Biomechanical design and long-term stability of trees: Morphological and wood traits involved in the balance between weight increase and the gravitropic reaction

Studies on tree biomechanical design usually focus on stem stiffness, resistance to breakage or uprooting, and elastic stability. Here we consider another biomechanical constraint related to the interaction between growth and gravity. Because stems are slender structures and are never perfectly symmetric, the increase in tree mass always causes bending movements. Given the current mechanical design of trees, integration of these movements over time would ultimately lead to a weeping habit unless some gravitropic correction occurs. This correction is achieved by asymmetric internal forces induced during the maturation of new wood.The long-term stability of a growing stem therefore depends on how the gravitropic correction that is generated by diameter growth balances the disturbance due to increasing self weight. General mechanical formulations based on beam theory are proposed to model these phenomena. The rates of disturbance and correction associated with a growth increment are deduced and expressed as a function of elementary traits of stem morphology, cross-section anatomy and wood properties. Evaluation of these traits using previously published data shows that the balance between the correction and the disturbance strongly depends on the efficiency of the gravitropic correction, which depends on the asymmetry of wood maturation strain, eccentric growth, and gradients in wood stiffness. By combining disturbance and correction rates, the gravitropic performance indicates the dynamics of stem bending during growth. It depends on stem biomechanical traits and dimensions. By analyzing dimensional effects, we show that the necessity for gravitropic correction might constrain stem allometric growth in the long-term. This constraint is compared to the requirement for elastic stability, showing that gravitropic performance limits the increase in height of tilted stem and branches. The performance of this function may thus limit the slenderness and lean of stems, and therefore the ability of the tree to capture light in a heterogeneous environment.     

Reduced wood stiffness and strength, and altered stem form, in young antisense 4CL transgenic poplars with reduced lignin contents

? Reduced lignin content in perennial crops has been sought as a means to improve biomass processability for paper and biofuels production, but it is unclear how this could affect wood properties and tree form. ? Here, we studied a nontransgenic control and 14 transgenic events containing an antisense 4-coumarate:coenzyme A ligase (4CL) to discern the consequences of lignin reduction in poplar (Populus sp.). During the second year of growth, trees were grown either free-standing in a field trial or affixed to stakes in a glasshouse. ? Reductions in lignin of up to 40% gave comparable losses in wood strength and stiffness. This occurred despite the fact that low-lignin trees had a similar wood density and up to three-fold more tension wood. In free-standing and staked trees, the control line had twice the height for a given diameter as did low-lignin trees. Staked trees had twice the height for a given diameter as free-standing trees in the field, but did not differ in wood stiffness. ? Variation in tree morphogenesis appears to be governed by lignin x environment interactions mediated by stresses exerted on developing cells. Therefore our results underline the importance of field studies for assessing the performance of transgenic trees with modified wood properties.     

Study of tension wood in the artificially inclined seedlings of <Emphasis Type="Italic">Koelreuteria henryi</Emphasis> Dummer and its biomechanical function of negative gravitropism

Key message

Stem reorientation is critical to tree survival. With anatomical observation and strain measurement, the tension wood formation and biomechanical behavior were studied to gain insights into tree uprighting process.

Abstract

Tension wood plays a role in maintaining the mechanical stability of angiosperm trees. Both biological and physical aspects of tension wood are essential in understanding the mechanism of trunk or branch reorientation. In this study, we worked on both tension wood formation and its biomechanical function in artificially inclined 2-year-old Koelreuteria henryi seedlings. The tension wood formation and reorientation process of the trunk last for about 3 months. With pinning method, we confirmed that at the beginning of inclination the cambial zone including the vascular cambium and the developing normal wood fibers on the upper side of the inclined trunk perceives the onset of mechanical change and starts to produce G-fibers that generate a strong contractile released growth strain (RGS) for gravitropic correction. Stronger contractile RGS and more tension wood were found at the trunk base than at the half-height, suggesting that the trunk base plays a key role in trunk uprighting of K. henryi seedlings. The eccentric cambial growth in the tension wood side increases the efficiency of gravitropic correction and the compressive strains measured in the opposite wood of some inclined seedlings also help the upright movement.

