, Volume 26, Issue 2, pp 421–433

Vertical and radial profiles in tracheid characteristics along the trunk of Douglas-fir trees with implications for water transport


    • School of Life SciencesUniversity of Nevada
Original Paper

DOI: 10.1007/s00468-011-0603-5

Cite this article as:
Schulte, P.J. Trees (2012) 26: 421. doi:10.1007/s00468-011-0603-5


The main stems of three young Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirbel) Franco) trees were dissected to obtain samples of secondary xylem from internodes axially along the trunk and radially within each internode. From these samples, measurements were obtained of tracheid diameter, length, the number of inter-tracheid pits per tracheid, and the diameter of the pit membranes. In addition, samples were obtained along the trunks of three old growth trees and also a small sample of roots for measurement of tracheid diameter. A gradient was apparent in all measured anatomical characters vertically along a sequence among the outer growth rings. These gradients arose not because of a gradient vertically along the internodes, but because of the strong gradients present at each internode among growth rings out from the pith. Tracheid characteristics were correlated: wider and longer tracheids had more numerous pits and wider pits, such that total pit area was about 6% of tracheid wall area independent of tracheid size. A stem model combining growth rings in parallel and internodes in series allowed for estimates of whole trunk conductance as a function of tree age. Conductance of the stem (xylem area specific conductivity) declined during the early growth of the trees, but appeared to approach a stable value as the trees aged.


Bordered pitConductanceResistanceTracheid anatomyXylem


Large trees among the conifers depend on imperforate tracheary elements within the xylem for long distance transport of water and nutrients. Tracheid characteristics such as diameter and length are important factors determining conducting ability. In addition, as imperforate xylem conducting elements, flow from cell-to-cell must occur through pits and therefore the pit numbers and their dimensions also become important components of the flow pathway (reviewed by Hacke and Sperry 2001; Sperry 2003). It is clear that some of these characters vary enormously over the flow pathway from roots to leaves. Tracheid diameters may vary from 20 to 60 μm with lengths ranging from 1 to 5 mm in roots and stems of conifers (Sperry et al. 2006). Within the leaves of conifers, tracheids may have diameters of 5–7 μm and lengths of <1 mm (Woodruff et al. 2008). Therefore, these characteristics will contribute to changes in hydraulic properties of the xylem along the flow pathway and also with age as the tree grows.

If the xylem pathway is analyzed as a network connecting a large system of roots to a large number of leaves, flow resistances throughout the network determine how flow and water potential vary. It has been suggested that a sufficient increase in tracheid diameter along the pathway from sites of evaporation in the leaves toward the roots may result in a root to leaf resistance that is invariant with size as the tree grows (West et al. 1999). Others have suggested that the extent of tracheid diameter change is insufficient for this property to arise (Becker et al. 2003). Tracheid anatomical characters such as diameter, length and pitting are also interrelated with respect to the water transport capability provided by these cells (Pittermann et al. 2006). Conifers have low resistance pit membranes and short lengths (in comparison with angiosperm vessels) and this combination leads to a comparable efficiency in the overall conduction system (Sperry et al. 2006). Tracheid diameter also appears to be related to their tendency to become cavitated following freeze–thaw cycles (Pittermann and Sperry 2003, 2006). These studies along with many others demonstrate the important roles that tracheid anatomy plays in conducting ability of the xylem.

Although anatomical data are available in the literature on tracheid diameters and lengths for a number of conifer species, a systematic survey of such characteristics along with details regarding pit sizes and numbers would be important for understanding the nature of the xylem network in trees and how it may vary with age and size of the tree. Therefore, this study was conducted to determine the variation in tracheid diameter, length, and pitting characteristics both axially and radially within the main stem (trunk) of Douglas-fir (Pseudotsuga menziesii var. menziesii (Mirbel) Franco) trees. While focusing primarily on three trees of ~20 m height, samples were also collected from the outermost growth rings of old growth trees (60 m height) and roots of both young and old growth trees. A model is also developed that combines these anatomical characters to estimate flow conductance of the total trunk as the trees aged.

Materials and methods

Three trees were collected from an even-aged stand on forest land near Oregon State University (site location ~44°43′N latitude, 123°20′W longitude, 250 m elevation). Trees ranged from 17 to 19 m in height and 30 to 34 cm diameter (DBH). Sections were cut from the center of each annual internode along the stem including the terminal leader. To make the project more manageable in size, every other internode disk was sampled from each tree and every other ring was sampled from each disk. The growth rings of each disk were sampled at two points; along the minor and major axes of the slightly elliptical sections. Wood samples were obtained from individual growth rings by band saw and chisel and transferred to 50% ethanol:water. Sampling of xylem tissue from individual growth rings focused on the earlywood portion of the growth ring [studies have suggested that perhaps 90% of the flow occurs through earlywood tracheids (Domec and Gartner 2002)].

