Leaf-stem allometry, hollow stems, and the evolution of caulinary domatia in myrmecophytes

Authors

  • C. Brouat,

    Corresponding author
    1. Centre d’Ecologie Fonctionnelle et Evolutive (UPR 9056), CNRS, 1919 route de Mende, 34293 Montpellier Cedex 5, France;
    • Author for correspondence: Carine Brouat Tel: +(33) 4 99 62 33 32 Fax: +(33) 4 99 62 33 45 Email:brouat@ensam.inra.fr

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  • D. McKey

    1. Centre d’Ecologie Fonctionnelle et Evolutive (UPR 9056), CNRS, 1919 route de Mende, 34293 Montpellier Cedex 5, France;
    2. Institut des Sciences de l’Evolution (UMR CNRS 5554), CC 065, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex, France
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Summary

  •  Leaf-stem size relationships over ontogeny were studied here in three different lineages of hollow-stemmed myrmecophytes in order to understand how a new stem function affects morphology.
  •  In each of six taxa, the primary cross-sectional area of a terminal internode and the area of the leaf borne by it were measured on plants representing all stages of ontogeny. Cross-sectional areas of both the cavity and the ring of wood were determined.
  •  The leaf-stem relationship over ontogeny was allometric, in contrast to the isometry previously found in solid-stemmed relatives. Stem cross-sectional area was initially larger relative to leaf area than for solid-stemmed species, increasing less than proportionally with increasing leaf size.
  •  Because mechanical stability requires a minimum ratio of t (thickness of the solid ring) to R (external radius of the cylinder), cross-sectional area of the ring of wood must vary with that of the cavity; both contributed to leaf-stem allometry. Relative to leaves, both are initially large and increase more slowly over ontogeny, suggesting that domatia are particularly costly for plants early in development.

Introduction

The focus of allometry is the relationship between dimensions of different traits of an organism. Two contrasting interpretations of allometric relationships can be discerned (Harvey & Pagel, 1991). Developmental correlations between different organs are sometimes viewed as being resistant to evolutionary change, potentially limiting the ability of each organ to evolve an independent response to sometimes divergent selection pressures (Primack, 1987; Midgley & Bond, 1989). However, allometric relations may themselves be the result of selection (Maynard Smith et al., 1985), defining a line of functional equivalence between dimensions of traits of an organism (Harvey & Pagel, 1991). The acquisition of a new function by an organ may thus change the relationship between dimensions of this organ and other organs of the organism: changes in function often imply changes in form.

Many important traits of plants vary in relation to the plant’s size and form (cf. Speck et al., 1990). Studies of plant biomechanics (Niklas, 1992, 1994, 1995), ecological strategies (King, 1991, 1998) and evolutionary design of reproductive structures (Primack, 1987; Midgley & Bond, 1989) have shown the interest of allometry in studies of plant evolutionary ecology. Here, we apply allometry to a plant trait not previously studied from this perspective, the caulinary domatia of myrmecophytes. In ant-plants with this type of domatia, which include representatives of over 65 genera of flowering plants (Davidson & McKey, 1993), stems have acquired a novel function: housing and protection of mutualistic symbiotic ants. Caulinary domatia are a key trait in the evolution of symbiotic ant-plant mutualisms (McKey, 1989, 1991; Fiala & Maschwitz, 1992; Davidson & McKey, 1993). If changes in function are associated with changes in form, how does acquisition by stems of this novel additional function affect their form in relation to other organs? In this study, we compare the relationship between leaf size and stem size over plant ontogeny in species possessing caulinary domatia (myrmecophytes) and in their solid-stemmed, nonmyrmecophytic relatives, in each of three lineages in which myrmecophytes have evolved independently. We address the following questions: What are the consequences of this novel function of stems for their size and form?; and How are these consequences expressed over plant ontogeny?

The relationship between the primary cross-sectional area of a stem (before secondary thickening) and surface area of the leaf borne by it was recognized almost 50 yr ago (Corner, 1949; Halléet al., 1978). However, White (1983a,b) was the first to examine this relationship in detail, in an interspecific comparison. In a previous study that extended White’s findings (Brouat et al., 1998), we reanalysed his data and showed that among species belonging to the same ecological group (White (1983a,b) compared gymnosperms, evergreen angiosperms and deciduous angiosperms of temperate North American forests), this relationship is isometric, that is the surface area of a terminal leaf is directly proportional to the primary cross-sectional area of the twig bearing it. In the same study, we reported for the first time data on this relationship over whole-plant ontogeny. To our knowledge, only one other study on the genus Acer (Ackerly & Donoghue, 1998) has tested the existence of such an ontogenetic relationship, but in that study the form of the relation was not described. For four tree species (two temperate, two tropical species), we showed the existence of an isometric ontogenetic progression in the leaf-stem relationship: as the tree develops, primary diameter (and thus cross-sectional area) of a terminal internode increases, and surface area at maturity of the leaf borne by it increases at the same rate. Size of the stem before secondary growth is determined by its functions, vascular supply and mechanical support for leaves and other appendages. Our finding of an isometric leaf-stem relationship is consistent with hypotheses supporting the ‘pipe model’ (Shinozaki et al., 1964). Abundantly described in forestry literature, this model predicts that the area of supported foliage will be proportional to the cross-sectional area of conducting tissues (typically sapwood, not heartwood (Niklas, 1992)). The ‘pipe model’ has been tested for angiosperm (Rogers & Hinckley, 1979) and gymnosperm (Waring et al., 1982) trees. It focuses on one function of stems – vascular supply. The isometric relationship we found between leaf area and the cross-sectional area of the stem bearing it over ontogeny is also consistent with theoretical expectations based on another function of stems, mechanical support (Niklas, 1992).

