Vulnerability curves (VCs) generally can be fitted to the Weibull equation; however, a growing number of VCs appear to be recalcitrant, that is, deviate from a Weibull but seem to fit dual Weibull curves. We hypothesize that dual Weibull curves in Hippophae rhamnoides L. are due to different vessel diameter classes, inter-vessel hydraulic connections or vessels versus fibre tracheids. We used dye staining techniques, hydraulic measurements and quantitative anatomy measurements to test these hypotheses. The fibres contribute 1.3% of the total stem conductivity, which eliminates the hypothesis that fibre tracheids account for the second Weibull curve. Nevertheless, the staining pattern of vessels and fibre tracheids suggested that fibres might function as a hydraulic bridge between adjacent vessels. We also argue that fibre bridges are safer than vessel-to-vessel pits and put forward the concept as a new paradigm. Hence, we tentatively propose that the first Weibull curve may be accounted by vessels connected to each other directly by pit fields, while the second Weibull curve is associated with vessels that are connected almost exclusively by fibre bridges. Further research is needed to test the concept of fibre bridge safety in species that have recalcitrant or normal Weibull curves.
Vulnerability curves (VCs) have been measured in many hundreds of species since the first VCs were published (Choat et al. 2012). A sizable majority of them seem to fit the Weibull cumulative distribution function (CDF):
where PLC is percent loss of conductivity, T is tension, and b and c are Weibull constants. The Weibull CDF equation is preferred because it fits a wide range of curve shapes from S-curves to R-curves (Sperry et al. 2012).
However, we have seen a growing number of VCs that seem recalcitrant, that is, do not appear to follow the ‘Weibull rule’. Some recalcitrant VCs might be the result of flawed measurement technique or just measurement error, but we started to think that some recalcitrant VCs might be explained by structural features of the xylem of ‘recalcitrant species’. Usually VCs are characterized by just a few points (4–10) of PLC versus T needed to induce the PLC (see Fig. 1, solid symbols). It is difficult to determine the exact shape of the VCs when only a few points are measured. So, in this paper, we characterize VCs with 20–40 points, which can be carried out quickly in a Cochard cavitron (Cai et al. 2010a), with a high degree of accuracy quantified in terms of low standard errors of the PLC and T-values (see Fig. 1, open symbols).
In this paper, we demonstrate that the recalcitrant VCs measured in two species can be characterized accurately by a double Weibull equation. In one case, the double Weibull consists of one S- and one R-shape curve with closely spaced ‘P50 values’ on the T-axis. In the other case, the double Weibull is two S-curves that are widely separated on the T-axis. In the latter case, we hypothesized that the two S-curves correspond structurally to different conduit types in the stems, that is, either vessels of different size class (Cai & Tyree 2010) or the differences in vessel-to-vessel connections via pits or maybe vessels versus fibre tracheids.
In this paper, we use ‘fibres’ and fibre tracheids synonymously. Hence, ‘fibres’ have pit pathways for water flow between fibres or between fibres and vessels. In contrast, fibres without pits will be explicitly called libriform fibres. Carlquist (1984) reported that woody species with solitary vessels tend to be surrounded by water conducting ground tissue (fibre tracheids). Hence, one objective of this paper was to test the possible function of fibres and whether fibres might have a role in explaining dual Weibull curves. We used dye staining techniques, hydraulic measurements and quantitative anatomy measurements to test the hypotheses that fibres might form fibre bridges between adjacent vessels and that this structure might account for the dual Weibull curves.
Materials and Methods
All measurements were carried out on 1-year-old shoots of Hippophae rhamnoides L. shrubs and Robinia pseudoacacia L. trees collected in the summer of 2012. Samples (30–50 cm long and 8–10 mm basal diameter) were collected from sun-exposed branches in the morning from 4 to 6 adult plants of each species, which were grown on the campus of Northwest A&F University, in Yangling, Shaanxi, China (34°16′N 108°4′E, elevation 457 m). Branches were placed in black plastic bags with wet paper and immediately transported into the laboratory. R. pseudoacacia was used only to obtain VCs, whereas all other methods below apply to H. rhamnoides.
