Hydraulic and mechanical stem properties affect leaf–stem allometry in mango cultivars

Authors

  • F. Normand,

    1. CIRAD-PERSYST, UPR Production Fruitière Intégrée, Station de Bassin-Plat, BP 180, F-97455 Saint-Pierre cedex, Réunion Island, France;
    Search for more papers by this author
  • C. Bissery,

    1. CIRAD-PERSYST, UPR Production Fruitière Intégrée, Station de Bassin-Plat, BP 180, F-97455 Saint-Pierre cedex, Réunion Island, France;
    Search for more papers by this author
  • G. Damour,

    1. CIRAD-PERSYST, UPR Production Fruitière Intégrée, Station de Bassin-Plat, BP 180, F-97455 Saint-Pierre cedex, Réunion Island, France;
    Search for more papers by this author
  • P.-É. Lauri

    1. UMR DAP, INRA-SUPAGRO-CIRAD-UM II, Equipe ‘Architecture et Fonctionnement des Espèces Fruitières’, 2 place Viala, 34060, Montpellier Cedex 1, France
    Search for more papers by this author

Author for correspondence:
F. Normand
Tel: +262 262 969364
Fax: +262 262 969368
Email: frederic.normand@cirad.fr

Summary

  • • Leaf size–stem size allometric relationships are important features of biomass allocation in plants and are affected by biological functions linking the two organs. They have been studied at specific and supraspecific levels, but not at the infraspecific level. It was hypothesized that allometric relationships link leaf size and stem size at the cultivar level, and are cultivar-specific in relation to distinctive functional stem traits: hydraulic conductivity and mechanical strength.
  • • Allometric relationships between leaf size and stem size were established for 3 yr, using the standardized major axis method, on current-year branches, composed of one to 16 growth units, for four mango (Mangifera indica) cultivars characterized by contrasting growth habits. The hydraulic and mechanical stem properties of these cultivars were also measured.
  • • The slopes of the relationships were similar among cultivars, but not the y-intercepts. Different y-intercepts in the stem mass vs branch cross-sectional area relationship and in the leaf mass vs stem mass relationship were related to mechanical and to hydraulic stem properties, respectively.
  • • These results showed that leaf–stem allometry in mango cultivars was shaped by hydraulic and mechanical stem properties, supporting a functional interpretation of the relationship between leaf and stem dimensions.

Introduction

How a plant distributes its biomass among structure (stem) and leaves has important consequences for plant architecture and functioning. Enquist & Niklas (2002) proposed a general allometric model which predicts scaling relationships among leaf, stem and root biomass of seed plants. Niklas (2006) generalized these relationships to equivalent organ categories of nonspermatophyte streptophytes (charophycean algae, bryophytes and pteridophytes), thus supporting the hypothesis of a single scaling relationship across eukaryotic photoautotrophs.

Such relationships have been used in several fields of research and applications. Allometric relationships have been established in horticulture, forestry and ecology to predict or estimate total canopy fresh weight (Westwood & Roberts, 1970), leaf biomass, leaf area and standing wood biomass (Kenefic & Seymour, 1999; Monserud & Marshall, 1999; Enquist & Niklas, 2001; Ketterings et al., 2001; Portéet al., 2002; Komiyama et al., 2005; Kajimoto et al., 2006) using simple, nondestructive variables such as trunk or branch diameter.

On a smaller scale, the leaf size–stem size relationship is an important aspect of biomass allocation which is widely debated in ecology. This relationship was first postulated for tropical trees by Corner (1949) and was then validated for temperate zone trees by White (1983a,b). It is known as the Corner's rule on axial conformity (Halléet al., 1978; Lauri & Térouanne, 1991; Brouat et al., 1998): ‘the stouter, or more massive, the axis in a given species, the larger and more complicated its appendages’ (leaves, inflorescences, fruits). This rule first concerned individual leaf size and was then extended to the total leaf area borne by an axis. Variation in the process of dry mass investment in leaves or in stem plays a key role in plants’ adaptive strategies. The leaf size–stem size spectrum is therefore a leading dimension of ecological variation among species (Westoby et al., 2002; Wright et al., 2007). Scaling relationships between stem size and leaf size have been investigated across species in relation to ontogeny (Lauri & Térouanne, 1991; Brouat et al., 1998), axial dimorphism (Lauri and Kelner, 2001), habitat (Preston & Ackerly, 2003; Shucun et al., 2006) and other spectra of variation (e.g. seed mass–seed output and specific leaf area–leaf lifespan) among species (Westoby & Wright, 2003, Wright et al., 2007).

Stem size is characterized by stem cross-sectional area, and/or by stem mass. Leaf size is generally characterized by individual leaf area (or mass), and/or by leaf area (or mass) summed at stem level. Leaf size and stem size are allometrically related. Allometric relationships are power functions:

yxβ(Eqn 1)

where y and x are variables, and γ and β are parameters. They can be linearized through a logarithm transformation of both variables:

Y=α+βX(Eqn 2)

where Y = log(y), α = log(γ) and X = log(x). The linear relationship is described by its slope β or scaling coefficient, and its y-intercept α or allometric constant. The slope is an important parameter of the relationship, as it describes the way two variables scale relative to one another. In particular, it determines whether the relationship is isometric (slope = 1, i.e. constant ratio between the variables), or allometric (slope ≠ 1). In the studies mentioned earlier, slopes of the log-log relationships were not significantly different between species or groups (ecological, morphological, phylogenetic) of species. On the contrary, the y-intercepts differed generally between species or groups of species, expressing differences in the leaf size–stem size allometry between these entities. Factors affecting the y-intercepts are not clearly identified. The two main hypotheses are related to the efficiency of stem-conducting tissues for the water supply of leaves, and to the role played by the stem in the mechanical support of leaves (Farnsworth & Van Gardingen, 1995; Brouat et al., 1998; Preston & Ackerly, 2003; Taneda & Tateno, 2004).

