Intraspecific changes in forest canopy allometries during self-thinning

Authors


*Correspondence author. E-mail: rjh208@cam.ac.uk

Summary

  • 1Leaves are the key active sites for energy and matter transfer in plants, and therefore the total one-sided area of leaves per square metre of ground (leaf area index, LAI) is a critical variable used for scaling up from plant to ecosystem level properties.
  • 2A commonly held belief is that LAI remains constant during the self-thinning phase of stand development, and allometric relationships between tree density, mean tree size and leaf area (or leaf mass) are frequently used to provide a mechanistic explanation for the observed thinning relationships.
  • 3We investigated variations in leaf allometry, stand LAI and other canopy properties along a developmental sequence of naturally occurring mono-specific self-thinning stands of mountain beech (Nothofagus solandri var. cliffortioides) in New Zealand.
  • 4Stand age had a consistent significant effect on both the slope and the intercept of both the leaf mass and the leaf area allometric relationships (increasing slope, decreasing intercept). This was due to trees of a given basal area having more leaf area (or leaf mass) when growing in a neighbourhood of smaller trees, than equivalently sized individuals surrounded by a lower density of trees larger than itself.
  • 5A peaked (non-constant) relationship was observed between LAI and stand age during self-thinning, with the mean LAI values peaking in intermediately aged large sapling stands (7·08) compared with the small sapling stands (5·42) and older pole stands (5·70). Stand level leaf mass per unit area (LMA) varied with canopy height and stand age, being highest at the top of canopies and in older stands.
  • 6We propose that the observed increase in canopy depth during the early stages of stand development (but after canopy closure has occurred) could be driving the increase in stand LAI due to a more even distribution of light within the canopy.
  • 7Our findings suggest that the commonly held assumption of constant LAI should be abandoned in favour of the notion of leaf area being at a dynamic maximum during self-thinning, with the maximum possible leaf area being influenced by age-related changes in canopy structure that occur during stand development.

Introduction

Competitive self-thinning is a widely accepted concept describing a fundamental relationship between tree density and mass during stand development that can be traced back to basic geometric and allometric principles (Yoda et al. 1963; Enquist, Brown & West 1998; Begon, Townsend & Harper 2004). The concept of self-thinning was initially developed in planted fully-stocked monocultures of mainly herbaceous species and has been since applied primarily to even-aged, mono-specific, closed canopy stands at or close to maximum density (Lonsdale & Watkinson 1982; Long & Smith 1984; Midgley 2001). There has been considerable debate surrounding the exact nature of such a relationship (i.e. the slope of the thinning line), and its generality and application to natural forest communities (White 1981; Long & Smith 1984; Osawa & Sugita 1989; Weller 1989, 1990; Lonsdale 1990; Midgley 2001; Enquist 2002; Roderick & Barnes 2004; Coomes & Allen 2007).

Both the earlier Euclidean approach of Yoda et al. (1963) and the recent fractal approach of Enquist et al. (1998) utilize allometric relationships between a plant's leaf area (or leaf mass), and its total biomass (or other proxies such as diameter or basal area) to predict the relationship between stand stem density and average mass. Both approaches assume that stem density (N) × leaf area (LA) = LAI = constant (Long & Smith 1984; Coomes 2006). Thus the maintenance of a constant leaf area index (which refers to its LAI, representing the one-sided leaf area per unit ground area (Chen et al. 1997)) following canopy closure has often been used as a mechanistic assumption to derive theories describing the changes in stem density and mean tree size that occur during self-thinning. A further assumption that is commonly made in such models is that total leaf area and total leaf mass are directly proportional to each other (Enquist et al. 1998; Enquist 2002). This implies that stand-level leaf mass per unit leaf area (LMA), or its inverse specific leaf area (SLA) remain constant during development.

