Trade-offs between net assimilation rate and specific leaf area in determining relative growth rate: relationship with daily irradiance




  • 1Three separate experiments were conducted, involving 27 herbaceous species and 14 woody species aged 15–30 days, in order to determine the relative importance of net assimilation rate (NAR), specific leaf area (SLA) and leaf weight ratio (LWR) in explaining interspecific variations in relative growth rate.
  • 2Daily quantum inputs were 31·12 mol m−2 day−1 in the first experiment and 33·17 mol m−2 day−1 in the second and third experiments. This is about twice the typical irradiance of most other experiments in this area, but only about 85% of the daily photon flux in nature. Plants were cultivated in hydroponic sand culture in a solution containing 5·8 mm nitrogen.
  • 3RGR was strongly and positively correlated with NAR in all three experiments. RGR was weakly and negatively correlated with SLA, while the correlation between RGR and LWR was weak and variable.
  • 4These results are compared to those already published in the literature: the commonly reported result that interspecific variation in RGR is determined primarily by SLA is partly due to the low irradiance used in most experiments, and the relative importance of SLA and NAR changes depending on irradiance.
  • 5A hypothesis is proposed in which direct and indirect effects of SLA on each of NAR and RGR are decomposed, and which leads to a trade-off between SLA and NAR as a function of daily irradiance.


There are large interspecific differences in relative growth rate (RGR, g g−1 day−1) (Grime & Hunt 1975) even when comparing plant species growing under identical environmental conditions and free of competition. Because plant size – and thus growth – is an important determinant of survival and reproduction in nature, these interspecific differences in RGR are now of central importance in plant ecology (Grime 2001; Tilman 1988; Westoby 1998). When the external environment is constant, interspecific differences in RGR must be due to interspecific differences in plant physiology and morphology. It is therefore important to know how physiological and morphological differences contribute to variation in RGR. To answer this question, many workers have used the classical decomposition into net assimilation rate (also called unit leaf rate; NAR, g cm−3 day−1); specific leaf area (SLA, cm2 g−1); and leaf weight ratio (LWR, g g−1). Specifically:

image(.eqn (1a))
image(eqn (1b))

NAR is a physiological component because it is a measure of whole-plant daily net photosynthetic rate weighted by the rate of change in plant carbon content (McKenna & Shipley 1999; Poorter 1989; Poorter & van der Werf 1998). SLA is a morphological component because it is determined by leaf dry matter concentration and leaf thickness (Shipley 1995; Witkowski & Lamont 1991). LWR measures the allocation of biomass to leaves vs other plant parts.

Many studies have measured interspecific RGR and the three components given in equation 1. Poorter & van der Werf (1998) reviewed most studies up to that date, and found that the majority showed RGR to be strongly correlated to SLA and weakly correlated to either NAR or LWR. Since then, a number of other studies have reported strong positive correlations between RGR and NAR, and weak correlations between RGR and SLA or LWR (Huante & Rincon 1998; Huante, Rincon & Acosta 1995; McKenna & Shipley 1999; Poorter 1999; Ryser & Wahl 2001; Saverimuttu & Westoby 1996; Taub 2002). The relative importance of SLA and NAR in determining RGR varies between studies – why might this be?

One possible explanation is that the relative importance of NAR and SLA depends on the ambient light environment, with interspecific differences in SLA being the main determinant of RGR at low irradiance, and interspecific differences in NAR being the main determinant of RGR at high irradiance. If this is true, the reason why SLA has been the most important determinant of RGR in the majority of studies reviewed by Poorter & van der Werf (1998) would be because most were conducted at low irradiance. Poorter & van der Werf (1998) evaluated this possibility in their original review, and rejected it. However, few studies published up to that date were conducted at high irradiance; average daily irradiance in the data compiled by Poorter & van der Werf (1998) was 15·5 mol m−2 day−1, and fully 80% of those studies were below 25 mol m−2 day−1, which is less than half the daily irradiance experienced by non-shaded plants in nature. I therefore explored the possibility that NAR is the main determinant of RGR at high irradiance, by growing a wide range of plant species at daily integrated photon flux densities that were approximately twice those used in most of the other experiments reviewed by Poorter & van der Werf (1998), and about 85% of those typically experienced in nature during the summer growing season.

Materials and Methods

Table 1 lists the species used in this study; taxonomy follows Gleason & Cronquist (1991). The results come from three separate experiments. The first two experiments contained only herbaceous species, while the third contained only woody species of trees or shrubs. Seeds used in the first experiment came from local populations near the Université de Sherbrooke (45°25′ N, 71°55′ E), while seeds used in the other two experiments came from commercial sources. In every case it is unlikely that the full intraspecific variation of each species was represented in the seed sources.