     

Effects of bending stress on taper and growth of stems of youngEucalyptus regnans trees

A glasshouse experiment investigated the effect of bending stress on stem radial and height growth and stem taper ofEucalyptus regnans seedlings. Eighteen-week-old, potted seedlings were bent continuously for 8 weeks with a static bending stress. The bending treatment was then removed and the seedlings grown for another 12 weeks. Other seedlings were stayed vertically throughout the experiment whilst control seedlings were neither bent nor stayed. Seedlings were rotated every 2 days to prevent reaction wood developing asymmetrically in the stems of bent trees. Bent trees had higher radial growth rates, developed more tapered stems and had higher safety factors (the ratio of stem radius to the minimum radius required to prevent the tree toppling over) than unbent seedlings. They produced a band of tension wood in their stems and ceased height growth whilst bent. When bending ceased, they resumed normal radial and height growth. Unbent trees developed more cylindrical stems. There were no differences in growth behaviour between stayed and control trees. Bent and unbent trees all developed a butt swell, the taper of which was not affected by treatment. It was concluded that bending stress has substantial effects on both the size and taper of tree stems. However, the development of butt swell is independent of the bending stress applied. The results were considered in relation to biomechanical theories of tree stem development.     

Identification of biomechanical factors involved in stem shape variability between apricot tree varieties

BACKGROUND AND AIMS: Stem shape in angiosperms depends on several growth traits such as elongation direction, amount and position of axillary loads, stem dimensions, wood elasticity, radial growth dynamics and active re-orientation due to tension wood. This paper analyses the relationship between these biomechanical factors and stem shape variability. METHODS: Three apricot tree varieties with contrasting stem shape were studied. Growth and bending dynamics, mechanical properties and amount of tension wood were measured on 40 1-year-old stems of each variety during one growth season. Formulae derived from simple biomechanical models are proposed to quantify the relationship between biomechanical factors and re-orientation of the stems. The effect of biomechanical factors is quantified combining their mechanical sensitivity and their actual variability. RESULTS: Re-orientations happened in three main periods, involving distinct biomechanical phenomena: (a) passive bending due to the increase of shoot and fruit load at the start of the season; (b) passive uprighting at the fall of fruits; (c) active uprighting due tension wood production at the end of the season. Differences between varieties mainly happened during periods (a) and (b). CONCLUSIONS: The main factors causing differences between varieties are the length/diameter and the load/cross-sectional area ratios during period (a). Wood elasticity does not play an important role because of its low inter-variety variability. Differences during period (b) are related to the dynamics of radial growth: varieties with early radial growth bend weakly upward because the new wood layers tend to set them in a bent position. The action of tension wood during period (c) is low when compared with passive phenomena involved in periods (a) and (b).     

The gravitropic response of poplar trunks: key roles of prestressed wood regulation and the relative kinetics of cambial growth versus wood maturation

In tree trunks, the motor of gravitropism involves radial growth and differentiation of reaction wood (Archer, 1986). The first aim of this study was to quantify the kinematics of gravitropic response in young poplar (Populus nigra x Populus deltoides, 'I4551') by measuring the kinematics of curvature fields along trunks. Three phases were identified, including latency, upward curving, and an anticipative autotropic decurving, which has been overlooked in research on trees. The biological and mechanical bases of these processes were investigated by assessing the biomechanical model of Fournier et al. (1994). Its application at two different time spans of integration made it possible to test hypotheses on maturation, separating the effects of radial growth and cross section size from those of wood prestressing. A significant correlation between trunk curvature and Fournier's model integrated over the growing season was found, but only explained 32% of the total variance. Moreover, over a week's time period, the model failed due to a clear out phasing of the kinetics of radial growth and curvature that the model does not take into account. This demonstrates a key role of the relative kinetics of radial growth and the maturation process during gravitropism. Moreover, the degree of maturation strains appears to differ in the tension woods produced during the upward curving and decurving phases. Cell wall maturation seems to be regulated to achieve control over the degree of prestressing of tension wood, providing effective control of trunk shape.     

Still rethinking the value of high wood density

? Premise of the study: In a previous paper, we questioned the traditional interpretation of the advantages and disadvantages of high wood density (Functional Ecology 24: 701-705). Niklas and Spatz (American Journal of Botany 97: 1587-1594) challenged the biomechanical relevance of studying properties of dry wood, including dry wood density, and stated that we erred in our claims regarding scaling. ? Methods: We first present the full derivation of our previous claims regarding scaling. We then examine how the fresh modulus of rupture and the elastic modulus scale with dry wood density and compare these scaling relationships with those for dry mechanical properties, using almost exactly the same data set analyzed by Niklas and Spatz. ? Key results: The derivation shows that given our assumptions that the modulus of rupture and elastic modulus are both proportional to wood density, the resistance to bending is inversely proportional to wood density and strength is inversely proportional with the square root of wood density, exactly as we previously claimed. The analyses show that the elastic modulus of fresh wood scales proportionally with wood density (exponent 1.05, 95% CI 0.90-1.11) but that the modulus of rupture of fresh wood does not, scaling instead with the 1.25 power of wood density (CI 1.18-1.31). ? Conclusions: The deviation from proportional scaling for modulus of rupture is so small that our central conclusion remains correct: for a given construction cost, trees with lower wood density have higher strength and higher resistance to bending.     