Recent evidence suggests that LAI may not remain constant during stand development in forest communities, especially natural forests (Ryan, Binkley & Fownes 1997; Turner et al. 2000; Bond-Lamberty et al. 2002b; Kashian, Turner & Romme 2005; Amiro et al. 2006; Coomes & Allen 2007). This may be due to some of the stands investigated not meeting the specific requirements given above that are needed to be classed as ‘self-thinning’. It may also be due to fundamental differences in stand development between herbaceous communities and forest stands, such as the tendency for increased vertical stratification within the canopies (Terborgh 1985). Increased vertical stratification enables increased light penetration which could result in older stands being able to support a greater LAI (Kitajima, Mulkey & Wright 2005). These considerations bring into question the accuracy and applicability of general models of stand development that are underpinned by the constant LAI rule (Enquist et al. 1998; Enquist 2002).

This paper will attempt to resolve an apparent conflict between allometrically- and resource-driven theories describing forest structure. LAI is difficult and time consuming to directly measure in forest stands (Pearcy et al. 1991). Allometric relationships between leaf mass (or leaf area) and either diameter, basal area or sapwood area are commonly used as a means of directly estimating stand-level LAI for mature forests (Turner et al. 2000). However, it is possible that unaccounted changes in these scaling relationships with stand age are confounding the stand-level LAI estimates (Tobin et al. 2006). This study uses both age-specific and overall allometric scaling relationships between basal area, leaf area and leaf mass in natural even-aged forest stands undergoing self-thinning to address the following four questions: (i) How equivalent are leaf area and leaf mass in terms of their allometric scaling relationships, and how do these change during self-thinning? (ii) Do changes in stand density and mean stem diameter during self-thinning follow the allometrically predicted trajectory associated with constant LAI? (iii) Is this prediction reflected in the actual stand LAI values during self-thinning? (iv) How might changes in the vertical leaf area and leaf mass profiles during development influence stand level LAI and LMA?

Materials and methods

study site

The study was carried out in the Craigieburn Range, central South Island, New Zealand (43°15′ S, 171°35′ E). The forest vegetation of this area occurs between valley bottoms at 650 m a.s.l. and tree line at 1400 m a.s.l. and consists of natural mono-specific stands of pure mountain beech (Nothofagus solandri var. cliffortioides (Hook. F.) Poole). Mean annual temperature and precipitation at 900 m a.s.l. are 8 °C and 1447 mm, respectively (McCracken 1980).

stand development sequence

The mountain beech developmental sequence used in this study was first established in 1991 as part of a larger experiment investigating nutrient storage and availability in mountain beech forest (see Allen, Clinton & Davis 1997 for a full description). The sequence consisted of even-aged mono-specific stands of pure mountain beech that, at the time of the establishment of the study, were c. 10, 25 and 120-years-old (Clinton, Allen & Davis 2002). Such stands occur naturally in mountain beech forest and are initiated by discrete large-scale catastrophic wind throw events (Allen et al. 1997; Harcombe et al. 1998; Martin & Ogden 2006). Although these stands have previously been referred to as being from the seedling, sapling and pole stages of stand development (Allen et al. 1997; Clinton et al. 2002), we refer to them in this study as small sapling, large sapling and pole stands, respectively, as this better reflects their current developmental stage (25, 40 and 135-years–old, respectively). Effort was taken to minimize between-stand environmental variation within this chronosequence. All stands were located on broad, relatively stable slopes of similar elevation (1015–1208 m), slope (7° to 24°) and aspect (98° to 170°) (Allen et al. 1997; Davis, Allen & Clinton 2004). Stands were all closed canopy and at maximum density (i.e. maximum site occupancy) as there were no obvious canopy gaps and no significant seedling recruitment had occurred in the 10 years leading up to this study (R. Allen unpublished data).

stem densities

During March 2007, stand size-structure and stem densities were assessed within a permanent plot sampling replicate stands of each age (Allen et al. 1997), by measuring stem diameter at 20 cm (basal diameter) for all live stems. Diameter at breast height (1·35 m) was also recorded for all stems > 25 mm at breast height. Plot size scaled with stem diameter, and was 20 × 20 m in the pole stands, 10 × 10 m in the large sapling stands and 5 × 5 m in the small sapling stands (Allen et al. 1997). A total of four plots from the pole stands, and three plots from the large sapling and small sapling stands were measured. In addition to these plots, three temporary harvest plots in which the destructive analysis was conducted (see below) were established for each age class in nearby stands. Considerable effort was taken to ensure that these plots were similar to the already established permanent plots (i.e. same aspect, density, age structure, canopy height). Stem diameters within these stands were measured in a similar fashion, giving a total of six to seven stands per age class.