Visualization of embolized vessels using stain
Stem segments used for staining were prepared in three different treatments: flushed, embolized in a cavitron at the end of the first Weibull (about 50% PLC or about 2 MPa) and near the end of the second Weibull (95% PLC or about 3.5–4.5 MPa). As a control, four 2 cm stem segments were flushed with degassed 0.1 m KCl at 130 kPa for 4 min. For each embolized treatment, four consecutive 2 cm segments were cut under water near the axis of rotation of the stem segment, which was embolized in the cavitron to the above tension or PLC. Then, 0.02% w/v stain (basic fuchsin + 0.1 m KCl) was perfused at a pressure of 3 kPa. Four segments in each treatment were perfused for 15 min, 30 min, 1 h and 2 h. Then, segments were flushed with 0.1 m KCl at 130 kPa for 5 min to remove excess stain. A microtome (Leica RM 2235; Leica, Nussloch, Germany) was used to cut 18-μm-thick cross sections from the middle of the 2 cm segments. Sections were washed with graded ethanol (35, 75 and 95%) for ≥4 s and mounted in glycerine on glass slides.
Cross sections were photographed under a microscope (Leica DM4000B; Leica) at 200× magnification with a digital camera (DFC 490; Leica Microsystem Ltd, Heerbrugg, Switzerland). The RGB colour values, exposure, gamma and colour saturation were adjusted to yield suitable image quality using the software called Leica Application Suite (Leica Microsystems Ltd). The same setting was used for all treatments.
A Cochard cavitron (a modified Allegra X-22R, Beckman Coulter centrifuge, Fullerton, CA, USA) made in the University of Vermont was used to measure VCs. Stems were cut under water into 27.4-cm-long sections with leaves and petioles removed, using a razor blade and then flushed with 0.1 m KCL at 130 kPa for 60 min to eliminate native embolism and embolism induced by cutting when collecting samples. Preliminary experiments proved that 30–60 min is enough to eliminate embolism. After that, stems were put into the cavitron and spun at the first tension of 0.12 MPa for 30 min to obtain a stable Kmax. Details about the construction and use of the Cochard cavitron are described in Cai & Tyree (2010) and the cavitron is now commercially available (EcoRenewables R&C LLC, Plainfield, VT, USA; contact M.T.T.). Preliminary estimates revealed that maximum vessel length in H. rhamnoides was about 35 cm, but vessel length analysis suggests that less than 3% were cut open at both ends of our 27.4 cm samples.
Quantitative wood anatomy
Vessel lengths were measured by the silicone rubber method in Sperry, Hacke & Wheeler (2005) and Cai, Zhang & Tyree (2010b). Five 40-cm-long stems with basal diameter of about 6 mm were collected and flushed with 0.1 m KCl at 130 kPa for 1 h in order to remove embolism, then injected with silicone rubber for 24 h and cured at room temperature for 3 d. The cured stems were cross-sectioned at several distances (from 0.2 to 23 cm) from the injection surface until less than 1 or 2% of the vessels were filled with rubber. Photographs were taken under UV light at 100× magnification for vessel length analysis. Analysis of the vessel length involved plotting the natural log of the number of rubber filled vessels (N) versus distance (x) from the injection surface and fitting to ln(N) = λx+ ln(No) by linear regression to determine λ, where No is the number of vessels at distance x = 0.The mean vessel length was equated to −2/λ and vessel length distributions were calculated as in Cai et al. (2010b).
Fibre conductivity was measured by filling vessels with rubber and then shaving off x = 0.5 mm of wood to remove excess rubber from vessels and fibres at the injection point. The hydraulic conductivity of the rubber filled stems was measured in a low pressure flow meter (LPFM) and equated to fibre conductivity after correction for conduction of vessels cut open by shaving off excess rubber. The fraction of vessels opened was computed from (1 – N/No) = 1 – eλx.
Vessel diameter (Dv) and contact fraction (Cf) were measured on stained sections cut 18 μm thick on a microtome. The excel histogram function was used to plot percentages of vessels versus bin diameter size classes, for example, the % of vessels in diameter classes of 10–20 or 20–30 μm. Excel solver was used to fit the plots to Weibull probability density functions (PDFs) (see Cai & Tyree 2010 for details).