Internode and ring numbering followed the convention shown in Fig. 1. Measurements from individual growth ring samples can be expressed along three possible series (Fig. 1) according to a scheme expressed earlier by Duff and Nolan (1953). Series A shows rings that were all produced by the cambium in the same growing season. For the example labeled as Series A, those growth rings were the outermost rings in the previous year (1 year before the tree was cut). Other series oriented parallel to Series A as shown would have been outermost growth rings in previous years. Series B shows rings from one particular internode as produced by the cambium in successive years. Series C shows rings that are located at the same number of rings from the pith at each internode along the trunk. These rings were produced by the cambium in successive years but at the same location (when produced) with respect to the top of the tree. For the example shown in Fig. 1 of Series C with the sequence running vertically through Ring 1, these growth rings were all produced when that internode was the uppermost internode of the tree.
Fig. 1

Numbering scheme for trunk internodes and rings. Moreover, shown are examples of the three series often used for comparing growth ring characteristics. Series A compares growth rings produced during the same growing season, at a fixed number of rings in from the bark. Series B compares growth rings within the same internode, with rings being produced in successive years radially out from the pith to bark. Series C compares growth rings at the same developmental distance from the pith along a series of internodes. Here, rings were produced in successive years but always at the same location relative to the top of the tree when the ring is produced. These series designations as A, B, and C correspond to the Duff and Nolan (1953) Type 1, 2, and 3 series, respectively

Samples were also obtained from three old growth trees that were recently wind-thrown on the Wind River Experimental Forest of the Gifford Pinchot National Forest within the southern Washington Cascade Range (45°49′N, 121°59′W, 560 m elevation). Blocks of the outer xylem were collected from these trees (60–65 m height, 0.9–1.2 m diameter, 400–500 years aged) at 3 m intervals along the stem for sampling the outer growth rings (it was not possible to readily observe the location of annual nodes along most of the trunk for these old growth trees). Additional samples were collected at this site from roots of both young trees and the old growth trees exposed by windthrow.

Anatomical measurements

Measurements of tracheid diameter (diameter of the lumen) were made from transverse hand sections of the wood samples following a brief staining (about 30 s) in 1% safranin. Sections were observed with an Olympus BX50 microscope and 8–10 digital images were saved from each section for later measurement using the ImageJ software ( Image scales ranged from 3 to 6 pixels per μm. Note that all references to the diameter or width of these cells refer to inner or lumen diameters not including the thickness of the cell wall.

Preliminary observations indicated that tracheids of Douglas-fir observed in cross section were rarely circular, with both elliptical and rectangular cells occurring. A common basis for comparing tracheid sizes was needed and because water transport is one of the primary functions of these tracheids, conducting ability was chosen as a basis. The hydraulic conductance (K) of simple conduits is nonlinearly related to the width of the conduit and is given for these shapes as (see Langlois 1964 and White 1991):
$$ K^{\text{circular}} = \frac{{\pi D^{4} }}{128\eta } $$
where D is the conduit diameter and η is the fluid viscosity;
$$ K^{\text{elliptical}} = \frac{\pi }{4\eta }\frac{{\left( {ab} \right)^{3} }}{{\left( {a^{2} + b^{2} } \right)}} $$
where a is the semi-major axis and b is the semi-minor axis;
$$ K^{\text{rectangular}} = \frac{{4ba^{3} }}{3\eta }\left( {1 - \frac{192a}{{\pi^{5} b}}\sum\limits_{i = 1,3,5}^{\infty } {\frac{{\tanh \left( {i\pi b/2a} \right)}}{{i^{5} }}} } \right) $$
where a is the semi-long side and b is the semi-short side of the rectangle. Equivalent diameters for elliptical conduits can be calculated by equating Eqs. 1 and 2, and for rectangular conduits by equating Eqs. 1 and 3 and solving for D, giving:
$$ D = \left( \frac{32( {ab})^{3} }{( {a^{2} + b^{2} } )} \right)^{\frac{1}{4}} \quad ( {\hbox{for ellipses}}) $$
$$ D = \left[ {\frac{{512ba^{3} }}{3\pi }\left( {1 - \frac{192a}{{\pi^{5} b}}\sum\limits_{i = 1,3,5}^{\infty } {\frac{{\tanh \left( {i\pi b/2a} \right)}}{{i^{5} }}} } \right)} \right]^{\frac{1}{4}} \left( {\hbox{for rectangles}} \right) $$
Fortunately, the series summation in Eq. 5 converges such that 32 terms (i up to 65) gives a sum accurate to at least 7 significant figures for rectangular conduits with sides ranging from 1:1 to 10:1. A program was developed (using Microsoft Visual C++ for Windows) to carry out these calculations along with statistical data such as mean cell diameter and standard deviation. For calculation of an average diameter for tracheids in a particular sample, diameter was weighted by its fourth power (see Supplemental materials online).

Measurements of tracheid length, diameter, and the number and size of pits were made on macerated tissue samples using Gifford’s method based on a 1:4:5 H2O2 (30%):DI water:glacial acetic acid solution (see Ruzin 1999). Observations of macerated tracheids were carried out on temporary slides with dispersed groups of tracheids mounted in water. The length, diameter, and number of pits for 50 tracheids were obtained from each sample using an ocular micrometer. Note that the diameter obtained in this process would not be identical to that obtained from measurements on tracheids in transverse section because the latter process involves both radial and tangential dimensions of the cell whereas the macerated cells generally lay on the slide on their radial faces because they were tapered on the tangential faces. Thus, the measurement gives the width of the wider cell face and does not incorporate aspects of the elliptical or rectangular shapes of the cells, as was done for diameter estimates from transverse sections. This orientation on their radial face was of course convenient for observing pits, which were found primarily on the radial walls. For measurement of pit sizes, images were obtained of ~100 pits per sample. Pits were circular to somewhat elliptical and therefore measurements were made (ImageJ program) of the major and minor axes for each pit membrane. These results were expressed as equivalent diameter circular pits and also as area per pit.

