On the Conservative Nature of the Leaf Mass–Area Relationship

Abstract

In a previous empirical study, Hughes and colleagues showed that for several herbaceous species there is apparently a unique species‐specific relationship between the area and mass of leaves. We tested this proposition using measurements from 15 broad‐leaved species. We found that to a reasonable approximation, leaf area was proportional to leaf mass within a given species despite relatively large variations in both leaf thickness and the mass fraction of liquid matter. These observations show that the inverse density–thickness of leaves from a given species, which we call the Hughes constant, is approximately conserved. We conclude that the Hughes constant is likely to be more conservative than other traits traditionally used to describe leaves.

INTRODUCTION

‘Leaf area and absolute water content’ was the title of an article published in 1970 in Annals of Botany (Hughes et al., 1970). This was a remarkable article for two main reasons. First, it showed that for a given species, the area of a leaf projected normal to the surface (A_n, m²) was approximately proportional to the mass of water within that leaf (m_q, kg). Their observed relation can be expressed as:

where K′ (m² kg^–1) is a species‐dependent constant. The remarkable aspect of this relation was that it held under a wide variety of conditions, e.g. variable light, nutrient and CO₂ regimes. The only factor that seemed to alter the relation was a slight, but nevertheless detectable, dependence on the texture of the rooting medium. Secondly, K′ was nearly constant despite variations in the water content of leaves of each species.

Surprisingly, the ‘Hughes et al.’ relationship has not received any attention in the ensuing 30 years. Instead, it has been standard practice during this period to express leaf measurements using the ratio of the projected leaf area to leaf dry mass, which is usually called the specific leaf area. Many thousands of studies have adopted this approach and numerous interpretations of the observed variation in specific leaf area have been developed based on those data. Nevertheless, if one accepts the ‘Hughes et al.’ relation [eqn (1)], then it would automatically follow, as pointed out in the original work (Hughes et al., 1970), that most of the variation in specific leaf area could actually be explained by variations in the water content of leaves. This has subsequently been shown on many separate occasions (Stewart et al., 1990; Garnier and Laurent, 1994; Shipley, 1995; Roderick et al., 1999b; Wilson et al., 1999; Garnier et al., 2001), in agreement with the general predictions made in the original paper. Furthermore, the fact that eqn (1) apparently held for a given species, despite variations in leaf water content, implies that there must be some other species‐specific quantity that is approximately conserved.

The aim of this paper is to assess whether the ‘Hughes et al.’ relationship holds in other species and, if so, to determine which quantity (as noted above) is approximately conserved. To do this, we initially describe, and then reformulate, the underlying theory to re‐express the original relation in terms of extensive variables. Following that, we report leaf measurements from 15 broad‐leaved species which are used to test the validity of the original relations shown in the 1970 paper.

THEORY

In the original work, the relation was expressed using A_n and m_q [see eqn (1)]. Neither of these are extensive variables. Appropriate extensive variables for this application are the (external) surface area (A_s, m²) and the mass (m, kg). [See Roderick (2001) for a general discussion about the use and importance of extensive variables.] Here, the original relation is re‐expressed in terms of extensive variables, which are then used to derive an algebraic expression for K′ [eqn (1)].

In most broad‐leaved species, the thickness of leaves is substantially less than either their length or width. Thus, to a very good approximation, the external surface area (A_s, m²) and projected area of broad leaves are related by:

Hence, for broad leaves, any expression given in terms of A_n can be related back to the underlying extensive variable, A_s. Accordingly, the volume (V, m³) of a broad leaf can be expressed as:

where z (m) is the thickness. Since the density (ρ, kg m^–3) is given by:

it follows from eqns (3) and (4) that:

Thus, if a plot of A_n vs. m for different leaves yielded a (more or less) straight line, then it would follow that the inverse density–thickness (1/ρz) of those leaves was (more or less) constant. As shown below, the measurements reported in the original paper imply this relation.

