Abstract
It is well known that leaf photosynthesis per unit dry mass (Amass) is positively correlated with nitrogen concentration (Nmass) across naturally growing plants. In this article we show that this relationship is paradoxical because, if other traits are identical among species, plants with a higher Amass should have a lower Nmass, because of dilution by the assimilated carbon. To find a factor to overcome the dilution effect, we analyze the Nmass–Amass relationship using simple mathematical models and literature data. We propose two equations derived from plant-growth models. Model prediction is compared with the data set of leaf trait spectrum obtained on a global scale. The model predicts that plants with a higher Amass should have a higher specific nitrogen absorption rate in roots (SAR), less biomass allocation to leaves, and/or greater nitrogen allocation to leaves. From the literature survey, SAR is suggested as the most likely factor. If SAR is the sole factor maintaining the positive relationship between Nmass and Amass, the variation in SAR is predicted to be much greater than that in Amass; given that Amass varies 130-fold, SAR may vary more than 2000-fold. We predict that there is coordination between leaf and root activities among species on a global scale.
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Introduction
Recent intensive studies have revealed convergence in the variation of leaf traits across vascular plant species on a global scale. At one end of the axis, species have higher photosynthetic capacity, a higher nitrogen (N) concentration, a greater leaf area on a dry mass basis, and a shorter leaf life span. The opposite is true at the other end (Reich et al. 1991, 1992, 1997; Wright et al. 2004, 2005). This convergence reflects a mixture of direct and indirect causal relationships (Wright et al. 2004). Higher photosynthetic capacity is beneficial for faster growth, whereas being tougher and less palatable for herbivores is needed to persist for a longer time. A leaf can hardly realize both at the same time, leading to a trade-off between photosynthesis and persistence (Reich et al. 1991; Wright and Cannon 2001; Hikosaka 2005).
The positive relationship between photosynthetic capacity and leaf N concentration seems reasonable in terms of biochemistry (Field and Mooney 1986; Evans 1989). Because about half of leaf N is invested in the photosynthetic apparatus, there is a strong correlation between photosynthetic capacity and N concentration within a species. Furthermore, species with a higher N concentration tend to have higher photosynthetic N-use efficiency (photosynthetic capacity per unit leaf N) (Hikosaka 2004; Wright et al. 2005). Because of these two factors, photosynthetic capacity increases more than proportionally with increasing leaf N concentration across species (Hikosaka 2004). In a survey on a global scale, the regression equation for photosynthetic capacity and leaf N concentration was Y = 36.3 X1.72 (Wright et al. 2004).
Most previous studies on the photosynthesis–N relationship have considered N concentration to be a determinant of photosynthetic capacity. However, N concentration is also dependent on photosynthesis. New leaves are constructed with allocated N and biomass (Fig. 1). N concentration will decrease if biomass allocation to leaves increases relative to N allocation. Thus, if there are two species with different photosynthetic rates, we can expect the species with a higher photosynthetic rate to have a lower leaf N concentration. However, this is discrepant to leaf-trait convergence. Why do species with a higher photosynthetic capacity have a higher leaf N concentration? In this article, using mathematical growth models, we theoretically show that the positive correlation between photosynthetic rates and nitrogen concentrations is paradoxical. Then we consider the mechanism that maintains the interspecific variation in leaf N concentration relative to photosynthetic rate, and discuss the factors responsible for leaf-trait convergence.
N concentration as a function of photosynthesis
Leaf N concentration per unit leaf dry mass (Nmass) is affected by various plant functions. Here Nmass is defined as the ratio of standing leaf N (LN) to standing leaf mass (LM) in the plant. LM at one point in time (LM t ) is determined by LM one step earlier (LMt−1) and by production (∆LMP) and loss of leaf mass (∆LML) during the step (LM t = LMt−1 + ∆LMP − ∆LML; Fig. 2). LN is also affected by the turnover of N. Nmass should thus be modeled as a function of these variables. To obtain simple solutions, we adopt several assumptions. First, we assume that LN and LM are balanced with each other such that each species has an inherent value of Nmass. Nmass is thus constant over short time periods (see “Assumptions in the model” for discussion).
