Trait correlation networks: a whole-plant perspective on the recently criticized leaf economic spectrum

Authors


Introduction

A decade ago, Wright et al. (2004) published a paper that described a ‘leaf economic spectrum’ (LES) of traits. Based on measurements of leaf area, leaf mass, photosynthetic capacity, dark respiration, nitrogen (N), phosphorus (P) and leaf lifespan (LL), collected for a wide range of plant species measured worldwide in their natural habitats, Wright et al. (2004) showed that ecophysiological variables form a spectrum of correlated traits. When parameters were expressed per unit dry mass, photosynthetic capacity scaled positively with N and P concentrations, but negatively with leaf mass per area (LMA) and LL. Recently, two groups have cast doubt on the biological significance of these correlations. Osnas et al. (2013) and Lloyd et al. (2013) independently drew attention to the statistical implications of using leaf biomass as the main factor for normalization. The basis for this concern dates back to the work of Pearson (1897) on ‘spurious’ correlations: if random variables X, Y and Z are uncorrelated with each other, then X/Z will often correlate positively with Y/Z, simply because the denominator Z will be small in some cases, with large values for both ratios as a consequence, and large in others, with small values for both ratios as a result. In terms of the LES: the rate of photosynthesis per unit leaf area may not or just weakly be correlated with the amount of N per unit leaf area, but if both are divided by LMA (or multiplied by specific leaf area (SLA), which is the inverse of LMA), a significant correlation is expected between the photosynthetic capacity per unit mass and the N concentration per unit mass. Both groups conclude that the significance of the correlation coefficient is misleading if the correction for randomly varying and unrelated values is not considered. They further conclude that leaf area is the logical basis for the expression of photosynthesis. In a response, Westoby et al. (2013) agree that the strong r2 between LMA and mass-based leaf traits can correspond with the same leaf traits on an area basis being uncorrelated with LMA, but claim an independent role for mass-based expressions in the comparative analysis of plant traits.

In this letter, we first discuss whether there is indeed a logical basis for expression of the photosynthetic process. We argue that most insight is gained by evaluating several normalizations. Subsequently, we draw attention to the fact that the LES is part of a larger whole-plant economic spectrum, with a biological model that requires transformation of carbon (C) gain per leaf area to a mass basis if we aim to understand the C-economy of the whole plant. Finally, we discuss ways forward to analyse the observed patterns of traits.

Is there a preferred basis for expression of leaf photosynthesis?

Everything else being equal, any measurement of photosynthetic CO2 uptake will be higher the more leaf tissue is present in the cuvette. Therefore, some way of normalization has to be applied. What then should be the basis of this normalization? Lloyd et al. (2013) reason that photosynthesis is strongly related to the flux of light, and therefore the area-based metric is the preferred basis of expression. Osnas et al. (2013) argue that the basis should be chosen such that the resulting expression does not show any correlation with leaf area, leaf mass or SLA. Based on a statistical analysis they also conclude that an area-based normalization is the preferred option. How prevailing is this option? In the literature, leaf photosynthesis is often expressed per unit leaf area, but also per unit fresh mass (McMillen & McClendon, 1983), dry mass (Jurik et al., 1979), protein, total or organic N (Evans, 1989), phosphorus (Lambers et al., 2010), chlorophyll (McMillen & McClendon, 1983), leaf volume (Charles-Edwards et al., 1974), mesophyll volume (Wilson & Cooper, 1969), cell or chloroplast volume (Dean & Leech, 1982) and Rubisco (Ghannoum et al., 2005). For the photosynthesis of vegetation or a crop, the basis of expression could also be per unit ground area (King & Evans, 1967). In all these cases the authors refer to ‘the rate of photosynthesis’, but the sense conveyed will critically depend on the normalization used. We illustrate this with an experiment where photosynthesis was studied for ten species that differed substantially in their SLA, and hence in their position on the LES. These species were grown in growth chambers at two contrasting light intensities. When comparing photosynthetic capacity between plants grown at low and high irradiance, averaged across species, high-light grown plants had a substantially higher photosynthetic capacity per unit leaf area (Fig. 1a), as is generally reported. Photosynthetic capacity per unit Rubisco, however, was lower for high-light grown plants, while photosynthetic capacity per unit dry mass was almost unchanged by growth irradiance. The situation is very different when we compare photosynthetic capacity for low- and high-SLA species, averaged over both growth irradiances (Fig. 1b). Now differences in capacity per unit leaf area are smaller than those per leaf dry mass. Differences per unit organic N were also smaller than those per unit leaf dry mass. For these two groups of species, the most stable basis was photosynthetic capacity expressed per unit Rubisco (Poorter & Evans, 1998).