Among the four solid-stemmed species that we previously studied (Brouat et al., 1998), two of them (Macaranga gigantea (Euphorbiaceae) and Leonardoxa africana ssp. gracilicaulis (Leguminosae: Caesalpinioideae)) are congeners of myrmecophytic plants (Fiala et al., 1994; Gaume et al., 1997, 1998; McKey, 2000). Here we compare each of these with related myrmecophytes and add a third lineage, producing the first comparative analysis of the evolution of the key plant adaptation, domatia, in a class of mutualisms that is widespread and biologically diverse in tropical forest ecosystems (Davidson & McKey, 1993).

Materials and Methods

Species studied

We studied three taxonomic groups in which ant-plants with caulinary domatia have evolved independently. In each group, we studied a nonmyrmecophyte (NM) and a specialized myrmecophyte (SM). In two of the three groups we also studied a morphologically ‘transitional’ myrmecophyte (TM), so termed because such species possess fewer morphological specializations for ant symbiosis. It is important to note that use of the term ‘transitional’ does not necessarily imply an evolutionarily intermediate state; the term is used in a morphological and ecological sense (Federle et al., 1998; Fiala et al., 1999; Brouat & McKey, 2000).

As currently circumscribed, the genus Leonardoxa (Leguminosae, Caesalpinioideae) includes a single polytypic species of small to medium-sized understorey trees of central African rainforests from Gabon to Nigeria (McKey, 2000). In addition to the nonmyrmecophytic L. africana (Baill.) Aubrév. ssp. gracilicaulis McKey (‘L. africana T1’ (Chenuil & McKey, 1996; Brouat et al., 1998)), which possesses solid stems (Brouat et al., 1998), we studied two myrmecophytic subspecies. Leonardoxa africana ssp. africana McKey (‘L. africana T4’ (Chenuil & McKey, 1996)) is a highly specialized myrmecophyte (McKey, 1984; Gaume et al., 1997) with domatia appearing very early in seedling development (McKey, 2000). Leonardoxa africana ssp. rumpiensis McKey (‘L. africana T2’ (Chenuil & McKey, 1996)), with fewer specializations, is a morphologically ‘transitional’ myrmecophyte (Chenuil & McKey, 1996). Domatia appear later in ontogeny in this taxon than in the specialized myrmecophyte (McKey, 2000).

The second genus we studied was Macaranga (Euphorbiaceae), the world’s largest genus of pioneer trees (Whitmore, 1984; Fiala & Maschwitz, 1992). Like the nonmyrmecophytic Macaranga gigantea Muell. Arg., with solid stems (Brouat et al., 1998), the two myrmecophytic species we selected for study occur in Borneo. One is a specialized myrmecophytic species, M. hullettii King ex Hook. f. (Fiala et al., 1991), in which domatia appear early in ontogeny. The other, M. hosei King ex Hook f., is a ‘transitional’ myrmecophyte (Fiala et al., 1991; Fiala et al., 1994), with fewer morphological specializations. In this species, hollow internodes appear relatively late in ontogeny.

The third group studied included two neotropical Polygonaceae, Triplaris cumingiana Fisch. & Mey., a specialized myrmecophyte with hollow stems, and Coccoloba uvifera (L.) L., which is nonmyrmecophytic. The two genera belong to different subfamilies (Roberty & Vautier, 1964). Stems of C. uvifera are not solid, but the central part of the stem is filled with a broad expanse of pith. This pith sometimes disappears (by autolysis?), producing truly hollow stems. The study of Coccoloba permitted us to examine whether differences in the leaf-stem size relationship are due to particular pressures linked to myrmecophytism or instead reflect mechanical constraints common to different types of hollow-stemmed plants.

Modelling leaf-stem size correlations

In allometric analyses, the relation between two parts of an organism that are correlated in size can be 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 (Huxley, 1932). The term a, the slope of the relation, is the allometric coefficient or rate of divergence (Huxley, 1932). The value of the slope establishes whether the relation is isometric (a = 1, no change of form over ontogeny) or allometric (a ≈ 1). The value of the Y-intercept does not determine the form of the relationship (Harvey & Pagel, 1991).

Our measurement of leaf area was shown to be more precise and repeatable than measurement of the cross-sectional area of the internode. Leaf area was therefore chosen as the explicative X variable, and we used Model I regression (which assumes there is no error in estimating the X variable (Harvey & Pagel, 1991)) to estimate the parameters of the allometric equations. The dependent variable Y was the cross-sectional area of the internode. The use of Model I regression permits comparison of the different parameters (intercepts and slopes) across species, by an analysis of covariance (ANCOVA).

Collection of samples

Each sample consisted of a terminal internode of a twig and the single leaf borne by it, dried in a plant press. Because all samples are similarly affected, drying mature leaves and internodes (already lignified) does not affect the form of the leaf-stem relationship (Brouat et al., 1998).