Cultivars of the same fruit tree species are characterized by different growth habits, yielding ability and ecological suitability, suggesting contrasted biological functioning, as shown, for example, for water utilization and plant hydraulic properties of coffee cultivars (Tausend et al., 2000) or for stem biomechanical properties of apricot (Alméras et al., 2004) or coffee (Cilas et al., 2000) cultivars. As leaf size–stem size relationships may be affected by the biological functions (vascular supply, mechanical support) linking the two organs (functional equivalence hypothesis, Harvey & Pagel, 1991; Brouat et al., 1998; Niklas, 2006), we presumed that these relationships differed among cultivars.

In the present study, we examined, at the level of current-year growth, the leaf size–stem size relationship of four mango (Mangifera indica) cultivars, grown in the same place. Our hypotheses were as follows: that scaling relationships linked leaf size and stem size at the cultivar level, and that these relationships were cultivar-specific in relation to distinctive hydraulic and mechanical functional stem traits affecting them. More specifically, we expected that cultivars with higher stem hydraulic conductivity bore larger leaf size, but had lighter stem, for a given stem size. We also expected that cultivars with higher stem mechanical strength bore larger leaf size, and had heavier stem, for a given stem size. We first analysed the relationships between leaf size and stem size for each cultivar during three consecutive years in order to determine whether the relationships were isometric or allometric, and how they were affected by cultivar and by year, the latter being the combination of environment and tree ontogeny. We then investigated the mechanical and hydraulic properties of the stem of each cultivar and examined their relationships with leaf–stem allometry.

Materials and Methods

Field site and plant material

The experimental orchard was located on a research station of the French Agricultural Research Centre for International Development (CIRAD) in Saint-Pierre, Réunion Island (20°52′S, 55°31′E) at 280 m asl. Trees of eight mango (Mangifera indica L., Anacardiaceae) cultivars grafted onto the same polyembryonic rootstock, Maison Rouge, were planted in May 2001. Homogeneous nucellar rootstock seedlings were visually selected during the nursery stage. Tree spacing was wide enough to avoid interactions between canopies. Trees of a cultivar were therefore genetically similar, and environmental differences between them were minimal. Cultural practices were those recommended by extension services. Water stress was avoided during the vegetative growth season with an appropriate irrigation.

Four of these cultivars were chosen for the study on the basis of their diverse origin, tree size and growth habits. José is an Indian type mango selected in the middle of the 19th century in Réunion Island and is grown locally (Vincenot, 2004). It is a medium-sized tree with an open canopy. Cogshall was selected in Florida (Campbell, 1992) and is grown locally for export. It is a medium-sized tree with a dense, compact canopy. Irwin was selected in Florida. It is a small to medium-sized tree with an open canopy (Campbell, 1992; Knight, 1997). It has a low branching density compared with the other cultivars (Normand et al., in press). Kensington Pride is a commercial cultivar selected and grown in Australia. It is a large, vigorous tree with a dense spreading canopy (Knight, 1997). The latter three cultivars were introduced in Réunion Island during the last 30 yr. José, Cogshall and Irwin are monoembryonic, whereas Kensington Pride is polyembryonic. Annual measurements of tree size and observations in the experimental orchard corroborate bibliographic data on tree size and growth habit of these cultivars (data not shown).

Under the subtropical climate of the southern hemisphere, mango trees flower from August to October, and harvest spreads from the end of December to March. Vegetative growth begins slowly with flowering and during fruit growth, and flushes after harvest during the hot, rainy season, until May. Vegetative rest occurs from June to July, just before flowering.

Mango trees have rhythmic and mainly sequential growth (Halléet al., 1978). Our plant materials in this study were branches developed during the current annual growth. During the growing season, a single bud of a terminal growth unit (GU) produces a structure, hereafter referred to as a branch, composed of one to several GUs resulting from both terminal growth and branching (Fig. 1). In this way a terminal GU may produce one to several branches according to the number of buds that burst.

Figure 1.

Schematic representation of three mango (Mangifera indica) branches stemming from two terminal growth units, (a) and (b), developed in the previous year's growth season. Terminal growth unit (a) bears two branches, composed of one and four growth units, respectively. Terminal growth unit (b) bears one branch composed of 10 growth units. Each segment represents the stem of one growth unit; leaves are not represented. Triangles indicate where branch basal cross-sectional area was measured.

Allometric relationships

Branches are composed of stem and leaves. We characterized the size of these components using the following variables: total leaf area borne by the branch, hereafter referred to as leaf area, for the major implication of leaf area in hydraulic demand; leaf mass, stem mass and branch (leaf + stem) mass, as these three variables represent the biomass of the whole branch and its parts and are related to the supporting function of the stem; and branch basal cross-sectional area, hereafter referred to as branch csa, as a measure of stem thickness at the branch base.

We measured the relationships between leaf size and stem size using bivariate allometry rather than a ratio between the studied variables. Allometric analysis is more informative than ratio, particularly as it takes into account size dependence of the leaf : stem size ratio in the case of a nonisometric relationship. Five allometric relationships were chosen, based on the following considerations:

  • • leaf area vs branch csa – this relationship is equivalent to the inverse of the Huber value (Tyree & Zimmermann, 2002) and is related to stem hydraulic functioning;
  • • leaf mass vs branch csa, stem mass vs branch csa and branch mass vs branch csa – these three relationships are related to stem mechanical strength and to biomass allocation to the branch and its components;
  • • leaf mass vs stem mass – this relationship is equivalent to the leaf : stem mass ratio and is related to biomass allocation between branch components.

Branch measurements

In order to detect a year effect on the allometric relationships, branches were sampled in June 2004, June 2005 and June 2006, during the rest period, after the last GUs had matured and leaves were completely expanded. Each year, 10–15 branches were sampled on three to five trees per cultivar. The number of branches studied per cultivar for the 3 yr varied from 30 to 35. Before cutting, two orthogonal diameters were measured with a digital calliper at the base of the first GU of the branch (Fig. 1). Branch basal diameter was the mean of these two measurements. Branch csa was calculated from basal diameter, assuming that this area was circular (ratio of the two orthogonal diameters ∼1). After cutting, branches were kept in plastic bags in a cooler and rapidly brought to the laboratory.

