The conifer-curve: fast prediction of hydraulic conductivity loss and vulnerability to cavitation

The relationship between relative water loss (RWL) and hydraulic conductivity loss (PLC) in sapwood is robust across conifer species. We provide an empirical model (conifer-curve) for predicting PLC from simple RWL measurements. The approach is regarded as a new relevant phenotyping tool for drought sensitivity and offers reliable and fast prediction of diurnal, seasonal, or drought-induced changes in PLC. For conifer species drought is one of the main climate risks related to loss of hydraulic capacity in sapwood inducing dieback or mortality. More frequently occurring drought waves call for fast and easily applicable methods to predict drought sensitivity. We aimed at developing a fast and reliable method for determination of the percent loss of hydraulic conductivity (PLC) and eventually the drought sensitivity trait P50, i.e., the water potential that causes 50% conductivity loss. We measured the loss of water transport capacity, defined as the relative water loss (RWL) together with PLC in trunk wood, branches, and saplings of eight different conifer species. Air injection was used to induce specific water potentials. The relationship between RWL and PLC was robust across species, organs, and age classes. The equation established allows fast prediction of PLC from simple gravimetrical measurements and thus post hoc calculation of P50 (r2 = 0.94). The approach is regarded as a relevant new phenotyping tool. Future potential applications are screening conifers for drought sensitivity and a fast interpretation of diurnal, seasonal, or drought-induced changes in xylem water content upon their impact on conductivity loss.


Introduction
Conifers are among the most endangered plant groups regarding forest dieback related to drought (Solberg 2004;Hentschel et al. 2014;Allen et al. 2015;Mencuccini and Binks 2015;McDowell and Allan 2015;Rosner et al. 2018;Klein et al. 2019). According to the International Union for Conservation of Nature (IUCN Red List), 34% of the world's conifers species are threatened (IUCN 2019). Facing global change (IPCC 2013), we urgently need fast and reliable screening tools for predicting drought sensitivity of conifer species and provenances thereof (David-Schwartz et al. 2016, Voltas et al. 2018. Screening tools should be economical, require little labor, not be time-consuming, easy in application and -last but not least -applicable to conifers worldwide. Recently, Rosner et al. (2019) presented an approach where hydraulic conductivity loss of angiosperm and conifer sapwood could be predicted from simple water loss measurements. The empirical predicting models in this preceding study were however species-specific. In the present study, we aimed at developing one single prediction curve that would be applicable for conifers with a wide range of natural occurrence. The idea for a conifer prediction model developed because the relationship between relative water loss and conductivity loss varied widely among angiosperm species; the curves of conifer species showed a quite stable relationship . Research on this plant group was also continued because their wood structure allows quite short sample lengths and application of several methods to measure hydraulic vulnerability that exists so far (Cochard et al. 2013. Hydraulic performance of (secondary) xylem under drought and its recovery from drought depends on (I) hydraulic vulnerability to embolism, expressed as, e.g., P 50 (i.e., the water potential resulting in 50% conductivity loss), (II) hydraulic safety margins, which is the P 50 in relation to the minimum water potential measured in the field Sperry 1988, Choat et al. 2012;Delzon and Cochard 2014;Choat et al. 2018), and on (III) the capability of refilling emptied tracheids, which is presumably related to the hydraulic capacitance (Johnson et al. 2012;McCulloh et al. 2014;Trifilò et al. 2015, or (IV) the potential to produce new xylem tissue (Magnani and Borghetti 1995;Cochard et al. 2001). Water storage capacitance is the amount of water released from a tissue due to a defined decline in water potential (Tyree and Yang 1990;Meinzer et al. 2003;Domec et al. 2006). In general, more knowledge exists about species or organ-specific P 50 and the shape of vulnerability curves (Choat et al. 2012), i.e., the percent loss of conductivity (PLC) plotted against the water potential (Ψ) , than about hydraulic capacitance (Trifilò et al. 2015). Capacitance can be expressed as the increase in the absolute mass of water lost from a sample of defined volume per unit Ψ change but also as the increasing relative water loss (RWL) per unit Ψ change. The RWL method allows the comparison of the samples differing in total water volume and wood density (Domec and Gartner 2001). Rosner et al. (2019) defined an additional capacitance parameter, the RWL at P 50 , i.e., the RWL that results from 50% conductivity loss. RWL at P 50 varies widely across angiosperm and conifer species and is negatively related to wood density, as found for other capacitance traits as well (Pratt et al. 2007;Scholz et al. 2007;McCulloh et al. 2014;Trifilò et al. 2015;Savi et al. 2017;Pratt and Jacobsen 2017).