Statistical analyses of the effects of the independent variables of location within the tree on measured anatomical variables were first conducted using 2- and 3-way ANOVA. For many cases, problems with the analysis arose because of unequal variances among the groups being compared. For those cases, log and square root transformations of the dependent variable were attempted but, typically, these did not resolve the problem. Where nonhomogeneity of variances remained, nonparametric procedures were used: including Kruskal–Wallace for one-way analysis, the Scheirer–Ray–Hare test for two-way analysis with replicates (Scheirer et al. 1976; Sokal and Rohlf 1995; Dytham 2003), and a procedure described by Gao and Alvo (2008) for carrying out nonparametric multiple comparisons within a two-way layout. Comparisons between dependent variables were made by correlation or regression analysis. All such statistical analyses utilized SPSS statistical software (IBM Corp.), except for the Gao and Alvo (2008) procedure which utilized a custom program written in the C language.

Stem model

Using an approach similar to that of Choat et al. (2008), this model describes the total flow resistance through the internodes of a Douglas-fir stem based on properties of the tracheids along with estimates of conducting areas for each growth ring within each internode of the stem. Tracheids are imperforate xylem conduits and flow from cell-to-cell depends on overlap between cells and the presence of pits in those regions of overlap. Although tracheid overlap was not specifically quantified, observations of partially macerated xylem suggested an overlap of between 1/3 and 2/3 of a tracheid length. Therefore, the model assumes 50% overlapping tracheids that present resistance in the form of a series combination of a lumen resistance (Rlum, MPa s m−3) and combined pit resistances (Rpit):
$$ R_{\text{tr}} = R_{\text{lum}} + R_{\text{pit}} $$
The lumen resistance to flow along the distance of one-half tracheid length is estimated from the Hagen–Poiseuille relation:
$$ R_{\text{lum}} { = }\frac{128\eta }{{\pi D_{\text{tr}}^{4} }}\frac{{L_{\text{tr}} }}{2} $$
where η is the dynamic viscosity (assumed to be 1.002e−09 MPa s), Ltr is the tracheid length (m), and Dtr is the tracheid diameter (m). The pit resistance for this tracheid is given by:
$$ R_{\text{pit}} = \frac{{2r_{\text{pit}} }}{{n_{\text{pit}} A_{\text{pit}} }} $$
where rpit is the pit resistivity (resistance per unit area, MPa s m−1), npit is the number of pits for this tracheid, and Apit is the area per pit. The factor of two is present because of the assumption that half of the total tracheid pits (in parallel) connect two tracheid centers. Note that the estimate of pit resistance does not distinguish between the actual pit membrane and the aperture of the pit canal. Some evidence exists that the pit canal component accounts for only a very small fraction of the overall resistance (Pittermann et al. 2006; Choat et al. 2008), although others have suggested that the pit canal may be a significant source of resistance (Domec et al. 2006). An estimate of the total resistance to flow over the length of the internode and for each growth ring is calculated from:
$$ R_{\text{ring}} = \frac{{2R_{\text{tr}} }}{{n_{\text{tr}} }}\frac{{L_{\text{int}} }}{{L_{\text{tr}} }} $$
where Lint is the length (m) of the internode and ntr is the number of tracheids that appear in a transverse section through the internode. The factor of two is present because the tracheid resistance calculation applies to half the distance of one tracheid length. The number of tracheids is calculated from the observed density of tracheids (ρtr) and area of the ring (Aring):
$$ n_{\text{tr}} = \rho_{\text{tr}} A_{\text{ring}} $$
The estimate of the total resistance to flow over the length of the stem is formed by combining each growth ring in parallel to form the internode:
$$ R_{\text{int}}^{j} = \frac{1}{{\sum\limits_{i = 1}^{I} {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {R_{\text{ring}}^{i} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${R_{\text{ring}}^{i} }$}}} }} $$
where \( R_{\text{int}}^{j} \) is the resistance of the jth internode as combining the resistances of each ith growth ring in parallel. Each internode is then combined in series:
$$ R_{\text{stem}} = \sum\limits_{j = 1}^{J} {R_{\text{int}}^{j} } $$
The model allows for choices in (1) the number of growth rings actually conducting within each internode, and (2) a pit resistivity for the pits through which water passes from tracheid to tracheid. Estimates of pit resistivity were obtained from the literature. The flow rate though tracheids in the xylem, given a particular pressure gradient, will be linearly related not to resistance but to conductance (inverse resistance). Therefore, conductance will be expressed in the graphs showing model results. In addition, conductance of stems is often expressed per area of the conducting tissue called stem-specific conductivity. For this estimate, Rring as calculated above is multiplied by the area of each growth ring. Note that samples were obtained from every other ring and every other internode and so tracheid anatomical data for the unsampled rings and internodes in the model were obtained by interpolation. As noted previously, the model was based on measurements from tracheids in the earlywood only; latewood tracheids are considerably narrower and the majority of flow would be due to conductance through earlywood tracheids (see Domec and Gartner 2002).