Fibre lengths (Lf) were measured on wood samples macerated by the Franklin method (Franklin 1945), from photographs on macerated fibres taken at 100× magnification. Photos of 5-μm-thick cross sections of stems were taken at 1000× magnification to measure fibre-lumen major-length and minor-length (width), lumen area and fibre diameter including wall thickness of fibre tracheids. Win CELL 2007 software (Regents Instruments Inc., Quebec City, Canada) was used to measure all fibre dimensions.
Lumen fraction of vessels was computed as , where Av is the lumen area of each vessel and As is the area of the analysed pie-shaped sector. Lumen fraction of fibres was computed using an elliptical approximation of area, , where L is the major length of the fibre lumen and l is the minor length (width) of the fibre lumen and As is the area of analysed pie-shaped sector.
The number of vessels or fibres in a specific area (Nv and Nf, respectively) was equated to the vessel or fibre count per unit area sampled (As). Contact fraction (= the fraction of vessel perimeter that is in contact with adjacent vessels) was calculated from photos of cross sections as in Hacke et al. (2006) and Wheeler et al. (2005).
Equivalent fibre bridge conductance (EFK)
H. rhamnoides vessels are arranged in narrow radial files separated by ray cells (see Plate 1). We assumed that water flow between adjacent vessels through fibre tracheids is more efficient than through a pathway crossing ray-cells (see section 2.2, Tyree & Zimmermann 2002). Adjacent vessels were connected to each other radially via 1 to 4 parallel bridges of fibres, where each bridge was 1–8 fibre-widths long. Stained photos at 200× were used to compute equivalent fibre bridge conductance using the following algorithm. We start with the concept of an average fibre hydraulic resistance = Rf. We counted the number of fibres in the i-th bridge (Ni); hence, the resistance of one bridge = NiRf. The EFK was calculated from the resistance of each bridge in parallel is given by .
The value of EFK is likely to underestimate the total conductance between adjacent vessels because some water could flow between vessels via longer bridges and via ray cells.
Theoretical vessel and fibre lumen hydraulic weight
Specific hydraulic weight of vessels was computed from , where Di is the vessel diameter and As is the area of analysed sector. Specific hydraulic weight of fibres was computed using an elliptical approximation of lumen conductivity , where L is the major length of the fibre lumen and l is the minor length of the fibre lumen (Cochard et al. 2007).
Vessel and fibre resistance calculation
Six 2-cm-long stem segments were flushed and mounted in a LPFM to measure Kmax. Then, they were injected for 3 h with silicone rubber to plug the vessels. After that, stems were immersed in water in small vials and placed in the oven (38 °C) for 12 h in order to harden the silicone rubber. A microtome was used to shave thin slices (0.5 mm) off of both ends of the stems to remove rubber coating the surfaces. Then, the stem segments were remounted in the LPFM and Kmax of plugged stems were measured after a 3 min flush. Kmax of plugged stems were corrected for evaporation rate and conductivity of vessels cut open by shaving off 0.5 mm slices to yield conductivity of fibres only (Kf,max) in the segments. The conductance of one fibre (kf) was computed from , where Lf is the average fibre length and Asw is the sapwood area of stem segment. Furthermore, Rf was equated to 1/kf. Based on the equivalent fibre bridge conductance (EFK), resistance of the fibre bridge was calculated (see the Discussion section).
A program called CavAnal was written by one of us (M.T.T.) that did least square fit of raw data from the Cochard cavitron; readers may write to M.T.T. to get a copy of CavAnal. The program fits single and dual Weibull curves and it allows for temperature correction and for selection of Kmax. The dual Weibull equation is shown in Eqn (2):
where W1 and W2 are the two Weibull curves, β is the maximum PLC for the first Weibull curve (see Fig. 2), T is the tension, b1 and c1 are the two Weibull constants for the first curve, and b2 and c2 are the two Weibull constants for the second curve. Each Weibull curve has a ‘P50’, which equals the half maximum value of (1 – exp[–(T/b)c], and hence is analogous to P50. In this paper, we use the symbol P1/2; hence, P1/2 = b[ln(2)]1/c. In Fig. 2, the values of P1/2 are 0.958 and 3.228 for H. rhamnoides and the values of P1/2 are 0.230 and 1.159 for R. pseudoacacia.