Only fully expanded, recently matured leaves and internodes were selected. Diameter of the internode was thus its primary diameter, unaffected by secondary growth. For myrmecophytic taxa, the just-mature hollow internodes we sampled were mostly not yet occupied by ants. Each of our samples came from a different individual tree. Sampled trees (ranging from 36 to 106, depending on the taxon: Table 1) were chosen to include the largest possible range of size, and thus of age, of the individuals. For example, for Macarangahosei, the samples were collected from individuals ranging in height from seedlings 10 cm tall to adult trees 8 m tall. Among samples of each species, we took care to minimize variation in light, humidity, and other environmental conditions. Samples of Leonardoxa were collected in rainforest understorey in Cameroon (L. a. gracilicaulis: Mont Kala (3°51′ N; 11°31′ E) near Yaoundé, Central province; L. a. rumpiensis: Dikome Balué (4°50′ N; 9°06′ E), in the Rumpi Hills, South-West province; L. a. africana: Ebodie (2°34′ N; 9°50′ E), Southern province). Samples of Macaranga were collected in Brunei (Kuala Belalong Field Studies Centre (4°56′ N; 114°49′ E), Temburong district, and near Kampong Badas (4°34′ N; 114°25′ E), Belait district). Samples of Triplaris were collected from planted adults and volunteer seedlings and juveniles, at Fairchild Tropical Garden in Miami, and in the Kampong of the National Tropical Botanical Gardens, Coconut Grove, Florida (25°45′ N; 80°15′ W). Samples of Coccoloba were collected from natural populations near Miami and from individuals growing in the Native Tree Nursery in southern Dade County. All samples were conserved and dried in a plant press.

Table 1. Relationship between the cross-sectional area of the stem and the area of the leaf borne by it for myrmecophytes and their nonmyrmecophytic relatives
GenusSpeciesStage r 2 VariableEstimate F (est. = 1) P
  1. Stage 1, pre-domatia stage, young individuals; stage 2, individuals bearing hollow stems. Linear regressions on log-transformed variables. Slopes were tested for departure from 0 and 1. N, sample size.

Leonardoxa L. a. gracilicaulis (NM) N = 46 0.85Intercept−3.85 ± 0.12  
    slope 1.07 ± 0.06  1.040.31
  L. a. rumpiensis (TM) N = 46Stage 1 N = 140.7Intercept−3.36 ± 0.26  
    slope 0.87 ± 0.17  0.50.49
  Stage 2 N = 320.8Intercept−3.04 ± 0.15  
    slope 0.80 ± 0.07  7.940.008
  L. a. africana (SM) N = 82Stage 1 N = 90.2Intercept−3.01 ± 0.37  
    slope 0.50 ± 0.33  2.210.18
  Stage 2 N = 730.63Intercept−2.25 ± 0.08  
    slope 0.44 ± 0.04203.70.0001
Macaranga M. gigantea (NM) N = 36 0.85Intercept−3.51 ± 0.17  
    slope 0.99 ± 0.07  0.010.92
  M. hosei (TM) N = 106Stage 1 N = 610.80Intercept−3.04 ± 0.07  
    slope 0.74 ± 0.05 24.90.0001
  Stage 2 N = 450.82Intercept−2.31 ± 0.15  
    slope 0.76 ± 0.07  9.70.005
  M. hullettii (SM) N = 57Stage 1 N = 80.56Intercept−2.76 ± 0.21  
    slope 0.43 ± 0.15 13.50.010
  Stage 2 N = 490.61Intercept−2.58 ± 0.20  
    slope 0.71 ± 0.08 11.30.001
Coccoloba C. uvifera (NM) N = 105Stage 1 N = 540.58Intercept−2.23 ± 0.06  
    slope 0.43 ± 0.05129.60.0001
  Stage 2 N = 510.63Intercept−2.46 ± 0.16  
    slope 0.67 ± 0.07 19.70.0001
Triplaris T. cumingiana (SM) N = 67Stage 1 N = 370.85Intercept−3.33 ± 0.08  
    slope 0.87 ± 0.06  4.70.037
  Stage 2 N = 300.73Intercept−2.36 ± 0.18  
    slope 0.67 ± 0.08 17.50.0003

Measurements of leaves and internodes, and calculation of cross-sectional areas

The surface of each leaf sampled was measured using a scanner (Hewlett Packard ScanJet 4c, Les Ulis, France) and an image analysis software package specially adapted for leaf surface measurements (DtScan, Hewlett Packard). Surface was expressed in cm2.

For each sample, we noted if the internode was swollen or not. Using an electronic caliper, each internode was measured to the nearest 0.1 mm at its apex (just below the attachment of the measured leaf). We measured the section along its widest and its narrowest axis, and approximated the cross-section of the internode as an ellipse (Fig. 1, formula 1).

Figure 1.

Measurements of leaf area and the stem cross-sectional area used in this study. We measured the cross-section at the apex of a terminal internode (1) and the area of the mature leaf borne by it (2). Formula 1, y =π(a/2) (b/2); formula 2, y =π(a − 2t) (b − 2t)/4; formula 3, y =[πab −π(a − 2t) (b − 2t)]/4. R

To see if an eventual difference in the leaf-stem relationship between myrmecophytes and their nonmyrmecophytic relatives was explained by the size of the cavity of hollow stems, we also wanted to consider the ontogenetic relationships between leaf area and cross-sectional area of the hollow part of the stem, and between leaf area and cross-sectional area of the solid part of the stem. For all samples with hollow stems, we thus measured the thickness (t) of the ring of tissue around the cavity, at the apex of the twig. The mean value of this thickness (measured at the narrowest and at the widest points of an apical section of the internode) was then used to estimate the cross-sectional area of the hollow part of the stem (Fig. 1, formula 2) and of the solid part of the stem (Fig. 1, formula 3).

Statistical methods

All analyses were done using SAS (SAS, 1996), performing backwards selections (Stevens, 1992). To determine if the appearance of hollow twigs during ontogeny has an effect on the form of the leaf-stem relationship, we tested, performing ANCOVA, whether two statistically distinct groups of samples could be recognized: those without hollow internodes (seedlings and/or juveniles, depending on the species) and those with (larger individuals).

Results

Data on L. a. gracilicaulis and M. gigantea (Brouat et al., 1998) are included in tables and figures to facilitate understanding of the new results.