Table 1.  Species means of estimated growth parameters in each of three separate experiments for plants aged 15–30 days
  1. Numbers in parentheses = number of plants used for that species.

  2. Parameters are average relative growth rate (RGR, g g−1 day−1); net assimilation rate (NAR, g cm−2 day−1); leaf area ratio (LAR, cm2 g−1); leaf weight ratio (LWR, g g−1); specific leaf area (SLA, cm2 g−1).

Achilleamillefolium (8)10·180·00411640·61248
Acoruscalamus (8)10·100·00072150·47436
Agrostisalba (7)10·230·0033 990·32286
Bromusinermis (7)10·180·0027 870·34244
Chrysanthemumleucanthemum (6)10·260·00261200·55208
Echinocloacrus-galli (8)10·220·00181220·30397
Epilobiumglandulosum (6)10·190·00051090·43257
Galiumpalustre (8)10·180·00181250·50256
Melilotusalba (7)10·210·0043 860·49186
Oenotherabiennis (8)10·180·00151400·69200
Phleumpratense (8)10·210·00241340·31392
Plantagomajor (7)10·080·00181160·65178
Rumexlongifolius (7)10·140·00131470·45299
Tanacetumvulgare (4)10·020·00061450·60238
Trifoliumpratense (8)10·230·0027 890·43219
Agropyrontrachycaulum (15)20·210·00221190·40292
Andropogongerardii (15)20·160·00121390·43325
Aquilegiacanadensis (15)20·220·00161750·59342
Asclepiasincarnata (15)20·230·00161490·52282
Asternovae-angliae (9)20·180·00111740·65269
Calamagrostiscanadensis (12)20·240·00151960·53385
Centaureamaculosa (13)20·330·00311380·68205
Elymuscanadensis (15)20·190·00191320·47273
Epilobiumglandulosum (13)20·330·00261700·72233
Eupatoriummaculatum (9)20·160·00072220·75298
Glyceriacanadensis (11)20·110·00081940·50387
Mimulusringans (9)20·290·00152530·71351
Oenotherabiennis (15)20·270·00241580·76212
Panicumvirgatum (14)20·210·00181480·46325
Rudbeckiahirta (9)20·230·00181740·72241
Acernegundo (6)30·140·00121340·57232
Acersaccharum (7)30·070·00031990·67297
Betulalenta (4)30·140·00081770·64274
Betulalutea (6)30·150·00082150·65330
Betulapapyrifera (7)30·050·00061640·67246
Celtisoccidentalus (8)30·150·00111510·69217
Fragusamericana (18)30·040·00031460·65225
Fraxinuspennsylvanica (14)30·090·00071480·65227
Rhusglabra (10)30·210·00161260·66191
Piceaglauca (27)30·100·00052080·78267
Pinusaristata (28)30·040·00031230·64191
Pinusbanksiana (27)30·090·00051720·66262
Pinusponderosa (25)30·040·0005 990·60165
Tsugacanadensis (10)30·210·00161260·66191


In experiment 1, light was supplied from three banks of lights: one bank of fluorescent lamps 2·1 m from pot height, which provided <10 µmol m−2 s−1 PAR at pot height because of shading with the other banks of lights; a second bank of fluorescent and incandescent lamps 1·2 m from the pots (providing 70 µmol m−2 s−1 PAR at pot height); plus a third bank of lamps consisting of one each of 1000 W metal halide and high pressure sodium lamps 0·9 m from the pots, which provided an additional 500 µmol m−2 s−1 PAR. The first bank of lamps remained switched on 24 h day−1. The second bank was on 16 h day−1, while the third bank was on 15 h day−1. This provided a total daily quantum input of 31·12 mol m−2. In experiment 2, the first bank was turned off but the second bank was on 24 h day−1 and the third bank was on for 15 h day−1. Thus plants in the second experiment received a total daily quantum input of 33·17 mol m−2. In experiment 3, the first bank was turned off and the second bank was on for 16 h day−1. This provided a total daily quantum input of 31·16 mol m−2: essentially the same daily amount as in the first experiment, but with a true dark 6 h period every 24 h. These combinations of light sources were used to provide as much daily photon input as possible without producing heat stress. As a comparison, the average daily quantum input in the Netherlands during the growing season is 37·5 mol m−2 day−1 (Krijnen 1992). These experimental irradiances were therefore ≈83–88% of typical values in nature.