Second, we consider two situations for plant growth. The first model (Exponential model) assumes that plants grow exponentially without any loss of tissues (no senescence) and recycling of N, in which the relative growth rate is constant. It represents initial growth of seedlings under ideal conditions, where there is no resource limitation, no mutual shading and no stress. The second model (Turnover model) assumes that LM is constant because of the same rate of leaf production and loss. This happens in climax vegetation, where the standing biomass is almost stable. These two situations are extremes in plant life and other situations may be regarded as intermediate between the two.
Exponential model
Here we use a simple plant-growth model that has been used for many growth-analysis studies (e.g., Hirose 1987; Garnier 1991). In the model, C and N are acquired by leaves and roots, respectively, and the unit rates of assimilation (photosynthetic rate per unit standing leaf mass, Amass, and N absorption rate per unit standing root mass, SAR) are constant. The fractions of biomass and N in each organ are also constant and the relative growth rate does not change (plants grow exponentially). There is no senescence in organs, i.e., no loss of organs.
As mentioned above, we assumed steady-state growth where standing leaf mass and leaf N are balanced with each other. Because there is no loss of N and biomass in this model, Nmass is obtained from the balance between N and biomass allocation to leaves:
where dLNP/dt and dLMP/dt are the rate of leaf N production (N allocated to leaves) and the rate of leaf mass production, respectively.
The rate of plant biomass production (dPMP/dt) is proportional to the product of photosynthetic rate per unit leaf mass (Amass) and standing leaf mass (LM):
where k is the coefficient of conversion from CO2 to biomass, which involves respiration (both construction and maintenance). Plant nitrogen uptake rate (dPNP/dt) is expressed as the product of specific absorption rate (SAR) and standing root mass (RM):
We define the fractions of acquired N and biomass that are allocated to leaves as LNF (= dLNP/dPNP) and LMF (= dLMP/dPMP), respectively. Note that LNF and LMF are not the ratio for standing N and mass. However, because steady-state growth without loss of biomass and N is assumed in this model, values of LNF and LMF are equal to those of the leaf-to-plant N ratio and the leaf-to-plant mass ratio, respectively (i.e., dLNP/dPNP ~ LN/PN and dLMP/dPMP ~ LM/PM, where PM and PN are the standing plant mass and N, respectively). Substituting Eqs. 2 and 3 into Eq. 1, Nmass is expressed as:
where RMF is the fraction of biomass allocated to roots, equal to the root-to-plant mass ratio in this model (i.e., dRMP/dPMP ~ RM/PM). Equation 4 indicates that Nmass increases with increasing root activity (SAR), biomass allocation to roots (RMR), and N allocation to leaves (LNR) because an increase in these variables increases the amount of leaf nitrogen. An increase in photosynthetic rates (Amass) decreases Nmass, because it increases biomass production. As an increase in LMF increases standing leaf mass, which not only increases biomass production but also dilutes nitrogen in leaves by increased leaf mass allocation, Nmass is inversely related to the square of LMF.
Turnover model
In mature vegetation, production of new leaves is balanced by loss of old leaves, leading to a constant leaf mass in the canopy (Hikosaka 2003; Oikawa et al. 2005). Assuming that the rate of leaf-mass production (dLMP/dt) is identical to the leaf loss rate for a certain value of leaf longevity (LL), LM is expressed as the product of leaf production rate and leaf longevity (Fig. 2; Ackerly and Bazzaz 1995; Hikosaka 2005):
Thus, standing leaf mass (LM) is greater if the leaf longevity is longer. Note that in this model, the value of LMF is not equal to that of standing mass ratio of leaf to total plant. Equation 5 can be modified as follows:
Similarly, RMF can be expressed as:
where RL is the root longevity. LN is expressed as:
where MRT is the mean residence time of N in the leaves (Berendse and Aerts 1987). MRT is higher if leaf longevity is longer and/or if plants recycle more N (Aerts and Chapin 2000). Then Nmass is expressed as:
RL and MRT positively relate to Nmass, because an increase in these factors increases the amount of leaf nitrogen. An increase in LL increases leaf mass, which in turn increases biomass production and dilutes leaf nitrogen.