We first verified that, for each of the six newly considered taxa, the primary cross-sectional area of the terminal internode and the surface area of the leaf borne by this internode increased with size of the plant. These two characters exhibit an ontogenetic progression, as shown for example for two species, M. hosei and L. a. rumpiensis (Fig. 2). In each species, values of these two measures reach a maximum and then remain more or less constant.

Figure 2.

Progression of (a) surface area of a terminal leaf; (b) internode primary cross-sectional area, with tree height (m). Circles, Leonardoxa africana rumpiensis; diamonds, Macaranga hosei. Variables are log transformed. Each point characterizes one individual tree. For each relationship, P < 0.0001.

Effect of presence of the cavity on the leaf-stem relationship

For each hollow-stemmed species, there is an effect of the ontogenetic stage (young individuals without cavity/larger individuals with cavities) on the relationship between leaf area and twig cross-sectional area. The relationships for each stage are different only in their intercepts for L. a. rumpiensis (Fig. 3a: F1;45 = 10.9, P = 0.002), L. a. africana (Fig. 3b: F1;81 = 11.2, P = 0.001), M. hosei (Fig. 4a: F1;79 = 1063.9, P = 0.0001) and Triplaris (Fig. 5b: F1;66 = 19.1, P = 0.0001). Stages were different only in their slopes for M. hullettii (Fig. 4b: F1;56= 35.1, P = 0.0001) and the nonmyrmecophyte Coccoloba (Fig. 5a: F1;104 = 7.1, P = 0.009).

Figure 3.

Linear regression (bold lines) between the area of a leaf and the primary cross-sectional area of the twig bearing it for Leonardoxa species (a) Leonardoxa africana rumpiensis, transitional myrmecophyte, and (b) L. a. africana, specialized myrmecophyte. Closed circles, individuals with solid internodes; open circles, individuals with hollow internodes. The regression line (thin lines) for the nonmyrmecophyte L. a. gracilicaulis (Brouat et al., 1998) is also presented. The figure next to the arrow gives the twig cross-sectional area just before the onset of production of hollow stems. Variables are log transformed. Each point characterizes one individual tree, trees sampled to represent the entire range of leaf and stem size over plant ontogeny.

Figure 4.

Linear regression (bold lines) between the area of a leaf and the primary cross-sectional area of the twig bearing it for Macaranga species, (a) Macaranga hosei, transitional myrmecophyte repeated from Brouat & McKey (2001) for purposes of comparison, and (b) M. hullettii, specialized myrmecophyte. Closed diamonds, individuals with solid internodes; open diamonds, individuals with hollow internodes. The regression line (thin lines) for the nonmyrmecophyte M. gigantea (Brouat et al., 1998) is also presented. The figure next to the arrow gives the twig cross-sectional area just before the onset of production of hollow stems. Variables are log transformed. Each point characterizes one individual tree, trees sampled to represent the entire range of leaf and stem size over plant ontogeny.

Figure 5.

Linear regression (bold lines) between the area of a leaf and the primary cross-sectional area of the twig bearing it for Polygonaceae species (a) Coccoloba, nonmyrmecophyte with hollow stems, and (b) Triplaris, specialized myrmecophyte. Closed squares, individuals with solid internodes; open squares, individuals with hollow internodes. The figure next to the arrow gives the twig cross-sectional area just before the onset of production of hollow stems. Variables are log transformed. Each point characterizes one individual tree.

Relationship between leaf area and cross-sectional area of the twig bearing it

In nonmyrmecophytic trees, slope of this relationship over ontogeny is not significantly different from one, and does not change over ontogeny (Brouat et al., 1998). Related myrmecophytic species present contrasts to these results.

Leonardoxa species

In the predomatia stage of L. a. rumpiensis, the slope of the relationship was not significantly different from one (Table 1). For L. a. africana, the small number of seedlings sampled before appearance of domatia was not sufficient to allow estimation of the relationship. After the appearance of domatia, there was negative allometry between the area of the leaf and the cross-sectional area of the twig in each of the two myrmecophytes (Table 1): during ontogeny, twig cross-sectional area was large relative to leaf area for small plants, and then increased relatively little as leaf area increased. The leaf–stem relationships differed significantly in slopes and intercepts between L. a. gracilicaulis and the second stage of each of the two myrmecophytes, L. a. rumpiensis and L. a. africana (Table 2). The relationships concerning the second stages of the two myrmecophytes also differed from each other in slopes and intercepts (Table 2). In the specialized myrmecophyte L. a. africana, the intercept was higher and the slope more different from isometry than in the transitional myrmecophyte L. a. rumpiensis.

Table 2. Comparison of leaf-stem relationships obtained for myrmecophytes and their non-myrmecophytic relatives
TaxonComparisonStageVariable F P
  1. Stage 1, pre-domatia stage, young individuals without hollow stems; stage 2, individuals bearing hollow stems. Results of backward selections from a general linear model on log-transformed variables.

Leonardoxa L. a. gracilicaulis (NM)/L. a. rumpiensis (TM)Stage 1slope  0.70.42
   intercept 13.90.0004
  Stage 2slope  5.80.018
   intercept 12.30.0008
  L. a. rumpiensis (TM)/L. a. africana (SM)Stage 1slope  0.880.36
   intercept  0.330.57
  Stage 2slope 24.90.0001
   intercept 24.60.0001
  L. a. africana (SM)/L. a. gracilicaulis (NM)Stage 1slope  1.70.20
   intercept  8.00.006
  Stage 2slope 70.70.0001
   intercept117.40.0001
Macaranga M. gigantea (NM)/M. hosei (TM)Stage 1slope  7.60.007
   intercept  7.70.006
  Stage 2slope  1.20.263
   intercept  8.10.006
  M. gigantea (NM)/M. hullettii (SM)Stage 1slope  0.510.481
   intercept  2.90.095
  Stage 2slope  5.20.025
   intercept 10.30.001
  M. hosei (TM)/M. hulletii (SM)Stage 1slope  8.010.006
   intercept  1.40.244
  Stage 2slope  0.110.739
   intercept 75.30.0001
Polygonaceae Coccoloba (NM)/Triplaris (SM)Stage 1slope 31.30.0001
   intercept135.10.0001
  Stage 2slope  0.0010.97
   intercept 17.10.0001