Young trees

A primary goal of the study was to assess trends in tracheid characteristics within each tree, and so an initial question with results concerned whether or not the trends within each of the three trees were similar such that a combination of the trees could be presented graphically. Although a 3-way ANOVA and nonparametric Kruskal–Wallace tests of tree effect (carried out because of issues with homogeneity of variances) for each anatomical property indicated that the tree effect was significant, this effect was small in comparison with the effects of internode and ring number. The most significant tree effect occurred with tracheid length: for Tree 2, tracheid length averaged 0.40 mm greater than found in Trees 1 and 3. Average tracheid diameter was slightly greater for Tree 2 (32.1 μm vs. 30.0 and 30.3 μm for Trees 1 and 3). Although there were slight differences apparent between trees, the overall trends suggested that the combined trees could be presented for consideration of vertical and radial trends.

Anatomical features of tracheids can be expressed as a function of internode along the main stem and ring out from the pith (Fig. 2). A nonparametric equivalent of two-way ANOVA with replicates, the Scheirer–Ray–Hare test (Scheirer et al. 1976; Sokal and Rohlf 1995; Dytham 2003) showed that internode and ring number effects were significant for all four measured tracheid characteristics (diameter, length, number of pits, pit diameter). A multiple comparison procedure was not available within SPSS for a two-way layout with replicates and so the procedure outlined by Gao and Alvo (2008) was employed to identify individual means which were significantly different in pair-wise comparisons. Tracheids were the narrowest near the top of the trees and in the first growth ring near the pith for all internodes. With increasing ring number from the pith (Series B, Fig. 1), tracheid diameter increased (note the left edge of the surface, Fig. 2a). But at any given ring number from the pith (Series C, Fig. 1), tracheid diameter is relatively constant along the stem (note the lower right edge of the surface, Fig. 2a). Similar trends were apparent for tracheid length, with the shortest tracheids near the tree top and within the first growth ring near the pith (Fig. 2b). An increase in tracheid length occurs with ring number out from the pith, but tracheid length is relatively constant with internode along the trunk for any given ring number from the pith. Tracheids near the top of the tree and within the growth ring near the pith had the fewest number of pits per tracheid (Fig. 2c). A nearly fourfold increase in number of pits per tracheid among the outer growth rings along the trunk of the tree is due to increasing pit numbers with ring number out from the pith. On the other hand, the number of pits in a given ring number did not increase with internode number down from the top of the tree. Similarly, the diameter of pits increased with ring number out from the pith for all internodes along the stem (Fig. 2d).
Fig. 2

Tracheid anatomical characteristics at each growth ring and internode from samples of the young tree main stems (data from the three trees were combined). The line intersections within each surface represent points where samples were obtained (a tracheid diameter, b tracheid length, c number of pits per tracheid, d diameter of tracheid pit membranes). Points connected by solid lines are significantly different at the p = 0.05 level whereas dotted lines indicate differences that are not significant. The nonparametric multiple comparison procedures of Gao and Alvo (2008) for a two-way layout were utilized because of nonhomogeneous variances between the groups (based on Levene’s test conducted during two-way ANOVA procedures)

Tracheid anatomical characteristics were also expressed as a function of tree age in order to provide a perspective of how these features change as the tree grows (Fig. 3). Tracheid diameter was lowest for the first ring formed near the pith for all internodes (Fig. 3a). Considering the outer growth rings as the trees aged, tracheid diameter increased such that a vertical profile gradually developed with wider tracheids toward the base of the tree. The increasing tracheid diameter apparent (Fig. 3a, Age 20 for example) with decreasing height down the trunk arises because of the increasing width of tracheids produced with increasing number of rings from the pith. However, this trend with height does not appear to continue the full length of the tree, but approaches a constant tracheid width. A reduction in tracheid diameter for the bottom internode was apparent among all three trees, particularly for Tree 2, where the base internode tracheid diameter average was 21% lower than the corresponding average for the third internode (28.4 compared to 36.1 μm). Tracheids were shortest near the top of the trees and within the first ring formed near the pith (Fig. 3b). As subsequent growth rings were produced, tracheid length increased dramatically, but similarly as for diameter, tracheid length approached a constant length in terms of a vertical profile along the lower 8–10 internodes. Tracheid diameter continues to increase with tree age (each age line continues to appear to the right of the previous lines), but the vertical gradient in tracheid length is largely found within the upper half of the tree. The number of pits per tracheid and the pit diameter (Fig. 3c, d, respectively) both increase with age such that a vertical profile also develops for these characters. A decline in the vertical gradient for pit number and diameter in the lower portion of the stem is apparent along with a similar reduction in the rate at which these characters increase with ring number from the pith as was noted previously for tracheid diameter and length.
Fig. 3

Tracheid anatomical characteristics from samples of individual rings obtained from internodes along the main stem of the young trees. Data points represent averages combining the three young trees studied. For each anatomical feature (a tracheid diameter, b tracheid length, c number of pits per tracheid, d diameter of tracheid pit membranes), internode number from the base of the tree is shown explicitly (along the vertical axis). The ages labeled at the left end of every other line indicate the age for which that line would have been the outermost ring along the tree stem (a Series A sequence from Fig. 1). In other words, observing from the Age 4 line to later lines shows how the anatomical character of the outermost ring changed as the tree grew. Ring number is shown implicitly, where the leftmost point in each line sequence (nearest the vertical axis) is Ring 2 and points along that sequence to the right are from subsequent rings (4, 6, 8,…). Within each line, points connected by solid lines are significantly different (p < 0.05) and dotted lines indicate a lack of significance (based on the Kruskal–Wallace nonparametric test followed by pairwise comparisons at the p = 0.05 level)