The aim of this study was to confirm the quite stable relationship between PLC and RWL ) across conifers species originating from different ecosystems around the globe. Such an approach should not only result in a fast prediction of species-, organ-, or age class-specific hydraulic vulnerabilities but will also allow us to establish the amount water remaining in xylem at P 50 and P 88 (Ψ at 88% PLC). We tested mature and juvenile trunkwood as well as branches of eight different conifer species with a broad range of natural occurrence from extremely wet environments (Taxodium distichum) to quite dry environments (Juniperus virginiana). We thus expected a wide range in P 50 . Most of the species investigated are also of high economical importance (Abies nordmanniana, Larix decidua, Picea abies, Pinus ponderosa, Pinus taeda, Pseudotsuga menziesii) which further substantiates the need for fast and reliable screening tools for selecting appropriate provenances with a higher drought tolerance.

Determination of conductivity loss and relative water loss
Either whole saplings or side branches (cut from larger supporting branches with a length varying from 0.5 to 1.5 m) were harvested in the morning and transported to the lab in black plastic bags containing wet towels. Internodes with a length of 200 mm were cut and debarked underwater. They were re-saturated under low vacuum for 24 h at 4°C in filtered, distilled water (Hietz et al. 2008) with 0.005% Micropur (Katadyn Products, Wallisellen, Switzerland). Prior to hydraulic measurements, specimens were shortened to 130 mm and then re-cut several times with clean razor blades. Sapwood area hydraulic conductivity (Ks, cm 2 s −1 MPa −1 ) was measured under a hydraulic pressure head of 5.4 kPa (540 mm water column) with distilled and filtered (0.22 μm) water containing 0.005% Micropur. The saturated weight (SW) was determined on a balance (resolution of 0.0001 g, Mettler-Toledo International Inc., Greifensee, Switzerland). Air overpressure was applied in a double-ended pressure chamber (PMS Instruments, Corvallis, OR, USA), thereafter the specimen was weighed again in order to determine the fresh weight (FW) at a given pressure application. The pressure in the chamber was gradually increased with steps of 0.5 MPa or 1.0 MPa. The duration of the pressure exposition was standardized to 1 min . Hydraulic vulnerability curves of trunk wood samples were achieved with the methods described by Spicer and Gartner (1998) and Domec and Gartner (2001). Results on PLC and RWL at given pressure applications for L. decidua and P. abies came from existing datasets . Tangential and radial faces of 200-mm long wood beams with a transverse surface of 100 mm 2 were shortened on a band saw and thereafter re-cut several times with a razor blade. Specimens were re-soaked as described above (Hietz et al. 2008). The final dimensions of the specimens were 6 mm (radial) × 6 mm (tangential) × 120 mm (longitudinal).
Samples were dried at 103°C for 24 h (Rosner 2017) in order to determine the dry weight (DW) on a balance. The relative water loss (RWL) at Ψ was calculated as: The correct determination of the SW is crucial because relating FW to a field in situ water content would obscure the relationship between RWL and PLC and would not allow correct projection of PLC ).

Sample numbers, data processing, and statistical analyses
Numbers of sampled trees, samples and datasets can be found in Table 1. The software SPSS™ 21.0 was used to carry out the data analyses. Normal distribution was tested with the Kolmogorov-Smirnov test. Relationships between traits were accepted as significant if the P value was < 0.05.