Macaranga species

For M. hosei and M. hullettii, the slopes of the leaf-stem relationships were allometric in each of the two stages (Table 1 and Fig. 4). However, it is important to note that in the second stage of M. hullettii, the relationship seems better described by a quadratic equation, individuals with the largest leaf size having larger stems than given by our linear regression (Fig. 4b). Intercepts and slopes were significantly different between M. gigantea and the second stage of the specialized myrmecophyte, M. hullettii (Table 2). The relationships concerning M. gigantea and the second stage of M. hosei differed significantly only in their intercepts (Table 2). For second stages of M. hosei and M. hullettii, only the intercepts are significantly different between these two species.

Polygonaceae species

For the nonmyrmecophytic but hollow-stemmed Coccoloba, the slopes of the leaf-stem relationships were allometric in each of the two stages (Table 1 and Fig. 5a), in contrast to the nonmyrmecophytic species in the two other lineages studied. For Triplaris, the myrmecophyte, the relationship between surface area of a leaf and cross-sectional area of the internode bearing it was also negatively allometric (Table 1 and Fig. 5b) in each of the two stages. When comparing second stages of Coccoloba and Triplaris, only the intercepts were significantly different (Table 2), the intercept for Coccoloba being lower.

To summarize, the relationship between the area of the leaf and the cross-sectional area of the twig is allometric for hollow-stemmed species, and the allometry is stronger for specialized myrmecophytes than for transitional ones and hollow-stemmed nonmyrmecophytes.

Relationship between leaf area and cross-sectional area of the hollow/solid part of the stem for hollow-stemmed species

For L. a. rumpiensis, L. a. africana, M. hullettii, Coccoloba and Triplaris (Table 3), the cross-sectional area of the hollow part of the stem, and the cross-sectional area of the ring of tissue around the cavity, both increase allometrically with the surface of the leaf over ontogeny (Fig. 6). For M. hosei (Table 3), a transitional myrmecophyte, the relationship between leaf area and cross-sectional area of the cavity is isometric, and the relationship between leaf area and cross-sectional area of the ring of tissue around the cavity is only marginally allometric.

Table 3. Relationship between leaf area and cross-sectional area of the solid (ring of tissue)/hollow (cavity) part of the stem bearing it for hollow-stemmed plants
GenusSpeciesPart of the stem r 2 VariableEstimate F (est. = 1) P
  1. Linear regressions on log-transformed variables. Slopes were tested for departure from 0 and 1. N, sample size.

Leonardoxa L. a. rumpiensis (TM) N = 32Cavity0.7Intercept−3.22 ± 0.20  
    slope 0.75 ± 0.09 7.080.01
        
  Ring of tissue0.82Intercept−3.43 ± 0.16  
    slope 0.83 ± 0.07 4.960.03
  L. a. africana (SM) N = 73Cavity0.6Intercept−2.53 ± 0.14  
    slope 0.45 ± 0.0768.40.0001
  Ring of tissue0.61Intercept−2.82 ± 0.15  
    slope 0.55 ± 0.0736.70.0001
Macaranga M. hosei (TM) N = 40Cavity0.61Intercept−2.79 ± 0.22  
    slope 0.86 ± 0.11 1.680.2
  Ring of tissue0.71Intercept−3.11 ± 0.18  
    slope 0.82 ± 0.08 4.00.053
  M. hullettii (SM) N = 48Cavity0.55Intercept−2.80 ± 0.23  
    slope 0.75 ± 0.10 6.510.014
  Ring of tissue0.63Intercept−3.09 ± 0.19  
    slope 0.71 ± 0.0812.30.001
Coccoloba C. uvifera (NM) N = 50Cavity0.50Intercept−3.13 ± 0.25  
    slope 0.77 ± 0.11 4.040.05
  Ring of tissue0.59Intercept−2.57 ± 0.17  
    slope 0.62 ± 0.0724.60.0001
Triplaris T. cumingiana (SM) N = 30Cavity0.64Intercept−2.40 ± 0.19  
    slope 0.60 ± 0.0822.70.0001
  Ring of tissue0.75Intercept−3.08 ± 0.19  
    slope 0.80 ± 0.08 5.30.029
Figure 6.

Relationships between area of a leaf and cross-sectional area of the solid part of the internode bearing it (closed circles), and between area of a leaf and cross-sectional area of the cavity of the internode bearing it (open circles), for each of the six hollow-stemmed species studied. Variables are log transformed. Each point characterizes one individual tree.

For each myrmecophyte, we note that the intercept of the relationship between leaf area and cross-sectional area of the cavity is always greater than the intercept of the relationship between leaf area and cross-sectional area of the ring of tissue around the cavity. It is the contrary for C. uvifera, a nonmyrmecophytic tree with hollow stems.

Discussion

For M. gigantea and L. a. gracilicaulis, nonmyrmecophytic species with solid stems, the leaf-stem size relationship was isometric (Brouat et al., 1998). In contrast to these results, for all myrmecophytes considered here (five taxa belonging to three families), the Y-intercept was greater than for nonmyrmecophytic species, and the leaf-stem relationship was negatively allometric. This means that early in development of a plant, the stem primary cross-sectional area is larger relative to leaf area and then increases relatively little with further increase in the size of the leaf borne by newly matured internodes. The earlier the onset of swollen twigs in plant ontogeny, the slower the rate of further increase of twig cross-sectional area over ontogeny.