Radial wood allocation in Schizolobium parahyba

? Premise of the study: Pioneer species of tropical trees allocate wood specific gravity (SG) differently across the radius. Some species exhibit relatively uniform, low SG wood, whereas many others exhibit linear increases in SG across the radius. Here, we measured changes in SG across the radius of Schizolobium parahyba (Fabaceae-Caesalpinioideae), a wide-ranging, neotropical pioneer, used extensively in land reclamation and forest restoration in Brazil. ? Methods: Pith-to-bark radial wood cores were extracted with increment borers from 42 trees at five sites, in Central and South America. Cores were cut into 1-cm segments whose specific gravities were determined and analyzed via linear and nonlinear regression. Wood specific gravity, very low initially at 0.15-0.20, doubled or tripled across the tree radius to 0.45-0.65 for large adults. ? Key results: Unlike linear increases in other tropical pioneers, the increases in Schizolobium were nonlinear (convex up). At one site with even-aged trees, the magnitude of the radial increase was similar in all trees, despite a 4-fold difference in diameter among trees, implying that the radial increases in Schizolobium were regulated by tree age, not by tree size. ? Conclusions: This unique pattern of development should provide an extended period of growth when SG is low, facilitating hyper-extension of the bole, at some risk of structural failure. Later in growth, the SG rate of increase accelerates, reinforcing what was a precarious bole. Overall, these results suggest a third model for xylem allocation in tropical trees, a model that may be associated with monopodial stem development and limited life span.     

Sanio's laws revisited. Size-dependent changes in the xylem architecture of trees

Early observations led Sanio [ Wissen. Bot. , 8 , (1872) 401] to state that xylem conduit diameters and lengths in a coniferous tree increase from the apex down to a height below which they begin to decrease towards the tree base. Sanio's law of vertical tapering has been repeatedly tested with contradictory results and the debate over the scaling of conduit diameters with distance from the apex has not been settled. The debate has recently acquired new vigour, as an accurate knowledge of the vertical changes in wood anatomy has been shown to be crucial to scaling metabolic properties to plant and ecosystem levels. Contrary to Sanio's hypothesis, a well known model (MST, metabolic scaling theory) assumes that xylem conduits monotonically increase in diameter with distance from the apex following a power law. This has been proposed to explain the three-fourth power scaling between size and metabolism seen across plants. Here, we (i) summarized available data on conduit tapering in trees and (ii) propose a new numerical model that could explain the observed patterns. Data from 101 datasets grouped into 48 independent profiles supported the notions that phylogenetic group (angiosperms versus gymnosperms) and tree size strongly affected the vertical tapering of conduit diameter. For both angiosperms and gymnosperms, within-tree tapering also varied with distance from the apex. The model (based on the concept that optimal conduit tapering occurs when the difference between photosynthetic gains and wall construction costs is maximal) successfully predicted all three major empirical patterns. Our results are consistent with Sanio's law only for large trees and reject the MST assumptions that vertical tapering in conduit diameter is universal and independent of rank number.     

Biomass accumulations and the distribution of nitrogen and phosphorus within three<Emphasis Type="Italic">Quercus acutissima</Emphasis> stands in central Korea

Above- and belowground biomass and nitrogen (N) and phosphorus (P) distribution within threeQuercus acutissima stands were investigated in central Korea. The average age (year) and diameter at breast height (DBH, cm) were 10.8 and 7.9 for Stand 1, 38.2 and 17.1 for Stand 2, and 44.0 and 20.7 for Stand 3, respectively. Fifteen trees were destructively harvested for dimension analysis of component biomass (stem wood, stem bark, foliage, branches, and roots) plus N and P concentrations. Total biomass (t ha^-1) was 88.7 for Stand 1, 154.9 for Stand 2, and 278.1 for Stand 3 while N and P contents in all tree components (kg ha^-1) were 483.3 and 52.2, 697.1 and 55.0, and 1113.9 and 83.7. Nitrogen concentrations were highest in the foliage, followed by the stem bark, branches or roots, and stem wood. In contrast, P concentrations were greatest in the roots, then foliage, branches, stem bark, and stem wood. In general, N and P concentrations in these components significantly decreased with tree age and DBH, while N and P contents significantly increased with age and size. These relationships were stronger for size than for age. Our current data could be utilized to estimate N and P budgets for silvicultural practices, including fertilization, thinning, and harvesting.     