Each branch was weighed, then leaves and stem were separated and weighed. The number of GUs per branch and the number of leaves per GU were recorded. Individual leaf area was determined with a planimeter (AM200, ADC BioScientific Ltd., Hoddesdon, UK). Leaf area of a branch was the sum of the individual areas of its leaves. The leaves and stems were then oven-dried at 80°C for 72 h, and weighed in order to record their dry mass and calculate their dry mass content. Branch dry mass content was calculated as the ratio of branch dry mass (stem + leaves) to branch fresh mass. Leaf mass per area (LMA) was calculated at the branch level as the ratio of leaf dry mass to leaf area. Hereafter, mass or biomass refers to dry mass or biomass.

Stem hydraulic and mechanical traits

Stem hydraulic conductivity and mechanical strength were determined on individual GUs in June 2006, independently of the measurements described in the previous section. As hydraulic parameters vary with stem diameter (Tyree & Zimmermann, 2002), measurements were performed on GUs of similar diameter, which is pertinent for comparing hydraulic properties among species or cultivars (Patiño et al., 1995; Vander Willigen et al., 2000). Stem mechanical properties such as modulus of elasticity or static load parameter are correlated with stem density (Niklas, 1992; Taneda & Tateno, 2004; Rosner et al., 2007). In our study, stem density was used as a surrogate for stem mechanical strength. Wood density and stem slenderness are also related to stem mechanical characteristics (Alméras et al., 2004) and were measured to assess their relationship with stem density and hydraulic traits.

For each cultivar, 20 mature terminal GUs of similar diameter, c. 6 mm, stemmed from lateral buds during the current-year growth season were chosen and cut. GU basal diameter was measured as previously before cutting. The leaves and stem fresh mass and dry mass were recorded as previously. Stem length and diameter at the middle of the stem were also measured. Stem volume was calculated from these data, assuming a cylindrical shape. Stem density was calculated as the ratio of stem dry mass to stem volume. Stem slenderness was calculated as the ratio of stem length to stem diameter at mid-length.

Saturated hydraulic conductivity, K, was determined using the XYL’EM apparatus (Xylem Embolism Meter, INRA Licensed Instrutec, Montigny-les-Cormeilles, France). Conductivity is defined as the product of stem segment length and conductance, which is directly calculated by the apparatus as the ratio of a measured flux to a known pressure gradient. A segment of c. 70 mm long was excised under water at the base of each stem. Still under water, each segment was defoliated, bark was removed at the two ends and the basal diameter without bark was measured. The whole segment was wrapped with Teflon tape to prevent lateral leak. KCl was added to distilled water to a concentration of 10 mmol l−1, in order to stabilize conductance measurements. Each segment was then flushed with the KCl solution at a pressure of 0.1 MPa for 90–120 s to expel air bubbles and saturate all vessels with water. Conductance of the segments are then measured with a hydrostatic pressure gradient of c. 2 kPa. Flush and measurement were repeated four times and saturated hydraulic conductance was determined as the maximum of these measurements. After measurements, segment length was measured and K was calculated. Two parameters were derived from K. Specific (KS) and leaf-specific (KL) saturated hydraulic conductivities were determined by dividing K by basal csa of the segment without bark, and leaf area distal to the basal end of the segment, respectively. Leaf area was measured on leaves distal to the base of the segment with a planimeter. The stem segment without bark represented wood, composed of conductive sapwood and nonconductive pith. We verified that pith diameter was not significantly different among cultivars (ANOVA, n = 20, P = 0.23). On these young GUs (2–4 months old), where secondary growth probably just began, the mean percentage of wood csa occupied by the pith was 38.8%. The actual specific hydraulic conductivity, related to sapwood csa, was therefore c. 1.63 times larger than the measured KS. However, we could compare KS among cultivars, as GUs had similar stem diameter and pith diameter. The bark was completely removed from the segments after measurement. Wood was oven-dried at 80°C for 72 h and weighed. Wood volume was calculated from fresh wood basal csa and length, assuming a cylindrical shape. Wood density was calculated as the ratio of wood dry mass to wood volume.

A priori hypotheses

On the basis of previous studies with distant taxa (cf. Introduction) and since environmental conditions were similar for all the cultivars, we expected that functional traits would affect the y-intercept of the allometric relationships rather than the slope. A set of 10 a priori hypotheses was chosen to test the correlations between leaf size–stem size allometry and hydraulic and mechanical functional stem traits (Table 1). The direction of the predicted correlations was specified on the basis of the following considerations: larger leaf area borne by a branch of a given csa requires larger hydraulic conductivity; larger leaf, stem and/or branch biomass require higher stem mechanical strength for a given stem csa; larger hydraulic conductivity for a given stem csa leads to lower stem mechanical strength because of larger and/or more numerous vessel lumens. There was no a priori direction in the correlation between branch mass vs branch csa y-intercept and stem hydraulic traits as the a priori directions of the correlations between stem mass vs branch csa y-intercept and hydraulic traits, and between leaf mass vs branch csa y-intercept and hydraulic traits, were opposed to each other.

Table 1. A priori hypotheses on the direction of the correlations between the y-intercept of the leaf size–stem size allometry and hydraulic (specific and leaf-specific hydraulic conductivities) and mechanical (stem density) functional stem traits
RelationshipHydraulic stem traitsMechanical stem trait
  1. csa, cross-sectional area.

Leaf area vs branch csaPositivePositive
Leaf mass vs branch csaPositivePositive
Stem mass vs branch csaNegativePositive
Branch mass vs branch csa?Positive
Leaf mass vs stem massPositiveNegative

Statistical analysis

For a given cultivar, some of the sampled branches came from the same trees and could be considered as pseudo-replications of trees and not as independent data. To determine if the nonindependence of branches from the same tree influenced our results, we tested for a tree effect for each cultivar and each allometric relationship. A linear mixed-effects model with a random tree effect on the y-intercept of the relationship was compared with a test of likelihood to a linear fixed-effect model without the random tree effect (Venables & Ripley, 2002). For each cultivar, data from the 3 yr were pooled to have a larger sample size per tree. The individual tree had no effect on the studied allometric relationships for a given cultivar (results not shown). Our data were therefore considered independent and suitable for further statistical analysis.