Figure 3 shows three representative VCs of H. rhamnoides, which fit a dual Weibull (Eqn (2)) and Fig. 2a gives the best fit Weibull curve and the two separate Weibull curves for a fourth typical VC. The VC started rising at 0.2 MPa tension, suggesting that some conduits in H. rhamnoides are very vulnerable to cavitation, and the second curve started rising again around 2.0 MPa, suggesting that some conduits are more resistant to cavitation. A total of 10 VCs were measured and Table 1 shows a summary of the best fit parameters of both single and dual Weibull curves. Dual Weibull curves fit the data four times more precisely than single Weibull curves, as measured by the root mean squares errors (RMSE = 6 versus 1.4 for single versus dual Weibull curves, respectively, t-test P < 10−5). The single Weibull has a mean P50 = 1.88 MPa; in contrast, the mean values of P1/2 = 0.90 and 3.52 for the first and second curves, respectively. The coefficient of variation (CV) on the first Weibull was greater than the CV of the second contrary to the impression gained from Fig. 3.
Table 1. The CavAnal program was used to fit both single and dual Weibull curves for 10 VC datasets of Hippophae rhamnoides; each dataset contains about 20–40 points
First dual Weibull
Second dual Weibull
Note: b and c are Weibull constants for a single Weibull and P50 has the usual meaning; b1, c1, b2and c2 are Weibull constants for the dual Weibull curves. The value β is maximum PLC for the first Weibull curve and the meaning of P1/2 is or for the first and second curve, respectively (see Eqn (2) and Fig. 2). Furthermore, RMSE = root mean square error of the best fit curve. The table shows the means, coefficient of variation (CV% = 100 SD/mean) and standard error (SE) of all the above parameters n = 10.
R. pseudoacacia also fitted a dual Weibull but the two curves overlap on the x-axis (Fig. 2b). We show the R. pseudoacacia data to illustrate that H. rhamnoides is not unique in being resolvable into two Weibull curves. We encourage readers to measure R-shaped curves with more points in the future to see if many R-shaped curves are really dual Weibull curves. As the objective of this paper is to find out the structural basis for dual Weibull curves, we will concentrate for the rest of this paper on H. rhamnoides, which has more distinct curves.
Quantitative vascular anatomy
Figure 4 shows the Weibull PDF fit for the different vessel bin size classes. The most frequent vessels are small vessels, <20 μm, but vessels >20 μm are responsible for most of the water flow, as measured by hydraulic weight. Four- to five-year-old stems in H. rhamnoides have ring-porous xylem structures (Zhang & Cao 1990; Jansen, Piesschaert & Smets 2000), but in current year stems of H. Rhamnoides, the boundary between small vessels and large vessels is much more gradual. Recently, Cai & Tyree (2010) were successful in obtaining good Weibull PDF fits of diffuse porous species. Cai & Tyree (2010) found that for Populus species, the range of vessel sizes was 10–50 μm, with a mode of 30 μm. The range of vessel sizes was the same for H. rhamnoides, but the mode was around 13 μm. We suggested that the poor fit of H. rhamnoides might be the consequence of a semi-ring porous structure.
Table 2 gives 11 other measurements of quantitative anatomy: for vessels and fibres, we give mean length, contact fraction, lumen fraction, density (number per unit area), lumen diameters and hydraulic weights. Of particular note is that even though there are 55 times more fibres than vessels, the vessels contribute most to hydraulic conductivity. The lumen fraction of vessels to fibres is in the ratio of 1.4, but the hydraulic weights are in the ratio of 73. Fibre lumens theoretically contribute about 1.4% (= 100%/73) to the stem hydraulic conductivity even though the sum of the lumen area of fibres is 69% (= Flf/Vlf) of that of vessels. This is because the hydraulic contribution of small lumina of fibres is far less than the larger vessels (3.8 versus 19 μm lumen diameters, respectively). In addition, the contact fraction (Cf = 0.03) is low compared to most other species (Wheeler et al. 2005; Hacke et al. 2006), where the range is 0.05–0.35, except one which is 0.01.
