2.1 STUDY AREA
The study took place in the Etosha Heights Private Reserve (EHPR) (19.2451 °S, 15.1921 °E), located in the Kunene region in northern Namibia, approximately 400 km north of the city of Windhoek. EHPR spreads over 480 km2 and shares an approximately 65 km long border with the Etosha National Park. The research site is part of a large-scale wildlife area.
The climate in the region is semi-arid (Peel et al., 2007). It is characterized by high air and soil temperatures with mean annual temperatures above 22°C and high solar radiation. Annual rainfall amounts to 300 - 350 mm and precipitation is highly variable in time and space. Annual evaporation rate ranges 2,500 - 2,600 mm, and thus an order of magnitude higher than the average levels of rainfall received (Atlas of Namibia Team, 2022). Temperatures and precipitation are changing seasonally, with the highest average precipitation during the wet season (November - March) and lowest average precipitation during the dry season (April - October). The soil is rich in carbonate and consists of limestone and dolomite rocks as well as sand and calcrete (Nortjé, 2019). The vegetation type in the area is a tree-and-shrub savanna with varying density, from large open grasslands with scattered trees up to dense, shrub-dominated landscapes (Atlas of Namibia Team, 2022). The most dominant shrub species in the region isColophospermum mopane , which occurs in high abundance throughout the reserve (Bester, 1996). Other prominent species in the area includeSenegalia mellifera, Dichrostachys cinerea, Vachellia nebrownii, Catophractes alexandri and Vachellia reficiens . The fauna within EHPR is rich and includes large populations of species from various taxonomic classes, including large mammalian grazers (Antelopes, Giraffes), browsers (Elephants, Rhinos), and predators (Lions, Leopards).
2.2 SHRUB SAMPLING AND MEASUREMENTS
We sampled all prominent shrub species, in total six species, in an area of approximately 164 km2 in central-east EHPR during March and April 2021. Sampling was assigned to 60 blocks, with a minimal distance between blocks of 500 m to control for local effects and to avoid spatial autocorrelation. Measured individuals and stems reflect the full range of sizes for each species occurring within EHPR. To avoid biases in shrub dimensions due to browsing, we sampled only individuals with minimal apparent damage, such as recently broken branches or a large portion of missing foliage caused by e.g., rhinos or elephants.
To establish allometric relationships between canopy area and sapwood area via stem diameter, we measured canopy area (CA) and stem diameter (DStem) for one individual of each of the six species (360 individuals in total, 60 per species) in each block. CA estimates relied on the average crown spread method (ACS) (Blozan, 2004), using measuring poles with a 1 cm scale. As stems are not necessarily round, DStem was measured by averaging two perpendicular diameters using a vernier scale with an accuracy level of 1 mm. In the case of a multi-stemmed individual, we measured all stems. Although DStem is commonly measured at breast height (i.e., 130 cm above ground level), the morphology of most shrub species included in this study did not allow for this measure, as shrubs are often either smaller or far too branched at this height. Since species differ in size and morphology, we selected appropriate heights for each species as follows: 20 cm (Catophractes alexandri, Vachellia nebrownii ), 50 cm (Dichrostachys cinerea, Senegalia mellifera, Vachellia reficiens ), 130 cm (Colophospermum mopane ). The validity and comparability of stem diameter measurements at different heights rely on the foundations of Leonardo da Vinci’s area-preserving rule, which states that the total cross-section area across all stems in an individual plant remains constant along the height axis (Richter 1970). This area-preserving rule has been repeatedly supported by different studies and methods (Minamino & Tateno. 2014; Oppelt, 2001).
