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. 2006 Jan;97(1):97–107. doi: 10.1093/aob/mcj004

The Leaf Size–Twig Size Spectrum of Temperate Woody Species Along an Altitudinal Gradient: An Invariant Allometric Scaling Relationship

SHUCUN SUN 1,*, DONGMEI JIN 2, PEILI SHI 3
PMCID: PMC2803375  PMID: 16254019

Abstract

• Background and Aims The leaf size–twig size spectrum is one of the leading dimensions of plant ecological variation, and now it is under development. The purpose of this study was to test whether the relationship between leaf size and twig size is isometric or allometric, and to examine the relationship between plant allometric growth and life history strategies in the spectrum.

• Methods Leaf and stem characters—including leaf and stem mass, total leaf area, individual leaf area, stem cross-sectional area, leaf number and stem length—at the twig level for 59 woody species were investigated along an altitudinal gradient on Changbaishan Mountain in the temperate zone of China. The environmental gradient ranges from temperate broad-leaved mixed forest at low altitude, to conifer forest at middle altitude, and to sub-alpine birch forest at high altitude. The scaling relationships between stem cross-sectional area and stem mass, stem mass and leaf mass, and leaf mass and leaf area at the twig level were simultaneously determined.

• Key Results Twig cross-sectional area was found to have invariant allometric scaling relationships with the stem mass, leaf mass, total leaf area and individual leaf area, all with common slopes being significantly larger than 1, for three altitudinal-zoned vegetation types under investigation. However, leaf mass was found to be isometrically related to stem mass and leaf area along the environmental gradient. Based on the predictions of previous models, the exponent value of the relationship between twig cross-sectional area and total leaf area can be inferred to be 1·5, which falls between the confidence intervals of the relationship at each altitude, and between the confidence intervals of the common slope value (1·17–1·56) of this study. This invariant scaling relationship is assumed to result from the fractural network and/or developmental constraints of plants. The allometric constants (y-intercepts) of the relationships between the stem cross-sectional area and leaf area (both total leaf area and individual leaf area) were found to decrease significantly along the altitudinal gradient. This suggests that the species would support less leaf area at a given twig cross-sectional area with increasing environmental stress.

• Conclusions This study demonstrated that plants respond to the environmental gradient by changing the y-intercepts of the relationship between leaf size–twig size, while keeping the exponent value of the allometric relationship as an invariant constant. The allometric growth in the twig size–leaf size spectrum is related to many other components of plant life history strategy, including the well established life history trade-off between efficiency and safety in the hydraulic transport of water.

Keywords: Allometric growth, altitudinal gradient, leaf area, stem mass, leaf mass, life history trade-off, scaling, twig cross-sectional area

INTRODUCTION

An important aim of plant ecology is to identify leading dimensions of ecological variation among species and to understand the basis for them. In addition to those of the leaf–height–seed (LHS) system (Westoby, 1998; Westoby et al., 2002), the leaf size–twig size spectrum recently has been recognized as one of the leading dimensions (Ackerly and Donoghue, 1998; Preston and Ackerly, 2003; Westoby and Wright, 2003; Pickup et al., 2005), and is still being explored (Westoby and Wright, 2003; Pickup et al., 2005). Compared with the other dimensions in the LHS system (Westoby, 1998), this spectrum is poorly understood in relation to plant life history strategies.

The leaf size–twig size relationship was first postulated >50 years ago (Corner, 1949) and it has become known as one of Corner's rules (Hallé et al., 1978; Brouat et al., 1998). According to the rule, it is claimed that thick stems will hold more leaf area, and larger appendages, and have fewer branches than thin stems (Corner, 1949). These plant architectural traits are usually influenced by ecological factors (e.g. Tomlinson, 1987). For example, leaf size and specific leaf area (SLA) tend to decrease with increased environmental stress (Chapin et al., 1993; Westoby et al., 2002), and the ratio of sapwood area to leaf area tends to increase with declining soil water availability (Cavender-Bares and Holbrook, 2001). However, although a scaling relationship has been found between twig sectional area and leaf area at both interspecific and intraspecific levels (Brouat et al., 1998; Brouat and McKey, 2001; Preston and Ackerly, 2003; Westoby and Wright, 2003), few studies have examined the scaling relationship in relation to environmental gradients.

Generally, there are two major approaches to characterize how plants respond to environmental changes in the leaf size–twig size relationship, i.e. changing the scaling slope value of the relationship, and/or shifting the slope horizontally or vertically. White (1983a,b) first examined the relationship in detail in an interspecific comparison. Brouat et al. (1998) reanalysed his data, showing that among species belonging to the same ecological groups, this relationship is isometric, i.e. the surface area of a terminal leaf is directly proportional to the primary cross-sectional area of the twig bearing it. However, recent studies have also found an allometric relationship between twig cross-sectional area and leaf area in either an interspecific comparison (Westoby and Wright, 2003) or an intraspecific comparison (Preston and Ackerly, 2003), in which the common log–log slope was significantly steeper than 1. Although these studies all claimed an invariant scaling relationship between leaf size and twig size, it is a dilemma whether or not to accept either of the two contrasting conclusions. If the scaling relationship is invariant, it should not be either isometric or allometric at the same time, and vice versa. Because no further study has simultaneously explored the scaling relationships among stem cross-sectional area, stem mass, leaf mass and leaf area at the twig level, it is hard to determine whether there is an invariant scaling relationship between leaf size and twig size. Moreover, the y-intercept of the scaling relationship has been found to be low for evergreen species (Brouat et al., 1998) and for species at sites with low soil water availability (Preston and Ackerly, 2003; Westoby and Wright, 2003). However, drawing the conclusion that species in stressful habitats tend to support less leaf area for given stem dimensions would be premature, because the scaling relationship has not been examined in relation to other environmental factors such as temperature and nutrient availability.