Table 2. Summary of hydraulic and quantitative wood anatomical values for stem segments of Hippophae rhamnoides
Note: Stem segments were 20 mm long and 6 mm in diameter (n = 6). As the mean physical diameter of vessel lumina (D) does not represent their hydraulic contributions (see Fig. 4), we computed hydraulically weighted mean vessel diameters also from the following equations: and .
Kmax with vessels filled with rubber (kg m MPa–1 s–1)
2.97 × 10–07
9.94 × 10–08
Hydraulic vessel diameter 1 (μm)
Hydraulic vessel diameter 2 (μm)
Vessel lumen diameter (μm)
Fibre lumen diameter (μm)
Fibre diameter with wall (μm)
Vessel hydraulic weight (m2)
1.74 × 10–10
0.174 × 10–10
Fibre hydraulic weight (m2)
2.40 × 10–12
2.38 × 10–13
Vessel lumen conductivity (kg m MPa–1 s–1)
2.22 × 10–05
1.32 × 10–06
Hydraulic conductance of one fibre (kg MPa–1 s–1)
5.82 × 10–09
1.97 × 10–09
Stem segment hydraulics
Table 2 shows hydraulic values worthy of comment. Most values are self-evident, but the estimation of fibre tracheid conductivity requires detailed comment. The maximum conductivity of stems (Kmax) is 2.26 × 10–5 kg m MPa−1 s−1, but the measured maximum conductivity of fibres contributes only about 1.3% of the total stem conductivity when the vessels are plugged with silicone rubber, which is very close to the theoretical value (see previous paragraph). To arrive at the 1.3% figure, we had to correct for evaporation from the lower reservoir on the balance of the LPFM and correct for residual vessel flow as explained below. In terms of raw numbers, the mean conductivity of stems after filling vessels with rubber and shaving off 0.5 mm of wood in order to open a pathway for fibre flow was 4.01 × 10–7 kg m MPa−1 s−1. After correcting for evaporation, the mean value increased about 12% to 4.47 × 10–7 ± 1.00 × 10–7 (SE) kg m MPa−1 s−1, which was 1.98% of the conductivity of the stems before filling vessels with rubber. However, about 0.6% of the vessels were cut open after shaving off 0.5 mm of the stem to remove rubber-filled fibres. The mean conductivity of 0.6% of the vessels was 1.37 × 10–7 ± 0.13 × 10–7 kg m MPa−1 s−1. After correcting for flow through cut-open vessels, we obtained a Kf,max of 2.97 × 10–7 ± 9.94 × 10–8 kg m MPa−1 s−1 (= 1.3% of the total stem conductivity); a t-test revealed that the computed fibre conductivity was significantly different from zero (P = 0.01).
From the above calculations, we conclude that fibre tracheids (1.3% of the total conductivity) cannot account for the second VC in H. rhamnoides (53% of the total conductivity, =100 – β in Table 1), but we feel that fibres have a role in water flow between vessels (fibre bridges) and may have a role in the dual Weibull curves (see Fig. 2 and the Discussion section). We estimated the conductance of a single fibre (kf) to be 5.82 × 10–9 kg MPa−1 s−1 and this is used to estimate EFK in Table 2 (see the Methods section). We argue in the discussion that some water flow between vessels occurs through vessel-to-vessel pits and some through fibre bridges.
Visualization of embolized vessels using stain
Plate 1 shows the staining pattern and tempo of three different treatments. In the flushed treatment, all the vessels and fibres were fully stained after 1 h, which confirmed that the flush was successful and that dye moves rapidly from vessels to fibre tracheids. In the second treatment (embolized at 2 MPa), only some vessels and fibres were stained after 2 h, which was expected because nearly half of the conduits were embolized. In the third treatment, the stem was embolized to 95% PLC = 4.5 MPa tension for the photos of Plate 1. In the third treatment, the stain moved more slowly and went through only a few vessels and fibres even after 2 h, as almost all conduits and fibre tracheids were not conductive. The staining pattern in H. rhamnoides was very different from that reported in Populus by Cai & Tyree (2010) because the stain in Populus was largely confined to vessels and penetrated into fibres very little (unpublished photos). We attribute the lack of staining of fibres in Populus to the presumed absence of pits between vessels and fibres in Populus; otherwise, stain should enter fibres as in H. rhamnoides (see discussion about fibre bridges and theory of stain movement in woody stems).