Preliminary regression analyses showed that the relationships between the variables in question followed a power curve like allometric relationships (Eqn 1). They were linearized with natural logarithms before analyses; that is, Y = loge(y), α = loge (γ) and X = loge (x) in Eqn 2. Allometric relationships were analysed in two steps. First we tested for a year effect for each cultivar. Then we pooled the 3 yr of data for each cultivar and tested for cultivar effect. To study these relationships, alternatives to linear regression were required, since we were seeking a functional rather than a predictive relationship between traits. The standardized major axis (SMA) method is appropriate for fitting bivariate lines in allometry, in that it calculates the line of best fit to summarize the relationship between two variables (Warton et al., 2006). This method also allows the presence of measurement errors on both traits (Sokal & Rohlf, 1995; Warton et al., 2006). The R (R Development Core Team, 2006) package SMATR (Standardised Major Axis estimation and Testing Routines, Warton & Ormerod, 2005) was used to estimate the SMA slope βSMA, the SMA y-intercept αSMA, and their respective 95% confidence intervals, of the linear functions Y = αSMA + βSMAX. Tests for isometry were computed using the test of slope equality to a fixed value, here 1, available in the SMATR package (Warton et al., 2006).

Year or cultivar effect may affect the allometric relationships in three ways (Warton et al., 2006): they can have an influence on the slope of the line of best fit; or, if slopes are similar (i.e. not significantly different between groups), there may be differences in y-intercept (shift in axis elevation) or shift along the common axis across different years or cultivars. We determined whether factor levels (different years or different cultivars) shared a common slope using the likelihood ratio test for common slope in the SMATR package. When slopes were similar, we tested for differences in y-intercept and shift along the common axis among factor levels. For these tests, a common slope value was used for each level. The two tests are quite similar and based on a Wald statistic (Warton et al., 2006).

If a significant shift was observed, post-hoc multiple comparisons were performed to determine which levels differed from others. For N levels of a factor (N = 3 yr or N = 4 cultivars), N(N − 1)/2 pairwise comparisons were computed. This was done, as previously, by testing for differences in y-intercepts or for shift along the common axis for two levels at a time. A Bonferroni correction of P-value threshold was done to avoid an increase in type I error as a result of the number of tests. For each comparison, the P-value threshold was P = (2 × 0.05)/N(N − 1).

Comparisons of branch characteristics and functional stem traits among cultivars were performed with single stratum analysis of variance with R. In case of heteroscedasticity, a one-way test of mean comparison was also carried out (Dalgaard, 2002). Differences among cultivars were evaluated with a Tukey's multiple comparison test.

A priori hypotheses were tested with the Pearson coefficient of correlation. The expected direction of the correlations (Table 1) allowed one-tailed significance testing for each correlation, except between branch mass vs branch csa y-intercept and stem hydraulic traits, which was performed with a two-tailed significance test. Correlations between hydraulic and mechanical stem traits were also assessed with the Pearson coefficient of correlation. In both cases, coefficients were computed on four points corresponding to the four cultivars. Given the small number of cultivar studied, correlations were considered meaningful when they were significant, with high coefficients (| r | > 0.9) and when the points were evenly distributed.

Results

Effect of year on allometric relationships for each cultivar

For each cultivar, the slopes of each relationship were similar for the 3 yr (data not shown), indicating that year had no effect on the scaling coefficient. The slopes of the relationships of leaf area, leaf mass, stem mass and branch mass vs branch csa were significantly greater than 1. On the contrary, the slopes for leaf mass vs stem mass relationship were significantly lower than 1. The relationships were therefore allometric and not isometric (i.e. paired variables were not proportional).

The y-intercepts of the five relationships were similar in the different years for Cogshall and José (data not shown), indicating that year had no significant effect on the relationships for these two cultivars. By contrast, a weak but significant effect of year was detected on y-intercept, mainly for relationships involving stem for Irwin and leaves for Kensington Pride. For Irwin, the 2004 y-intercepts of the relationships of stem mass and branch mass vs branch csa were higher than the 2005 and 2006 ones (Table 2). For Kensington Pride, the y-intercepts varied significantly among years in four of the five relationships: leaf area, leaf mass and branch mass vs branch csa, and leaf mass vs stem mass (Table 2). In each case, the 2006 y-intercept was higher than those for 2004 and 2005. A year effect was present for these two cultivars, but it was not the same in the sense that the year with the highest intercept was 2004 for Irwin and 2006 for Kensington Pride. This is addressed in the ‘Discussion’ section. Data for the different years were then pooled for each cultivar to compare allometric relationships between cultivars.

Table 2.  Effect of year on the standardized major axis (SMA) y-intercept of the five allometric relationships related to leaf and stem size of branches (current-year growth) of Irwin and Kensington Pride mango (Mangifera indica) cultivars
RelationshipIrwinKensington Pride
200420052006P200420052006P
  1. csa, cross-sectional area.

  2. Year did not affect the slope of the relationships and the common slope value is given. Sample sizes in 2004, 2005 and 2006 are, respectively, 15, 10, 10 for Irwin, and 13, 10, 10 for Kensington Pride. Relationships were loge– loge linearized before SMA analyses. Within the same line and for a given cultivar, y-intercept values followed by different letters are significantly different (post-hoc multiple comparison test).

Leaf area vs branch csa
 Common slope1.261.261.261.171.171.17
 y-intercept−3.15−3.29−3.090.15−2.90 b−2.95 b−2.53 a< 0.001
Leaf mass vs branch csa
 Common slope1.361.361.361.251.251.25
 y-intercept−3.02−3.20−3.150.13−2.81 b−2.90 b−2.50 a< 0.001
Stem mass vs branch csa
 Common slope1.721.721.721.661.661.66
 y-intercept−5.61 a−6.01 b−6.17 b< 0.001−5.27−5.55−5.340.26
Branch mass vs branch csa
 Common slope1.441.441.441.371.371.37
 y-intercept−3.06 a−3.29 b−3.25 b< 0.01−2.86 b−3.02 b−2.69 a< 0.01
Leaf mass vs stem mass
 Common slope0.810.810.810.750.750.75
 y-intercept1.401.541.730.061.17 b1.29 b1.53 a< 0.01

For all cultivars, no significant lateral shift along the common axis was detected among years.