Using eqn (5), we can derive an expression for K′ [eqn (1)] as follows. First, the total mass (m, kg), which is an extensive variable, is given by:

where m_q (kg) and m_d (kg) are the mass of liquid matter and dry matter, respectively. Defining the mass fraction of liquid matter (Q) as:

we can rewrite eqn (5) as follows:

By inspection of eqns (1) and (8), it follows that K′ must be given by:

In the original work, Hughes et al. (1970) gave the range in m_q/m_d for each species they reported (see their Table 1, p. 262). That range can be converted to a range in Q using the following relation:

Table 1.

Estimates of the Hughes constant (K ± 1 s.d.) for the 15 species in this study

Number	Species name	K (cm2 g–1)	R 2	z (µm) (min–max)	Q (min–max)
1	Eucalyptus ficifolia F. Muell.	32·9 ± 0·5	0·97	220–400	0·47–0·74
2*	Hedera helix L.	55·6 ± 0·8	0·98	170–350	0·67–0·80
3	Betula jacquemontii Spach.	47·1 ± 0·6	0·96	230–380	0·56–0·62
4	Melia azedarach L. var. australasica	60·3 ± 1·1	0·95	110–200	0·65–0·69
5	Populus nigra L. ‘Italica’	56·7 ± 0·4	0·99	140–250	0·66–0·69
6	Alnus rhombifolia Nutt.	47·9 ± 0·6	0·97	180–330	0·57–0·66
7*	Ginkgo biloba L.	36·3 ± 0·6	0·94	250–480	0·67–0·75
8*	Eucalyptus pauciflora Sieber ex. Sprengel	19·6 ± 0·5	0·91	390–620	0·50–0·63
9*	Callistemon viminalis Sweet ex. G.Don	36·7 ± 0·4	0·97	270–370	0·48–0·76
10*	Convolvulus mauritanicus Boiss.	54·7 ± 1·0	0·88	220–340	0·71–0·79
11*	Salix babylonica L.	51·5 ± 0·5	0·96	360–470	0·63–0·74
12*	Cercis occidentalis Torr.	60·4 ± 0·8	0·94	180–290	0·57–0·67
13	Hypericum calycinum L.	37·3 ± 0·4	0·95		0·56–0·59
14	Acer platanoides L.	95·4 ± 2·6	0·94		0·52–0·59
15	Vinca minor L.	43·6 ± 1·0	0·95	140–300	0·74–0·82

The minimum and maximum estimates of leaf thickness (z) and mass fraction of liquid matter (Q) for the 30 leaves of each species are also noted. (Note that there were only 29 measurements available for species 1 due to a gross error in one of the measurements.)

* Species for which earlier measurements were available for comparison purposes (Roderick et al., 1999b).

If this is done for each species listed in Table 1 of Hughes et al. (1970), we find that Q is restricted to a typical range for each species, and that Q is also generally high (mostly >0·90) for each species, implying that most of the matter in the leaves is water. Thus, for most of the original data, 1/Q was generally near unity. Since Hughes et al. also found that K′ was approximately constant, it follows that the inverse density–thickness must have also been approximately constant. Thus, rewriting equation (5) we have:

where K (m² kg^–1) must be equal to the inverse density–thickness, i.e.:

It follows from the above that the ‘Hughes et al.’ relation implies that K should be (more or less) constant. We call K the Hughes constant and test whether it is (more or less) constant in a number of different broad‐leaved species.

MATERIALS AND METHODS

Measurements

We measured leaves collected from 15 broad‐leaved species growing on the campus of the Australian National University between December 2000 and April 2001. For each species, we recorded the mass, area, thickness and dry mass of ten individual leaves in three separate groups, giving a total of 30 leaves per species. The leaves were selected from different parts of the plants to span a large range of mass, area and age. For seven of the species studied, we had previously reported the mass and area of two sun and two shade leaves (Roderick et al., 1999b). Those measurements were used to check the robustness of the area–mass relationship.

Leaf thickness was measured in three places on each leaf using a dial thickness gauge while the leaves were still attached to the plant. An average of these measurements was used as an estimate of leaf thickness. Note that the thickness of some of the leaves was difficult to measure accurately in this way because of the leaf structure (e.g. protruding veins, etc.). Thus, our estimate of leaf thickness may not be very accurate for some species, but is precise enough for our purpose because the thickness measurements were only used to determine whether the thickness of leaves from each species was (roughly) constant. Once thickness measurements were complete, the leaves were removed from the plant and taken immediately to the laboratory where the mass and projected area of each was measured. Within each group of ten leaves, we visually selected the largest leaf and measured the mass of that leaf at 2 min intervals over an 8 min period. These measurements were subsequently used to estimate the loss of mass that would have occurred while the leaves were transported to the laboratory, and then to assess whether this would lead to significant errors. The leaves were oven‐dried at 80 °C for at least 48 h after which the dry mass of each was determined.