destructive leaf area analysis

Whole trees were selected from within each of the harvest plots in a stratified manner so as to sample a wide range of diameters. A total of 87 trees were sampled, 54 from small sapling stands, 26 from large sapling stands and 7 from pole stands, covering a range of diameters (measured at 20 cm) of 0·5 to 31·5 cm. All trees were harvested during March and April 2007 after the spring flush of leaves had fully developed. Relatively few large trees were sampled due to the considerable practical difficulties and time consuming nature of sampling. Each tree was felled and leafy branches were divided into 1-m height classes and taken back to the laboratory in plastic bags. For each height class, leaf dry mass was either directly measured by removing all the leaves, drying them at 60 °C for 3 days, and weighing them, or it was estimated by subsampling. Subsampling involved taking all the leafy branches from a given height class, cutting them into small sections that had similar branch to leaf proportions (assessed visually) and weighing to obtain the total leafy branch mass. A random subsample of leafy branches was taken (c. 10% or 50–80 g), weighed, and all the leaves were removed, dried at 60 °C for 3 days, and weighed. Subsample dry leaf mass as a percentage of fresh leafy branch mass was then used to calculate total leaf dry mass for the given height class.

Leaf area was determined using a random subsample of c. 100 fresh leaves (0·8–1·5 g) for each height tier within each tree. Digital images of the area subsamples were obtained within 24 h of harvest using a scanner (Canon CanoScan N1220U), and subsample leaf area was determined using ImageJ software (default settings). Scanned leaf samples were then dried (60 °C for 3 days), weighed and subsample area per gram dry weight was used to calculate total leaf area for each height tier within each tree. Total tree leaf area and total tree leaf mass were then calculated by summing all the leaf areas from each height class. Leaf mass per unit area (LMA) within each height tier within each tree, and mean tree LMA were then calculated by summing the total area and dividing it by the total mass for each height tier or tree, respectively.

stand lai, lmi and lma calculations

Total tree leaf mass and leaf area are usually related to tree basal area (B) by fitting the power functions log (leaf area) = log (a) + b × log (B) and log (leaf mass) = log (c) + d × log (B), where a, b, c and d are regression parameters (Turner et al. 2000; Enquist 2002). The parameters a, b, c and d were estimated by standardized major axis (SMA) regression using the smatr package (Warton et al. 2006) in r (v2·6·0, R Foundation 2007), and correspond to the slopes and intercepts of the log–log regression between leaf area or leaf mass and B. We fitted two types of line, using either (i) the general scaling relationship using all 87 trees; or (ii) age-specific scaling using only trees from the age class in question. Stand leaf area index (LAI), leaf mass index (the amount of leaf mass per unit ground area (LMI)) and stand leaf mass per unit (leaf) area (LMAstand) were then calculated by applying these relationships to all the trees within a plot (n) as follows:

image( eqn 1)
image( eqn 2)
image( eqn 3)

stand level lai and lma vertical profiles

Stand level LAI profiles were calculated using the individual harvested tree leaf area profiles, by creating an average leaf area profile for four size class bins within each stand. These bins had diameters (at 20 cm) of 0–1, 1–2, 2–4 and > 4 cm for small sapling stands, 0–2, 2–4, 4–6 and > 6 cm for large sapling stands and < 15, 15–20, 20–25, 25–30 and > 30 cm for pole stands. For each stand, these leaf area profiles were then adjusted to account for the relative abundance of trees within each diameter bin, and also corrected for their relative contributions to the total stand leaf area by using the estimated leaf area of the median diameter tree within each size bin as a correction factor. LMA profiles within the canopy were calculated by binning the tree-level LMA values and adjusting for relative abundances as described above to get stand-level mean LMA values for each height tier within the canopy.