Effect of cultivar on allometric relationships

The cultivars did not affect the slope of each relationship (Table 3). They were significantly greater than 1 for the variables regressed against branch csa. Stem mass vs branch csa had the highest slope (1.68) and leaf area vs branch csa had the lowest (1.22). The slope for the leaf mass vs stem mass relationship was significantly lower than 1 (0.76).

Table 3.  Effect of mango (Mangifera indica) cultivar on standardized major axis (SMA) parameters of the five allometric relationships related to leaf and stem size of branches (current-year growth)
RelationshipCogshallIrwinJoséKensington PrideCommon value (95% CI)P
  1. csa, cross-sectional area.

  2. Cogshall, n = 34; Irwin, n = 35; José, n = 30; Kensington Pride, n = 33. Relationships were loge– loge linearized before SMA analyses. Within the same line, values followed by different letters are significantly different (post-hoc multiple comparison test). When a parameter was not affected by cultivar, its estimated common value is given with its 95% confidence interval (CI).

Leaf area vs branch csa
 Slope1.171.271.191.221.22 (1.16;1.29)0.71
 y-intercept−2.77 a−3.01 b−2.87 ab−3.04 b< 0.001
 Lateral shift7.73 b7.19 b7.52 b9.09 a< 0.001
Leaf mass vs branch csa
 Slope1.231.371.251.271.30 (1.24;1.37)0.28
 y-intercept−2.60 a−2.86 bc−2.70 ab−3.01 c< 0.001
 Lateral shift8.59 b7.99 b8.37 b9.91 a< 0.001
Stem mass vs branch csa
 Slope1.571.751.831.691.68 (1.60;1.76)0.08
 y-intercept−5.39 b−5.71 c−5.08 a−5.47 bc< 0.001
 Lateral shift9.00 b8.25 b9.16 b11.15 a< 0.001
Branch mass vs branch csa
 Slope1.301.441.421.391.39 (1.33;1.46)0.34
 y-intercept−2.72 a−2.98 b−2.68 a−3.00 b< 0.001
 Lateral shift9.26 b8.64 b9.17 b10.83 a< 0.001
Leaf mass vs stem mass
 Slope0.780.780.680.760.76 (0.72; 0.80)0.27
 y-intercept1.63 a1.60 a1.29 b1.30 b< 0.001
 Lateral shift4.38 ab3.53 b4.36 ab5.61 a< 0.001

Cultivar had a significant effect on the y-intercept for the five relationships (Table 3, Fig. 2). Cogshall and José had generally higher y-intercepts than Irwin and Kensington Pride in the relationships between branch characteristics and branch csa. This indicated that for the same branch csa, the former two cultivars had higher leaf area, leaf mass, stem mass and branch mass than the latter two cultivars. For the leaf mass vs stem mass relationship, Cogshall and Irwin had a higher y-intercept than José and Kensington Pride, indicating that a given stem mass supported a larger leaf mass in Cogshall and Irwin than in José and Kensington Pride.

Figure 2.

Standardized major axis (SMA) lines for four mango (Mangifera indica) cultivars, Cogshall (Cog, closed circles, n = 34), Irwin (Irw, open squares, n = 35), José (Jos, open circles, n = 30) and Kensington Pride (KP, closed squares, n = 33), between leaf area and branch cross-sectional area (csa) (a), leaf mass and branch csa (b), stem mass and branch csa (c), branch mass and branch csa (d), and leaf mass and stem mass (e). Data are loge-transformed.

Lateral shifts along the common axis were detected for each relationship (Table 3). For the variables regressed against branch csa, Kensington Pride had significantly higher values along the common axis than the other cultivars. For the leaf mass vs stem mass relationship, Kensington Pride also had the highest lateral shift (5.61), but it was only significantly different from Irwin's (3.53).

Branch characteristics of mango cultivars

The branch characteristics, pooled over 3 yr, differed significantly among cultivars for all variables (Table 4). Kensington Pride branches were larger than the branches of the other cultivars for branch csa, number of GUs per branch and stem mass of individual GU, denoting the higher vigour of this cultivar. Mean branch csa of Kensington Pride was about twice that of the other cultivars, and the maximum number of GUs for this cultivar was double that of the others. Irwin had the smallest number of GUs per branch, probably because of its low branching density. Leaf, stem and branch dry matter contents were contrasted among cultivars, with highest values for José.

Table 4.  Branch (current-year growth) characteristics of the four mango (Mangifera indica) cultivars
VariablesUnitsCogshallIrwinJoséKensington PrideP
  1. csa, cross-sectional area; GU, growth unit; LMA, leaf mass per area.

  2. Data are measurements recorded during 3 yr (Cogshall, n = 34; Irwin, n = 35; José, n = 30; Kensington Pride, n = 33). Within the same line, means followed by different letters are significantly different (Tukey's test).

Branch csamm292.0 b81.2 b89.1 b189.3 a< 0.001
Branch dry matter content%40.2 ab37.6 b44.7 a41.3 ab< 0.001
Leaf : stem mass ratiog g−13.5 ab4.1 a2.6 bc2.1 c< 0.001
Mean nb of GUs3.12 ab2.11 b3.10 ab4.12 a< 0.05
[mini–maxi]  [1–8] [1–7] [1–8] [1–16] 
Stem mass of individual GUg2.84 b2.92 b4.14 b7.62 a< 0.001
Stem dry matter content%34.3 b29.9 c40.3 a35.9 b< 0.001
No. of leaves per GU12.3 b12.9 b13.8 ab15.7 a< 0.001
Individual leaf massg0.69 ab0.70 ab0.56 b0.74 a< 0.01
Leaf dry matter content%42.5 c40.5 d46.7 a45.0 b< 0.001
Individual leaf areadm20.41 a0.43 a0.33 b0.48 a< 0.001
Branch leaves areadm215.8 b11.4 b13.8 b31.8 a< 0.001
LMAg m−2167.8 a162.6 ab168.5 a154.1 b< 0.001

Irwin and Cogshall had large leaf : stem mass ratio. By contrast, this ratio was low for José and Kensington Pride, indicating that these latter cultivars tend to allocate biomass in stem rather than in leaves in current-year branches. The number of leaves per GU was the largest for Kensington Pride, but was not significantly different from José. The GUs of Cogshall had the lowest number of leaves. José leaves were the smallest on the basis of individual area and dry mass. However, this latter variable did not differ significantly from Cogshall and Irwin. Kensington Pride had the largest leaves, both on a dry mass and on an area basis. As a consequence of these results, Kensington Pride leaf area at the branch level was significantly larger (two times) than that of the other cultivars. LMA was the lowest for Kensington Pride, the highest for Cogshall and José, and intermediate for Irwin.

