Leaf size, which varies by several orders of magnitude among taxa, has numerous physiological (e.g., carbon assimilation rates and water budgets) and biomechanical implications (e.g., response to wind, gravity, and other mechanical stresses; Niklas, 1992; Ackerly et al., 2002; Olson et al., 2018). Due to hydraulic and biomechanical selective pressures coupled with leaf attachment requirements, small twigs cannot support large leaves (Shinozaki, 1964; Westoby et al., 2002). The observation that twig diameter increases with leaf size, referred to as Corner's rule of axial conformity (Corner, 1949), is well supported by data (White, 1983; Ackerly and Donoghue, 1998; Brouat et al., 1998; Cornelissen, 1999; Westoby and Wright, 2003; Fajardo et al., 2020). We investigated whether plants economize on these investments by constructing large-diameter twigs with thick cores of pith, a low density, and low cost tissue.

Pith has received relatively little attention from researchers and has even been portrayed as functionless (Jane et al., 1970). Despite frequent disregard, pith is recognized as valuable water-storage tissue in some stem-succulent species (Mauseth, 1993, 2004). For taxa with chloroplast-containing pith, such as species of Fraxinus and Populus, pith photosynthesis reportedly helps plants mitigate anaerobiosis in stem interiors (Pfanz et al., 2002). Pith is also an important food source for a wide range of animals from mountain gorillas (Elgart-Berry, 2004) to cerambycid beetles (Strauss, 1991) and harbors many species of fungi (Huse, 1981). Hollow piths of numerous species provide caulinary domatia for ants (Davidson and McKey, 1993; Brouat and McKey, 2001). Finally, before the advent of polystyrene foam and other modern materials, Sambucus pith was used by anatomists to hold samples for hand-sectioning, and Aeshynomene aspera pith served as the core material for tropical sun helmets.

Pith, a tissue of typically low density that is sometimes absent due to autolysis (Sachs, 1882), occupies the centers of woody stems where mechanical strains are minimal and rigidity and sturdiness are not structural requisites for stem stiffness. Instead, by displacing structural tissues (i.e., wood and bark) away from the neutral axis (e.g., Niklas, 1992), an investment in pith represents a metabolically inexpensive way to increase the second moment of area (I) of twigs. We therefore hypothesized that across species, the cross-sectional area of pith increases with leaf size.

MATERIALS AND METHODS

Leaf-bearing twigs from wild and cultivated trees and shrubs were collected in warm, temperate Gainesville, Florida, United States (29.65°N, 82.32°W) where mean annual precipitation is 1430 mm (Hoenstine and Lane, 1991). From each species (Appendix S1), we collected the first mature leaf (as determined by size, texture, and color) and the subtending internode from sun-lit twigs. Effort was placed on sampling a wide phylogenetic range of angiosperms; we sampled 81 species representing 75 genera and 51 families. Leaf areas were measured for an average of three leaves per species on a LI-COR 3100 Leaf Area Meter (LI-COR Inc., Lincoln, NE, USA). Twig traits (width of the pith, width of wood, width of bark; Appendix S2) were measured at the middle of the internode in free-hand sections using a dissecting microscope equipped with stage and ocular micrometers. For species with pith that is star-shaped (e.g., Quercus falcata), triangular (e.g., Ardisia crenata and Cinnamomum camphora), elliptical (e.g., Ficus elastica and F. altissima), or otherwise not circular in cross section, we calculated cross-sectional absolute areas using multiple measurements and the appropriate geometrical equation. To reveal how tissue dimensions likely affect twig biomechanical properties (e.g., resistance to bending), we expressed them as second moments of area (I; Appendix S3). To test for the hypothesized relationship between leaf and pith size, we used standardized major axis regression (SMA; Warton et al., 2006). Components of the allometric (log-log) equations were calculated using SMA methods with the sma function in the R package smatr version 3.4-8 (R Core Team, 2021; Warton et al., 2012). Because SMA methods do not work well in the presence of outliers, we used Huber's M estimator as suggested by Taskinen and Warton (2013), instead of least squares. Species with more than one individual sampled (to gauge within species variation) had their leaf areas, twig traits, and moments of areas averaged before type II regression was performed.