For all tracheid characteristics described above (Fig. 3), the vertical trends in outer growth rings approach a constant in the lower portion of the tree because although the growth rings contain wider and longer tracheids with more numerous and wider pits as the cambium ages, those increases are gradually reduced. For all of the characters in Fig. 3a–d starting at the leftmost point in any age sequence, note the distance to the next point to the right horizontally (thus for the same internode). Progressing further to the right, the increases in the character tend to get smaller. In other words, the character increases with ring from the pith but subsequent increases get smaller. A set of graphs showing these same anatomical characters plotted against ring number instead of internode (not shown) displays this initially increasing trend whose increase declines, but the lines for the different tree ages tend to collapse together because as noted previously, the characters do not change with internode number.

Old growth trees

Variations in tracheid diameter for the outer growth rings of old growth trees with height along the stem have two trends depending on location with respect to the crown of the tree (Fig. 4). In the upper 10–20 m, tracheid diameter increases with distance down from the top, covering a range in diameter similar to that found in the younger trees. Starting in the vicinity of the crown base, however, tracheid diameter no longer increases with height down the stem, becoming nearly constant. The tree labeled OG2 had narrower tracheids (40–45 μm for most of the stem) than the other two trees and the crown occupies a smaller fraction of the total tree height. These observations suggest that this tree might have represented a lesser dominance in the stand than the other two trees. The old growth trees labeled OG1 and OG3 contained 45–55 μm average diameter tracheids all along the stem below the base of the crown except for a reduction at the trunk base for tree OG1. The branches of old growth trees showed a steep gradient of declining tracheid diameter with distance from the main stem (Fig. 4).
Fig. 4

Tracheid diameter from samples of old growth trees where the outer xylem rings were sampled along the trunk. Tracheids were also sampled from two branches, whereby the indicated height refers to the path length along the trunk and out the branch. Error bars show the standard error of the mean at each point (unless smaller than the symbol). Solid symbols along the top indicate the approximate location of the crown base for each of the trees (estimated from the presence of living branches along the trunk)


Two roots were sampled from one of the old growth trees (OG3) ~1–2 m from the base of the trunk (38 mm diameter root with 52 growth rings and 73 mm diameter root with 89 growth rings). Although variation in tracheid diameter was apparent from ring to ring, an overall trend from the innermost growth ring of secondary xylem to the bark was not observed except for the innermost 2 or 3 rings (Fig. 5). Tracheid diameter averaged over all growth rings was 50.9 μm for the root with 52 rings and 62.1 μm for the root with 89 rings. Two smaller roots (4.5 and 2.8 mm diameter) from the same old growth tree contained somewhat narrower tracheids than found in the older roots, averaging 40.0 and 44.2 μm (not included in Fig. 5). Two roots were also sampled from young (~23-year-old) trees. No clear trend in tracheid diameter with growth ring number was apparent except for narrower tracheids in the innermost 2 growth rings (Fig. 5). Tracheid diameter averaged 55.9 and 53.8 μm for all rings sampled from these two roots.
Fig. 5

Tracheid diameters from root samples of old growth (open symbols) and young trees (solid symbols). The inset in the lower left shows a portion of the same data magnified. The standard error of the mean for each group is shown by the error bars

Anatomical property interactions

Similarities between the vertical and radial profiles of tracheid anatomical properties suggested that these measures would be correlated with one another. Therefore, relationships between tracheid diameter and length and relationships between diameter and measures of pitting were examined. Tracheid length and tracheid diameter were significantly correlated (Fig. 6a). Relationships were not significantly different between the three trees. For all trees combined, the relationship appears to be linear (r2 = 0.793).
Fig. 6

Relationships between tracheid diameter and anatomical characteristics of a tracheid length for the three young trees, where each data point represents the mean for tracheids from each ring within each disk as sampled, b pit diameter (data shown only from the first internode at the base of each trunk), and c the ratio of pit diameter to tracheid diameter (data shown only from the first internode at the base of each trunk). Lines show regressions for data from all trees combined. For c, the curve fit choice is justified because if a linear relationship exists between pit diameter and tracheid diameter, as in b, the ratio of pit to cell diameter will have an inverse relationship with tracheid diameter

Tracheid pit diameter was related to tracheid diameter (Fig. 6b). These relationships did not differ significantly between the three trees and so the data were combined for presentation. Although wider cells had pits of greater diameter, the pit diameter did not increase in direct proportion. For example, tripling cell diameter from 20 to 60 μm resulted in pit diameter increasing only 1.5-fold. The relationship between the ratio of pit diameter to cell diameter and the diameter of the cell indicates that for narrow tracheids, pits are roughly ¾ the width of the cell, whereas for wide tracheids, the pits are less than half the width of the cell lumen (Fig. 6c). Observations indicated that narrow tracheids had only one row of pits, whereas for wide tracheids there were often two rows of pits. However for the tracheids observe in stem xylem, it appears that pits in multiple rows within a tracheid are not likely connecting a single pair of tracheids, but connect one tracheid to a pair of tracheids oriented radially to one another. However as will be noted later, wide tracheids in roots with two rows of pits often do appear to connect the same pair of tracheids. Pit area will scale with pit diameter squared, and so the relationship between pit area and cell diameter (not shown) does show an approximate doubling of pit area with a doubling of cell diameter. Total pit area for an individual tracheid can be estimated by multiplying the area of the average pit by the average number of pits per cell. When compared with an estimate of total cell area (cells approximated as cylinders), a relationship appears between total pit area and cell area (Fig. 7). Over a sixfold range in cell area, the total pit area appears to be a constant fraction of cell area: ~6%.
Fig. 7