Stem hydraulic and mechanical traits of mango cultivars

The stem csa was not different among cultivars (Table 5), as GUs of similar basal diameter were chosen for this independent experiment. José had the largest stem density and Irwin the lowest, although this latter was not significantly different from Cogshall and Kensington Pride. Wood density was also significantly higher for José and lower for Irwin. Stem slenderness was significantly higher for José than for the other cultivars, indicating long and thin GUs for this cultivar. By contrast, Cogshall, and particularly Irwin, had low stem slenderness and short stems, denoting squatter GUs.

Table 5.  Hydraulic and mechanical traits of growth unit stems of the four mango (Mangifera indica) cultivars (n = 20)
VariablesUnitsCogshallIrwinJoséKensington PrideP
  1. csa, cross-sectional area; K, saturated hydraulic conductivity, KS and KL, specific and leaf-specific saturated hydraulic conductivity, respectively. Within a same line, means followed by different letters are significantly different (Tukey's test).

Stem csamm226.526.326.328.50.26
Stem lengthcm14.5 b13.2 b19.2 a18.1 a< 0.001
Stem slenderness28.7 bc24.4 c39.5 a32.6 b< 0.001
Stem densityg cm−30.45 b0.41 b0.53 a0.44 b< 0.001
Wood csamm212.5 b10.9 b11.0 b14.5 a< 0.001
Wood csa/stem csa%47.2 a41.5 b42.1 b50.6 a< 0.001
Wood densityg cm−30.36 bc0.35 c0.46 a0.39 b< 0.001
Kmmol m (s MPa)−12.35 a2.02 b0.66 d1.66 c< 0.001
KSmol (m s MPa)−1189.3 a180.3 a59.8 c113.1 b< 0.001
KLmmol (m s MPa)−166.6 a78.0 a27.8 b44.7 b< 0.001

Although stem csa did not vary among cultivars, wood csa was significantly larger in Kensington Pride than in the other cultivars (Table 5), in relation to differences in bark thickness. However, Kensington Pride and Cogshall had a significantly larger ratio of wood csa to stem csa than Irwin and José. K varied significantly among cultivars (Table 5). Cogshall had the highest value, followed by Irwin, Kensington Pride and José, whose K was particularly low compared with the other cultivars. KS and KL were significantly higher for Cogshall and Irwin than for Kensington Pride and José. These latter two cultivars had similar KL, and significantly different KS, José having the lowest values.

Correlations among functional traits, and between functional traits and y-intercepts

Specific (KS) and leaf-specific (KL) saturated hydraulic conductivities were highly correlated (Table 6). Stem density was significantly correlated with stem slenderness and wood density, but the correlations were weaker than the correlation between the latter two variables. As expected (third consideration for a priori hypotheses), mechanical traits were negatively correlated with hydraulic traits for these stems of similar csa. However, correlations between stem density and hydraulic traits were not significant and weaker than those between wood density or stem slenderness and hydraulic traits.

Table 6.  Pairwise Pearson coefficient of correlation between hydraulic and mechanical traits measured on growth unit stems of the four mango (Mangifera indica) cultivars (n = 4)
 KSKLStem densityWood density
  1. Bold text indicates a significant correlation.ns, P > 0.05; *, P < 0.05; **, P < 0.01.

KL0.96*   
Stem density−0.75 ns−0.83 ns  
Wood density0.95*0.95*0.91* 
Stem slenderness0.93*0.99**0.91*0.97*

The direction of the correlations between the y-intercepts of the allometric relationships and functional stem traits (Table 7) were as expected (Table 1). However, only three correlations were high and significant (Table 7, Fig. 3): the one between stem density and the y-intercept of the stem mass vs branch csa relationship, and the ones between KS, KL and the y-intercept of the leaf mass vs stem mass relationship. The correlations between functional traits and the y-intercepts of relationships involving leaf area or leaf mass were particularly weak. The y-intercept of the branch mass vs branch csa relationship was negatively correlated with KS and KL, probably as a result of the higher negative correlation of these traits with the y-intercept of the stem mass vs branch csa relationship rather than the poor positive correlation of these traits with the y-intercept of the leaf mass vs branch csa relationship.

Table 7.  Pairwise Pearson coefficient of correlation between the y-intercept of the five studied relationships and functional traits measured on growth unit stems of the four mango (Mangifera indica) cultivars (n = 4)
 y-intercept
Leaf area vs branch csaLeaf mass vs branch csaStem mass vs branch csaBranch mass vs branch csaLeaf mass vs stem mass
  1. KS and KL, specific and leaf-specific saturated hydraulic conductivities, respectively. Bold text indicates a significant correlation.

  2. ns, P > 0.05; *, P < 0.05.

KS0.15 ns0.15 ns−0.76 ns−0.26 ns0.94*
KL−0.03 ns0.03 ns−0.86 ns−0.39 ns0.93*
Stem density0.41 ns0.42 ns0.97*0.75 ns−0.64 ns
Figure 3.

Relationships between standardized major axis (SMA) y-intercept of the stem mass vs branch cross-sectional area (csa) relationship and stem density (a), between SMA y-intercept of the leaf mass vs stem mass relationship and specific (KS) (b) and leaf-specific (KL) (c) saturated hydraulic conductivities. Mango (Mangifera indica) cultivars: Cogshall (Cog), Irwin (Irw), José (Jos) and Kensington Pride (KP). Bars, 95% confidence interval for y-intercept, and standard error for stem density, KS and KL.