In order to examine the response of the leaf size–twig size relationship to environmental variations, we investigated leaf and stem characters—including leaf and stem mass, total leaf area, individual leaf area, stem cross-sectional area, leaf number and stem length—at the twig level for 59 woody species along an altitudinal gradient on Changbaishan Mountain in the temperate zone of China. The environmental gradient ranges from temperate broad-leaved mixed forest at low altitude, to conifer forest at middle altitude, and to sub-alpine birch forest at high altitude, with the stressfulness of habitat apparently increasing with altitude. To explain the relationship between twig cross-sectional area and total leaf area further, we also determined the scaling relationships between stem cross-sectional area and stem mass, stem mass and leaf mass, and leaf mass and leaf area at the twig level. The specific questions we asked were (a) whether the scaling relationship between leaf size and twig size is invariant along the gradient; and, if so, (b) whether the scaling relationship is isometric or allometric; and (c) whether plant species support less leaf area for a given stem cross-sectional area with increasing environmental stress, for example from low-altitude to high-altitude environments.

MATERIALS AND METHODS

Site description

The study site is located along the northern slope of Changbaishan Natural Reserve in Jilin Province, northeastern China (41°42′N–42°10′N, 127°38′E–128°10′E). The reserve has an elevation varying from 720 to 2691 m above sea level (asl) and a temperate continental montane climate. Annual rainfall is approx. 700 mm at lower elevations and increases to approx. 1400 mm at Tianchi Lake, the top of Changbaishan Mountain. The mean annual air temperature decreases from 4·9 °C at the foot of the mountain to −7·3 °C at the top. Influenced by the climate, the Changbaishan Natural Reserve has obvious vertical vegetation zones, including Korean pine and broad-leaf mixed forests at low altitude (720–1100 m), spruce and fir conifer forests at middle altitude (1100–1800 m), birch (Betula ermanii) forests in the sub-alpine zone at high altitude (1800–2100 m), and alpine tundra at elevations above 2100 m.

Generally, the species at high elevations experience more stressful environments than do those at low elevations, due to low temperature and soil nutrient availability (Cheng et al., 1981). The vertical zonation of vegetation distribution on the mountain has been interpreted in relation to ecological factors including temperature, soil water and nutrient availability (Chen and Feng, 1985).

Twig sampling

Three forest types, i.e. the mixed forest, the conifer forest and the birch forest, were investigated in the natural reserve. Eight sites were sampled in total, with three of them being in the mixed forest (720, 790 and 1050 m asl, at low altitude), three in the conifer forest (1350, 1550 and 1650 m asl, at middle altitude) and two at the birch forest (1850 and 2050 m asl, at high altitude). A total of 41, 29 and 14 species were sampled for the three forest types (Table 1), respectively. The total number of species was 59, belonging to 36 genera of 23 families, with the low altitude sharing 13 and three species in common with the middle and high altitudes, respectively, and the middle altitude sharing six species in common with the high altitude. In each site, all woody species were investigated, except those in which fewer than three individuals could be sampled.

Table 1.

Trait means for the 59 study species at the twig level along an altitudinal gradient on Changbaishan Mountain, northeastern China