Why is the leaf-stem size relationship over ontogeny allometric for myrmecophytic plants?

For myrmecophytic plants, two complementary hypotheses could explain the allometric form of the leaf-stem size relationship. First, at the beginning of their ontogeny, myrmecophytic plants have few caulinary domatia. Small mutualistic ant colonies that inhabit these domatia are thus more vulnerable to predators such as insectivorous birds or monkeys that open domatia to eat ants (McKey, 1974; Freese, 1976; Federle et al., 1999). To protect their mutualists from predation, juvenile hosts may require relatively thicker stems, with a thicker ring of tissue around the domatia. At older stages, domatia and mutualistic ants being more numerous, predation would have a weaker impact on the mutualists. Costly investment in additional tissues around the cavity would be unnecessary for these larger plants. At older stages, the stem cross-sectional area would thus be smaller in proportion to leaf size than at juvenile stages, leading to an allometric leaf-stem size relationship over ontogeny.

A second hypothesis is based on the fact that there is a minimum diameter (varying with the ant species) below which a cavity cannot be inhabited (Moog et al., 1998). Presence of a relatively large cavity (or thick pith, easily excavated by some mutualistic ants to create a cavity (Agosti et al., 1999)) is thus a prerequisite for the establishment of a mutualistic relationship. Field observations suggest that cavities of very young individuals of specialized Macaranga and Leonardoxa myrmecophytes are often colonized by founding queens. In myrmecophytes, selective pressures acting on domatia could have favoured cavities for protective ants that were of habitable size at seedling stages and then increased relatively little in size over ontogeny. The form of leaf-stem size relationships observed in myrmecophytic species could thus reflect the allometric relationships between leaf size and cavity size.

However, this hypothesis is not sufficient to explain our results, because the relationship between leaf size and the cross-sectional area of the solid part of the stem is also allometric. Moreover, the allometric form of the leaf-stem size relationship is not restricted to myrmecophytes. Coccoloba, a hollow-stemmed nonmyrmecophyte, also presents an allometric relationship over ontogeny between leaf surface area and stem primary cross-sectional area, in contrast to other (solid-stemmed) nonmyrmecophytic species examined in our previous study (Brouat et al., 1998). Aside from Coccoloba, we were unable to obtain for our study any other woody nonmyrmecophytic angiosperm with hollow stems. Despite this, our results suggest that the form (isometric or allometric) of the leaf-stem relationship could be associated with the structure (solid or hollow) of stems, regardless of whether plants are myrmecophytes.

Why do hollow-stemmed plants show ontogenetic allometry in leaf-stem size relationships – presence of a cavity, changes in the cross-sectional area of wood, or both?

The first of the two hypotheses presented above implies that leaf-stem allometry in these hollow-stemmed plants is due to the ring of woody tissue around the cavity, while the second implies that allometry is due to the central cavity. Which of these components of hollow stems are responsible for allometry?

The size of the stem before secondary growth is supposed to be determined by its functions, vascular supply and mechanical support for leaves and other appendages. Vascular supply should not depend on the form of the stem (hollow or solid), as long as the cross-sectional area of individual conducting elements and the total cross-sectional area of conducting tissues remain constant. For hollow-stemmed species, conducting tissues are organized in a ring that circles the cavity. One hypothesis to explain leaf-stem size allometry for hollow-stemmed species is based on the ‘pipe model’ (Shinozaki et al., 1964), in which the cross-sectional area of conducting tissues is expected to be proportional to the area of supported foliage. Based on this model, the cross-sectional area of the ring of tissue around the cavity would be proportional to the surface area of the supported leaf, over the ontogeny of a hollow-stemmed plant. Here, allometry over ontogeny in hollow-stemmed plants would result if size of the central cavity varies little over a large range of leaf size. Our data (Fig. 6, Table 3) show that while size of the central cavity is not invariant, it does vary less than proportionally with leaf size: the relationship is allometric.

However, our results show that cross-sectional area of the solid part of the stem also increases less than proportionally with leaf size over ontogeny: this relationship is also allometric (Fig. 6, Table 3). The solid part of the stem and the cavity both contribute to allometry in the leaf-stem relationship, and the hypothesis that allometry is simply due to the presence of a cavity of invariant or weakly varying size is thus falsified.