If longevity terms (MRT, RL, and LL) are assumed to be infinite, Eq. 4 is identical to Eq. 8. Therefore, the Turnover model can be regarded to include the Exponential model.
The paradox of the N–photosynthesis relationship
Here we analyze the relationship between Nmass and Amass mainly according to the Turnover model. We define X, which is equal to (SAR RMF LNF RL MRT)/(k LMF2 LL2) in Eq. 8. Then Eq. 8 is simplified as follows:
Equation 9 suggests that, if other variables (X) are constant, Nmass decreases with increasing Amass, i.e., Nmass is negatively correlated with Amass (line b in Fig. 3). This is, however, inconsistent with previous studies showing a positive correlation between Nmass and Amass. Thus, X is not constant and varies along Amass. Here we use a dataset for a number of species growing in natural vegetation collected by the global plant trait network (Glopnet; Wright et al. 2004). The slope of the log–log relationship between Nmass and Amass across 712 species was 0.58 (line a in Fig. 3). From this, therefore, the slope of the log–log relationship between X and Amass is predicted to be 1.58. This suggests that the variation in X is greater than that in Amass. In the Glopnet dataset, Amass varied 130-fold (5–660 nmol g−1 s−1), suggesting that X varied more than 2000-fold (line c in Fig. 3).
Which term contributes to the variation in X?
Equation 8 suggests that to have a higher Nmass species with higher Amass should have smaller biomass allocation to leaves than to roots (related to LMF and RMF), greater nitrogen allocation to leaves (LNF), and/or higher nitrogen uptake rate in roots (SAR). Variables related with longevity (LL, RL, and MRT) potentially affect the relationship; Nmass increases with increasing RL and MRT and with decreasing LL. Hereafter, we discuss which of these factors contributes to the actual relationship.
Longevity terms
MRT is expressed as: MRT = LL/(1 − R), where R is the nitrogen resorption efficiency in the leaf (Aerts and Chapin 2000). It has been suggested that R is related neither to growth form nor to leaf-trait convergence (Aerts 1996; Aerts and Chapin 2000; Wright and Westoby 2003). The MRT/LL ratio is thus regarded as a constant fraction along the variation in Amass. Studying leaf and root traits in grassland and savannah species, Tjoelker et al. (2005) found that LL were positively correlated with RL. This implies that the RL/LL ratio is also a constant fraction along the variation in Amass. These facts suggest that the longevity terms less contributes to the variation in X.
Biomass allocation
Biomass allocation has a large effect on the Nmass–Amass relationship, i.e., a decrease in allocation to leaves leads to concentration of nitrogen in the leaves, and an increase in allocation to roots increases nitrogen uptake rate at the plant level (Eq. 8). It should be noted that LMF and RMF in our models are not the ratio of standing mass but the fraction of assimilated biomass that is allocated to the target organ. Thus the presence of large stems does not mean low LMF. In the Glopnet survey, the Nmass−Amass relationship is less affected by the presence of large stems (trees versus herbs; Wright et al. 2005).
The contribution of biomass allocation to leaves can be estimated from the Glopnet dataset. In the turnover model, LL can be expressed as follows (see Eq. 5):
It has been shown that the slope of the Amass−LL relationship on a log-scale was −0.73 (Wright et al. 2004, 2005). Substituting Eq. 10 into the Amass−LL relationship in the Glopnet dataset suggests that the slope of the LMF−Amass relationship was positive (0.38; Wright et al. 2005; see also Givnish 2002). However, the positive relationship between LMF and Amass is inconsistent with the model prediction; if this relationship is positive and other variables are constant, Nmass should decrease with increasing Amass (see Eq. 9). Furthermore, previous studies that analyzed plant growth under controlled conditions have also shown that interspecific variation in the leaf-to-plant mass ratio is either unrelated or positively correlated with Amass or growth rates (Poorter and Remkes 1990; Garnier 1991; Aerts and Chapin 2000; Wright and Westoby 2000; Shipley 2006). This evidence suggests that biomass allocation has no positive contribution to the positive relationship between Nmass and Amass.