Forest type Life form Family Species TCSA (mm2) TSM (mg) TLM (mg) ILA (mm2) TLA (mm2) LN
Mixed forest EC Pinaceae Picea jezoensis 1·32 22·3 100·18 861·48
EC Pinaceae Abies nephrolepis 2·18 40·54 203·66 22·54 1500·29 67
EC Pinaceae Pinus koraiensis 4·85 76·82 751·86 91·11 3315·55 72·5
DB Aceraceae Acer barbinerve 2·58 21·79 361·57 2589·54 10 421·74 4·1
DB Aceraceae Acer mandshuricum 2·28 32·2 362·3 2863·3 11 453·2 4
DB Aceraceae Acer mono 2·73 24·01 357·36 2138·75 10 803·75 4·9
DB Aceraceae Acer pseudo-sieboldianum 1·73 15·06 204·2 3052·77 6060·58 2
DB Aceraceae Acer tegmentosum 5·02 53 548·57 9256·89 18 513·78 2
DB Aceraceae Acer triforum 1·82 36·07 302 5126·35 10 252·7 2
DB Araliaceae Acanthopanax senticosus 9·62 82·56 780·78 6376·52 24 778·9 3·6
DB Araliaceae Arala mandashriea 10·95 794·28 3388·88 11 127·68 13 0541·4 11
DB Berberidaceae Berberis amurensis 5·67 10·52 261·68 935·52 6854·09 7·6
DB Betulaceae Betula platyphylla 2·15 28·46 183·28 499·3 3317·3 6·5
DB Betulaceae Corylus mandshurica 2·28 26·19 309·85 3687·84 10 700·29 2·9
DB Caprifoliaceae Lonicera caerulea var. edulis 2·84 41·4 269·2 589·21 6481·3 11
DB Caprifoliaceae Lonicera chrysantha 0·91 23·8 95·35 701·87 2807·48 4·2
DB Caprifoliaceae Lonicera praeflorens 1·45 49·1 362·3 940·16 7521·3 8
DB Caprifoliaceae Lonicera ruprechtiana 1·45 17·03 96·13 629·05 3760·53 5·7
DB Caprifoliaceae Viburnum burejaeticum 2·99 22·81 181·01 1825·55 4051·72 2·2
DB Celastraceae Euonymus alatus 2·84 69·5 184·17 678·48 4961·28 7·1
DB Celastraceae Euonymus verrucosus var. pauciflorus 2·3 32·02 186·94 1267·05 5645·21 4·5
DB Fagaceae Quercus mongolia 2·97 69 631·81 3852·32 18 134·89 4·6
DB Leguminosae Maackia amurensis 9·62 226·3 1875·63 14 386·95 64 700·97 4·5
DB Myrsinaceae Ardisia japonica 2·99 31·3 134·9 1082·18 4328·7 4
DB Oleaceae Fraxinus mandschurica 9·91 181·57 1151·63 6211 28 132·95 5
DB Oleaceae Syringa reticulata var.· mandshurica 2·23 46·55 298·11 1085·41 6394·91 5·8
DB Rosaceae Crataegus cuneata 3·22 41·96 368·98 1867·3 9989·63 5·4
DB Rosaceae Malus baccata 2·78 52·23 287·67 1184·77 6768·93 5·6
DB Rosaceae Prunus padus 2·93 67·86 369·32 1395·28 8375·38 6·2
DB Rosaceae Rosa davurica 2·28 36·5 215·66 1120·99 3907·08 3·6
DB Rosaceae Sorbus alnifolia 2·2 37·94 240·66 2564·87 9204·14 3·6
DB Rosaceae Sorbus pohuashanensis 6·78 114·91 1043·94 7214·73 30 815·41 4·1
DB Rosaceae Spiraea elegans 0·88 20·84 68·9 365·24 2663·8 7
DB Salicaceae Populus davidiana 2·58 14·48 310·42 1716·29 6970·44 4
DB Saxifragaceae Philadelphus schrenkii 2·11 26·37 197·99 1321·38 6589·59 5
DB Saxifragaceae Ribes komarovii 1·09 7·82 70·36 624·36 1846·93 3·1
DB Saxifragaceae Ribes mandshurica 3·14 19·6 276·8 2997·07 8991·2 3
DB Staphyleaceae Euscaphis japonica 8·18 54·36 1514·9 32 686·9
DB Tiliaceae Tilia amurensis 2·97 25·77 298·77 4933·64 18 399·47 3
DB Ulmaceae Ulmus laciniata 1·84 13·55 251·75 1966·23 6955·45 3·5
DB Ulmaceae Ulmus macrocarpa 1·26 14·5 189·86 1188·34 5074·43 4·2
Conifer forest EC Pinaceae Picea jezoensis 1·49 17·32 70·19 16·65 733·76 43·2
EC Pinaceae Abies nephrolepis 2·33 22·03 79·52 19·78 1214·2 60·5
EC Pinaceae Pinus koraiensis 4·76 59·27 488·06 109·95 5820·98 50
DB Aceraceae Acer barbinerve 2·75 46·5 164·46 1413·46 5660·38 4
DB Aceraceae Acer mono 3·36 61·12 359·26 2704·8 10 864·32 4
DB Aceraceae Acer tegmentosum 5·8 81·62 430·08 8157·06 16 314·12 2
DB Aceraceae Acer ukurunduense 5·69 131·04 1020·55 4542·29 27 354·95 5·9
DB Berberidaceae Berberis amurensis 7·77 16·07 289·57 878·98 7430·6 8·7
DB Betulaceae Alnus hirsuta 4·57 107·16 481·8 2102·23 10 937·42 5
DB Betulaceae Betula ermanii 2·41 38·15 141·91 1125·23 4022·87 3·9
DB Caprifoliaceae Lonicera caerulea var. edulis 1·46 27·22 125·57 482·8 3286·95 6·9
DB Caprifoliaceae Lonicera nigra var. barbinervis 0·82 26·73 39·62 333·08 2262·4 7
DB Caprifoliaceae Lonicera ruprechtiana 1·87 28·85 134·36 692·55 3780·65 5·4
DB Caprifoliaceae Viburnum sargentii 6·2 115·47 466·93 5606·68 14 378·71 2·5
DB Celastraceae Euonymus verrucosus var. pauciflorus 1·69 21·12 146·64 1303·38 6002·64 4·4
DB Rosaceae Crataegus cuneata 1·61 14·53 129·1 724·14 3620·68 5
DB Rosaceae Malus baccata 2·1 50·75 208·38 791·01 4659·38 5·8
DB Rosaceae Prunus padus 2·6 1966·1 7853·63 4
DB Rosaceae Rosa davurica 2·05 9·3 161·83 1878·67 7256·66 3·8
DB Rosaceae Sorbus alnifolia 2·94 81·36 182·44 1502·75 6381·64 4·1
DB Rosaceae Sorbus pohuashanensis 9·2 150·41 1207·16 7497·11 32 897·93 4·3
DB Salicaceae Populus davidiana 4·88 218·14 223·5 795·72 6472·48 8·4
DB Salicaceae Salix raddeana 3·79 68·92 378·18 1628·59 7148·44 4·2
DB Salicaceae Salix xerophila 5·76 176·12 363·82 477·83 5202·16 9·4
DB Saxifragaceae Ribes burejense 1·67 22·7 97 658·39 3770·07 5·7
DB Saxifragaceae Ribes komarovii 1·67 43·3 86·4 394·63 2079·01 9·8
DB Saxifragaceae Ribes maximowiczianum 1·21 3·8 33·5 638·87 1575 2·7
DB Thymelaeaceae Daphne koreana 4·17 21·8 139·32 326·85 4673·24 13·8
DB Tiliaceae Tilia amurensis 4·57 125·36 439·34 4045·81 15 661·7 3·8
Birch forest BE Ericaceae Rhododendron chrysanthum 16·07 62·65 457·63 753·23 4537·74 5·8
BE Ericaceae Rhododendron mucronulatum 3·46 54·5 432 269·06 3496·53 12·8
BE Ericaceae Rhododendron parvifolium 2·15 17·37 121·08 69·45 787·72 11
EC Pinaceae Picea jezoensis 2·55 36·24 117·02 15·59 1016·58 65·2
EC Pinaceae Abies nephrolepis 1·34 10·94 45·44 7·56 467·78 59·8
DB Betulaceae Alnus mandshurica 6·13 74·1 284·23 1202·41 3149·13 2·8
DB Betulaceae Betula ermanii 4·89 135·69 282·83 862·76 4375·19 5·3
DB Caprifoliaceae Lonicera caerulea var. edulis 2·78 69·74 276·62 606·47 5987·82 9·6
DB Ericaceae Arctous ruber 1·17 12·24 34·32 35·89 235·66 6·6
DB Ericaceae Vaccinium uliginosum 1·62 26·46 61·08 105·48 786·12 7·6
DB Ericaceae Vaccinium vitisidaea 1·03 15·34 60·76 77·32 742·48 9·3
DB Rosaceae Rosa davurica 2·22 35 183·1 1898·28 4678·3 2·5
DB Salicaceae Salix matsudana 5·27 329·2 462·35 580·89 8482·66 14·6
DB Salicaceae Salix xerophila 7·12 223·63 269·25 446·13 5064·36 11
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BE = broad-leaved evergreens; DB = deciduous broad-leaved species; EC = evergreen conifers; TCSA = twig cross-sectional area; TSM = twig stem mass; TLM = twig leaf mass; ILA = individual leaf area; TLA = total leaf area; LN = leaf number