Sapwood area-specific hydraulic conductivity at a given Ψ was divided by the sapwood area-specific hydraulic conductivity at full saturation in order to calculate the percent loss of conductivity (PLC). PLC was plotted against the negative of the applied pressure (Ψ). For some species, organs or age classes only mean values for PLC and RWL at a given pressure application were available. Hydraulic vulnerability curves were fitted by an exponential sigmoidal equation (Pammenter and Vander Willigen 1998), and the P 50 and P 88 (Domec and Gartner 2001), i.e., the pressure application at which 50% or 88% of conductivity loss occurred, were calculated. We used the following equation: The parameter "a" corresponds to the slope of the linear part of the regression and "b" is the P 50 . P 88 was calculated from these parameters. Ψ in Eq. (2) is used here and thereafter for water potential. In Table 2, results for "a" and P 50 are provided with their standard error and the 95% confidence interval (CI 95%).
The relationship between point measurements and mean PLC and RWL were tested by the "curve estimation" function in SPSS™ 21.0, where linear, quadratic, or cubic regressions were chosen according to their predictive quality. The chosen equation was used to calculate RWL at P 50 for each species, organ, or age class. In Table 3, the CI 95% and 95% individual prediction intervals (PI 95%) for RWL at P 50 or RWL at P 88 are provided. Species, organ, and age class-specific mean values of PLC (PLC pred ) and RWL were fitted by a Weibull equation (e.g., Lopez et al. 2005): The parameter "c" corresponds to the mean RWL across all conifers investigated in the study that causes~63% of PLC.
Water loss curves, i.e., the RWL plotted against Ψ (RWL-Ψ curve) were fitted by the "curve estimation" function in SPSS™ 21.0. The fittings with the highest predictive quality (r 2 ) and the most reliable shape were chosen. The "curve estimation" function was also used to establish the relationship between Ψ and RWL in order to predict Ψ at a given RWL, for instance the RWL at P 50 or at P 88 . In these curves, the Ψ was plotted against the RWL (Ψ-RWL curve, Table 4).
The predictive quality of the RWL for PLC at the species, organ and age class level was tested by calculating empirically modeled P 50 parameters from the RWL at P 50 and the relationship between Ψ and RWL (Ψ-RWL curve). The same procedure was performed for P 88 . The predicted values of P 50 and P 88 are provided with their 95% CI and 95% PI (Table 4). By means of the Eq. [3], PLC was predicted from RWL point measurements (if available) and mean values (Table 1). Thereafter, P 50 and P 88 parameters (Table 5) were calculated using Eq. [2]. Modeled P 50 and P 88 were related to the corresponding traits from directly measured datasets. Linear regression analysis was performed to meet the 1:1 slope requirement. A flow chart of the two different approaches is shown in Fig. 1.

Results
Conifer species investigated varied widely in their vulnerability to cavitation (Fig. 2, Table 2). In saplings, A. nordmanniana had the lowest P 50 (− 8.1 MPa) and P. menziesii grown in Austria had the highest P 50 (− 5.0 MPa). In branches, P 50 ranged from -5.8 MPa in P. menziesii to − 2.4 MPa in T. distichum. In general, P 50 was highest in the wood of the main trunk, ranging from -4.9 MPa in P. menziesii to − 2.2 MPa in P. abies. The species investigated varied as well in their RWL at a given pressure application (Fig.  2). For instance, whereas RWL increased only slightly with each pressure application in A. nordmanniana saplings (Fig. 2b), RWL had large increases over narrower pressure ranges in P. abies trunk wood (Fig. 2d).
PLC was strongly related to RWL at the species/organ/agespecific level (Table 3). Mean species/organ/age-specific PLC for a given Ψ and PLC predicted from the corresponding RWL dataset (Table 3) were therefore strongly linearly related (Fig.  3b). The RWL at P 50 had values ranging from 15% in L. decidua saplings to 36% in J. virginiana trunk wood. By means of the species/organ/age-specific RWL at P 50 and the relationship between Ψ and RWL (Table 4), P 50 values could be predicted which correlated strongly (almost 1:1) with those calculated from the measured dataset (Fig. 4a). Predicted P 88 was as well strongly related to P 88 derived from measured datasets (r 2 = 0.98, P < 0.0001).