Discussion

Effect of year on allometric relationships

The effect of year on allometric relationships differed according to the cultivar. Differences were found on the y-intercept of different years for only two cultivars, Irwin and Kensington Pride. These differences concerned relationships involving stem size for Irwin, and leaf size for Kensington Pride. For each relationship, the year with the highest y-intercept was the same for a given cultivar: 2004 for Irwin and 2006 for Kensington Pride. The range of variation of y-intercept among years for Irwin and Kensington Pride was similar to the one among cultivars (Tables 2 and 3). These results suggested that the observed year effect was not an artefact.

Two likely causes for the year effect are tree ontogeny and environment. The year effect on y-intercept for Irwin and Kensington Pride did not look like ontogenetic variation, as there was no regular change over the years. Similarly, Brouat et al. (1998) did not find any ontogenetic variation on leaf–stem allometry of four species belonging to different families. On the other hand, the climate was quite stable over the years, as was confirmed by climatic records on the orchard (data not shown), in particular mean temperature and global solar radiation during the vegetative growth season (January to May). Rainfall was higher in 2005 (678 mm) than in 2004 and 2006 (348 and 415 mm, respectively) during the same season. Consequently, the lack of year effect on two out of four cultivars was not surprising. But our yearly data on branch characteristics did not allow us to propose a satisfactory explanation for Irwin and Kensington Pride.

We disregarded the year effect on these two cultivars by pooling data over the 3 yr. We did so with the assumption that, for Irwin and Kensington Pride, ‘normal’ years were the 2 yr with similar y-intercepts, and the ‘abnormal’ third year had a higher y-intercept. It tended, therefore, to increase the y-intercept of these two cultivars in the study of cultivar effect. In this study, Irwin and Kensington Pride had the lowest y-intercepts among cultivars in relationships where they were concerned by a year effect (Table 3). Therefore, the year effect on Irwin and Kensington Pride, although difficult to explain, did not alter the conclusions on the cultivar effect on allometric relationships.

Effect of mango cultivar on allometric relationships

Mango cultivars exhibited a large range of branch (current-year growth) size, which confirms the large variability between branches of individual plants noticed by Westoby & Wright (2003) and Shucun et al. (2006). Whereas other studies at species or community level averaged this variability, we showed that, within a large range of number of GUs per branch (one to 16), leaf size and stem size are allometrically, and not isometrically, related at the branch level for each cultivar. The large range of branch size may be related to branch location within the tree canopy, that is, to their exposure to environmental factors (light, wind), to their topology with more or less vigorous units, or to their time of growth. Indeed, vegetative growth is asynchronous on mango trees, and branches that appear late during the vegetative growth season have a lower probability to branch further and to be composed of more than one GU (unpublished results).

The largest slope values were found in the stem mass vs branch csa relationship (1.68) and branch mass vs branch csa relationship (1.39), probably in relation to secondary growth. As a branch develops, stem mass is not just the result of additional GUs, but also of secondary growth on the branch's older GUs.

The slopes of the relationship of leaf area and leaf mass vs branch csa were significantly greater than 1 (1.30 and 1.22 respectively; Table 3). A slope of 1 is predicted by hydraulic models assuming that area-based hydraulic capacity and demand are size-independent (Shinozaki et al., 1964; Farnsworth & Van Gardingen, 1995; Tyree & Zimmermann, 2002). This is observed, for example, on twigs just after primary growth (Brouat et al., 1998). Our observed slopes, larger than this predicted value, indicated that leaf area or mass and branch csa were size-dependent and that leaf area or mass increased more rapidly than branch csa. This suggested that area-based hydraulic capacity, which is only one aspect of the whole-plant hydraulic functioning, was not limiting in mango cultivars with respect to demand. The demand was then probably limited by other hydraulic properties of the whole plant, but also by biomechanical aspects in relation to the support of leaves, inflorescences and, in particular, fruits. The importance of these biomechanical aspects in the partitioning of biomass or in branch geometry has been recognized in angiosperms and in Picea sitchensis (Farnsworth & Van Gardingen, 1995; Taneda & Tateno, 2004). The hydraulic and biomechanical properties shaping the slopes of these relationships are probably species-specific, as cultivars shared similar slopes.

The slope of the leaf mass vs stem mass relationship was 0.76, not different from the theoretical 3/4 scaling exponent between leaf mass and stem mass at the plant level (Enquist & Niklas, 2002). This suggested that the general allometric model of global allocation rules for biomass partitioning in seed plants (Enquist & Niklas, 2002; Niklas & Enquist, 2002; Niklas, 2006) remains valid at a smaller scale, that is, at the level of mango cultivars’ current-year branch.

For each relationship, cultivar significantly affected the y-intercept and the lateral shift along the common axis. Kensington Pride always had a significantly larger lateral shift than the other cultivars, because of its higher vigour (Knight, 1997). Its current-year branches were larger, heavier and bore larger leaf area compared to those of the other cultivars (Table 4). Despite larger mean values for these variables, Kensington Pride followed the same relationships (common slopes) as that of the other cultivars, indicating common functional relationships between studied variables among these mango cultivars. Differences in y-intercept revealed differences in biomass allocation to branches and to their components, stem and leaves, among cultivars. For the same branch csa, more biomass was allocated to branches in José and Cogshall than in Irwin and Kensington Pride. Similarly, for a given stem mass, Cogshall and Irwin bore higher leaf mass than José and Kensington Pride, indicating that they allocated more biomass to leaves vs stem than José and Kensington Pride. This was corroborated by a higher leaf : stem mass ratio for these two cultivars (Table 4).

The four mango cultivars therefore had distinct behaviours with respect to two gradients: a gradient of biomass allocation to the branch for a given branch csa, and a gradient of biomass allocation to leaves and to stem within the branch. This is illustrated in Fig. 4, where leaf and stem masses were estimated for each cultivar from the allometric relationships for a 100 mm2 cross-sectional area branch. The graph shows the large variability among cultivars for leaf mass and stem mass allocated in a branch of a given csa. There was a factor of 1.5 in leaf mass between Kensington Pride and Cogshall, and a factor of 2 in stem mass between Irwin and José. All cultivars were well above the y = x line of equal distribution of biomass among leaves and stem, indicating that, for this branch csa, they allocated more biomass to leaves than to stem within branches. However, there were differences in this distribution. Cogshall and Irwin allocated about three times more biomass to leaves than to stem, whereas this ratio was c. 2 for José and Kensington Pride. Figure 4 also illustrates that Cogshall and José, located near the upper right-hand corner of the graph, allocated more biomass to branches than Irwin and Kensington Pride.