For each species, five randomly selected individuals were located and then three branches with tips at the outer surface of the plant's crown were chosen at random. In this study, twig was defined as a first-year shoot of selected branches, consisting of a terminal set of internodes and the leaves borne by them. The terminal set was located back to the first side branch. One twig without apparent leaf area loss was selected from each chosen branch for measurement. Leaf number and twig length were recorded. Twig diameters were measured in the middle of the internodes using a vernier caliper, and each internode was measured to the accuracy of 0·1 mm. Twig cross-sectional area was calculated from the diameters. All leaves on the twigs were taken off for leaf area and mass measurements. The leaves were scanned to computers, and the pictures were digitized using MapInfo software, and then leaf area was recorded. The leaves were dried to constant mass and weighed.

Data analysis

The collected data on plant functional traits, including leaf size and twig size, were log transformed to fit a normal distribution before analysis. Because no significant difference across species was found in the functional traits measured between different elevations within any specified forest type, data were pooled for each forest type. Moreover, a hierarchical analysis of variance (ANOVA) was conducted for the mixed forest. Variance between species was found to be consistently the largest component, and variance between individual plants was always less than that between twigs on an individual plant. Consequently, in interspecific comparisons, traits were averaged arithmetically within species, and then species averages were log10 transformed to determine the leaf size–twig size relationship.

The relationships between any two functional traits in this study were described by a mathematical equation of the type y = bxa, linearized under the form log(y) = log(b) + a log(x), x and y being the dimensions of the two parts considered. The term b is the y-intercept of the relationship and the term a, the slope of the relationship, is the allometric coefficient or rate of divergence. The value of the slope determines whether the relationship is isometric (a = 1, no change of form among species) or allometric. The value of the y-intercept does not determine the form of the relationship and, if two lines of the same slope are compared, the difference between their respective values of b indicates the differences independent of size.

Model type II regression analysis was used to estimate the parameters of the allometric equations. Slopes of the allometric relationship were calculated as standardized major axis (SMA) (Falster et al., 2003), which is also known as reduced major axis (RMA) (Sokal and Rohlf, 1995). The values for a and b were computed using the formulae a = aOLS/r and log(b) = log(Y) – a log(X), where aOLS is the ordinary least square (OLS) scaling exponent (slope), r is the OLS correlation coefficient, and X and Y denote the mean values of x and y, respectively. Confidence intervals for individual regression slopes were calculated following Pitman (1939). Tests for heterogeneity of regression slopes and calculation of common slopes where homogeneity of slopes was demonstrated followed Warton and Weber (2002). Differences in elevation of regression slopes (y-intercept) and in shifting along the slope were tested by ANOVA (and post hoc Tukey tests where appropriate). The calculation related to allometric equation parameters was conducted using (S)MATR Version 1.0 (Falster et al., 2003. http://www.bio.mq.edu.au/ecology/SMATR). This software has proved to be successful in several previous studies (e.g. Wright et al., 2002; Westoby and Wright, 2003). In this study, because conifer species were found to depart far from the slope line, and because there were too few (only two or three) conifer species within each forest type to generate a slope line for this ecological group, they were excluded from calculation of the allometric relationship. However, three evergreen broad-leaved species were found alongside deciduous broad-leaved species in the birch forest, and the scaling relationships among the functional traits were not significantly different whether they are included or excluded. These species therefore were included in the analysis.