In order to guarantee equal weight of each species-, organ-, and age class-specific PLC-RWL relationship, mean values for a given Ψ were used for the pooled data analysis (Fig. 3a). The relationship between PLC and RWL across all samples was fitted with the function: PLC pred is the predicted percent loss of hydraulic conductivity (Fig. 3c). More information on the parameters of Eq. (4) can be found in the legend of Fig. 3. RWL of 30.49% corresponds to a PLC pred of~63% across all conifer specimen investigated. RWL of 25.18% would then result in PLC pred of 50%, and RWL of 45.12% would result in PLC pred of 88% across species, organs, and age classes.
From RWL point measurements and the conifer-curve, PLC pred values were calculated. PLC pred values and the corresponding Ψ, was used to project P 50 (Table 5). The correlation between P 50 and the empirically modeled P 50 (P 50pred ) was tight (r 2 = 0.94, P < 0.0001), but no 1:1 relationship could be reached for specimens with low P 50 (Fig. 6, in the Annex). A linear regression was therefore used for reliably predicting P 50 (Fig. 4b).
where P 50pred' corresponds to P 50pred after slope correction. P 88pred was as well strongly related to P 88 calculated from measured data (r 2 = 0.98, P < 0.0001). Conifer species, organs or age classes with higher RWL at P 50 or P 88 were more vulnerable to cavitation: The positive relationship with P 50 was however much stronger with RWL at P 88 (Fig. 5). P 88 showed as well an increase with increasing RWL at P 88 (r 2 = 0.44, P < 0.01).

Discussion
This study tested whether an empirical relationship between the loss of water transport capacity and the loss of water content could be established across temperate conifer species. We found that it was possible to predict conductivity loss and eventually P 50 or P 88 for different conifer species, organs, and age classes with a coefficient of determination of 94% from quite simple RWL and Ψ measurements using one empirical model (conifer-curve, Fig. 3a). Although the RWL curves and the vulnerability curves differed widely between species, organs, or age classes (Fig. 2), the relationship between RWL and PLC is presumably quite conservative (Fig. 3). We discuss why this may be the case in conifers but not in angiosperms , explore the relationship between hydraulic capacitance and vulnerability to cavitation, and propose how the technique could be further developed as a fast and reliable phenotyping tool.

Why is the relationship between RWL and PLC so robust?
Conifer wood is quite homogenously constructed and solely one-cell type, the tracheid, fulfills the different functions of water transport and mechanical support (Braun 1970;Lachenbruch and McCulloh 2014). Species, organ, or age class-specific variability in late wood percent, lumen diameter, cell wall thickness, tracheid length, and pit properties result in different hydraulic vulnerabilities and water release curves (Domec and Gartner 2001;Hacke et al. 2001;Domec et al. 2009;Bouche et al. 2014;Hacke et al. 2015). We found a wide range in P 50 values in the current study. In that regard, it was remarkable how the young trunk of A. nordmanniana saplings, with P 50 of -8.1 MPa and trunk wood from the upper crown of mature P. abies trees with P 50 of − 2.2 MPa (Fig. 4) could be fitted into one PLC-RWL curve (conifer-curve, Fig. 3a) from which the species-and age class-specific PLC at a given Ψ could be reliably predicted from RWL data. This suggests that wood design in conifers is quite conservative concerning the PLC-RWL relationships. However, even if a given RWL results in a quite similar conductivity loss across different cambial age, anatomy can be adjusted to the hydraulic safety demands that are necessary for tree survival. The distance from the apex/tip influences tracheid size; tracheid lumen diameters are thus much smaller in saplings than at the lower trunk of mature trees of a given species (Anfodillo et al. 2013;Rosner 2017;Prendin et al. 2018); therefore, a stable PLC-RWL relationship suggests shorter tracheids and smaller pit aperture diameters with a higher torus overlap in saplings, which could additionally increase the hydraulic safety (Rosner 2013;Bouche et al. 2014;Hacke et al. 2015). Extreme shifts from the species mean PLC-RWL curve may come from the presence of  1 Flow chart of the