Figure 4.

Leaf dry mass and stem dry mass calculated for four mango (Mangifera indica) cultivars for a branch with a 100 mm2 basal cross-sectional area. Allometric relationships between leaf mass (stem mass) and branch cross-sectional area were used for this computation. Cultivars within the solid line ellipse allocate more biomass to leaves in relation to stem than those within the dotted line ellipse.

Relationship between stem functional traits and leaf–stem allometry

The present allometric study on mango showed different patterns of biomass allocation to and within the branch depending on the cultivar. Our hypothesis was that these differences were related to cultivar-specific functional traits linking stem and leaves: vascular supply and mechanical strength. Branch characteristics and hydraulic and mechanical stem traits varied widely among cultivars (Tables 4 and 5). In particular, specific and leaf-specific hydraulic conductivity varied strikingly. Their range of variation among cultivars was as wide as that among species from contrasting habitats within a genus (Cavender-Bares & Holbrook, 2001; Woodrum et al., 2003), or among species of different families (Vander Willigen et al., 2000; Jacobsen et al., 2007). On the other hand, KS and KL of coffee cultivars with contrasting crown architecture and shoot morphology are not very different (Tausend et al., 2000). Nevertheless, our results were not consistent with the hypothesis that KL is driven by environment and should be similar under the same environmental conditions (Vander Willigen et al., 2000). Stem density, related to mechanical strength, varied among cultivars, but not as much as hydraulic traits.

Correlations between hydraulic and mechanical stem traits showed that wood density, stem slenderness, KS and KL were closely correlated to one another, more than stem density was correlated to each of them. This suggested that wood density and stem slenderness were indicators of KS and KL. This was expected for wood density, but not for stem slenderness, which is a morphology parameter generally related to stem mechanical strength (Alméras et al., 2004).

Stem density integrates conductive and nonconductive tissues, in particular supporting tissues located in the cortex. This could explain that stem density was not highly correlated with KS and KL. It was therefore appropriate to retain this variable as a surrogate for stem mechanical strength. This result also suggested that there was no tradeoff between hydraulic and mechanical stem properties of these mango cultivars, in agreement with previous results (Woodrum et al., 2003; Jacobsen et al., 2007; Rosner et al., 2007).

The y-intercepts of only two allometric relationships were related to functional stem traits (Table 7). On the one hand, the stem mass allocated by a cultivar to a branch of a given csa depended on the stem density of the cultivar. Eqn 1 then became:

stem mass =γ(ρ)Bcsaβ, β >1(Eqn 3)

where γ(ρ) is a parameter which depends on stem density ρ, and Bcsa is branch csa.

On the other hand, the leaf mass of a branch with a given stem mass depended on stem hydraulic properties, probably in relation with water supply. Eqn 1 became then:

leaf mass =γ′(κ) (stem mass)β′, β′ <1(Eqn 4)

where γ′(κ) is a parameter which depends on KS or KL, symbolized by κ.

Combining Eqns 3 and 4 led to:

leaf mass = γ′(κ)γ(ρ)β′ Bcsaββ′, β > 1, β′ < 1(Eqn 5)

Equation 5 shows that allometric relationships between leaf mass, and the related variables leaf area and branch mass vs branch csa depended on both mechanical and hydraulic stem properties. The y-intercepts of the leaf area and leaf mass vs branch csa relationships were more correlated with stem density than with stem hydraulic properties, supporting the idea that stem mechanical strength was more important than hydraulic properties to shape the leaf size vs branch csa relationship (Farnsworth & Van Gardingen, 1995; Taneda & Tateno, 2004). The diversity of functional stem traits among mango cultivars and the rules of biomass allocation to and within the branch (Eqns 3 and 4) led to a wide pattern of biomass allocation to the branch and its components (Fig. 4), with probable consequences on plant architecture and global functioning.

Although this study should be extended to a larger number of cultivars to confirm these results, our conclusions were strengthened by the fact that correlations were computed between two independent datasets.

Strong allometric relationships can be viewed as constraints on the independent evolution of the related traits (Harvey & Pagel, 1991). Variation among taxa is then expected to be a lateral shift along a common axis, and not a variation in y-intercept, which would require more change in one trait than in the other. Preston & Ackerly (2003) showed, however, that the y-intercepts of leaf–stem allometry of congeneric species evolve easily, in association with the evolution of stem hydraulic capacity. Our results showed that very close, recently diverged, taxa as mango cultivars did not appear allometrically constrained as they displayed differences in y-intercepts. This suggested that leaf–stem allometry in mango cultivars might rather be viewed as lines of functional equivalence (Harvey & Pagel, 1991, Brouat et al., 1998), as assumed in this study, determined by mechanical and hydraulic stem traits. These functional traits resulted from adaptive processes specific to each cultivar (Tausend et al., 2000), possibly having to do with different centres of diversification of mango in contrasted eco-regions (Bompard & Schnell, 1997). The selection of the four cultivars did not follow long genetic improvement schemes, but rather was a selection among seedling trees, sometimes from unknown parents, driven by considerations on fruit quality and yield (Campbell, 1992; Knight, 1997; Vincenot, 2004). Therefore, the functional traits of these cultivars, and the related leaf–stem allometry, probably reflected the adaptation to the climatic conditions of the habitat where they, or their ancestors, have evolved. Further studies on the subject would help improve the ecological suitability of mango cultivars.

Acknowledgements

We thank Clarisse Magne and Armelle Renard for their helpful contribution to field work, and Philippe Cabeu for leaf area measurements. We also thank anonymous reviewers and Prof. David Ackerly for their helpful comments and suggestions. The authors acknowledge Alison Bissery for kindly editing the English in the manuscript.

Ancillary