Photos from the second treatment (embolized at 2 MPa, 30 or 60 min stain) were used to analyse the diameter of stained and unstained vessels. The calculation of theoretical PLC based on the staining pattern was 46%, which was in agreement with the value measured by Cochard cavitron (42%). Figure 5 shows the plot of the percent embolized vessels against bin diameter-size class. The plot can be divided into two linear regions. For vessel diameter ≤27.5 μm, the regression was negatively correlated with vessel diameter; for vessel diameter ≥27.5 μm, the regression was positively correlated. The dual linear relationship (Fig. 5) is in marked contrast to Populus, where % embolized vessels is positively correlated with bin vessel diameters from 12.5 to 62.5 μm (Fig. 5 in Cai et al. 2010a). Figure 5 might be explained if we suppose that the kind of vessel-to-vessel connections changes with vessel size.
Theory of stain movement in stems
A growing body of evidence about the movement of sugars and xenobiotic molecules in plants helps considerably in interpreting the movement of xenobiotic dyes in stems. Some stains work because they bind to specific sites in living or dead cells. Others accumulate without binding but move around within living cells through other known mechanisms (Tyree, Peterson & Edgington 1979). Dyes that accumulate in ray cells might be phloem mobile if there are plasmodesmata, for example, safranin that accumulates in ray cells and stains (binds to) tracheids (Sperry & Tyree 1990) and fluorescein that accumulates in ray cells but does not bind to vessel walls (Cirelli, Jagels & Tyree 2008); hence, not all of these substances make suitable dyes to distinguish embolized from non-embolized xylem conduits.
Xylem conduits and structural fibres are chemically unique compared to other plant cells because they have lignin deposits in secondary walls. Hence, a suitable dye for tracing water flows is one that binds to lignin and remains confined to water-filled conduits. Basic fuchsin met these requirements in recent studies on the effect of vessel size on the vulnerability to embolism in Populus species (Cai & Tyree 2010; Cai et al. 2010a). However, basic fuchsin can, in principle, pass through primary cell walls in pits. So, the fact that basic fuchsin did not pass into adjacent fibre cells in Populus suggests either a scarcity of vessel-to-fibre pits or air-filled fibre lumina in Populus. Cirelli et al. (2008) have also demonstrated that molecules the size of sucrose (376 MW) do not pass through lignified cell walls and that also explains why basic fuchsin (338 MW) and 2 fluorescein dyes (342–389 MW) tend to be confined to water-filled vessels provided there are no pits between vessels and wood fibres. In Plate 1, basic fuchsin clearly spreads into fibres and this is consistent with the existence of many pits between vessels and fibres and fibre-to-fibre.
A successful staining technique needs to select an ‘optimum’ time for dye perfusion based on knowledge of how fast dyes move through conduits at any given applied pressure. The Hagen–Poiseuille equation can be used to calculate the average sap velocity (v) in a conduit of radius (r) as a function of pressure gradient (dP/dx):, where η = the viscosity of water. The average velocity is defined as the volume flow rate divided by the conduit lumen area. From this, it follows that the ratio of velocity (v1/v2) in conduits of radius r1 and r2 is given by (v1/v2) = (r1/r2)2. The velocity of sap at the conduit wall is zero and the peak velocity occurs near the centre of the lumen. Taylor (1953) has proved both theoretically and experimentally that dye moves at the average velocity of the sap provided the dye does not chemically react with the conduit wall. So, we would expect a non-reactive dye in stems of H. rhamnoides to move slower in fibre tracheids than in vessels because tracheid radius is less than vessel radius (1.9 versus 9.6 μm); hence, dye should move 0.04 times the rate of dye in the average vessel. A similar ratio can be calculated from hydraulic measurements and the percent of vessel and tracheid lumens as a percentage of stem cross section [0.019 = Kf,maxVlf/(KmaxFlf)].