Patterns of auxin distribution during gravitational induction of reaction wood in poplar and pine

Gravistimulation of tree stems affects wood development by unilaterally inducing wood with modified properties, called reaction wood. Commonly, it also stimulates cambial growth on the reaction wood side. Numerous experiments involving applications of indole-3-acetic acid (IAA) or IAA-transport inhibitors have suggested that reaction wood is induced by a redistribution of IAA around the stem. However, in planta proof for this model is lacking. Therefore, we have mapped endogenous IAA distribution across the cambial region tissues in both aspen (Populus tremula, denoted poplar) and Scots pine (Pinus sylvestris) trees forming reaction wood, using tangential cryosectioning combined with sensitive gas chromatography-mass spectrometry analysis. Moreover, we have documented the kinetics of IAA during reaction wood induction in these species. Our analysis of endogenous IAA demonstrates that reaction wood is formed without any obvious alterations in IAA balance. This is in contrast to gravitropic responses in roots and shoots where a redistribution of IAA has been documented. It is also of interest that cambial growth on the tension wood side was stimulated without an increase in IAA. Taken together, our results suggest a role for signals other than IAA in the reaction wood response, or that the gravitational stimulus interacts with the IAA signal transduction pathway.     

Strain distribution during anchorage failure of Pinus pinaster Ait. at different ages and tree growth response to wind-induced root movement

Winching tests were carried out on 5- 13- and 17-year-old tap rooted Maritime pine (Pinus pinaster Ait.) in order to determine how the mode of anchorage failure changes throughout the life of a tree. As trees were pulled sideways, strain along the lateral roots was recorded using strain gauges attached to a strain indicator. Measurements of strain in the root system, taken during winching, provide information about root movement when loaded by wind. The mode of mechanical failure appeared to depend on tree age. The youngest trees bent over completely during winching, but did not break due to the plasticity of their trunks. The 13-year-old trees either broke at the base of the tree (due to the presence of grafting scar tissue) or at the base of the tap-root. The oldest trees broke at the base of the tap-root and sounds of roots breaking were also heard. Strain was twice as great in the trunk compared to the roots in the 5- and 13-year-old trees and was three times greater in the compression roots of 17-year–old trees compared to that in the trunk. In one 17-year-old tree, strain was found to increase at a distance of 35 cm in tension roots before decreasing again. Although the mode of failure changed with tree size, anchorage strength increased proportionally with the third power of trunk diameter, therefore another reason why failure differs with tree age must exist. In order to determine if different types of wood were being laid down in the lateral roots in response to wind loading, maturation strains, indicating the existence of mechanical stress in developing wood cells, were measured at different points along the roots. A high correlation was found between maturation strain and strain measured during winching, in roots that lay in the wind direction only. Therefore, trees appear to be able to respond to external loading stress, even at a local level within a root. This revised version was published online in June 2006 with corrections to the Cover Date.     

A model to simulate the gravitropic response and internal stresses in trees,considering the progressive maturation of wood

Key message

The developed model of gravitropism takes non-instantaneous maturation of wood into account which enabled to correctly simulate different gravitropic phases and realistic internal stress profiles.

Abstract

A new biomechanical model of tree movement in relation to gravity (gravitropism) is proposed in this study. The modelling of the progressive maturation of wood cells is taken into account, as well as spatio-temporal variations in maturation strains (MS) and mechanical properties. MS were identified using an inverse method that allows the model to fit the gravitropic reaction observed experimentally. For this purpose, the curvature during righting movement, the geometry and the mass distribution of a two-year-old poplar tree was measured. The identified MS are higher than expected, which shows the underestimation of MS by usual measurements. By using the same mechanical parameters and MS as an input, the model gives satisfying results in terms of shape modelling for different trees up to 32 days after tree tilting. The model is able to simulate the latency phase observed in the tree righting movement, and the internal stress profile in the trunk is realistic (low compressive value in the central part of the trunk and zero stress in newly formed cells). The next development of the model will aim to simulate the end of the gravitropic phase in relation with the regulation of MS by the tree.     