measuring procedure for the two model approaches for calculating the P 50 or P 88 . Hatched lines indicate the modeling procedure for the "conifer curve", solid lines for the speciesspecific modeling approach to predict P 50 or P 88 . The dataset comprised the water potential (Ѱ), the RWL (relative water loss) and the PLC (percent loss of conductivity) reaction wood. Compression wood (Fig. 7, in the Annex) has a high wood density, lower conductivity (Spicer and Gartner 1998), but is more vulnerable to cavitation than opposite wood (Mayr and Cochard 2003). For instance, L. decidua branches had a higher conductivity loss at given relative water loss compared with other species (Fig. 3a). RWL at P 50 was only 15.1%. PLC in L. decidua predicted for a given Ψ with the conifer-curve was lower than the measured PLC (Fig. 3c). Therefore, P 50 was lower (more negative) than the P 50 calculated from predicted PLC values of the species-specific L. decidua curves (Fig. 4).
Such shifts in the PLC-RWL curves result in different hydraulic capacities, thus in differences between RWL at P 50 or P 88 .

Relationship between hydraulic capacitance and vulnerability to cavitation
Although the relationship between PLC and RWL is more stable in conifers than across angiosperm species , species-, organ-, and age class-specific differences in the RWL at P 50 do exist (Fig. 5). The RWL at P 50 Fig. 2 Point measurements of percent loss of hydraulic conductivity (PLC) and the estimated vulnerability curves described in Table 2 in the Annex (a, c, e, g) and of relative water loss (RWL) and the estimated water loss curves described in Table 4 in the Annex (b, d, f, h) plotted against the water potential for different conifer species, organs or age classes can be regarded as a capacitance parameter , which is very useful for comparing different species because no absolute values are used (Domec and Gartner 2001). We found a positive trend between P 50 and the RWL at P 50 and a significant positive relationship between P 50 and RWL at P 88 (Fig. 5). Similarly, McCulloh et al. (2014) found that mature conifer trunks had greater hydraulic vulnerability together with higher hydraulic capacitance than branches of the same species. Angiosperm branches with higher hydraulic capacitance also show less negative (higher) mean daily minimum water potentials (Meinzer et al. 2003). Species with higher P 50 may therefore have more pronounced diurnal changes in conductivity loss (Trifilò et al. 2015). Within a plant, woody parts with higher hydraulic vulnerability but higher hydraulic capacitance may act as important storage compartments for water (Holbrook 1995). We have no sound explanation why a stronger relationship existed between P 50 and RWL at P 88 than between P 50 and RWL at P 50 , because in conifers, P 50 is regarded as a "point of no return" for the recovery from drought (Choat et al. 2018), even though some species can survive much lower conductivity losses (e.g., Hammond et al. 2019). It might be that the presence of reaction wood (Mayr and Cochard 2003) masks the relationship at high Ψ. The presence of reaction wood but also the distance from the apex/tip (Anfodillo et al. 2013;Rosner 2017;Prendin et al. 2018) may explain some different P 50 values than those found in literature. Branch P 50 values for L. decidua, P. abies, P. ponderosa, P. taeda, and T. distichum corresponded to those published earlier (reviewed in Choat et al. 2012, Bouche et al. 2014. We found however much higher (less negative) P 50 for J. virginiana branches but slightly lower P 50 in P. menziesii branches (reviewed in Choat et al. 2012). Fig. 3 Relationship between mean measured PLC and RWL across conifer species, organs and age classes for a given pressure application (Ψ): the "conifer-curve" (a), predicted mean PLC using species, organ and age specific curves (

Phenotyping: limits of application and further development of the method