Why does the cross-sectional area of the solid part of the stem increase at a rate different from that of the leaf area? While vascular supply to leaves may be independent of the form of the stem, increasing in isometric proportion with leaf area over ontogeny, mechanical properties of the stem change depending on whether it is hollow or solid (Niklas, 1992). Hollow stems are more likely to break (brazier buckling (Spatz et al., 1990; Niklas, 1992)) – because of the supported weight or environmental stresses such as wind – than solid ones (Mattheck et al., 1994; Spatz & Speck, 1994). Using engineering mechanics, it is easy to show that the principal determinant of the failure of hollow tubes subjected to various types of stresses is the ratio between the thickness of the wall of the tube (t) and the external radius of its cross-section (R) (Spatz et al., 1990; Niklas, 1992; Mattheck et al., 1994). Below a critical value of this ratio, failure is much more likely to occur. The requirement to maintain a minimum value of the t : R ratio may introduce size-dependence into leaf-stem relationships for hollow-stemmed species. For solid stems, the cross-sectional area required to support and supply a leaf is a function of surface area and mass of the leaf. The size ratio of the two organs should thus be independent of size (isometry). For a hollow stem, however, the requirement for the cross-sectional area of wood could be set not only by dimensions of the leaf it supports and supplies, but also by the cross-sectional area of the internal cavity. In a hollow stem with a given cavity size (Fig. 7), the cross-sectional area of tissues needed to supply and support a big leaf will probably already be enough to satisfy the critical t : R ratio. By contrast, the smaller the leaf, the more additional tissues to those necessary for supporting and supplying the leaf will be needed to satisfy the critical t : R ratio. Because they do not contribute directly to energy production, supporting tissues are considered to be costly for the plant (Givnish, 1982; Rich et al., 1986). Selection should thus favour formation of sufficient stem tissue to perform these functions, but not more. Under this hypothesis, a young plant, with small leaves, is more likely to require an investment in additional supporting tissues than is an older plant with bigger leaves. If the cross-sectional area of the internal cavity increases over ontogeny at a rate different from that of surface area and mass of a leaf, then the optimal ratio between stem and leaf dimensions will be size-dependent, resulting in allometry. This hypothesis of a cost of hollow stems that varies over ontogeny could explain leaf-stem size allometry in hollow-stemmed plants. However, we present it very tentatively. In this study, we have not considered variation in mechanical and physical properties of the various tissues that compose stems (Wainwright et al., 1976; Kull et al., 1992; Speck, 1992; Niklas, 1993), or in other stem traits such as stem length, internodal distance, or presence of septa at intervals in hollow stems (Spatz et al., 1990). Such details are crucial for understanding biomechanical properties of stems. Subsequent biomechanical and histological studies are thus needed.

Figure 7.

Why hollow stems can be more costly for young plants with small leaves than for older plants with bigger leaves. Graphical representation for a given and constant cavity size. The cross-hatched portion of the drawing represents the cross-sectional surface of vascular tissue needed to supply the leaf. This area increases isometrically with leaf size. Cavity size is represented as constant to simplify the argument. However, the same point holds as long as cavity size increases less than proportionally to leaf size over whole-plant ontogeny, as we found in our sample (see Appendix 1 for details).

As a first test of the hypothesis that the cost of hollow stems varies over ontogeny because t : R must be held above some critical value, we present analytical considerations (Appendix 1) on the form of the relationship between the leaf area and the cross-sectional area of the solid part of the internode bearing the leaf, assuming that t : R is held constant over whole-plant ontogeny. We also assume that the relationship between leaf area and the cross-sectional area of the cavity is allometric, as suggested by our data (Table 3). Under these hypotheses, we show that the relationship between the leaf size and the cross-sectional area of the solid part of the internode bearing the leaf is allometric, with a slope equal to that of the corresponding relationship concerning the cross-sectional area of the cavity. Values of intercepts calculated for three of our species (Appendix 1) based on these assumptions show good correspondence with intercepts reported in Table 2, for t : R ratios near those reported in the literature (t : R near 0.2; Niklas, 1992; Mattheck et al., 1994). Our measurements allow us to calculate t : R ratios for each hollow-stemmed individual of the different taxa we studied (Fig. 8). Although variable for each taxon, the t : R ratio appears not to vary with leaf size or whole-plant ontogeny. Moreover, for the relationship between the leaf area and the cross-sectional area of the ring of tissue, the calculated intercepts that are closest to those found by measurement (Appendix 1, in boldface) correspond in each case to a t : R-value that is similar to the measured mean t : R (Appendix 1, Fig. 8). These analyses support our hypothesis that selection to maintain a critical minimum t : R ratio introduces size-dependency in the cost of constructing hollow stems.

Figure 8.

Relationships between the t : R ratio of each internode measured and the surface area of the corresponding leaf, for each of the six hollow-stemmed taxa studied. In no case did the ratio show a trend to vary with the area of the associated leaf (which reflects whole-plant ontogeny).

Consequences for the evolution of ant-plant mutualisms

The relationship between stem and leaf size affects the cost to the plant of woody tissues that support the plant’s photosynthetic surfaces (White, 1983a). If optimal dimensions of hollow twigs relative to leaves do vary over the development of the plant, as we speculate, then costs of producing domatia may be different at different points in ontogeny. Domatia would be more costly for seedlings and juveniles with small leaves than for plants at later stages of ontogeny, and the larger the cavity in these small plants, the greater the cost. Examining this question may help explain the observed variation among myrmecophytes in the timing of onset of production of domatia during ontogeny (McKey, 1991; Fiala & Maschwitz, 1992; Brouat & McKey, 2000). For example, among the species we studied, M. hosei and L. a. rumpiensis develop domatia relatively late in their ontogeny, in comparison with related specialized myrmecophytes, which already develop domatia as young as seedlings (10 cm high (Brouat & McKey, 2000)). For L. a. rumpiensis, domatia first appear on individuals taller than 50 cm. For M. hosei, depending on the individual, domatia appear at tree heights between 50 cm and 90 cm. The mean size of the initial cavity (Ci) is always larger in specialized myrmecophytes than in related transitional myrmecophytes (L. a. africana: Ci, 0.017 cm2 vs L. a. rumpiensis; Ci, 0.013 cm2; M. hullettii; Ci, 0.041 cm2 vs M. hosei; Ci, 0.033 cm2) as we calculated for the five smallest individuals bearing domatia of each taxon. Furthermore, the leaf-stem relationship is only slightly allometric for the two transitional myrmecophytic species. The Y-intercept is greater than for nonmyrmecophytic species, but smaller than for specialized myrmecophytes. Transitional species seem thus at an intermediate state between myrmecophytic and nonmyrmecophytic species for leaf-stem size relationships. According to the hypothesis that the cost of producing hollow stems is size-dependent, hollow stems of transitional myrmecophytes, appearing relatively late in ontogeny with a smaller cavity, would be less costly for the plant than hollow stems of specialized myrmecophytes (Brouat & McKey, 2000). At this stage of ontogeny, little additional tissue is needed to support the cavity, and the leaf-stem size relationship is thus nearer isometry. The presence of large domatia very early in ontogeny in specialized myrmecophytes may thus reflect the action of strong selective pressures, such as herbivory, on juvenile trees. As these plants are associated with specialized, host-specific ants that provide better protection than do generalists (McKey, 1984; Fiala et al., 1994; Gaume et al., 1997), the costs of producing domatia very early in ontogeny may be compensated by greater benefits of ant protection (Brouat & McKey, 2000). Our study of leaf-stem size relationships completes other observations in both Leonardoxa (McKey, 1991, 2000) and Macaranga (Fiala et al., 1994): a number of characters related to ants and not just the domatia-appear to be less specialized, or intermediate, in ‘transitional’ myrmecophytes.