Results

leaf area and leaf mass of individual trees

Using data from all 87 harvested stems, a highly significant allometric relationship between overall tree leaf area and basal area was found over five orders of magnitude of basal area (r2 = 0·97, P < 0·001, Fig. 1a) with the exponent of the relationship being 0·98, which was not significantly different to one (95% CI 0·94–1·01). However, when each age class was analysed separately (Fig. 1b), regression lines were found to differ with stand age, with the intercept getting smaller with increasing age (P < 0·001), and the slope of the trees from the pole stands being significantly steeper than the younger small sapling and large sapling stands (P = 0·04) (Table 1). This essentially meant that a tree of a certain size (e.g. one having a basal area of 10 500 mm2) has more leaves if it is growing within a younger large sapling stand than a tree of equivalent size growing in an older pole stand. A similar pattern was observed with tree leaf mass scaling with basal area (Fig. 1c,d), with the intercepts getting lower (P < 0·001) with increasing age and much steeper slopes being observed for the pole stands (P = 0·03). Residual plots and formal tests for heteroscedacity conducted on the above-mentioned regressions showed no significant trends (see Appendix S1 in Supplementary material).

Figure 1.

Scaling relationships between tree leaf area (a, b) and tree leaf mass (c, d) with basal area measured at 20 cm above-ground; (a) and (c) have lines fitted using all the data, while (b) and (d) have lines corresponding to the different age classes (inline image, small sapling, inline image, large sapling and +, pole stands). See Table 1 for slopes, intercepts and standard errors.

Table 1.  Slope and intercept values of allometric relationships between total tree leaf area (cm2) and tree basal area (mm2), and between total tree leaf mass (g) and tree basal area, estimated by SMA regression of the form y = log (a) + b × log (B). The slope value equates to the exponent (b) and the intercept to the co-efficient log (a). 95% confidence intervals (CI) are given in brackets
 Slope95% CIIntercept95% CI
Leaf area
Overall0·98(0·94, 1·01)2·13(1·91, 2·36)
Small sapling1·06(1·00, 1·13)1·79(1·45, 2·13)
Large sapling1·07(0·98, 1·15)1·44(0·89, 1·99)
Pole1·34(1·09, 1·65)−1·86(−4·76, 1·05)
Leaf mass
Overall1·08(1·04, 1·13)−3·07(−3·32, −2·81)
Small sapling1·22(1·15, 1·29)−3·60(−3·95, −3·24)
Large sapling1·20(1·12, 1·29)−3·98(−4·53, −3·44)
Pole1·49(1·25, 1·78)−7·66(−10·41, −4·92)

The exponents of scaling relationship between leaf mass and tree basal area (B) were all significantly larger than those from the respective leaf area scaling relationship (Table 1). Indeed, total tree leaf area scaled with total tree leaf mass in a very tight log–log relationship (Fig. 2a) with a scaling exponent of 0·90 (95% CI 0·89 to 0·91), indicating that a 10-fold increase in leaf mass resulted in only a ninefold increase in leaf area; this relationship was independent of stand age (P = 0·77). Since mean tree size, and hence mean total tree leaf mass increased during development, this resulted in a significant increase in the mean LMA with stand development (Fig. 2b).

Figure 2.

Relationship between total leaf area and total leaf mass for 83 trees, (a) and (b) changes in mean stand level LMA with developmental stage. The solid fitted line in (a) is the SMA regression line with a slope of 0·90 (95% CI 0·89–0·91) and an intercept of 4·89 (95% CI 4·85–4·94), while the dashed line is a 1 : 1 relationship fitted through the centroid of the data. The significant increase in mean stand level leaf mass per unit area (LMA) during development, as shown in (b), is expected given the increase in mean tree size during development (see Table 2) and the fact that leaf mass increases faster than leaf area, as shown in (a). Error bars are ± standard error.