The pattern of dye movement in Plate 1 suggests that dye moves rapidly through vessel lumina and then moves either by diffusion and/or mass flow into fibre lumina via pit membranes (see the faint red halo around vessels at 15 min). With time (30 min to 2 h), the halo of stained fibres around vessels becomes broader and darker until nearly all fibres are red. As the time of perfusion of the first and last picture is the ratio of 15 min : 2 h = 0.125, we conclude that dye could not have moved into fibres by flow exclusively through a catena of fibres, which would be about 67 times slower than vessels and hence would take about 16 h to travel the same distance through a fibre catena. We conclude this also because dye first appears in fibres adjacent to vessels and eventually spreads outward to all fibres even when about half the vessels are embolized in Plate 1.
A possible connection between fibre tracheid flow and vulnerability curves
One hypothesis we considered was that fibre tracheids might account for the second VC in H. rhamnoides. The first Weibull curve accounts for 47 ± 3% of the hydraulic conductivity of stems (Table 1); hence, if the second Weibull curve is due to fibre tracheids, then fibre flow should account for about half of the total water flow in stem segments. Flow through vessels was inhibited by filling them with rubber and the measured residual flow was only about 1.3% of the total stem hydraulic conductivity (Table 2). Hence, we can eliminate the hypothesis that fibre tracheids account for the second Weibull curve. Nevertheless, the dye experiments suggested that a considerable amount of dye reaches and stains the lignified secondary walls of fibre lumina. Could the fibres be acting as a hydraulic bridge between adjacent vessels? And is that why they acquire stain so rapidly?
The conceptual advantage of a fibre bridge is that it offers more safety against embolism propagation between adjacent vessels than do vessel-to-vessel pits. According to the pit area hypothesis, the largest pit pore between an air-filled vessel and a water-filled vessel seeds the cavitation. Large vessels are likely to have more pits than small vessels and hence are more likely to cavitate than small vessels (see Cai & Tyree 2010). However, the paradigm changes if there are fibre bridges because in that case the embolism would propagate into a rather small fibre lumen and the likelihood that it would propagate from that fibre to the adjacent vessel is rather small because there are few pits in the embolized fibre in contact with the adjacent water-filled vessel. The small size of the fibre confers the safety. In contrast, when adjacent vessels are connected by pit fields, the vessel lumens are much bigger than fibre lumens; hence, an embolized vessel presents many more pits to the adjacent water-filled vessel; therefore, the probability of one of those pits having a large pit pore is more than in a small fibre lumen. The question is do fibre bridges have low-enough hydraulic resistance compared to vessel lumina to be functional?
In order to evaluate the hydraulic functionality of fibre bridges, we computed the average fibre conductance of a single fibre from LPFM measurements and the equivalent fibre conductance (EFK) from photographs of stem cross sections (Table 2). We need to compare the resistance of fibre bridges to resistance of vessel lumens, which can be computed from EFK and the vessel lumen hydraulic conductivity, respectively (Table 2). Let us consider a fibre bridge model for the average vessel, which is about 0.15 m long. Half the vessel length will be receiving water from a vessel below it and the other half will deliver water to the vessel above through fibre bridges. The hydraulic resistance of the vessel lumen will be 0.5Lv/Kv = 7.7 × 106, where Kv is the conductivity of one vessel catena = Kh,v/NvAsw. In comparison, the resistance of the fibre bridge would be 8.42 × 105 [= Lf/(0.5LvEFK)]. Hence, the fibre bridge resistance is only one-ninth of the vessel lumen resistance of an average vessel and hence is quite efficient for vessel to vessel water transport.
In Fig. 6a–c, we computed this comparison for the range of most probable vessel lengths. Figure 6a shows the PDF of the vessel length distribution. Figure 6b shows the computed vessel lumen resistance for half the vessel length and the fibre bridge resistance for the same half-length. It can be seen that the fibre bridge resistance exceeds the vessel lumen resistance for vessels <0.06 m and fibre bridge resistance is less than vessel lumen resistance for vessels >0.06 m. In Fig. 6c, we plot the hydraulic resistance of each vessel length class weighed by the PDF value in Fig. 6a. The area under the two curves gives the average fibre bridge resistance and the vessel lumen resistance in current year H. rhamnoides stems: 7.53 × 106 versus 1.85 × 106 for vessel lumen resistance and fibre bridge resistance, respectively. From this, we conclude that fibre bridge paradigm is a possible mechanism of connection between vessels in H. rhamnoides stems.