Figure 1.

The response of photosynthesis of (a) low- and high-light grown plants averaged across 10 species and (b) low- and high-specific leaf area (SLA) species averaged from two growth irradiance treatments. The rate of photosynthesis is normalized on the basis of seven variables. In order to allow comparison of the different normalizations, the grand mean for each expression was scaled to 100%. Numbers next to the lines refer to the average percentage change comparing high-light grown plants against low-light grown plants, or when low-SLA species are compared against high-SLA species. Details of species and measurements are given in Poorter & Evans (1998) and Evans & Poorter (2001).

Which variable is the preferred basis of expression? We contend that there is no preferred basis, but that there is much to be learned from using various normalizations. In the first contrast, where photosynthetic capacity expressed per unit mass is similar for leaves grown under high and low light, the higher photosynthetic capacity per unit area reflects a larger investment of biomass per unit leaf area in high-light grown plants (i.e. a lower SLA; Poorter et al., 2009). Because leaf N concentration was unaffected by growth irradiance, the leaf chemical composition on a dry mass basis apparently is not strongly different. Consequently, the higher photosynthetic capacity per unit area is then driven by the larger N content per unit leaf area in high-light grown plants, caused by a larger number of cells per leaf area. Because leaves grown under high light allocate a greater proportion of leaf N to Rubisco, photosynthetic capacity per unit Rubisco is reduced. In the second contrast, high-SLA species tend to have greater photosynthetic capacity per unit organic leaf N or leaf dry mass than low-SLA species, but their rate of photosynthesis per unit Rubisco is very similar. This implies that high-SLA species have a relatively larger investment in Rubisco than low-SLA species. Thus, it is by changing the basis of expression, and analysing how that alters the rate of photosynthesis, that a good understanding of the consequences of different investment patterns in leaf mass, N, chloroplasts or cells by different groups of plants can be obtained.

The whole-plant economic spectrum

Analysing statistical correlations between various normalized traits can be valuable and informative, but correlation does not mean causation and – as outlined by Osnas et al. (2013) and Lloyd et al. (2013) – can be spurious or misleading in some situations. Biological models allow one to structure the relevant variables before statistical analysis. Westoby et al. (2013) in a reply to Lloyd et al. (2013) pointed out that there is an economic perspective in the expression of photosynthesis per unit mass, as it relates C-gain by a leaf in return for a given unit of biomass invested in that leaf. This is a valuable point, which we want to take a step further: the traits of the LES are an essential subset of traits which together form a ‘whole-plant economic spectrum’. The additional traits are variables related to allocation of biomass, and physiology, chemical composition, as well as morphology of stems and roots. These traits are as important for whole-plant performance as the leaf traits, and correlate with LES traits in a systematic manner. Thus, across a wide range of species, plants with high SLA also have lower stem density (Méndez-Alonzo et al., 2012), a lower allocation to roots, higher root N concentrations and a higher nutrient uptake rate per unit root mass (Lambers & Poorter, 1992). Together they constitute an axis of slow vs fast growth, which has been paramount in the ecological theories of, for example, Grime (1979) and others (Lambers & Poorter, 1992; Chapin et al., 1993). Species with a low potential relative growth rate (RGR; biomass increase per unit existing biomass per unit time) are generally found in stressful environments, whereas species that show a high RGR under optimal growth conditions are generally found in habitats where the environment is more favourable (Grime, 1979).

A frequently-used approach in growth analysis factorizes RGR into a so-called ‘physiological’ component, which essentially is the growth rate expressed per unit leaf area, and a ‘morphological’ component, which indicates how much leaf area there is per unit plant mass (Evans, 1972). A further factorization, which is not often made, is to link RGR directly to the various components of the C-economy:

math image(Eqn 1)

(Lambers & Poorter, 1992; Poorter et al., 2013). The first term in the right-hand part of Eqn 1 (∫Aa) represents the gross daily whole-plant C-gain expressed per unit total leaf area. Multiplication by SLA (specific leaf area, leaf area per unit leaf dry mass) converts this into the daily C gain per unit leaf dry mass. Further multiplication by the fraction of plant biomass allocated to leaves (LMF, leaf mass fraction, leaf dry mass per total plant dry mass) subsequently transforms this rate to the daily C gain per unit total plant mass. To obtain net C gain, one needs to account for C-losses from the shoot and roots, mainly in respiration, but also including root exudation and volatile losses. Carbon-use efficiency (CUE) represents the fraction of daily C fixed that is retained after accounting for all these losses. Finally, to convert net C fixation into biomass, the C-concentration of the newly-formed biomass ([C]) has to be considered.