Note that the empirical models for predicting PLC from RWL measurements and eventually P 50 are applicable to functioning sapwood solely. In that regard, and except in Douglas-fir, the advantage of conifer wood is that many annual rings are used for conducting water (Bertaud and Holmbom 2004). However, reliable, standardized, sampling may be easier for wood of the main trunk than for small branches and shoots because the sapwood zone is easier to detect, and reaction wood can be avoided. However, when trunkwood is sampled, the distance from the apex/tip has to be considered (Anfodillo et al. 2013;Prendin et al. 2018). Even though branches used in general for vulnerability curves have a small diameter, they may be quite old (Schweingruber et al. 2008), and not all annual rings will necessarily transport water. It is thus important to harvest branches where the woody part consists of sapwood solely, which can be easily tested by staining techniques (Hietz et al. 2008). Moreover, we suggest performing experiments only during the growing season because (1) the bark is easier to remove from the woody parts, and (2) wood of temperate species harvested during the winter time shows a poorer ability to refill artificially, presumably because of natural pit aspiration (Mayr et al. 2014). The reliable prediction of the weight at full saturation is of utmost importance for the proposed technique, as already pointed out in a preceding study . In a specimen that contains heartwood, the tracheids will not refill properly because many pits are permanently aspirated. Dehydration behavior of such "oversaturated" regions, i.e., artificially refilled regions that did not contribute to the sapflow in the living tree anymore (Pivovaroff et al. 2016), might be different. Moreover, the application of positive pressure may result in water loss but not necessarily to a loss in hydraulic conductivity. The method presented is much less labor intensive than repeated flow measurements and less prone to errors resulting from tracheids clogged with resin or other organic substances.
Nevertheless, the procedure could still be improved, regarding the time that was necessary to measure one specimen. It should be possible to collect the xylem sap that is released due to the pressure application in pre-weighed vials (Ennajeh et al. 2011;Savi et al. 2019) and calculate the fresh weight at a given Ψ from subtracting the mass of water. A whole vulnerability curve could thus be produced within less than a quarter of an hour. Consensus should be about the time of pressure application and the prepreparation of the specimens (Mayr et al. 2006), because this can influence the relationship between the RWL and Ψ. The method of stress application that leads to conductivity loss (e.g., bench top dehydration, pressure collar) has no influence on the relationship between RWL and PLC ), but for predicting P 50 , Ψ-RWL datasets are necessary, which simulate the situation in the living tree. In that regard, it is likely that the conifer-curve is not applicable for RWL datasets of very small wood samples where Ψ is measured in a small chamber of a thermocouple psychrometer (Meinzer et al. 2003;Barnard et al. 2011;McCulloh et al. 2014;Jupa et al. 2016;Pratt and Jacobsen 2017), because the curve shapes often differ from those measured on bigger samples Gartner 2001, 2002;Domec et al. 2006;Gleason et al. 2014;Blackman et al. 2016). Due to the high amount of cut open surfaces in relation to volume, dehydration in small wood samples will proceed quite fast and probably not from the more vulnerable to the less vulnerable tracheids but from the outside to the inside of the specimen ).

Conclusions
We were able to construct one empirical model equation in order to predict conductivity loss and eventually P 50 for different conifer species originating from different ecosystems. The method offers fast and reliable prediction of PLC from quite simple and fast RWL and Ψ measurements and could be thus applied as an efficient phenotyping tool for P 50 . Future research should test this PLC-RWL in conifer species not included in this study to Fig. 5 Relationship between positive pressure that is necessary to result in 50% conductivity loss (P 50 ) and the RWL at P 50 (a) and at P 88 (b) for different conifer species, organs and age classes determine if the relationship is universal. The knowledge of this relationship can help interpret decent indirect anatomy-based techniques such as X-ray micro-computed tomography or neutron radiography. Future potential applications of the new method presented are screening trees for drought sensitivity and a fast interpretation of diurnal, seasonal, or drought-induced changes in xylem water content upon their impact on conductivity loss.