By measuring twigs just below the first mature leaf, we avoided the many changes in cross-sectional characteristics of twigs due to secondary growth. Twig dimensions and bark and wood thickness change rapidly with distance from the apical meristem and with twig age, but given our focus on a primary tissue, we sampled where primary tissues still dominate. Measurements of twig properties at the end of a year's growth or at a set distance from the apex and all of the leaves above those points provide other insights into the functional ecology of twigs such as the contributions of bark to twig rigidity (Rosell et al., 2013; Olson et al., 2018).

To account for character correlations that result from phylogenetic relationships, we also evaluated trait correlations using phylogenetic independent contrasts (Felsenstein, 1985; Garland et al., 1992). To construct a phylogenetic hypothesis for the sampled species with trait data, we first extracted data from the six-gene multiple sequence alignment of Smith et al. (2011) for taxa representing 79 of our 83 sampled species, and we extracted sequences from GenBank for an additional two sampled species. We performed maximum likelihood phylogenetic analysis on the 81-species alignment using RAxML-VI-HPC version 7.2.8 (Stamatakis, 2006) and made the branch lengths ultrametric using penalized likelihood, implemented in r8s version 1.71 (Sanderson, 2003). We ran all phylogenetic independent contrast analyses using the PDAP module in Mesquite (Midford et al., 2002; Maddison and Maddison, 2011) and ran an ordinary least squares linear regression through the origin for each pair of standardized contrasts (e.g., Garland et al., 1992). Details about tree construction and phylogenetic independent contrast methods are provided in the Supplementary Materials (Appendix S4). The multiple sequence alignment, tree, and character data used for the phylogenetic independent contrast analysis are placed in the Dryad Digital Repository (https://doi.org/10.5061/dryad.xksn02vgh [Larios Mendieta et al., 2021]).

RESULTS

For the 81 species included in this study (Appendix S1), cross-sectional areas of twigs ( = 38.5 mm², range: 1.3–240.1 mm²), bark ( = 11.7 mm², range: 0.6–62.5 mm²), wood ( = 12.1 mm², range: 0.3–95.2 mm²), and pith ( = 14.6 mm², range: 0.2–209.2 mm²) as well as leaf sizes ( = 150.5 cm², range: 1.6–872.9 cm²) all varied over several orders of magnitude. While twig characteristics were consistent within species, leaf size varied substantially both among and within species (Appendix S2). Twig characteristics are highly correlated positively with one another and leaf size (Table 1). The correlation coefficients were significantly different from zero for all twig characteristics and leaf size, a condition that is required for SMA regression (Legendre and Vignette, 1998). In keeping with Corner's rule of axial conformity, twig cross-sectional area increased with leaf size (R² = 0.60, P < 0.001, Figure 1A). As hypothesized, pith area increased with leaf area (R² = 0.53, P < 0.001; Figure 1B) as did the thickness of both wood (R² = 0.52, P < 0.001, Figure S1) and bark (R² = 0.48, P < 0.001, Appendix S5). Although pith diameter tends to increase with leaf size, Cnidoscolus chayamansa (pith: 4%, wood: 89%, bark: 7%) and Clusia rosea (pith: 17%, wood: 48%, bark: 35%) produced smaller pith area (relative to twig sizes) than predicted (Appendix S1).

Results from phylogenetic independent contrast analyses were consistent with the nonphylogenetic regressions for twig trait absolute areas, which indicate that the character correlations are not driven by phylogenetic relatedness. More specifically, when phylogenetic relationships are taken into account, positive correlations were maintained (Figure 2) between twig and leaf area (R² = 0.31, P < 0.001), pith and leaf area (R² = 0.41, P < 0.001), and wood and leaf area (R² = 0.09, P < 0.01), but not between bark and leaf area (R² < 0.01, P = 0.99). Decreased strength of the correlations may be due to unequal representation of taxa across the phylogeny. Also simplifying the interpretation of the data was the finding that pith areas in species with compound (mean pith area = 14.6 mm², N = 17) and simple leaves (mean pith area = 15.1 mm², N = 66) did not differ (t = 0.08, P = 0.93). See Appendix S6 for phylogenetic independent contrast values.