It is clear from Eqn 1 that the product of the area-based photosynthesis and SLA is not just a statistical manipulation to arrive at significant correlations between some otherwise randomly related variables. Rather, the rate of photosynthesis per unit leaf – or per unit whole plant mass – are compound variables in the C-economy of a plant that generally contain the largest part of the variation in RGR (Table 1; Walters et al., 1993). Given the underlying biological model, as well as the high explanatory power of mass-based photosynthesis in positioning plants along the slow to fast return axis, we therefore are of the opinion that if photosynthesis is measured with the aim to understand and/or manipulate the growth and C-economy of the plant, it would be a missed opportunity not to calculate these variables.

Table 1. Species variation in the variables of Eqn 1 and in two component variables, as measured in 24 herbaceous species, grown in a growth chamber, correlation with relative growth rate (RGR) and the estimated contribution of variation in each growth component to variation in RGR
  UnitsHighest/lowest value across speciesCorrelation with RGRContribution to the total RGR difference (%)
  1. For this analysis, average values per species were used. The sensitivity analysis assumed that the five components of the RGR equation could be varied independently of each other, which will in reality not be completely true. Data are from Poorter & Remkes (1990) and Poorter et al. (1990).

RGRRelative growth ratemg g−1 d−13.22  
∫AaGross daily assimilation per unit leaf areamol C m−2 d−11.880.064
SLASpecific leaf aream2 kg−1 leaf2.190.8143
LMFLeaf mass fractiong leaf g−1 plant1.530.5822
CUECarbon use efficiencymol mol−11.540.7723
[C]C-concentrationmol g−1 plant1.21−0.658
∫AmGross daily assimilation per unit leaf massmol C g−1 leaf d−12.420.6647
∫ApGross daily assimilation per unit total plant massmol C g−1 plant d−13.110.9069

Possible ways to proceed

In the previous sections we have illustrated that there is no preferred way of normalization, or, alternatively, that the preferred basis of expression depends on the research question at hand. However, Osnas et al. (2013) and Lloyd et al. (2013) make the perfectly valid point that as compared to the weak area-based correlations, the main driver that causes the strong correlations among the mass-based traits is variation in SLA. How could we proceed from here to better understand the observed correlation patterns across species? We have a number of suggestions.

(1) First, it would be helpful to have a graphical representation of the trait network, preferably with as many leaf, stem and root traits considered relevant for plant performance as possible. One way to do so is an undirected correlation network, as often used in systems biology (Villa-Vialaneix et al., 2013). Fig. 2(a) shows such a network for all the observations compiled for the LES; Fig. 2(b) does the same for the experiment described in the whole-plant economic spectrum section.

Figure 2.

The correlation network of (a) the variables from the leaf economic spectrum (LES) and (b) across a range of slow- to fast-growing herbaceous species. Blue lines, positive correlations; red lines, negative correlations. Thin lines explain between 25–50% of the variation (0.50 < |r| < 0.71), intermediate lines 50–75% (0.71 < |r| < 0.87) and thick lines > 75% of the variation (|r| > 0.87). Note that statistically significant correlations with an r2 < 0.25 were not shown, because we expect them not to have a strong mechanistic basis. This is especially true for data sets with high degrees of freedom, such as the Wright et al. (2004) database. Yellow-coloured nodes, mass-based LES variables; grey-coloured nodes, area-based LES variables; blue-coloured nodes, additional variables. Data for (a) are from Wright et al. (2004), data for (b) pertain to the 24 species as detailed in Table 1 or as follows: Aa, light-saturated photosynthesis per unit leaf area; Am, light-saturated photosynthesis per unit leaf mass; gs, stomatal conductance; LL, leaf lifespan; SLA, specific leaf area; CUE, carbon use efficiency; RGR, relative growth rate; LMF, leaf mass fraction; [C], C-concentration, ∫Am, gross daily assimilation per unit leaf mass; ∫Ap, gross daily assimilation per unit total plant mass; ∫Aa, gross daily assimilation per unit leaf area; Na and Pa, nitrogen and phosphorus content per unit leaf area; Nm and Pm, nitrogen and phosphorus concentration on a leaf mass basis.

(2) Two factors are required for a correlation to exist: there has to be variation within each variable, and covariation amongst them. Some variables are more constrained than others, and it is good to know what the actual range in variation is. With the five growth factors of Eqn 1 analysed, variation in C-concentration, for example is much smaller than that in LMF, which in turn is smaller than the variation in SLA (Table 1). It is relevant to understand why some variables differ, while others are relatively similar among species (Poorter et al., 2013). Why, for example, is variation in the C-concentration of plant material so constrained, especially within growth forms, whereas the evolutionary leeway for variation in SLA is much larger?