Hydroponic Methods

Each plant was grown in its individual drained container in washed silica sand. Containers in the first experiment were 1·3 l; those in the second and third experiments were 0·79 l. Each individual was ≈8 cm from the next. All containers sat in a large plastic basin. The nutrient solution was pumped into this basin four times per day, at 6:00, 12:00, 18:00 and 24:00 h, in experiment 1; and twice a day, at 12:00 and 24:00 h, in experiments 2 and 3. In each case, the sand initially became saturated and then drained to field capacity over a 30 min period. The nutrient solution consisted of 2 mm KNO3, 1·5 mm Ca(NO3)24H2O, 2 mm MgSO47H2O, 0·38 mm (NH4)2SO4, 1 mm KH2PO4, 10 µm MnSO4H2O, 1 µm Na2MoO42H2O, 46 µm H3BO4, 1 µm ZnSO47H2O, 1 µm CuSO4 and 68·1 µm EDTA-Fe. The pH was measured daily and adjusted to 5·8. Nitrate concentrations were also monitored daily using a nitrate-selective electrode, and the solution was changed when nitrate concentration decreased below 3 mm. Because large volumes of solution were used (200l), this did not occur often. Temperatures were 26 °C during the day and decreased to 19 °C at night. Relative humidity was ≈60%.

Sampling Strategy

Each interspecific relationship between RGR and its components follows a multilevel (Bryk & Raudenbush 1992; Goldstein 1995) or mixed-effects model (Pinheiro & Bates 2000) possessing two hierarchical levels of random variation: interspecific and intraspecific. In a true multilevel model, these two sources of random variation are estimated separately as variance components. The test on the interspecific slope between RGR and its component is then based only on the interspecific variance component, whose precision is based on the number of species rather than on the total number of observations. Unfortunately, both RGR and its components are estimated as species means rather than based on individual plants, and this confounds the two sources of variance. In such cases, it is important to maximize variation at the level for which the variance component is largest (Goldstein 1995). Shipley (1995) estimated variance components for SLA and found that the interspecific variance component was over 10 times larger than the variance component measured at the individual level. Meziane (1998) found that 79, 70 and 79% of the total variance in SLA, LWR and leaf net photosynthetic rate, respectively, were explained by interspecific differences even when nutrient and light supply were varied. Hunt (1984) reported that interspecific variation in RGR was five times larger than intraspecific variation in RGR. It is therefore more important to maximize the interspecific variation than to maximize intraspecific replication when these two sources cannot be estimated separately. In experiments with a fixed number of individuals, increasing the number of individuals per species will increase the precision with which the growth components of that particular species are estimated, but this necessarily reduces the number of species and therefore the most critical level of variation. For these reasons, I chose to increase the number of species even though this meant reducing the number of plants per species. In general, seven plants per species were used in the first experiment; 13 in the second experiment; and nine plants per species of woody angiosperms and 23 plants per species of woody gymnosperms in the third experiment. Reduced germination rates resulted in fewer plants for some species. More woody gymnosperm plants were used because it was expected that they would have lower RGR and would therefore require more replication (Table 1). Plants were harvested at 15 and 30 days after planting. At each harvest, roots were washed clean of sand, and biomass was separated into leaf blades, roots and structural tissues (stems, petioles, leaf sheaths), dried at 70 °C for at least 72 h, and then weighed. Leaf surface areas were measured using an image analyser before drying. For the Pinus species, surface areas were calculated assuming that the leaves were longitudinal prisms, calculated from projected needle area and average needle thickness per plant, and that two-thirds of the full surface would be able to intercept directional light; for these needle leaves the winseedle image analysis program was used (Regents Instruments, Quebec, Canada).

RGR, NAR, SLA and LWR were estimated from these primary data using the improved formulae of Hunt (Hunt 1990; Hunt & Cornelissen 1997).


Table 1 lists the mean values of RGR, NAR, SLA and LWR in the three experiments. Figure 1 plots the relationships between RGR and each of its components based on average values of plants aged 15 and 30 days, and Table 2 lists the Pearson correlation coefficients between RGR and its components. RGR was strongly positively correlated to NAR in all three experiments, was never significantly correlated to LWR, was not significantly correlated to SLA in experiments 1 or 3, but was significantly negatively correlated to SLA in experiment 2.

Figure 1.