Relationship between the total pit area per tracheid and tracheid wall area (estimated from tracheid diameter and length assuming cylindrical cells). Total pit area is estimated from the number of pits per tracheid and their average pit membrane area. Data are from all rings sampled from the bottom internode of each trunk

Pits were found exclusively on the radial walls of the earlywood tracheids studied here. For xylem samples with relatively wide tracheids, pits often occurred in two (rarely three) rows. Although macerations of tracheids often showed radial files of still-attached tracheids, links between tracheids with multiple pit rows were more readily observed in transverse sections which by chance would often show pits in the walls of connected tracheids. From images of transverse sections, tracheids containing multiple rows of pits were counted with respect to whether their pits connected to two distinct tracheids or connected to the same neighboring tracheid. For the above ground stems of young trees, multiple pit rows always connected with distinct tracheids (Fig. 8), whereas multiple pit rows in tracheids of old growth stems were about equally likely to connect to distinct tracheids or the same adjacent tracheid. For the wide tracheids in old growth roots and young tree roots, multiple pits rows were most commonly connecting a single pair of tracheids.
Fig. 8

Pit connections between tracheids having two rows of pits. Shown is the fraction of such connections that occurred to distinct tracheids. Numbers at the top of the bars show mean tracheid diameter for that source. Like letters above the bars indicate non-significant differences (p > 0.05)

Stem models

Models of the young tree stems were not only based on anatomical properties of the tracheids as functions of internode and growth ring, but also depend on macroscopic characteristics such as internode length, ring area, and the density of tracheids within each ring. For brevity, the macroscopic data are available in tabular form online. The rate of flow through the xylem, assuming a given pressure driving force, will be linearly related with conductance while inversely related to resistance, and so model results will be presented using conductance (inverse resistance) units.

Models of each tree could predict the conductance of each internode and the contribution made by each growth ring. Therefore, an estimate could be made of conductance through the entire trunk (rings in parallel and internodes in series) from year-to-year as the tree grew. Of course as the tree grows larger, the main stem is supporting an increasing foliage area. A useful measure of stem conducting ability expresses conductance per unit stem area (stem specific conductivity) or leaf area (leaf-specific conductivity). Although foliage area was not available from this study, conductance of individual rings and internodes could be expressed per unit area of that growth ring. Models were developed expressing from 1 to 8 of the outermost rings as being functional for conduction. Total stem conductance per xylem area (stem-specific conductivity) shows a decline with age as the trees grew larger (Fig. 9). However, this decline tapered off beyond about age 10 and approached a constant value as the trees continued to grow larger. It was also apparent that the number of rings conducting would affect total stem conductivity; however, conductivity with 4 to 8 rings conducting showed little further increase. As a comparison with sapwood depth in other studies, for the young trees considered here, the 4–5 outermost growth rings correspond to the outer sapwood and the 6–7 outermost growth rings would correspond to the combined outer and inner sapwood (to at least 45 mm depth) as defined by Domec et al. (2005). Models expressing total conductance (as opposed to stem-specific conductance shown here) were also developed. An overall trend of increasing conductance with age was apparent, but this result would be less useful by itself because the foliage area supplied by the trunk would also have been increasing with age.
Fig. 9

Model results of estimated stem-specific conductivity (conductance divided by stem xylem area) for the three young trees from base to top internode as the trees grew (top to bottom graph pairs show trees 1–3). The effect of the number of rings conducting is shown in the left 3 graphs (for rpit = 0.1). The effect of pit membrane resistivity is shown in the right 3 graphs (for 4 rings conducting)

As noted in the “Materials and methods” earlier, estimates of pit resistivity were drawn from the literature (Lancashire and Ennos 2002; Hacke et al. 2004; Pittermann et al. 2005, 2006). Given the wide range of values apparent in the literature for various conifer species, models were developed with three values of pit resistivity (0.1, 1.0, and 10.0 MPa s m−1). Pit resistivity had a great effect on total stem conductivity, although the trends with tree age noted earlier were also apparent (Fig. 9).

The relative contribution of the pits in overall flow resistance was calculated as the ratio of pit resistance to the combination of pit and lumen resistances. The pit fraction of the total resistance depended strongly on the value of pit resistivity used in the model. For rpit values of 0.1, 1.0 and 10.0, the pit fraction (for all three trees combined) averaged 25.9, 76.6 and 97.0%, respectively. For all three trees and at all three rpit values, pit fraction was not significantly correlated with tracheid diameter (p > 0.05). For trees 2 and 3 (but not tree 1), there were slight negative correlations between pit fraction and tracheid length (r2 values ranged from 0.17 to 0.27). It may be of casual interest to note that the measurements of tracheid density together with ring areas for each internode can yield an estimate of the total number of tracheids in the trunks of the young trees; 548 million, 463 million and 470 million for trees 1, 2 and 3, respectively.