stand densities, size distributions and self-thinning

Average densities, mean tree basal area and total stand basal area values are given for the different aged stands in Table 2. Mean tree basal area and canopy height both increased during development, and total stand basal area was significantly greater in large sapling and pole stands than the small sapling stands (anova P < 0·001). Stem size distributions within stands were relatively narrow in the small sapling stands but became increasingly spread out with increasing stand age (Fig. 3). The relationship between mean basal area and stem density, across all age classes (Fig. 4) had a slope of −0·93 which was significantly < 1 (P = 0·002, 95% CI −0·89 to −0·97). When combined with the overall scaling exponent for leaf area in terms of basal area, this self-thinning slopes suggest that LAI increases during development (LAI~BA0·05). Although the fit was statistically strong (r2 of 0·99), the regression line still slightly underestimated the density in large sapling stands and overestimated it in small sapling stands (Fig. 4a). A nonlinear model with a quadratic term provided a significantly better fit (P < 0·001), reducing the residual SS by 51%. The relationship between mean tree leaf area (calculated using the age–SLA scaling relationships) and stem density (Fig. 4b) had a slope of −1·004 which was indistinguishable from 1 (95% CI −0·96 to −1·05). This would seem to predict constant LAI during self-thinning. However, again a nonlinear model with a quadratic term provided a significantly better fit (P = 0·002). Residual plots for both the linear and the nonlinear models described here are given in Supplementary Appendix S1.

Table 2.  Summary stand data for the different developmental stages. Stand age (in 2007) is determined from wood cores (Allen et al. 1997), N, number of stands sampled. Mean and total basal area (BA) values are calculated from diameter measurements taken at 20 cm above-ground for all live stems > 30 cm high. Standard errors are given in brackets
 Age (years)NDensity (stem/m2)Mean BA (cm2)TotaI BA (cm2/m2)
Small sapling 25639·6 (3·1)  1·58 (0·09)61·9 (12·1)
Large sapling 406 6·3 (0·83) 16·69 (1·84)98·4 (11·1)
Pole13570·26 (0·02)374·43 (18·29)96·9 (8·0)
Figure 3.

Mean size distributions for (a) small sapling, (b) large sapling and (c) pole stands based on diameter at 20 cm above-ground. Diameters are binned into 1 cm size classes with the maximum value shown on the axis labels (e.g. 1 refers to 0–1 cm size bin). Densities are scaled to stems per m2 for all stands.

Figure 4.

Relationships between stem density and mean basal area (at 20 cm) for all stands (a) and mean tree leaf area (b). In (a), the slope of the self-thinning line (solid line), fitted through the mean data as all stands were assumed to be at maximum density, is −0·93, (95% CI −0·89 to −0·97, r2 of 0·99). Dashed lines represent LAI isoclines for LAI values of three and eight for the lower and upper lines, respectively, calculated using the overall scaling relationship between leaf area and basal area. Both dashed lines have slopes of −0·98 (see Table 1). The mean tree leaf area for each stand (b) is calculated using the appropriate age-specific scaling relationship (see Table 1), and the slope of the fitted line in (b) is 1·004 (95% CI −0·96 to −1·05).

changes in lai and lmi with stand development

Stand LAI values ranged from 3·4 to 7·8 and varied with stand age (Fig. 5a). Using the overall scaling relationships, there was a significant difference between age groups (P < 0·001), with small sapling stands having much lower LAI than large sapling or pole stands (Tukey's HSD, P < 0·001 for both). Using the more accurate age-specific scaling relationships, however, we found that there was actually no difference in LAI between small sapling and pole stands, but the large sapling stands remained significantly greater than both small sapling and pole stands (Tukey's HSD, P = 0·006 and P = 0·01, respectively). These results were robust to both the inclusion of the errors associated with the predictions of individual tree leaf area values from the leaf area vs. basal area scaling relationships, and to changes in the regression technique used to estimate the slope and intercept parameters (see Supplementary Appendix S2).

Figure 5.

Mean stand LAI (a) (dimensionless) and LMI (b) (units of grams per m2) for different stages of stand development, showing the different results obtained when using either the overall scaling relationship or the more appropriate stand-age specific scaling, both using SMA regressions. Error bars are ± standard error and are based on plot as the unit of replication.