Second moments of area (I) were used to analyze each twig's traits as strain-bearing structures (Appendix S3). Twig resistance to bending or twisting varies with the product of I (measure of bending resistance due to geometry or shape) and Young's modulus (E; a measure of material stiffness) of the component tissues (i.e., EI; Niklas, 1992). Stresses due to bending or torsion are largest near twig peripheries and diminish to zero at their centers (Spatz and Niklas, 2013); even low E pith can contribute substantially to twig stiffness by its low tissue cost contributions to I. The observed log-log slope of 0.82 (Appendix S7) between pith and twig dimensions suggests that a 10-fold increase in pith cross-sectional area is accompanied by a 76% increase in twig size. Additionally, leaf area was correlated positively with all I-transformed traits (pith: R² = 0.56, P < 0.001; wood: R² = 0.58, P < 0.001; bark: R² = 0.58, P < 0.001; twig: R² = 0.61, P < 0.001; Figure 3). Similarly, tree stems with low-density wood reportedly meet their mechanical demands through increased diameter (Niklas, 1992; Rosell et al., 2012; Kempe et al., 2014).

DISCUSSION

Large leaves inserted on thick twigs that branch sparingly are often associated with rapid stem elongation (Olson et al., 2009). Stems that rapidly and economically elongate benefit from the production of twigs with low tissue densities (Lauri, 2019). Our data agree with this assertion insofar as twigs of many small-leaved species we sampled were thickened more by bark than wood or pith, whereas many of the large-leaved species are pith-rich. Of the species with the 10 thinnest twigs, eight had bark that contributed >50% of the twig cross-sectional area. This finding reflects that while the hydraulic conduction of xylem can be augmented (e.g., by increased vessel diameter and length) and pith can be virtually done without, inner bark functions require more consistent tissue investments. In contrast to species with small leaves, large-leaved species have twigs that are often thickened disproportionately by pith. In the 10 species with the thickest twigs, pith comprised >50% of the cross-sectional areas of 5. This result reveals how dynamic and diverse investments in twig biomass can be at the high end of the twig size–leaf size spectrum. Pith is a low-density tissue and thus a low investment alternative to wood or bark for twig thickening. Production of large-pithed twigs should also be associated with rapid stem growth rates but may have some long-term costs in terms of resistance to mechanical and other stresses (Briand et al., 1999). Among the sampled species, those with the largest piths are famously fast-growing, light-demanding, small-statured, and short-lived. These species included Carica pubescens (pith area = 209.2 mm², leaf area = 640.3 cm²), Cecropia peltata (pith area = 138.3 mm² and leaf area = 549.4 cm²), and Aralia spinosa (pith area = 36.3 mm² and leaf area = 720.5 cm²). The costs and benefits of providing symbiotic ants with caulinary domatia notwithstanding, the substantial biomechanical demands imposed by the extremely large leaves of Cecropia spp. are satisfied by production of thick twigs with hollow piths (Brouat and McKey, 2001).

Twig traits are associated with many plant life-history characteristics including growth rates, leaf display (especially the avoidance of self-shading), and responses to wind loading (Gartner, 2001). Although bark constitutes most of the cross-sectional area of most young twigs (Rosell et al., 2013) and contributes substantially to the stiffness of young twigs (Niklas, 1999), pith should be explicitly considered when evaluating resource allocation patterns and the consequences for leaf size. The observed positive correlation between bark and pith thickness suggests that the pith's effects on I and consequent contributions to the mechanical support of leaves should also be considered. While this study highlights the contributions of pith and twig characteristics to the second moments of area (I) of twigs, we did not consider material stiffness (E) of each respective tissue. Future research on stem mechanics should examine the contribution of pith, wood, and bark to Young's modulus (E) and overall flexural stiffness (EI), especially since the material stiffness of pith likely varies with tissue turgor, hydraulic conductance, cell number, and transverse area (Niklas, 1988). Additionally, future pith-related research might focus on pith shape and its contributions to the flexural stiffness of twigs and on how leaf–pith relationships relate to other characteristics such as susceptibility to crown damage, leaf lifespans, and hydraulic conductivity.

AUTHOR CONTRIBUTIONS

F.E.P. devised the project. K.A.L.M. collected plant samples and measured leaf areas, twig, bark, wood, and pith dimensions. J.G.B. conducted plant trait phylogenetic independent contrast analyses. K.A.L.M. wrote the initial draft. All authors contributed to data analysis, interpretation of results, literature review, and editing of the manuscript.