General trends in the vertical and radial profiles for the tracheid properties of diameter, length and the number and size of pits are surprisingly similar (Fig. 2). Cells are wider and longer toward the base of the tree and also out from the pith to the bark. Moreover, the number of pits per tracheid and the diameter and area of those pits increases toward the base of the tree and radially from the pith toward the bark. Although tracheid diameter and length both increase with distance from the top of the trees, this trend is not the result of inherently wider and longer tracheids in lower internodes. For any given ring number from the pith held constant, such characteristics are approximately constant with internode and hence height above the ground. These features tend to increase as the cambium extends producing new growth rings. Thus, the internodes near the base of the trees have outer rings with wider and longer tracheids because those rings are farther developmentally from the pith and not because they are farther down from the top of the tree. The vertical trends in tracheid features (including pitting) arise because of the dominant trends present from ring-to-ring at all heights along the stem (Fig. 3). Referring to the series portrayed earlier (Fig. 1), the trends observed in sequences of Series A are present because of a gradient occurring in Series B and not in Series C. This is of course a natural occurrence because of the pattern of cambial production of cells from the outer edge of the stem xylem. In principal, the observed gradient of tracheid features with height could arise from a gradual reduction in cell diameter, length, pit numbers and sizes as the tree grows taller, but this is clearly not the case. The young tree is dominated by narrow, short tracheids with relatively few and narrow pits. Tracheids continue to be produced by newly formed growth rings through activity of the vascular cambium. As the vascular cambium ages (greater ring number from the pith), tracheids are produced that are wider, longer and with a greater number and diameter of pits. Thus for a tree where transport along the length of the trunk in the xylem is primarily a function of outer growth rings with more recently produced tracheids, a gradient in all of these anatomical features develops as the tree ages. There does appear to be a limit at least for diameter, length, and the number of pits, because all of these characters do not continue to increase in the lower part of the trunk, perhaps in part related to the location of the base of the crown (Fig. 4). Tracheid diameter does, however, increase within the root system in comparison with above ground stems (Fig. 5). Although the earlywood as studied in the present work may dominate from the conduction aspect, studies of latewood characteristic profiles might be useful for consideration of mechanical support functions.

A close relationship was apparent between tracheid length and diameter (Fig. 6a). Pittermann et al. (2006) describe this as evidence of an optimal scaling of this relationship toward minimizing the overall resistance for transport with respect to the length of a tracheid. Similarly, Hacke et al. (2004) suggest that tracheids in conifers can achieve a comparable hydraulic efficiency as found in vessels because their low resistivity pit membranes lead to an approximate balance in lumen versus pit resistance components for lengths attainable by the individual tracheids. In the present study, pit membrane area was closely related to tracheid wall area (Fig. 7). Pit membrane area is significant for water transport and would become limiting if tracheid diameter increased without increases in membrane area. Pitterman et al. (2006) found that pit area was 8.6% of tracheid wall area, somewhat comparable to that noted in the present study (5.6%). This constant ratio of pit area to tracheid wall area contributes to a constant fraction of pit resistance as part of the total tracheid resistance (Sperry et al. 2006). Domec et al. (2008) have suggested that increases in diameter of the torus relative to the pit membrane with height in old growth trees may be important for increasing embolism safety, but also then could become limiting for transport as this would reduce the area of the pit membrane available for flow between tracheids.

Pits in the tracheids of conifers are generally located only on the radial walls except for occasionally in the latewood portion of a growth ring (Siau 1971; Panshin and de Zeeuw 1980). The overlap between tracheids and flow through pits on the radial walls allows for flow axially along a stem. Flow in a tangential direction around the growth ring across the stem would also be possible because of the pit locations, although one would expect the resistance to flow in the tangential direction to be higher than in the axial direction. A tracheid with more than one row of pits that are connected to distinct neighboring tracheids (oriented radially with respect to one another, see Fig. 8) would appear to allow for some flow in a radial direction as well. Thus, features in the arrangement of pits may contribute to lateral flow within stems. Flow through ray tracheids and perhaps ray parenchyma cells might also contribute to radial flow. Radial tension gradients have been estimated within the trunks of Douglas-fir trees (Domec et al. 2005) and if a measure of radial conductivity was available, these could be combined to predict radial flow rates. Lateral flow between growth rings in conifers may also be an important factor in determining which growth rings supply needles of different ages (Maton and Gartner 2005).

Model results suggest that the resistance of pits as a fraction of the total tracheid resistance remains remarkably constant over a range of tracheid diameters from <20 to >45 μm and also for tracheids ranging from 1 to 4 mm length. Although lumen resistance would decrease with increasing tracheid diameter, wider tracheids also had a greater number and increased area of pits. Similar results have been noted for a wide range of coniferous species (Pittermann et al. 2006; Sperry et al. 2006). The apparent constancy of this relationship over a wide range of tracheid sizes would suggest an endogenous control over pit development. The model did not consider (due to lack of data from the present study) that pit resistivity might vary with internode and ring within the trunk, however. There is evidence that pit membrane resistance varies with height in Douglas-fir due to both the changes in pit membrane area but also the size of pores in the margo of the pit membrane (Domec et al. 2006). The pit fraction of total resistance from the model varied tremendously depending on the chosen value for pit resistivity, suggesting that this is clearly a parameter needing further study.