To study the relationship between stem diameter and sapwood area, we randomly selected between 20 and 23 individuals per species (visiting 25 blocks: 0-1 individual per block per species, 130 individuals in total). We removed one branch per individual using branch shears or a handsaw. To ensure that our data set for developing the allometries contained samples from the complete spectrum of Dstem values, we sampled a large range of branch sizes (3.9 mm – 111.4 mm). Measurements of stem diameter and sapwood area were achieved via staining of stem cross sections. Immediately after cutting, the ends were shaved with fresh razor blades, thus reducing the possibility that damage to the xylem during harvest would affect our results. The sample was immediately inserted into a tube containing a staining solution of methylene blue 0.5% (w/v) and distilled water with a concentration ratio of 1:20. The amount of diluted solution varied according to the diameter of the sample and the tubes used for staining, between 10 ml for very small samples (twigs) and 200 ml (large branches). Tubes were sealed to prevent evaporation and samples remained in the solution for at least 24 hours to allow uptake of the dye into the stem via active transpiration by the remaining foliage. After removing and drying the samples in the air, cross-sections were made approximately 1 cm above the bottom of each sample using branch shears or an electric hand saw. The cross-sections were placed on a clear background adjacent to a ruler with 1 mm marks for consistent scaling. Images were taken using a digital Canon SX540 HS camera placed on a tripod. Visual analysis was done using ImageJ (Fiji is Just) version 2.1.0/1.53c (Abramoff, 2004; Schindelin et al., 2012). Representative examples for staining samples for each species are illustrated in Fig 1. In every sample, the borders of the following three areas were marked manually and the resulting areas measured digitally with an accuracy of 1 mm2: A) total area (the entire area of the cross-section including bark), B) wood area, and C) heartwood area (Fig. 2). The outer limits of the heartwood were defined as the first innermost tree ring of the cross-section not containing traces of blue staining (Fig. 2). While our staining approach dyed the active part of the sapwood only, this procedure enabled us to identify the entire sapwood area that has been formed. Sapwood area was mathematically obtained by subtracting the heartwood area from the wood area. Stem diameter (Dstem) was derived based on total area (Atot), assuming circularity of the cross-section.
2.3 DATA ANALYSIS
Species-specific allometric relationships were modeled using the power law equation (Niklas, 1994)
\(Y\ =\ {b\bullet X}^{a}\), (1)
where \(X\) is the size measure (Dstem or CA), \(b\) a normalization constant, \(a\) the scaling exponent, and \(Y\) the estimated sapwood area (SA or SAtot). We considered the total sapwood area (SAtot) of each study shrub for the allometry between canopy area (CA) and SA. To obtain SAtot we measured the Dstem of all stems, applied the corresponding species-specific allometric relationship between Dstem to SA to each stem, and summed up the estimates. To identify the scaling exponent and to enable a comparison with the WBE prediction, we applied log-transformation and fitted a linear model, as
\(\ln\left(Y\right)=\ a\bullet ln\ \left(X\right)+ln(b)\). (2)
Models were assessed using both, R2 and the regression coefficient \(a\) (the scaling exponent) and its significance (P < 0.05 of F-value). Additionally, 95% confidence intervals of the scaling exponent were calculated and plotted for each species-specific model.
The equations were back-transformed into their ‘natural’ exponential form to simplify the application of the allometric relationships. To prevent underestimation bias of the logarithmic regression estimate (Niklas, 1994), a back-correction factor CF was introduced based on Sprugel (1983), as
\(CF\ =exp(\frac{\text{SEE}^{2}}{2})\) (3)
where SEE is the standard error of the scaling exponent estimate \(a\).
The final equation for the prediction of sapwood area from the respective size measure will then have the following form:
\(\ln\left(Y\right)=CF\bullet\left(\text{\ ln}\left(b\right)+\ a\bullet ln\ \left(X\right)\right)\overset{\Rightarrow}{}Y=b^{\text{CF}}\bullet X^{a\bullet CF}\), (4)
To identify species-specific structural characteristics of sapwood formation due to drought and their relation to plant age, we also calculated the relative sapwood area (\(\frac{\text{SA}}{\text{wood\ area}}\)) and fitted an additional linear model for the relationship between relative sapwood area and Dstem for each species.
Data processing, data visualization and statistical analysis were performed with R version 4.0.5 (2021-03-21) and R-Studio version 1.1.423 (R Core Team, 2019). Used packages included ‘car’ (Fox & Weisberg, 2019), ‘dplyr’ (Wickham et al., 2023a), ’FSA’ (Ogle et al., 2023) ‘ggplot2’ (Wickham, 2016), ‘ggpubr’ (Kassambara, 2020), and ‘tidyr’ (Wickham, 2023b).
RESULTS
In total, we stained and measured 130 individual plants for sapwood area and stem diameter, and measured canopy area and total stem diameter of 360 individuals of six savanna bush encroacher species. A detailed summary of the measurements is found in Appendix Table A1.
In all six species, sapwood area was positively correlated with stem diameter. Dstem accounted for almost the entire variation in C. alexandri (99%), C. mopane (98%),S. mellifera (97%), V. reficiens (97%), V. nebrownii (97%) and D. cinerea (78%) (Fig. 3, Table 1). The very high values of R2 for all species established Dstem as a strong independent variable to estimate sapwood area. Apart from D. cinerea , all species included the regression line predicted by the WBE model within the 95% confidence interval of the slope.
The relative sapwood area to Dstem relationship varied substantially between species (Fig. 4). While this ratio was constant inC. mopane, S. mellifera , and V. reficiens , a significant positive relationship was found in C. alexandri ,V. nebrownii and a significant negative one in D. cinerea . On average, D. cinerea invested clearly the least of all species in water conducting sapwood compared to heartwood.