It is interesting to note that Coccoloba, the sole nonmyrmecophytic species with hollow stems studied, is also the sole species in which the intercept of the relationship between leaf area and cross-sectional area of the ring of tissue around the cavity is greater than the intercept of the corresponding relationship concerning cross-sectional area of the cavity. Myrmecophytic species seem thus to have larger cavities relative to the solid part of the stem than do nonmyrmecophytic species with hollow stems. This could reflect the influence of selective pressures acting on domatia for larger habitable volume for protective ants.

Leaf-stem size correlations: developmental constraint or the product of selection?

Our results allow us to choose between two competing interpretations of allometric relationships, as developmental constraints or as lines of functional equivalence that are products of selection. When stem morphology is subjected to selection acting on a new function, such as providing nest sites for ants in hollow stems and mechanical protection of these mutualists, or when hollow stems are advantageous because this morphology allows more rapid extension growth (Niklas, 1992), the leaf-stem size relationship over ontogeny is modified. The leaf-stem relationship thus appears not to be a constraint, but rather a line of functional equivalence. The appropriate size ratio is modified by changes in function of stems, and the allometric relationship is responsive to this new selective pressure.

Conclusions

Over ontogeny, the primary cross-sectional area of a terminal internode and the surface area of the leaf borne by it increase in isometric proportion, when the functions of the twig are limited to vascular supply and biomechanical support of the leaf. Our data show that when a new selection pressure acts on twigs, for example to provide shelter for symbiotic ants, the leaf-stem size relationship is modified, and becomes allometric.

Despite the need for more studies on nonmyrmecophytic hollow-stemmed plants, our results suggest that the allometry of the leaf-stem size relationship could be general for all hollow-stemmed plants, whether myrmecophytic or not. Several hypotheses could explain our results, based on the roles of stems in relation to the leaves they support. Comparative histological and biomechanical studies on hollow- and solid-stemmed plants are now necessary to better understand the allometry decribed here and its evolutionary implications.

Acknowledgements

We thank the Ministry of Research and Higher Education of the Republic of Cameroon for permission to carry out research in Cameroon. Universiti Brunei Darussalam provided logistical support in Brunei. The research was funded by a grant from the French government (CNRS program ‘Environnement, Vie, Sociétés’) in Cameroon and by a Brunei Shell Environmental Studies Fellowship in Brunei. We thank for help in collection of samples Bruno DiGiusto, Edmond Dounias, Laurence Gaume, and Alain Ngomi in Cameroon; Peter Becker, Colin Maycock, Muja Ngambat, and Sariwan Anak Dom in Brunei; Martine Hossaert-McKey and Didier Vernet (of the CEFE), Chuck Hubbuch and Benoit Jonckheere (both of Fairchild Tropical Garden), Larry Schokman (of the Kampong of the National Tropical Botanical Gardens), Roger Hammer (manager of Protected Areas, Dade County), and Rob Campbell and Hugh Forthman (Native Tree Nursery) in Florida. Peter Becker, Stuart Davies, Laurence Gaume, Martine Hossaert-McKey, Emmanuelle Jousselin, Finn Kjellberg and Nick Rowe are acknowledged for their helpful comments on various drafts of the manuscript. Jean-Dominique Lebreton gave advice on statistical analysis. Comments by Katherine Preston (Stanford University) and by an anonymous reviewer improved the final version.

Appendix

Appendix 1

The form of the allometric relationship between leaf area (Lx) and the cross-sectional area of the solid part of the internode bearing the leaf (Wx), when t : r is constant.

We Suppose that cross-sections of the entire internode (radius: Rx) and of the cavity (radius: dx) are circular, so that the area of each can be assimilated to that of a disk. We also assume that the relationship between leaf area and the cross-sectional area of the cavity of the internode (Dx) is allometric, as observed for the six species we studied. Thus,

image(Eqn 1)

(tx, the thickness of the ring of tissue around the cavity; Rx, tx + dx.) Assume that tx : Rx, k, with k, constant, then:

image(Eqn 2)

(Wx, πRx2 − πdx2.) From Eqn 1 and Eqn 2, we can say that:

inline image

inline image

Conclusions

The slope of the relationship between leaf area and cross-sectional area of the solid part of the stem is the same as that of the relationship between leaf area and the cross-sectional area of the cavity. Knowing the t : R ratio and the intercept of one relationship (e.g. leaf area and cross-sectional area of the cavity), the intercept of the other relationship (e.g. leaf area and cross-sectional area of the solid part) can be calculated.

Numerical example

Calculation of the intercept of the relationship between Lx and Wx, for three k (= t : R), and comparison with the value (M) obtained with measurements.

TaxonLog ak = 0.1k = 0.2k = 0.3M
L. a. rumpiensis −3.22−3.843.47−3.20−3.43
M. hosei −2.79−3.423.04−2.77−3.11
Coccoloba −3.13−3.76−3.37−3.12−2.57

Ancillary