Statistical analysis

In the original work, Hughes et al. (1970) found that the best‐fit linear regression usually had a slightly positive intercept. In exploratory analysis (using mass instead of liquid mass), our results confirmed this finding. However, when plotting leaf area as a function of mass, the relationship must, by definition, pass through the origin. Thus, using linear relations, the best‐fit composite relation must be composed of at least two straight lines, one through the origin and the other through the majority of the data. Based on inspection of the plots in the original paper, the two lines must intersect somewhere very close to the origin. From a practical viewpoint, we found that there was only a very small error involved in assuming that the data could be summarized by a single regression line passing through the origin. We adopted this approach and the method described in Zar (1984) was used to estimate K.

RESULTS

Using our measurement of the change in mass of the leaves, we found that over an 8 min period the maximum and average relative reduction in mass was approx. 4 and 1 %, respectively. The maximum time that elapsed between harvest and measurement of leaf mass was 13 min, and over that length of time the maximum and average relative reductions in mass would have been approx. 6 and 2 %, respectively. Errors of this magnitude will not have a material impact on estimates of K (see Fig. 1) and were ignored in the analysis.

Fig. 1. Relationship between mass and area of leaves (crosses) for the 15 species (numbers on top of each plot) listed in Table 1. Measurements for two sun (triangles) and two shade (diamonds) leaves (see plots for species 2 and 7–12) made 2 years earlier (Roderick et al., 1999b) also shown.

Initially, we analysed each group of ten leaves separately, and estimated three different values of K for each species. Those estimates were generally more or less the same, and we subsequently grouped all the measurements together to determine a single value of K for each species (see Fig. 1 and Table 1). The coefficients of determination were generally high (R² mostly >0·90). The worst fit was for species 10 (R² = 0·88, Table 1), which had very small leaves (see Fig. 1) so that small measurement errors would have been more significant. Note that while K was approximately constant for each species (but see below for exceptions), there were relatively large variations in the mass fraction of liquid matter and leaf thickness amongst the individual leaves from each species (Table 1).

For five (species 7, 8, 10–12) of the seven species for which we had made leaf measurements 2 years earlier (Roderick et al., 1999b), the older measurements more or less fell onto the regression line although there was more scatter than in the current measurements. The exceptions were species 2 and 9. In the case of species 9, a regression through the older measurements would have yielded a smaller value of K, implying that the inverse density–thickness of the leaves was generally smaller (hence the density–thickness was greater) in the older measurements. Species 2 (Hedera helix) was more interesting because the estimates for the two original shade leaves more or less fell on the regression line but the estimates for the two original sun leaves fell well below the regression line (Fig. 1). It is apparently well known that H. helix plants have two distinct leaf types (M. Canny, pers. comm.), commonly called ‘tree leaves’ (which have a smooth leaf margin) and ‘ground leaves’ (which have a serrated leaf margin). In the earlier study, we had traced the outlines of the sun and shade leaves onto our field sheets and, on inspection of those sheets, we found that the original shade leaves were ‘ground leaves’, whereas the sun leaves were ‘tree leaves’. To verify this, we measured a further five leaves of each type. The extra measurements confirmed that there were distinct differences in K between the two leaf types (Fig. 2), and that the ‘ground leaves’ had a larger K implying a greater inverse density–thickness (and hence a lower density–thickness) than the ‘tree leaves’.

Fig. 2. Relationship between mass and area of leaves for species 2 (Hedera helix). Symbols as in Fig. 1, plus an extra five measurements for ‘tree leaves’ (asterisks) and for ‘ground leaves’ (squares). The upper line is the regression depicted in Fig. 1, while the lower (dashed) line is the regression for the ‘tree leaves’. See text for discussion.