The fibre bridge paradigm is further supported by publications on the anatomy of 4- to 5-year-old H. rhamnoides stems that describe frequent vessel-to-fibre and fibre-to-fibre pits (Zhang & Cao 1990; Jansen et al. 2000). We have confirmed these observations in our current-year stems (unpublished). Scanning electron microscope (SEM) photographs of vessel ‘pit fields’ tend to be in the form of linear files of pit apertures which connect to narrow fibre tracheids that average 8 μm diameter (including cell walls). Furthermore, 5-μm-thick cross sections viewed at 1000× in a light microscope revealed frequent bordered pits connecting vessels to fibres and fibres to fibres. There are likely to be pit fields between adjacent vessels as the contact fraction between vessels is about 0.03 in current year stems (Table 2). Figure 7 is a scale drawing (artist's conception) of the connection between fibres and vessels. Figure 7a shows the possible pathway water might take between vessels separated by two to three fibres. Figure 7b shows details of the fibre-to-fibre and fibre-to-vessel pits. Pitting is revealed only in thin sections (≤5 μm thick) and is rarely all in the same plane. The pit apertures are elongated slits that join up with pit chambers about 3–5 μm in diameter with a pit membrane in the middle. Fibres contain pits in linear files along the fibre length (413 μm) between adjacent fibres or vessels with an estimated 30–50 pits per linear file.
We cannot definitively identify which vessels ‘groups’ account for the two Weibull curves. However, we tentatively propose that the second Weibull curve is associated with vessels that are connected almost exclusively by fibre bridges. The first Weibull curve may be accounted for by vessels connected to each other directly by pit fields. The P1/2 of the first Weibull curve is about 0.9 MPa in H. rhamnoides, which is similar to hybrid cottonwoods (1.0–1.6 MPa) (Arango-Velez et al. 2011), and cottonwoods have vessel diameters that are similar to H. rhamnoides. Fibre bridges might account for the higher P1/2 = 3.5 because fibre bridges are safer. There is direct connection between vessels because the contact fraction is 0.03; hence, we also have to hypothesize that there is a transition between vessels that have traditional pit-field connections to vessels connected by fibre bridges. That may explain the strange behaviour in Fig. 5 because the negative correlation between % embolism and vessel diameter (for small vessels) may be due to the transition from vessels connected by pit fields to vessels connected by bridges.
The fibre bridge paradigm does not replace previous concepts about how wood is designed to provide cavitation resistance. Previous paradigms embodied in the pit area and the rare pit hypotheses are also valid for some species. However, if the fibre bridge hypothesis passes the test of time, then it will provide a new dimension to concepts about how resistance to cavitation is related to xylem structure and function. Carlquist (1984) had advanced a vessel-grouping hypothesis: Species with mainly solitary vessels have fibre tracheids (water conducting ground tissue), while species with higher levels of vessel grouping show fibres (libriform fibres) that are not contributing to transport (see also Mencuccini et al. 2010 and Martínez-Vilalta et al. 2012). Sano et al. (2011) have demonstrated that fibres in general do not contribute much to total hydraulic conductance on their own, which is in agreement with our data (fibres contribute 1.3% to total Kmax), but they can still act as efficient hydraulic bridges between vessels (Fig. 6). In this regard, the low conductance of fibre tracheids are similar to the low conductance of vessel-to-vessel pits which occupy 10−4–10−6 of the transport path-length but contribute half to the hydraulic resistance of vessels. Cai & Tyree (2010) have remarked in the past that regressions of P50 versus pit area have an R2 = 0.75 close to the R2 of P50 versus vessel diameter (= 0.72), which should not be the case if the pit area hypothesis is true. Cai & Tyree (2010) suggested that one reason for this is that the centrifuge method is not well suited to measuring P50 when vessels are longer than 4 cm. To this, we can add the further suggestion that the pit area hypothesis will not apply to species that use fibre bridges to connect adjacent vessels. Additional research is needed to confirm or reject this new concern.
The authors wish to acknowledge the following grants that made this research possible: Natural Science Foundation of China (Grant No. 31270646) and National Undergraduate Innovation Training Project (1210712053) to J.C. and State Forestry Administration of China (Grant No. 201004036) to S.Z. and the thousand talent program grants to M.T.T. Many thanks to Zaimin Jiang for his technical assistance.