In addition, in order to determine whether the correlation between different functional traits varied with evolutionary divergence, phylogenetically independent contrasts were conducted using the PDTREE module of PDAP version 6.0 (http://mesquiteproject.org/pdap_mesquite/index.html). The calculation method of PDAP followed Garland and Ives (2000). The phylogenetic tree was constructed following Institute of Botany, Academic Sinica (1980) and Hou (1998). Regression of evolutionary divergence data used standard model I techniques.

RESULTS

Twig cross-sectional area in relation to stem mass, leaf area and mass

Twig cross-sectional area was strongly related to stem mass of the twigs in all three forests [r2 ranging from 0·441 (conifer forest) to 0·848 (birch forest), P < 0·01 for all forests], with a common slope of 1·504 [the 95 % confidence interval (CI) = 1·278–1·770], significantly larger than 1·0 (Fig. 1A). No significant shift was found among forests in either y-intercept (P = 0·741) or x-intercept (P = 0·565). The relationship was also strong when expressed as correlated evolutionary divergences (mixed forest only, regression through origin, r2 = 0·67, P < 0·001, Fig. 2A).

Fig. 1.

Fig. 1.

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Cross-species relationships between twig cross-sectional area and the traits including (A) twig stem mass, (B) twig leaf mass, (C) total leaf area and (D) individual leaf area for the woody species along an altitudinal gradient on Changbaishan Mountain, northeastern China. The solid lines are the reduced major axis (RMA) regression curves. Individual regression lines were non-heterogeneous for all the four relationships. No significant difference in the y-intercept of the regression line was found in (A) and therefore only the common regression line is shown. However, the y-intercept was significantly higher at low altitude in (B) and therefore the regression line of low altitude and the common regression line of middle and high altitudes are shown. In (C) and (D), the y-intercept was found to be higher at low than middle altitudes, which was in turn significantly higher than at high altitude, and therefore all the three regression lines are shown. For habitats: diamonds, low altitude; circles, middle altitude; triangles, high altitude. For life forms: filled symbols, evergreen conifer species; shaded triangles, evergreen broad-leaved species; others, deciduous broad-leaved species.

Fig. 2.

Fig. 2.

Fig. 2.

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Correlations of evolutionary divergences between twig cross-sectional area and other traits including (A) twig stem mass (r2 = 0·67, P < 0·001); (B) twig leaf mass (r2 = 0·87, P < 0·001); (C) total leaf area (r2 = 0·77, P < 0·001) and (D) individual leaf area (r2 = 0·68, P < 0·001) for the deciduous woody species (n = 38) on Changbaishan Mountain (the mixed forest only), northeastern China. Symbols for nodes in the phylogenetic tree: Rosaceae, squares; Aceraceae, triangles; Caprifoliaceae, diamonds; and circles for both the families having only one comparison and high-order nodes.

The cross-sectional area of twigs was significantly correlated with the total leaf area (Fig. 1B; r2 from 0·634 in birch forest to 0·703 in mixed forest, P < 0·05 for all forests), and leaf mass (Fig. 1C; r2 from 0·756 at mixed forest to 0·787 in birch forest) supported on the twig. SMA slopes ranged from 1·21 (conifer forest) to 1·68 (birch forest) for total leaf area, and for leaf mass they ranged between 1·25 (birch forest) and 1·37 (mixed forest). No significant difference was found in the SMA slopes between any two forests. Assuming homogeneity of slopes, the best-fit common regression slope was 1·351 (CI = 1·173–1·555) for total leaf area, and was 1·34 (CI = 1·187–1·501) for leaf mass, both significantly steeper than 1·0. The y-intercept of the relationship for leaf area was lowest in the birch forest, followed by mixed, and then by conifer forests (all P < 0·01). The y-intercept for leaf mass was higher in the mixed forest than in the other two forests (both P < 0·001). These results indicate that less leaf area and more leaf mass are supported by a given cross-sectional area for species in the birch forest. The relationships between twig cross-sectional area, leaf mass and total leaf area were also strong when expressed as correlated evolutionary divergences (mixed forest only, r2 = 0·77 and r2 = 0·87, respectively, both P < 0·001, Fig. 2B, C).

A strong relationship was also found between twig cross-sectional area and individual leaf area [r2 ranging from 0·337 (conifer forest) to 0·539 (mixed forest), P < 0·05 for all forests] (Fig. 1D), with a common slope of 1·541 (CI = 1·293–1·835). A significant shifting in the y-intercept was found between the birch forest and the other two forests (P < 0·001 for comparisons), and between the mixed and conifer forests, indicating that thick stems support large individual leaves, consistent with Corner's rule. However, there was no significant relationship between twig cross-sectional area and leaf number (r2 ranging from 0·001 to 0·121), indicating that the relationship between twig cross-sectional area and total leaf area was driven mainly by the size of individual leaves, not by the number of leaves. The relationships between twig cross-sectional area and individual leaf area were strong when expressed as correlated evolutionary divergences (mixed forest only, r2 = 0·68, P < 0·001, Fig. 2D).