Nitrogen allocation
An increase in allocation of plant nitrogen to leaves (LNF) increases Nmass (Eq. 8). It is known that the leaf nitrogen concentration is positively correlated with the root nitrogen concentration across species (Craine et al. 2005; Tjoelker et al. 2005). Thus, it is not likely that Nmass increases at the expense of root nitrogen concentration. These facts suggest that the contribution of LNF is not large.
Root activity
SAR varies among species for two reasons. One is different soil nitrogen availability, which directly affects SAR (Hirose 1987). This may contribute to the variation in X because species with a higher Amass tend to inhabit fertile soils (Poorter and Remkes 1990; Reich et al. 1991). However, such a positive relationship in Nmass and Amass is found within a single habitat (Wright et al. 2001), suggesting that the relationship is explained not only by soil fertility.
The other reason is the inherent difference in SAR. Previous studies have shown that SAR varies greatly among species even when they are grown at the same nutrient availability and that SAR is positively related to Amass in such experiments (Garnier 1991; Poorter et al. 1991; Reich et al. 1998; Comas et al. 2002). Figure 4 shows our experimental results from 11 herbaceous and tree seedlings grown under the same nitrogen condition (data from Osone et al. 2008). Amass was correlated with neither leaf-to-plant mass ratio nor leaf-to-plant N ratio, but positively with SAR. The slope of the log–log relationship between SAR and Amass was 1.40 (Fig. 4). Similar values were obtained in studies by Poorter and coworkers (2.1) and by Reich and coworkers (1.7). These values are equivalent to the predicted slope of the X−Amass relationship in the Glopnet dataset, 1.58. These experimental results strongly suggest that the inherent difference in SAR contributes to the positive relationship between Nmass and Amass.
Inherent differences in SAR may partly be ascribed to root morphology. In general, roots with higher specific root length have higher SAR (Jackson et al. 1990; Eissenstat 1992; Reich et al. 1998; Osone and Tateno 2005), but are less resistant to physical disturbance and herbivory (Eissenstat 1992; Ryser 1996; Wells and Eissenstat 2001; van der Krift and Berendse 2002). Thus, there may be a trade-off between activity and persistence in root traits, and in the leaf traits mentioned above.
Coordination between leaf and root traits has been suggested by several field studies (Craine et al. 2005; Tjoelker et al. 2005). In should be noted, however, that the positive relationship between SAR and Amass lacks direct support from field experiments. Comas and Eissenstat (2004) found no trends in the phosphate uptake rate between fast-growing and slow-growing tree species growing in the field.
Assumptions in the model
We assumed a steady state in N and biomass allocation to leaves, i.e., Nmass is constant over short time periods (Eq. 1). This is not strictly true because Nmass often changes with ontogeny over longer time frames. However, if the N and biomass allocation were far from steady state, we would not find leaf-trait convergence, as observed in previous studies. For example, Nmass in species with a high Amass would decrease faster than that in species with a low Amass. Contrary to this, it is generally found that fast-growing species have higher Nmass than slow-growing species, suggesting that the balance between N and biomass allocation to leaves is largely fixed in each species. Our assumption is thus appropriate for addressing the question of which physiological traits are necessary for maintaining such interspecific variations. Furthermore, our results may be applicable to plants in a changing environment. Wikström and Ågren (1995) showed that results predicted by a growth model assuming steady-state growth can be applied even to cases in which growth conditions suddenly changed, because plants rapidly adjust their traits to the environmental change.