Relationships between relative growth rate (RGR), net assimilation rate (NAR), leaf area ratio (LAR), specific leaf area (SLA) and leaf weight ratio (LWR) in three separate experiments conducted at high irradiance. Each point is a species mean for plants aged 15–30 days. □, Experiment 1, herbs; ○, experiment 2, herbs; •, experiment 3, woody gymnosperms; ♦, experiment 3, woody dicots.

Table 2.  Pearson correlation coefficients between growth components in each of three separate experiments
  1. Experiment 1 involved 17 species of herbs; experiment 2, 20 species of herbs; experiment 3, 14 species of trees and shrubs. Values in bold are significant at the 5% level.

RGR, NAR 0·56 0·82 0·90
RGR, SLA−0·01−0·53−0·17
RGR, LWR−0·46 0·50−0·14
NAR, SLA−0·30−0·690·49
NAR, LWR−0·11 0·17−0·23
SLA, LWR−0·600·49 0·01


Comparisons with the Literature

The conclusion that interspecific differences in RGR are most strongly associated with interspecific differences in SLA appears to be entrenched in the literature, and is now even found in textbooks (Lambers, Chapin & Pons 1998). The results reported here contradict this conclusion. Poorter & van der Werf (1998) reviewed the available literature up to that date, and concluded that there was no evidence for NAR to increase in importance at higher irradiance levels, although 80% of the studies in that review had daily integrated irradiances below 25 mol m−2. Their conclusions were based on calculating a ‘growth response coefficient’ (GRC), defined as the slope of a regression of ln(growth component) on ln(RGR). Because some glasshouse studies did not report the daily quantum input, they took typical values from the literature (Poorter & van der Werf 1998, p. 318), and I have used these values as well. However, most of the studies reviewed had only a few species. Figure 2 shows the results from Appendix 2 of Poorter & van der Werf (1998) for studies in which there were at least four species or genotypes, plus all those newer studies for which the actual data were provided, including the three experiments reported here (Antunez, Retamosa & Villar 2001; Campbell & Rochefort 2002; Huante & Rincon 1998; Huante, Rincon & Acosta 1995; Meziane & Shipley 1999; Poorter 1999; van Rijn 2001; Ryser & Wahl 2001; Taub 2002; Tjoelker, Oleksyn & Reich 1998; Volin, Reich & Givnish 1998; Watling, Ball & Woodrow 1997; Wright & Westoby 2000). Because studies with more species provide better tests of the interspecific trend, I have scaled the size of the points to inline image where S is the number of species in the study. This scaling factor was chosen because the residual degrees of freedom for the slopes (Fig. 3a,b) and correlation coefficients (Fig. 3c,d) are equal to this amount. As RGR is essentially independent of irradiance once the daily quantum input is about 20 mol m−2 (Poorter & van der Werf 1998), it is useful to compare the results relative to this value in the literature. At irradiances below 20 mol m−2, the majority of studies involving herbaceous species report weak effects of NAR (GRC < 0·5) and strong effects of SLA (GRC > 0·5). Above 20 mol m−2, the trend is reversed. There are large amounts of scatter in Fig. 2, presumably due to the many other factors that affect the strength of the relationships, including nutrient supply rates as well as the types of species chosen in any one study. In particular, those studies involving trees (Fig. 2, open circles) tend to find NAR to be important even at low levels of irradiance. This may be because many trees reach light saturation at lower irradiances than most herbs.

Figure 2.

Growth response coefficients (GRC) and Pearson correlations of NAR (a,c) and SLA (b,d) relative to RGR from various studies plotted against daily quantum input (mol m−2 day−1). Studies involved •, herbaceous species; ○, trees. The size of the symbol is proportional to inline image, where S is the number of species included in that study. Horizontal lines are added for visual reference; vertical line marks the level at which RGR becomes largely independent of irradiance.

Figure 3.

Growth response coefficients for NAR and SLA relative to RGR. Each point represents a single published study. The size of the circles is proportional to inline image, where S is the number of species included in that study. The line represents a perfect negative trade-off between NAR and SLA in determining RGR.

In general, it appears that SLA is most strongly associated with RGR when plants are grown at low irradiance, while NAR is most strongly associated with RGR when plants are grown at higher irradiance, although there are exceptions to this trend. A good example of this general pattern is given by Poorter (1999), who measured the growth parameters in a set of tropical trees at three different irradiances: 3, 25 and 100% of full daylight. NAR was weakly correlated with RGR at the lowest irradiance (3% daylight), which is probably less than 50 µmol m−2 s−1, or ≈1 mol m−2 day−1. As irradiance increased to 25% (≈375 µmol m−2 s−1, ≈10 mol m−2 day−1) the importance of NAR increased while that of SLA decreased. At 100% irradiance (≈1500 µmol m−2 s−1, ≈40 mol m−2 day−1) NAR was strongly correlated with RGR, while SLA was weakly and non-significantly correlated with RGR.