Using the overall scaling relationship, leaf mass per unit ground area (LMI) showed a strong increasing trend with stand age (P < 0·001), and this trend was still evident when the age-specific scaling was used, with large sapling and pole stands having considerably more leaf mass per unit ground area than small sapling stands (Fig. 5b) (P < 0·001 and P = 0·002, respectively). There was no significant difference in LMI between the large sapling and pole stands, as the increase in stand level LMA (Fig. 2b) counterbalanced the decline in stand level LAI (P = 0·13).

within-canopy lai and lma profiles

Average within-canopy partitioning of LAI for small sapling, large sapling and pole stands are shown in Fig. 6a–c. Total canopy depth increased with stand development, as did overall canopy height, and LAI distribution within these vertical canopy layers became increasingly less concentrated in one layer with increasing stand age (co-efficient of variation = 3·6, 2·1 and 0·97 for small sapling, large sapling and pole stands, respectively). Calculated for each height class, LMA showed a strong increasing trend with increasing relative height in the canopy (Fig. 6d, P < 0·001), and both the slope and the intercept of the relative height profiles depended significantly upon stand age (P < 0·001 for both). These results reflect an increase in variation between top of canopy and bottom of canopy LMA during stand development, which was primarily driven by an increase in the maximum LMA recorded at the top of the canopy (Fig. 6d).

Figure 6.

Canopy leaf area profiles showing the percentage stand LAI (one-sided leaf area per unit ground area) in each height class for small sapling, large sapling and pole stands (a–c, respectively) and (d) distribution of LMA (leaf mass per unit leaf area) with relative height in the canopy (expressed as a fraction of the total canopy height) for the three age classes (inline image, small sapling, inline image, large sapling and +, pole stands).

Discussion

The observed pattern of changing stand LAI (and to a lesser extent LMI) during development, of increasing to a peak and then declining, is similar to that reported for many other studies of forest development (Ryan et al. 1997). Since all stands in our study were deemed to be at or near maximum density and undergoing competitive self-thinning (Osawa & Allen 1993), our findings constitute evidence against one of the central assumptions of the specialized self-thinning literature, namely the maintenance of a constant LAI during self-thinning (Yoda et al. 1963; Long & Smith 1984; Enquist 2002). This finding enhances our understanding of how LAI changes during stand development in natural forests, and has potentially important flow-on effects for ecosystem modelling, especially since LAI is a key parameter in most models of total ecosystem productivity, transpiration, carbon dioxide flux and global climate change (e.g. Chase et al. 1996, Williams et al. 1998, Aragao et al. 2005, Raddatz 2007).

age-specific allometric relationships

Generalized allometric relationships for leaf mass and/or leaf area are key attributes used in ecology to scale leaf and plant level phenomena to stand or ecosystem level (Enquist 2002; Brown et al. 2004; Kerkhoff & Enquist 2006), and are important practical tools for calculations of LAI in forests (Deblonde, Penner & Royer 1994; Turner et al. 2000; Goulden et al. 2006; Xiao et al. 2006). Although tree-level leaf allometric relationships are known to vary with changing environment (Kostner, Falge & Tenhunen 2002), and between species (Turner et al. 2000), the explicit effects of stand age have seldom been tested (but see Tobin et al. 2006). Age-related effects, and the associated changes neighbourhood density, are potentially very important to take into account when utilizing species-specific allometric relationships to calculate stand level LAI for sites of different developmental stage (Bond-Lamberty, Wang & Gower 2002a; Bond-Lamberty et al. 2002b; Goulden et al. 2006). Our results show that stand age has a consistent effect on both the slope and the intercept of both the leaf mass and the leaf area allometries for mountain beech (increasing slope, decreasing intercept). This equates to a tree of a given basal area having more leaf area (and leaf mass) when it is growing in a neighbourhood of smaller trees, than a similar sized tree surrounded by a lower density of trees larger than itself.