Leaf mass in relation to leaf area and stem mass

Leaf area was highly correlated with leaf mass [r2 from 0·856 (conifer forest) to 0·926 (mixed forest), P < 0·001 for all the three forests, Fig. 3B], with a common slope of 0·978 (CI = 0·902–1·06) which is very close to 1, indicating these two traits are linearly related. Significant shifts both in the y-intercept and along the common slope were found between the birch forest and the other two forests (P < 0·01 for all). Although all the forests shared a common slope, species in the birch forest were smaller in leaf area, but higher in leaf mass, suggesting that they were characterized by a high specific leaf area. The evolutionary divergence correlation analysis also showed a significant relationship between them (mixed forest only, r2 = 0·85, P < 0·001, Fig. 4A).

Fig. 3.

Fig. 3.

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Cross-species relationships between (A) stem mass and leaf mass, and (B) leaf area and leaf mass for the woody species along an altitudinal gradient on Changbaishan Mountain, northeastern China. The solid lines are the reduced major axis (RMA) regression curves. Individual regression lines were non-heterogeneous for both the relationships. In (A), the y-intercept of the regression line was significantly higher at low altitude, and therefore the regression line of low altitude and the common regression line of middle and high altitudes are shown. In (B), however, the y-intercept was found to be lower at high altitude, and therefore the regression line of high altitude and the common regression line of low and middle altitudes are shown. Note that there is a shift in both the y-intercept and x-intercept for the species at high altitude. For habitats: diamonds, low altitude; circles, middle altitude; triangles, high altitude. For life forms: filled symbols, evergreen conifer species; shaded triangles, broad-leaved species; others, deciduous broad-leaved species.

Fig. 4.

Fig. 4.

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Correlations of evolutionary divergences (A) between twig stem mass and leaf mass (r2 = 0·85, P < 0·001) and (B) between stem leaf area and leaf mass (r2 = 0·94, P < 0·001), for the deciduous woody species (n = 38) in the Changbaishan Mountain (the mixed forest only), northeastern China. Symbols for nodes in the phylogenetica tree: Rosaceae, squares; Aceraceae, triangles; Caprifoliaceae, diamonds; and circles for both the families having only one comparison and high-order nodes.

A significant scaling relationship was found between leaf mass and stem mass [r2 = 0·550 (conifer forest) to 0·650 (mixed forest), Fig. 3A], with a common slope of 0·908 (CI = 0·785–1·049), not significantly different from 1, suggesting the relationship perhaps is isometric. Significant differences were found in the y-intercept between the birch forest and the other two forests (P < 0·01). The evolutionary divergence correlation analysis also showed a significant relationship between them (mixed forest only, r2 = 0·94, P < 0·01, Fig. 4B).

DISCUSSION

The present study showed that the relationship between twig cross-sectional area and leaf area was more allometric than isometric, similar to the results of Preston and Ackerly (2003) and Westoby and Wright (2003), but in contrast to those of Brouat et al. (1998). The scaling relationship was found to be a constant along the environmental gradient, indicating that the relationship was invariant among different habitats. However, the y-intercept was lower at high altitude than at low and middle altitudes, indicating that plants might support less leaf area at a given twig cross-sectional area with increasing environmental stress.

The invariant allometric relationship

Allometric relationships between different organs of plants have been demonstrated in many studies from individual to community levels (Niklas, 1994; Enquist and Niklas, 2001, 2002; Enquist, 2002; Niklas and Enquist, 2002). One of the important hypotheses available for interpreting the relationship is that of developmental constraint (Harvey and Pagel, 1991). This hypothesis attributes biological allometric relationships to developmental correlations between dimensions of these organs, which might limit the ability of each organ to evolve an independent response, even if selection pressures might act on different organs of the plant in opposing directions with regard to size or some other dimension. The developmental correlations between different organs are therefore sometimes viewed as resistant to evolutionary change and as a potential source of further evolutionary constraints (Harvey and Pagel, 1991; Niklas, 1994). For example, size correlation among stems, leaves and reproductive structures may limit the plant's ability to respond independently to environmental variation both temporally and spatially, and possibly further influence the fitness of the plants (Watson and Casper, 1984). The invariant allometric scaling relationship found in the present study indicates that leaf size always increases with stem size at a constant and disproportional rate, which could be established by the size correlation between leaf and stem at the plant twig level. Developmental constraints prohibit the change of the scaling slope in response to environmental changes, but allow change in the y-intercept of the scaling relationship. We therefore believe that the slope and the y-intercept have evolved in response to different selective forces, and that the slope may be controlled by a more fundamental mechanism (that is perhaps related to the second hypothesis). Watson and Casper (1984) have also suggested that developmental constraints might limit plant plasticity and plant modular autonomy. However, in an elegant evolutionary analysis of caulinary domatia in hollow-stemmed myrmecophytes, Brouat and McKey (2001) argued that leaf–stem size correlations were not a constraint, but rather a line of functional equivalence, and they attributed the altered twig leaf–stem allometric relationship they observed to requirements for mechanical stability in this ecological group. How developmental constraints evolve is not clear so far, and costs and benefits are not fully understood. Another hypothesis to explain the invariant scaling relationship is allometric relationships between different dimensions resulting from the fractal network in plants. Plants have evolved hierarchical branching vascular networks that terminate in a size-invariant unit, leaves (West et al., 1997; Enquist, 2002). Natural selection tends to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. On this assumption, a general model has been proposed to predict the relationship between different parts of plants and animals (West et al., 1997). Later, theoretical models based on the evolution of fractal-like networks were developed that specifically predict numerous allometric scaling relationships, and many of these predicted relationships have been demonstrated (Enquist et al., 1999; Enquist and Niklas, 2001, 2002; Enquist, 2002). Recent studies on plant allometry have shown that the scaling relationships observed for animals apply equally well to plants (West et al., 1997; Retta et al., 2000; Niklas and Enquist, 2001, 2002). The allometric relationship found in this study might be one of those resulting from evolution of such a fractal network system.