DISCUSSION

For each species we found there was a relatively large range of both the mass fraction of liquid matter and the thickness of the leaves. Despite that, K was much more conservative, and to a reasonable approximation was approximately constant for each species. However, for species such as H. helix that have different leaf types, it is more appropriate to determine a value of K for each leaf type. For species 9 (Callistemon viminalis), measurements of leaves from the same plant made about 2 years earlier all fell below the regression line (Fig. 1). This indicates a bulk shift in the area–mass relationship for those leaves, presumably due to a bulk change in the degree of hydration. For example, assuming that the (projected) area of fully expanded leaves remains approximately constant, then it would follow that as the mass increases, the value of K will decline, and vice versa. Thus, for a leaf of (approximately) constant projected area, the state of maximum mass of the leaves, often called the saturated mass (Cornelissen et al., 1997; Garnier et al., 2001), will also represent the minimum value of K. Thus, it is more appropriate to talk of the minimum value of K. Nevertheless, the data (with the exception of species 9) suggest that the value of K is sometimes reasonably conservative for a given species. With these exceptions, and the caveat that our analysis is in terms of an extensive variable (mass as opposed to the use of liquid mass in the original 1970 study), the results reported here are generally consistent with the earlier findings of Hughes et al. (1970).

The conclusion that K, which we have called the Hughes constant, is approximately constant despite variations in leaf thickness and water content, is a little surprising at first glance. However, it is consistent with many well known trends. For example, we showed earlier that K is equal to the inverse density–thickness. Thus, if K is (more or less) constant then the density–thickness must also be (more or less) constant. This can be easily understood as follows. During the daylight, leaves often lose water and become thinner (Tyree and Cameron, 1977). At the same time, leaves also gain carbohydrate by photosynthesis at a rate that is generally correlated with the rate of water loss (Wong et al., 1979). Thus, the mass fraction of carbohydrate‐based materials should increase during daylight and these materials are generally denser than water (Roderick, 2001). Consequently, the density of the non‐gaseous phase within leaves will generally increase during daylight. Thus, the decrease in thickness and the increase in density are opposing and will act to (at least partially) cancel one another out, so that the product of density and thickness should be approximately conserved. In other words, we would generally expect K to be roughly constant for a given species, and that expectation is generally consistent with the observations.

In the original paper, Hughes et al. (1970) noted that if the mass fraction of liquid matter and leaf thickness varied, then K could only be constant if (in their terminology) the relative volumes of intercellular (i.e. gaseous) spaces and dry matter change in a regular way with leaf area over time. However, note that the dry matter (or liquid matter) does not occupy a unique space, so the term, ‘relative volume of dry matter’ (or liquid matter) has no macroscopic meaning. Nevertheless, the conclusion of Hughes et al. can easily be recast in terms of the air space, solution and structure within leaves which are unique spaces (Roderick et al., 1999a; Roderick, 2001). The obvious implication is that the volume fraction occupied by gaseous spaces within a leaf must generally co‐vary with the volume fraction occupied by the cell wall matrix (i.e. the structure), but for a given species, the product of leaf density and leaf thickness remains approximately constant over time. This is an important deduction largely made in the original 1970 paper and which is confirmed here.

These results show that for a given species, the Hughes constant is likely to be much more conservative than other functional attributes (e.g. leaf area per unit dry mass, leaf water content, etc.) traditionally used to describe leaves. As such, the Hughes constant may represent a very useful way of summarizing the leaf characteristics of different species. More generally, the results show that variations in both the mass fraction of liquid matter and the volume fraction occupied by gaseous spaces must be considered when interpreting leaf measurements.

ACKNOWLEDGEMENTS

Helpful comments by Dr Hans Cornelissen improved the manuscript. We thank Professor Martin Canny for bringing our attention to the difference between ‘tree leaves’ and ‘ground leaves’ of ivy. We also thank Dr Ken Cockshull, who explained some of the background behind the original 1970 paper, and who graciously agreed to us calling K, the Hughes constant, in honour of Dr Tony Hughes who died a young man very shortly after publication of the 1970 paper.

Received: 25 October 2001; Returned for revision: 8 January 2002; Accepted: 31 January 2002.