One can consider how the tracheid properties and characteristics of growth ring area might combine to determine how the overall conductance of a tree from base to top changes with age (and hence tree height). Work starting with West et al. (1999) introduced the idea that flow capability might be tree size invariant if characteristics of the conduits varied in the right manner (sufficient taper along the flow pathway, in their terms). Model results presented here suggest that xylem-specific stem conductance does decline initially with increasing tree height, but may approach a constant value that does not decrease further with tree age (Fig. 9). The initial declines in conductance reflect the rapid height growth of the trees and hence increasing path length while the uppermost internode at any given age contains narrow tracheids, dominating the overall flow pathway. With increasing age, the production of wider and longer tracheids in the outer growth rings acts to reduce the extent to which conductance declines with increasing path length. Although the overall path length increases, the ring area for conduction increases as rings are added in the internodes below the growing tip, but presumably the supplied foliage area is also increasing. Thus, a more complete consideration of the whole tree would of course have to consider that the transport system is delivering greater flow with distance down from the top because the total foliage area is increasing as each internode supplies more and more branches. Foliage area attached per node was not available in the present study, but this would be a useful addition to a consideration of network properties in trees. McDowell et al. (2002) have shown that leaf area to sapwood area decreases with age and height in Douglas-fir and suggest that this decrease may help to compensate for the decline in conductance as these trees grow taller. A detailed analysis of the hydraulic network in the angiosperm Fraxinus americana by Weitz et al. (2006) did suggest that the increase in vessel diameter from the tip of branches to the base represented a stable hydraulic pattern independent of tree age. The present model for young Douglas-fir trees does indicate that although conductance may decline in the initial years of growth, the increases in tracheid diameter and length with ring might lead to a stable value of conductance with age. Studies of a number of angiosperm and gymnosperm species by Anfodillo et al. (2005) suggested that although trees appeared to show similar tapering with height, for trees approaching their maximal height, this tapering would not be sufficient to compensate for increases in path length. The present results for old-growth Douglas-fir also suggest that tracheid diameter and length do not continue to increase (taper) with height for large trees.

For tree stems as a delivery network, the presence of higher resistance at the tips of the branching system might provide a balancing of flow to the various branches. This network feature is primarily the result of tracheid diameter changes along the stems. A similar concept was expressed earlier by Ewers and Zimmermann (1984a, b) with respect to the hydraulic architecture of a tree determining the distribution of xylem sap to the terminal as opposed to lateral portions of the crown. The lack of an overall trend in tracheid diameter with growth ring among roots, along with the suggestion that tracheid width in young roots is nearly as great as found in old roots might reflect the nature of the roots system as a source as opposed to the sink end of the overall xylem network. Distance along the trunk may be important for the overall conducting path, particularly with respect to the role of gravity in xylem tension. On the other hand, for balancing the distribution of flow throughout a stem network, perhaps increases in tracheid diameter along the pathway are of greatest significance only between points where branching occurs. From this latter perspective, the lack of tracheid diameter increase below the tree crown may not matter with respect to network properties. Lower tensions would be present in the root system along with reduced structural demands, and this may help account for the presence of the widest tracheids within the roots (Pittermann et al. 2006). The trends of tracheid diameter with growth ring number in the roots showed a rapid increase from the first and second growth ring to relatively constant values among the remainder of the rings. In contrast, as noted previously, tracheid diameter among above ground stems of the young trees increased steadily with ring number. Tracheid diameter among outer growth rings also increased with internode down from the top of the young trees, but the increase appears to stabilize in the lower part of the crown for large old growth trees. Thus the observed vertical and radial trends in tracheid characteristics undoubtedly play a significant role in the overall tree hydraulic network, although these patterns appear to be different in root versus shoot portions of the tree. Future work incorporating estimates of pit membrane resistivity over similar vertical and radial profiles into a whole-tree model along with estimates of foliage area supplied would be useful to enhance our understanding of xylem transport in trees. Although the model shown here did not distinguish between the contributions of the pit canal, margo, and torus to overall pit resistance, recent evidence suggests that the relative role of these components may vary among related species (Pittermann et al. 2010) and further efforts to incorporate pit anatomy and particularly pit membrane pores in models would be useful in understanding the contribution of pits to flow resistance.


The author wishes to thank the staff of the Wind River Canopy Crane Research Facility (, including Ken Bible, for assistance with locating suitable old growth trees and for the use of laboratory space for initial anatomical work. Also, the efforts of JC Domec in securing disks from internodes of the young trees are greatly appreciated. Lastly, the assistance of Kaushik Ghosh in the Department of Mathematical Sciences at UNLV with statistical procedures is gratefully acknowledged.

Supplementary material

468_2011_603_MOESM1_ESM.pdf (19 kb)
Supplementary material 1 (PDF 19 kb)
468_2011_603_MOESM2_ESM.pdf (115 kb)
Supplementary material 2 (PDF 114 kb)
468_2011_603_MOESM3_ESM.pdf (127 kb)
Supplementary material 3 (PDF 126 kb)
468_2011_603_MOESM4_ESM.pdf (75 kb)
Supplementary material 4 (PDF 75 kb)

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© Springer-Verlag 2011