Equation 2 assumes that part of assimilated carbon is respired for construction and maintenance of tissues, where the conversion coefficient was regarded as constant (k). It is known that the construction cost of tissues varies among functional types but the difference is generally small (e.g., Poorter and Villar 1994). It is also known that in mature leaves, the respiration rate (maintenance respiration) is almost proportional to the photosynthetic rate; for example, the slope of the log–log relationship between Amass and respiration rate per unit mass was 1.18 (Wright et al. 2005). At a plant level, however, respiration rates may be affected by biomass allocation, because maintenance respiration rates vary among organs. Because respiration rates are higher in leaves than in roots and stems (e.g., Kinugasa et al. 2005), if leaf mass fraction is greater, plant respiration rates may be higher, lowering k. However, the degree of change in k may be smaller than that of changes in LMF, and its effect to Nmass would be canceled by the change in LMF2 (Eqs. 4 and 8).
Amass values determined in leaf-trait studies are generally measured instantaneously under saturating light, whereas Eq. 8 assumes daily carbon gain for Amass. Theoretically the daily carbon gain of a leaf shows a saturating curve when plotted against the light-saturated rate of photosynthesis (Hirose and Werger 1987). The slope of the relationship between Nmass and daily carbon gain may thus be greater than that of the relationship between Nmass and the light-saturated rate. On the other hand, there is an opposite factor; Amass shown in previous studies was determined for young individual leaves only while our models consider the whole plant, including older leaves. Mediavilla and Escudero (2003) showed that the slope of the relationship between mean Nmass and mean Amass was smaller than that for the relationship between Nmass and Amass of young leaves. Here we assume that these two effects cancel each other. In a data set by Osone et al. (2008), the slope of the log–log relationship between photosynthetic capacity and NAR (rate of biomass increment per unit leaf mass) was close to 1 (0.91; r 2 = 0.81), which supports our idea.
Conclusion
This study indicates that leaf-trait convergence is not only a leaf matter. If leaf carbon gain were not coordinated with other factors, we would not observe such a beautiful correlation between Nmass and Amass across species in the field. We predict that the convergence is supported mainly by the coordinated variation in root activity. If SAR is the sole factor to overcome the nitrogen dilution effect, its interspecific variation is expected to be greater than that in Amass. This prediction is consistent with previous laboratory experiments, but is not yet supported by field observations. Thus, it still remains unclear what brings about the positive correlation between Nmass and Amass on a global scale. Further studies are needed to understand how leaf-trait convergence is maintained.
Abbreviations
- Amass :
-
CO2 uptake rate per unit standing leaf mass
- k :
-
Conversion coefficient from CO2 to biomass
- LL:
-
Leaf life span
- LM:
-
Standing leaf mass
- LMF:
-
Fraction of biomass allocated to leaves
- LMP:
-
Leaf mass production
- LN:
-
Standing leaf N
- LNF:
-
Fraction of N allocated to leaves
- LNP:
-
Leaf N production
- MRT:
-
Mean residence time of N in leaves
- Nmass :
-
Leaf N concentration per unit leaf dry mass
- PM:
-
Standing plant mass
- PMP:
-
Plant biomass production
- PN:
-
Standing plant nitrogen
- PNP:
-
Plant N production
- R :
-
N resorption efficiency
- RL:
-
Root life span
- RM:
-
Standing root mass
- RMF:
-
Fraction of biomass allocated to roots
- RMP:
-
Root mass production
- SAR:
-
N uptake rate per unit standing root mass
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Acknowledgment
We thank H. Nagashima, N.P.R. Anten and Y. Yasumura for valuable comments. This study was supported in part by grants from the Japan Ministry of Education, Culture, Sports, Science and Technology and by the Global Environment Research Fund (F-052) from the Japan Ministry of the Environment.
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Kouki Hikosaka is the recipient of the BSJ Award for Young Scientist, 2006.
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Hikosaka, K., Osone, Y. A paradox of leaf-trait convergence: why is leaf nitrogen concentration higher in species with higher photosynthetic capacity?. J Plant Res 122, 245–251 (2009). https://doi.org/10.1007/s10265-009-0222-z
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DOI: https://doi.org/10.1007/s10265-009-0222-z