The most likely reason for this is due to size-specific competition within the canopy, especially for light. A sub-dominant tree is likely to be overtopped by larger neighbouring trees which would reduce the amount of light reaching its foliage, resulting in a decline in photosynthesis and a lower leaf area. This process is commonly thought to be responsible for the size-specific increase in mortality of smaller stems often observed in competitively thinning stands (Hutchings & Budd 1981). A change in leaf area of a tree may well be reflected by diameter independent changes in its sapwood area, given that trees with lower leaf area are likely to be growing less and hence, assuming a constant rate of heartwood production per unit diameter, would have less sapwood area than a similar sized, but faster growing tree in a better neighbourhood environment (Turner et al. 2000). This hypothesis remains to be tested for mountain beech as very limited data are available on the ratios between sapwood and heartwood area for this species. Evidence for other species generally indicate that sapwood area is very variable for trees of a given size, and is a better predictor of total leaf mass for large trees than total basal area (Turner et al. 2000). We speculate that the variability in sapwood area with diameter is due to neighbourhood effects on local resource availability.

mean tree allometry and self-thinning

In this study, the slope of the self-thinning line between stem density and mean tree basal area was found to have an exponent of −0·93, which is slightly greater than a recently reported value based on actual time-series data of −0·88 (recalculated in terms of basal area at 20 cm from Coomes & Allen 2007– see Supplementary Appendix S3). This discrepancy could possibly be explained by the fact that our density data included trees of all sizes while Coomes & Allen (2007) only included stems bigger than 2·5 cm d.b.h. in their analysis. This would tend to increase the density of the youngest stands, resulting in a slightly steeper overall slope. Both our ‘mean tree’ predictions (Fig. 4) and those previously published (Coomes & Allen 2007) suggest constant or increasing stand LAI during self-thinning. This does not agree with our more accurate, direct estimates of stand LAI (Fig. 5). This highlights the inherent difficulties in using general allometric relationships between stem density, mean tree size and leaf area to accurately infer changes in stand LAI during self-thinning. These difficulties are mainly due to the fact that in such relationships, mean size and density commonly vary over 4–5 orders of magnitude, while LAI has a comparatively small range of ecologically possible values. This means that very small changes in the slope of the thinning line or the distribution of residuals can result in significantly large changes to stand LAI (Figs 4 and 5). In addition, bias may be introduced into the calculations when using the mean tree approach as a result of Jensen's inequality (Duursma & Robinson 2003). Our findings add to existing warnings against the use of the mean tree approach to investigate changes in LAI during stand development, an approach that has been commonly employed in the self-thinning literature (Long & Smith 1984; Osawa & Allen 1993; Enquist et al. 1998; Enquist 2002).

possible causes of changing lai

Leaf area is thought to reach a peak at which light, water, space or nutrients become limiting, causing competition that results in mortality of the weaker individuals (Long & Smith 1984; Ryan et al. 1997). Our data suggest that the peak in leaf area is reached after the competitive thinning process has been initiated, which implies that mountain beech stands are able to increase their access to scarce resources (particularly light) following the point of canopy closure, at least during the early stages of stand development. Stand-level canopy profiles show that the greatest increase in crown depth occurs when going from the small sapling to large sapling stages of development (Fig. 6). We propose that increases in LAI between small sapling and large sapling stands is due to a more even distribution of light through the canopy, driven by the increase in canopy depth and more regular layering of leaves within the canopy. This prediction could be tested by coupling the leaf area profiles presented in this paper with measurements of light availability and photosynthetic rates for leaves at different heights within the canopies of different aged stands, and also including changes in leaf angle and inclination with stand age (Niinemets, Cescatti & Christian 2004; Hirose 2005). The increase in LAI during the early stages of stand development might also be due to increased nutrient availability caused by the breakdown of woody material left over from the previous generation (Allen et al. 1997; Clinton et al. 2002).