(3) The network could be further scrutinized by investigating correlations when one or more of the other traits are statistically controlled for. Osnas et al. (2013), for example, showed that part of the observed correlation network in the LES could be achieved by randomly taking SLA values from the data set and multiply them with photosynthesis per unit area and N per unit area (Osnas et al., 2013, fig. 1). However, from that figure it can also be seen that the actually observed correlations can be stronger than the simulated ones, sometimes with different slopes. The random model could then be used as a null model to test against the real observations (Brett, 2004). This permits testing any effect beyond what would be expected purely on the basis of a multiplication. Partial correlation networks follow a similar procedure, but extend the correction to all other variables in the network (Villa-Vialaneix et al., 2013).

(4) The suggestions so far only pertain to correlations and do not go into the causal structure among variables. The virtue of a correlation approach is that no a priori assumptions are made that may not be justified (see also point 8). However, in the end a cause–effect model of how these traits are related to each other – and to growth or fitness – is highly desirable. A powerful technique to differentiate between various cause–effect relationships in multivariate models is the technique of Structural Equation Modelling (Shipley, 2000). This approach has been applied successfully to analyse a range of multivariate biological problems, including an analysis of some of the LES variables (Peterson et al., 1999; Shipley et al., 2006) and some of the variables measured in the experiment shown in Fig. 1 (Shipley et al., 2005).

(5) A question that still largely goes unanswered is how different subgroups of species perform (Fyllas et al., 2012). For example, do herbaceous grasses and eudicots show the same network topology? If so, how do the strengths of each feed-forward effect or trade-off compare? And how is the network topology affected when woody species are compared to herbs?

(6) The LES is based on plants measured in the field, and hence there is an environmental component in the data that may partly drive the observed correlations. For example, plants grown at low nutrient supply generally have lower concentrations of leaf N or P than those with a high nutrient supply, and lower rates of photosynthesis per unit dry mass. As some of the species in the Wright et al. (2004) database normally occur in nutrient-poor habitats and others at nutrient-rich sites, at least part of the network could be shaped by a plastic response of plants to the availability of nutrients. It would therefore be good to establish first to what extent a variable is affected by a given environmental factor (Poorter et al., 2010) and second, whether the same network topology exists when plants are all grown under common conditions.

(7) SLA as a trait is still a kind of black box, relating light interception area to the biomass invested in the leaves. Given its importance, we need greater insight into how leaves of different species are built, from an anatomical viewpoint (Castro-Díez et al., 2000; Villar et al., 2013) and from a chemical perspective (Poorter et al., 2009). In the slow-growth part of the spectrum, is SLA reduced simply by the addition of more cell-wall material, or are there investments in additional cells and cytoplasmic compounds (Shipley et al., 2006)?

(8) A hidden assumption in the analysis of RGR is that the C-budget is driving the growth of plants, and thus that any change in one of the right-hand parameters of Eqn 1 will affect growth. However, in many cases where nutrient availability, water availability or temperature is low, or where species with an inherently slow growth rate are the focus, it may actually be growth that sets the pace of photosynthesis, rather than the other way around (Körner, 2013; Poorter et al., 2013). This does not invalidate Eqn 1, since the net C-flux must still be there for a plant to grow and could be measured, but a problem could arise if photosynthesis was being predicted from other parameters or prior measurements. To enhance our understanding of the growth patterns, we might have to scrutinise different parts of the plants, like roots or developing leaves, or metabolic pathways other than those involved in photosynthesis. This may shed a very different perspective on the control of the leaf and whole-plant economic spectrum.

Conclusions

There are different ways to express biological data, and for the process of photosynthesis, normalization for leaf area has been a very useful one. However, different questions require different approaches, and as such, there is no single ‘best’ basis of expression for every situation. Often, improved understanding of the system can be gained by using various ways of normalization.

Biological models are more important than statistical considerations. In the model that relates C-fixation to whole-plant C-budgets, the rate of photosynthesis per unit leaf mass or total plant mass plays an important explanatory role. Expressing photosynthesis per unit mass is not a statistical artefact. Importantly, however, it is often variation in SLA that accounts for a large part of the variation in growth rate, and also for the mass-based correlations across species.

Finally, we conclude that we need more insight into the interdependence of the multitude of physiological and morphological traits that plants optimize to succeed in a given environment.

Acknowledgements

Thanks to Ian Wright, Onno Muller, Mascha van der Sande and three anonymous reviewers for insightful comments on a previous version of the manuscript.

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