Trade-Offs Between NAR and SLA

Why might this switch in importance between NAR and SLA occur as irradiance increases? At an ecological level, it is common for a plant to experience a variable light environment during its growth and for different individuals of the same species to grow in different light environments. As growth is important for survival and reproduction, it would be advantageous for a plant if growth were maintained over a wide range of irradiances, rather than being severely depressed whenever the light supply decreases. Such a buffering of RGR would occur if NAR and SLA trade-off.

There are good empirical reasons to expect such a trade-off. Poorter & van der Werf's (1998) literature survey found that RGR changes very little once the daily irradiance reaches about 20 mol m−2, but that both SLA and (especially) NAR continue to change with increasing irradiance. As, by definition, RGR = NAR · SLA · LWR, a constant RGR and changing values of its components require that these components trade-off in importance. Figure 7(a) of Poorter & van der Werf (1998) shows that NAR is both low and has little interspecific variance at low irradiance. With increasing irradiance, the average NAR and the interspecific variation around this average increase, as some species increase their NAR very little while others increase NAR greatly with increasing irradiance. The physiological origin of the trend for NAR is easy to understand with reference to typical curves of net leaf photosynthetic rate vs irradiance. Such curves follow a non-rectangular hyperbola in which the light-compensation points of different species are much less variable than the light-saturation points. As NAR is largely determined by whole-plant daily net photosynthesis, it is likely that NAR describes a similar relationship.

Figure 7(c) of Poorter & van der Werf (1998) shows the opposite trend for SLA; SLA is high and variable at low irradiance, and low and relatively similar across species at high irradiance. Poorter & van der Werf (1998) comment on this trade-off, which is still found when newer studies are included (Fig. 3). The line in Fig. 3 represents the expected trend if GRCSLA and GRCNAR showed a perfect trade-off; in other words, a change in either NAR or SLA completely compensates for the other. Despite a few outliers, the trade-off is quite pronounced and also exists between different species grown at a constant irradiance (McKenna & Shipley 1999; Meziane & Shipley 1999). Finally, as NAR is largely a measure of whole-plant net photosynthetic rate, one would expect that leaf net photosynthetic rate would also have a negative relationship with SLA, and this is indeed the case, both in the field (Reich et al. 1999) and when light and nutrients are manipulated experimentally (Meziane & Shipley 2001).

A Hypothesis to Explain the Trade-Off

McKenna & Shipley (1999) proposed a path model relating RGR and its components. With respect to RGR, NAR and SLA, the path model is as shown in Fig. 4, with the path coefficients represented by letters. From the rules of path analysis (Shipley 2000) one can relate the covariances (σ) and correlations (ρ) between RGR and each of NAR and SLA:

Figure 4.

Hypothesized path model relating specific leaf area (SLA), net assimilation rate (NAR) and relative growth rate (RGR). Letters represent path coefficients; ɛ, residual variances of the path model.

image(eqn 2)
image(eqn 3)
image(eqn 4)
image(eqn 5)
image(eqn 6)

As RGR is largely independent of daily irradiance after ≈20 mol m−2, interspecific differences in RGR will not change after this point, so inline image will remain approximately constant in equations 5 and 6. However, increasing daily irradiance above 20 mol m−2 will continue to increase inline image and to decrease (though perhaps less severely) inline image. Meziane & Shipley (1999) found that the path coefficients themselves did not change with irradiance or nutrient supply, although the means and variances of each variable did. This means that the correlation between SLA and RGR will decrease and the correlation between NAR and RGR will necessarily increase, given this hypothesized structure, with increasing daily irradiance. This does not occur because the structural relationships between the variables change, but rather because the interspecific differences in these variables change in a compensatory fashion.

The question should not be: which is more important, NAR or SLA, in determining RGR? Both are important but their importance changes with irradiance, and this is what allows RGR to be largely buffered from changes in irradiance. If this hypothesis is correct the intraspecific plasticity in these growth parameters across variable environments is particularly important in nature, and interspecific constraints on this plasticity will affect the relative success of different species across light gradients.


The Natural Sciences and Engineering Research Council of Canada financially supported this research. Soumadi Mounirattinam and Patrice Laliberté provided technical help. Hendrik Poorter kindly provided the data from his original literature review.