The allometric relationship between twig cross-sectional area and total leaf area at the twig level is convincing in this study because it can be inferred from the scaling relationships among twig cross-sectional area, stem mass, leaf mass and leaf area. First, we found that twig cross-sectional area was related to stem mass with a common slope of 1·464, very close to 1·50, a commonly known constant that relates cross-sectional area and volume of a given cylinder. This scaling relationship has been widely confirmed and is well understood in forestry studies. Allometric studies have indicated that stem diameter (D) commonly scales as plant height (H) raised to a power of 1 (Farnsworth and Niklas, 1995), and it apparently scales as stem area to a power of 2. Stem mass is usually directly related to stem volume (D2H), therefore leading to a 3/2 power scaling relationship between stem area and stem mass. Secondly, leaf mass is strongly related to stem mass in the present study, with a common slope of 0·91, and CI between 0·79 and 1·05, suggesting an isometric relationship. This exponential constant significantly differs from 3/4, the expected value predicted by Enquist and his colleagues (Enquist et al., 1999; Enquist and Niklas, 2001, 2002), who have developed models and shown how the 3/4 power scaling of metabolic rate with body mass in both animals and plants results from physical and biological constraints on the distribution of resources through fractal-like vascular networks. Enquist and Niklas (2002) have analytically derived the scaling relationships among standing leaf, stem and root (belowground) biomass by first noting that the amount of resource used per individual plant approximates metabolic demand and gross photosynthesis (B). Because B is predicted to scale proportionally to total leaf mass (ML) (B ∝ ML), the theory predicts that the surface areas over which resources are exchanged with the environment (e.g. leaf surface area, which correlates with leaf mass) are proportional to the 3/4 power of the total plant biomass, stem mass and root mass. However, the 3/4 power scaling relationship might not be applicable to the twig level addressed in this study. Nevertheless, the isometric relationship between stem mass and leaf mass is consistent with a recent model prediction on annual allocation. Based on the 3/4 power rule and a series of calculations, Niklas and Enquist (2002) also predicted isometric relationships among annual leaf biomass production, annual stem and root biomass production, regardless of leaf phenology. A large synoptic data set for standing plant organ biomass and organ biomass production spanning 10 orders of magnitude in total plant body mass has confirmed this prediction. In the present study, because all data were collected from first-year shoots, it is reasonable that our result supports this model prediction. In addition, leaf mass was found to relate linearly to total leaf area, because the common slope is 0·98, close to 1·0. This is consistent with the assumption that leads to the theory of Enquist et al. (1999), in which leaf mass is assumed to represent the area of exchange with environments. Transferring the relationships among stem area, stem mass, leaf mass and total leaf area, it could be expected that the scaling exponent between twig sectional area and leaf area is 1·5. This exponent value falls between the CIs of the scaling relationship at each altitude, and falls between the CIs of the common slope in this study. It seems to also fall between the CIs of the scaling relationship between twig cross-sectional area and leaf area in the studies of Westoby and Wright (2003), who reported a common slope of 1·45 in an interspecific comparison, and of Preston and Ackerly (2003), who reported a common slope of 1·46 in an intraspecific comparison. However, the exponent constant of the relationship found by Brouat et al. (1998) is significantly less than 1·5. A possible explanation is that twig diameter was measured at different positions. Preston and Ackerly (2003), Westoby and Wright (2003) and the present study all measured it at the middle of the internodes below the most basal leaf on the stem (back to the first branching point), showing an allometric relationship. However, Brouat et al. (1998) and Brouat and McKey (2001) made measurements at the apex of terminal internodes within first-year shoots, showing an isometric relationship. It is possible that Brouat et al. (1998) and Brouat and McKey (2001) underestimated the scaling constant. In addition, Brouat and McKey (2001) and Preston and Ackerly (2003) measured the section along both the widest and narrowest axes at the apex of the internodes, and approximated the cross-sectional area of the internode as an ellipse. This method seems more precise than that of the present study. The effect of measuring position on the scaling constant is not clear.