Moreover, sapwood area was positively correlated with canopy area. CA accounted for most of the variation of SAtot in C. alexandri (82%), C. mopane (84%), S. mellifera (80%),V. reficiens (86%), V. nebrownii (81%) and a bit less again in D. cinerea ( 71%) (Fig. 5, Table 2).Although R2 values were high for all species, they were lower than for the correlation between Dstem and SA (Fig. 3, Table 1).
DISCUSSION
Sapwood area is a key component in quantifying canopy transpiration and allometric equations for estimating sapwood area using tree size parameters have been developed for various woody ecosystems. And yet, in the case of Southern African savannas, only few exist (Lubczynski et al., 2017), although various allometric relationships have been extensively studied in recent years (Fregoso, 2002; Issoufou et al., 2015; Moncrieff et al., 2011; Tredennick et al., 2013). Scaling exponents of these size-correlated trends often rely on the universal value predicted by the West-Brown-Enquist model (West et al., 1999; Niklas, 1994). Nevertheless, the model itself is a point of dispute (Brown et. at., 2005; Kozlowski & Konarzewski, 2004) because it does not incorporate features specific for different plant taxa or for different environments. As sapwood formation is likely governed by low water availability, establishing species-specific relationships between sapwood area and tree dimension for Southern African savanna woody species may be essential to accurately estimating transpiration rates (Ter-Mikaelian & Korzukhin, 1997; Yaemphum et al., 2022). In this study, we established allometric relationships between tree dimension and sapwood area in six shrub species involved in savanna bush encroachment in Namibia.
Our results illustrate that sapwood area can be reliably predicted based on stem diameter in all six species tested. Comparing our results with the prediction of the WBE model (West et al., 1999) showed that the model holds true in most cases.
Various findings illustrate that despite the unique conditions in savannas and other drylands, the scaling relationships between stem diameter and sapwood area in drought resistant plants are similar to those of plants found in other climates (Fregoso, 2002; Gebauer et al., 2009; Patino et al., 1995; Wang et al., 2010). However, the relationship between stem diameter and sapwood area in D. cinerea revealed an exponent substantially lower than the other five bush species tested. This is not exclusive for the Etosha region. In the eastern Kalahari in Botswana, D.cinerea revealed the smallest slope of nine species (Lubczynski et al., 2017), although authors fitted a linear function rather than a power function (in accordance to the WBE model) to the relation between sapwood area and stem diameter. Petit and Anfodillo (2009) illustrate an anatomical reason why actual sapwood area fails to scale with the stem diameter raised to 2.33 sometimes. What we usually consider as sapwood does not actually correspond to the conductive tissues in the WBE model. Conduits (vessels and tracheids) are always embedded in a matrix of wood fibers (stabilization function) and parenchyma (storage and embolism repair function). If the general assumptions of the WBE theory regarding geometric and hydrodynamic constrains (West et al., 1997) are valid, smaller allometric exponents as in D. cinerea arise if there is more genuine conductive tissue and less parenchyma and wood fibers on the same surface. More genuine conductive tissue can arise either with wider conduits or with more conduits in total. Such a sapwood composition at the expense of parenchyma is, however, more vulnerable to cavitation and -embolism (Brodersen & McElrone, 2013), even if the same conductivity across the stem is reached compared to species exhibiting the allometric exponent of 2.33 of the WBE theory. Parenchyma cells in sapwood serve as large water storage reservoirs and are linked to osmotically driven embolism repair mechanism (Broderson & McElrone, 2013). The vulnerability to cavitation and embolism might be partly compensated by a decrease in conduit size. The higher wood density of D. cinerea compared to other savanna species (Fernandez-Ortuño et al., 2015) supports indeed a smaller conduit size. That these vessels are small, although probably high in number, finds also support since D. cinerea has a low sap flow velocity relative to other savanna shrub species (Zziwa 2003), and estimations of transpiration rates of vegetation plots in areas predominated by D. cinerea were lower than areas with similar shrub density predominated by other common shrubs (Chavarro-Rincon, 2009). Although the size and number of conducting vessels per stem area of D. cinerea is unknown, the allometric exponent and sap flow velocity taken together indicate that the species might be relying on this to compensate for a reduced sapwood area. Thus, D. cinereaseems to be less efficient in water uptake and might be more water dependent than the other bush encroacher species in our study. IndeedD. cinerea does almost not increase in biomass and is less abundant in areas with less soil moisture and higher temperature (de Klerk, 2004; Shikangalah et al., 2021). Its main distribution in Namibia as bush encroacher extends to savannas with MAP > 550mm (de Klerk, 2004). Questions remain regarding the underlying causes of its dominance in these moister areas as well as the functional driver of the unusual small allometric exponent. In any case, D. cinerea ’s striking anatomy is supported by our results on low relative sapwood area and by previous results showing that D. cinerea has an unusual small sapwood to heartwood ratio than other woody savanna species (Shikangalah et al., 2021; Zziwa, 2003). A large heartwood area might relate to an adaptation mechanism, which increases the stem stability, because heartwood is generally stiffer than sapwood. A strong argument for this view is our observation that relative sapwood area decreased with age (stem diameter as a proxy of age or growth). However, if central heartwood was to increase flexural stiffness, the heartwood would need to have a inordinately lower elasticity than sapwood (Niklas, 1997), a trait which we do not know. Moreover, high wind velocities as a driver of stability traits are not typical for the main distribution areas of D. cinerea (Atlas of Namibia Team, 2022).
