlation is found when the comparison is restricted to herbaceous species growing in a constant environment (r = 0·48). For community ecologists, this result is unfortunate as NAR, a rate that is related to whole-plant net photosynthetic rate on an area basis, is more difficult to measure that either SLA or LMR. It will therefore be important to find easily measured attributes that correlate well with NAR.

However, the above conclusion is more complicated because, within herbaceous species at least, the strength of the growth-response coefficients of both NAR and SLA varies quite closely with the daily quantum input and trades off (Figs 5 and 6). Figure 7 plots the predicted values of the GRC values. For herbaceous species, SLA is the most important determinant of RGR in experiments conducted at low irradiance (below ≈15 mol m−2 day−1); SLA and NAR are of about equal importance until about 25 mol m−2 day−1; and NAR is the most important determinant of RGR in experiments conducted above 25 mol m−2 day−1. Villar et al. (2005) measured DQI continuously for the first 100 days of the year in Spain: their DQI values varied from 10 to 50 mol m−2 day−1, the average being ≈30 mol m−2 day−1. This means that the relative importance of SLA and NAR in determining RGR might have changed daily and over the growing season. The same trade-off was not detected in the woody species, but this may be because relatively few experiments involving woody species were conducted at higher irradiance levels.

Figure 7.

Predicted values of the growth-response coefficients as a function of daily quantum input.

Given that the growth-response coefficients for NAR and SLA trade off with daily quantum input, the most important general growth component of RGR is the product of NAR and SLA: NAR calculated on a leaf mass basis [NARmass = (1/ML)(dMP/dt)]. This follows from the observation that LMR almost always has a small effect on RGR. Indeed, regressing ln(NARmass) on ln(RGR) using a mixed model results in a GRC of 0·86 for the woody species, irrespective of DQI, and GRC = 0·35 + 0·15 ln(DQI) for the herbaceous species; this translates to values of 0·70, 0·80, 0·86 and 0·96 at DQI = 10, 20, 30 and 60 mol−2 day−1. NARmass is related to whole-plant net photosynthetic rate calculated on a leaf mass basis. One can predict the mass-based net photosynthetic rate per leaf (Amass) from a combination of SLA and leaf nitrogen content (Reich et al. 1997; Wright et al. 2004) and so, if NARmass is also related to leaf-level Amass, then perhaps interspecific RGR could be predicted by a combination of SLA and leaf N per leaf dry mass. I cannot evaluate this possibility with the current data set, but both these variables are easy to measure on leaf samples, so perhaps Westoby's (1998) model could be extended by replacing SLA with the predicted value of NARmass.

Finally, there was still substantial between-experiment variation in all the growth-response coefficients, even after taking into account differences in DQI. This means that there are other experiment-specific differences that cause the GRC values to vary. Two likely differences are the ages and sizes of the plants used in the different experiments; and the nutrient supply rates provided. Unfortunately, not enough papers provided this information to allow these variables to be included in the analysis.

Acknowledgements

This study was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Hendrik Poorter kindly provided the data from his original meta-analysis and contributed significantly to the writing of this paper.

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