The variation in the elevation of the scaling relationship

In this study, although the scaling relationship between the cross-sectional area and leaf area was constant along the altitudinal gradient, the y-intercept decreased significantly with increasing altitude. This presumably results from the combined effect of environmental stress. Conditions at low altitude are relatively favourable for plant growth (Chi et al., 1981), while at middle and high altitudes, plant performances are limited by low temperature and soil nutrient availability (Cheng et al., 1981). The pattern of vegetation distribution along the altitudinal gradient appears to be controlled by ecological factors, including temperature, rainfall and soil nutrient availability (Cheng et al., 1981; Chi et al., 1981). Moreover, leaf economy models indicate that plants usually employ a conservative strategy in stressful environments, and evergreen species tend to occupy the habitats with low soil nutrient availability (Chabot and Hicks, 1982; Kikuzawa, 1991). This is because they are efficient in nutrient use, for example in tropical rainforests and Taiga forests in cold temperate zones. In this study, along the altitudinal gradient, evergreen species increase in both diversity and abundance in communities, and three species of evergreen broad-leaved species even dominate forests at high elevations of the mountain. However, it is difficult to determine whether the shifting in the y-intercept at the high altitude relative to low and middle altitudes results from environmental difference among habitats, or from the difference among ecological groups. Because the vegetation pattern is primarily controlled by climatic and edaphic conditions, we presently tend to attribute the lowered y-intercept of the scaling relationship at high altitude to the stressful habitats due to low temperature and low soil water and nutrient availability.

The difference in y-intercept among different habitats can be interpreted using a hypothesis based on hydraulic models (e.g. Harvey and Pagel, 1991; Niklas, 1994; Brouat et al., 1998), another aspect that may constrain relationships (Harvey and Pagel, 1991). This hypothesis assumes that area-based hydraulic capacity and demand are size independent (Niklas, 1994; Brouat et al., 1998). According to this hypothesis, the cross-sectional area of the vascular tissues in the twig (which is correlated with the flux density of sap flow) should be proportional to the leaf surface area that is supplied, because the majority of vascular tissue present in the stem of the twigs functions to supply leaves borne by it before secondary growth. To some degree, this hypothesis is similar to the ‘pipe model’ (Shinozaki et al., 1964), which predicts that the area of supported foliage will be proportional to the cross-sectional area of conducting tissues (typically sapwood, not heartwood) (Niklas, 1992). However, a major trade-off should be incorporated into the hydraulics hypothesis to explain the variation in the intercepts of the scaling relationship along the environmental gradient.

A general trade-off between efficiency and safety in the hydraulic transport of water is becoming increasingly well established across diverse taxa (Sobrado, 1997; Hacke et al., 2001). In optimal environmental conditions with highly competitive systems and in the absence of water stress, hydraulic conductance is maximized, presumably to maximize gas exchange and growth. However, under xeric conditions, resistance to cavitation appears to be maximized at the expense of efficiency in water transport. Variations among closely related species in xylem structure and hydraulic architecture have been shown to be related to habitat gradients in water availability (Villar-Salvador et al., 1997; Cavender-Bares and Holbrook, 2001). The observation that the y-intercept of the scaling relationship between twig cross-sectional area and total leaf area at the low altitude was significantly higher than those at the middle and high altitudes might result from the relatively high soil water availability at low altitude. At high altitude, the temperature often goes down to less than −20 °C during winters (Cheng et al., 1981), and hence soil water availability can be significantly reduced. Moreover, the trade-off between efficiency and safety of tracheary elements should favour larger cross-sectional areas of smaller diameter, less efficient, but injury-resistant conducting elements in temperate evergreens. These tend to reduce water transport capacity but maintain relatively constant hydraulic conductivity during cold and/or dry seasons, to increase resistance to freezing-induced xylem cavitations (Davis et al., 1999), for example for the species at high altitude in this study. This is a possible explanation for the observation that the y-intercepts declined along the altitudinal gradient, in which the proportion of temperature evergreens increased strongly from the low to high altitudes. Sobrado (1997) also found in the seasonal tropics that drought deciduous species maximized hydraulic conductivity in the short term at the expense of seasonal occurrences of embolism.

In addition, leaf life span (LLS) might have an effect on y-intercepts of the scaling relationship. In low altitudes, we observed a higher elevation of the scaling relationship between twig cross-sectional area and leaf area, but a lower elevation for the relationship between leaf mass and total leaf area, compared with high altitudes. This contrasting pattern apparently is due to the decreased SLA in the species at high altitude. According to leaf economy models (Kikuzawa, 1991), the species can also be expected to have long LLS at high altitudes rather than low altitudes, even for the deciduous species, although we did not investigate LLS in this study. The long-lived leaves, for example in temperate evergreen species, usually need to be mechanically tough and to tolerate biotic and abiotic damage (Reich et al., 1992; Westoby et al., 2002; Wright et al., 2004). Requirement for physical support can depend on numerous factors, including individual leaf area, leaf number and SLA. We argue that a long LLS would require an additional physical vascular support from twig stems because the species with a long LLS have to experience many adverse environmental conditions, such as strong cold wind during winters. Nevertheless, Enquist et al. (1999) reported a higher y-intercept of the scaling relationship between leaf and stem mass in gymnosperm, and they attributed this to the fact that conifers typically retain three cohorts of leaves that have less well-developed aerenchymatous mesophyll compared with angiosperm leaves. This may not be applicable to the present study because we only sampled the first-year shoots including only one cohort of leaves.

Acknowledgments

We thank Xubin Zhu, Lu Chaoqun, Yan Li and Zhenglin Yang for field assistance, and Dr Mac Sisson, Dr Karl J. Niklas and Dr Doyle McKey for critical comments on an early version of this manuscript. Thanks are also due to the staff of Changbaishan Mountain Natural Reserve for permitting this study to be conducted. This study was supported financially by the National Science Foundation of China (30000023 and 30370257).

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