An adaptation in flexural stiffness or any other reason for relatively more heartwood was not detected in C. mopane , S. melliferaand V. reficiens . Furthermore, the small shrubs V. nebrownii and C. alexandri even decrease the relative amount of central heartwood with stem age, promoting a higher flexibility instead of stiffness, which might be affordable if the increase in overall woody biomass contributes to stability already. If sapwood area is correlated with storage capacity for water (Scholz et al., 2008), lower water availability could be a driver distinguishing their local occurrence. While definitive conclusions regarding C. mopane , S. mellifera and V. reficiens based on these findings are currently hard to make, our results could help understanding what conditions drive which shrub species during bush encroachment.
Based on the overall strong relationship between stem diameter and sapwood area, we were also able to establish strong relationships between crown area and sapwood area in all six species. This result is meaningful because it supplies further support for the potential of estimating sapwood area based on aerial imagery (Mitra et al., 2020). Whereas previous studies found a linear relationship between crown size and properties of water conductance (Ahongshangbam et al., 2020; Quiñonez-Piñón & Valeo, 2019; Tziaferidis, 2021), the relationships detected in our study were slightly exponential, presumably due to the inclusion of smaller samples. Another reason for a divergent allometric relationship might be the time of sampling. We carried out data collection and measurements at the end of the rainy season. Deciduous phenology of savanna trees and shrubs has been shown to be strongly influenced by seasonality (Dahlin, 2016), meaning that the relationships between crown area and total sapwood area may vary seasonally. Continuous measurements of crown area and stem diameter as a base for total sapwood area are therefore necessary to adapt the relationship described above to different seasons and years.
In addition, since our measurements of plant dimensions were taken within a nature reserve, where browsing pressure by large African mammals such as Giraffes, Elephants, and Rhinos is present, a comparison of crown area across different land-use types with different browsing pressures might be required to understand to what degree crown area is affected by the presence of large browsers. Nevertheless, we believe that our allometric relations are sufficiently reliable and universal due to our selection of apparently unharmed individuals, as well as due to the sampling of shrubs from multiple plots covering a large area with many different local conditions.
CONCLUSIONS
The assessments of six main bush encroacher species of Namibia proposed here indicate that sapwood area can be reliably predicted based on stem diameter, crown dimensions and the universal WBE model. Our allometric equations offer the prospect of vastly increasing our knowledge about transpirational water losses in semiarid bush-encroached savannas. Robust species-specific models predicting individual shrub sapwood area from shrub size are, however, critical for accurate estimating of stand- and landscape-scale transpiration in shrub encroached regions, in particular when D. cinerea is involved. A subsequent extension of our research may apply these species-specific total sapwood area-crown area or sapwood area-stem diameter allometric equations to estimate woody transpiration for different bush encroachment scenarios in the studied region. Such analysis remains highly relevant for all Southern African savannas given the widespread shift in vegetation composition via bush encroachment by different species but also considering climate change, in particular as droughts are projected to become longer and more frequent (IPBES, 2018; IPCC, 2023).
ACKNOWLEDGMENTS
This work was supported by the German Federal Ministry of Education and Research (BMBF) project ORYCS (FKZ 01LL1804A). We thank the Ministry of Environment, Tourism and Forestry (Namibia) and the Namibian National Commission for granting research permission [certificate number RCIV00032018 with authorization numbers: 20190602, 20190808] and Andre Nel (the owner) and the team of Etosha Heights Private Reserve, for their manifold support.
We gratefully acknowledge the German Research Foundation (DFG) for their generous support through open access funding, enabling us to freely disseminate our research findings.