Statement on data availability The dataset for the "conifer-curve" is available from the corresponding author on reasonable request.
Funding Information Open access funding provided by University of Natural Resources and Life Sciences Vienna (BOKU). This study has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 645654 (Topwood). DMJ was partially supported by NSF IOS-165731 and JCD and DMJ were partially supported by NSF IOS-1754893.

Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of interest.
Abbreviations CI 95%, 95% confidence intervals; DW, dry weight; FW, fresh weight; P 50 , positive pressure resulting in 50% conductivity loss; P 50pred , positive pressure resulting in 50% conductivity loss calculated from PLC pred ; P 50pred' , P 50pred after slope correction; P 88 , positive pressure resulting in 88% conductivity loss; P 88pred , positive pressure resulting in 88% conductivity loss calculated from PLC pred ; PI 95%, 95% individual prediction intervals; PLC, percent loss of conductivity; PLC pred , PLC predicted from RWL; RWL, relative water loss; RWL at P 50 , RWL at Ψ when 50% conductivity is lost; RWL at P 88 , RWL at Ψ when 88% conductivity is lost; SW, water-saturated weight; Ψ, xylem pressure Annex Branches came either from the base of the crown (branch base) or from its top (branch top). Datasets are marked with *where only mean value datasets were available The parameter "a" corresponds to the slope of the linear part of the regression and "b" is the P 50 , i.e., the pressure that is necessary to result in 50% conductivity loss P 88 is the pressure that would result in 88% conductivity loss (Domec and Gartner 2001). Results for a and P 50 are given with ± standard error and the 95% confidence interval (CI 95%) is given in brackets. Information on the sample and dataset numbers is given in Table 1  Table 3 Parameters for linear (b0, b1), quadratic (b0, b1, b2) or cubic (b0, b1, b2, b3) equations for the relationship between percent loss of conductivity (PLC, independent variable) and the relative water loss (RWL, dependent variable) (P < 0.0001), the calculated RWL resulting in 50% (RWL at P 50 ) and 88% (RWL at P 88 ) of conductivity loss and their 95% confidence intervals (CI 95%) and 95% individual prediction intervals (PI 95%) for different conifer species and different age classes  Equation parameters are given either for linear (b0, b1), quadratic (b0, b1, b2), or cubic (b0, b1, b2, b3) equations for branches, saplings, or trunk wood of different conifer species. The predicted values of P 50 and P 88 are given with their 95% confidence intervals (95% CI) and 95% prediction intervals (95% PI). P is < 0.0001 for all equations listed  Fig. 2a. The parameter "a" corresponds to the slope of the linear part of the regression and "b" is the P 50 , i.e., the pressure that is necessary to result in 50% conductivity loss. P 88 is the pressure that would result in 88% conductivity loss. Results for a and P 50 are given with ± standard error, and the 95% confidence interval (CI 95%) is given in brackets. Information on the sample and dataset numbers is given in Table 1 Fig. 6 Predicted pressure application that is necessary to result in 50% conductivity loss (P 50 ) from the conifer-curve 1 [Eq. 4] related to P 50 derived from experimental datasets. Detailed information on the predicted values can be found in Table 5. The gray dashed line indicates the 1:1 relationship Fig. 7 Transverse sections of Larix decidua branch wood (a) and Picea abies young trunk wood (b). L. decidua contains compression wood that is common for conifers on the lower part of branches. Compression wood is characterized by higher density zones in the earlywood. Due to different shrinkage properties of wood differing in density, the L. decidua branch shows a concave bending at the compression wood side and a convex bending at the side of the opposite wood after drying at 103°C (c, above), whereas it was straight at full saturation. The young trunk wood sample of a P. abies sapling remained straight after drying at 103°C because the amount of late wood was quite consistent in each annual ring (c, below) Open Access This article is distributed under the terms of the Creative Comm ons Attribution 4.0 International License (http:// creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.