Three mechanisms have been widely proposed to account for the decline in leaf area at later stages of development (Ryan et al. 1997). The first is due to a reduction in nutrient availability (Binkley, Smith & Son 1995), caused by immobilization of nutrients in increasing amounts of woody material. Reduced nutrient availability generally results in an increase in below-ground allocation (Gower, McMurtrie & Murty 1996). For our developmental sequence, total cation storage in woody material was highest in our pole stage and lowest in our large sapling stage of stand development (Allen et al. 1997) and nitrogen availability was greater in our large sapling stands than in our pole stands (Clinton et al. 2002). This is consistent with the idea that reduced nutrient availability is contributing to the decline in leaf area at latter stages in development. The second possible mechanism causing the decline in leaf area in the pole stands is increased canopy height resulting in increased crown movement and abrasion during strong winds (Long & Smith 1992), which has received recent empirical support in lodgepole pine stands (Meng et al. 2006). This is definitely a possibility in our sites as trees are frequently subject to severe gales, and pole stands exhibit considerable crown shyness (R. Holdaway personal observation). A third possibility is an increase in unfilled canopy gaps caused by the inability of existing trees to fully occupy free space (Peet 1992). Future research is required to separate out the relative contributions of these three potential mechanisms to the observed decline in leaf area when going from the large sapling to pole stages of stand development.

changes in lma during stand development

Since leaf mass and leaf area scaled non-isometrically with each other, tree level LMA increased with increasing tree size, as did mean stand-level LMA (Figs 2 and 6). This meant that leaves were generally thicker in the older stands than in the younger stands. The increase in stand level LMA during development could also be driving the decline in LAI observed when going from the large sapling and pole stands, particularly since the LMA was found to remain constant during this period (Fig. 5). LMA also varied systematically down the canopy, being highest at the top of the canopy in the oldest stands (Fig. 6). The increase in LMA (or decrease in SLA) with increasing canopy height is consistent with many other studies (Day, Greenwood & White 2001; Koch et al. 2004; England & Attiwill 2006) and has historically been attributed to the increase in light availability between the bottom and top of a forest canopy (Hollinger 1989; Niinemets 1999). Recent evidence suggests that gravitation effects on within-plant water transport and resulting leaf turgor are the primary determinants of the increase in LMA with canopy height. This, however, was for some of the tallest trees on Earth (in excess of 100 m), and these effects are unlikely to be significant for our developmental sequence as the maximum height is only 17 m (Koch et al. 2004).

The variation in leaf LMA with canopy height and stand age observed in this study is likely to be the result of complex trade-offs between water use and carbon dioxide uptake. Thin, flat leaves tend to maximize light capture and carbon dioxide uptake, but quickly become water limited in high-light environments. Thicker leaves have a lower surface area to volume ratio and hence lower rates of transpiration in high-light environments, but also have lower rates of carbon dioxide uptake (Niinemets 1999; England & Attiwill 2006). In young stands, canopies are much denser and therefore relatively decoupled from the atmosphere. This would reduce transpiration and allow leaves situated in high irradiance conditions to have lower LMA values without becoming water limited. As stands develop they become more open and exposed to drying winds which would select for larger LMA values and greater water use efficiency (Irvine et al. 2004).

concluding remarks

The LAI of a stand is known to depend upon a range of site, species and environmental factors (Beerling & Woodward 2001). Our results suggest that, contrary to some of the ideas underlying the self-thinning literature (Long & Smith 1984; Enquist et al. 1998), it is also highly dependent upon the developmental stage of the stand. We propose that the idea that stand leaf area (or leaf mass) remains constant during development following the onset of competitive self-thinning needs to be replaced with the notion of leaf area (or mass) is at a ‘dynamic maximum’ during this phase of stand development. Here, the principles that too few leaves will free up resources (light) for competing plants to use, and too many leaves will result in declines in net photosynthetic gains due to self shading and increased metabolic costs still hold. However, the exact leaf area (or leaf mass) that a stand can support (i.e. the position of the dynamic maximum) varies systematically with stand development, potentially due to changes in the vertical structure of the canopy and resulting trade-offs between leaf area and leaf mass which alter the relative rates of resource use and acquisition within the forest canopies as they develop.

Acknowledgements

We would like to thank Laura Young for being a great help with fieldwork. Thanks go also to Matthew Turnbull and Canterbury University for providing advice and assistance during fieldwork and to Ed Tanner and David Hanke for providing helpful comments on the manuscript. Funding was provided from the New Zealand Foundation for Research, Science and Technology (Ecosystem Resilience Outcome Based Investment) and the Woolf Fisher Trust.

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