Wood mechanics, allometry, and life-history variation in a tropical rain forest tree community

Wood density plays a central role in the life-history variation of trees, and has important consequences for mechanical properties of wood, stem and branches, and tree architecture. Wood density, modulus of rupture, modulus of elasticity, and safety factors for buckling and bending were determined for saplings of 30 Bolivian rain forest tree species, and related to two important life-history axes: juvenile light demand and maximum adult stature. Wood density was strongly positively related to wood strength and stiffness. Species safety factor for buckling was positively related to wood density and stiffness, but tree architecture (height : diameter ratio) was the strongest determinant of mechanical safety. Shade-tolerant species had dense and tough wood to enhance survival in the understorey, whereas pioneer species had low-density wood and low safety margins to enhance growth in gaps. Pioneer and shade-tolerant species showed opposite relationships between species traits and adult stature. Light demand and adult stature affect wood properties, tree architecture and plant performance in different ways, contributing to the coexistence of rain forest species.     

Mechanosensing is involved in the regulation of autostress levels in tension wood

Key message

The level of stresses of tension wood changes during the gravitropic movement. These changes are induced by the perception of strains experienced by the tree during reorientation to the upright position.

Abstract

In most hardwood species, tension wood is produced to ensure tropic movements in radially growing organs. Tension wood exhibits internal tensional forces (autostresses) greater than those of normal wood, which enable the trunk to restore its verticality. During the gravitropic response, there is a first phase when the trunk curves upwards and a second phase when the trunk decurves to reach a final vertical and straight shape. Tension wood appears to be of varying strength, but the source of these variations remains partly undefined. We set out to assess the involvement of mechanosensing in the regulation of the strength of tension wood. Autostress levels characterise the strength of tension wood and can be indirectly estimated by measuring the associated residual longitudinal maturation strains (rlms) after the autostresses release. The higher the tension, the higher the measured associated shrinkage. To look for the involvement of mechanosensing in the regulation of tension wood strength, rlms were measured in different types of experiments in which the trunk mechanical state was modified. Results showed that (1) bigger trees exhibited higher levels of rlms, (2) there was a quantitative relationship between the rlms and the sum of strains experienced by the trunk, (3) artificial curving induced an increase in rlms and (4) in tilted staked trees, rlms increased towards negative values for 3 weeks and then remained constant. These findings are consistent evidence for the regulation of rlms values by mechanosensing. This brings new insight into gravitropism.     

Allometric relationships for Eucalyptus nitens (Deane and Maiden) Maiden plantations

Allometric relationships between stem, leaf area and crown dimensions were determined for Eucalyptus nitens (Deane and Maiden) Maiden using 81 trees sampled from 13 post-canopy closure sites and 34 trees sampled from 6 pre-canopy closure sites. These sites differed in site quality, stand age, fertiliser treatment, stand density and levels of weed infestation. Overall, tree age ranged from 2 to 13 years, tree height from 1.4 to 26.1 m and diameter at breast height from 0.6 to 38.7 cm. Pre-canopy closure trees exhibited site-specific relationships which were to some extent confounded with tree age. However, post-canopy closure trees had relationships which were independent of site, age and silvicultural treatments. Strong relationships between structural components were found for both stem and crown. Stem diameter at breast height was non-linearly related to tree height and crown length. Stem sapwood area (breast height or crown base) could be predicted from stem cross-sectional area. For post-canopy closure trees, a functional relationship between sapwood area (breast height and crown base) and leaf area was site-independent. The lack of specificity in terms of both site and management techniques enables these relationships to be applied generally to E. nitens plantations in Tasmania.     

Genotypic variation in wood properties and growth traits of triploid hybrid clones of Populus tomentosa at three clonal trials

To better understand the genetic control of growth traits (tree height, dbh, and stem volume) and wood properties (basic wood density and fiber length) in triploid hybrid clones of Populus tomentosa, genetic relationships among selected wood properties with growth traits were examined in 5-year-old clonal field trials located in Yanzhou, Gaotang, and Xiangfen, northern China. In total, 180 trees from 10 clones were sampled from the three sites. The site had a moderate effect on basic wood density (BWD), stem wood dry weight (DWT), and tree growth and had a highly significant effect on fiber length (FL) (P?<?0.001). Clonal effects were also significant (P?<?0.05) for all studied traits (except for diameter at breast height (DBH) and stem volume (SV)). Clone × site interaction was significant for all the studied traits except for FL. The estimated repeatability of clonal means for FL (0.91) was higher than for BWD (0.71), DWT (0.62), tree height (0.62), DBH (0.61), and SV (0.55). Intersite genetic correlation estimates indicated that wood properties were more stable than growth traits. Phenotypic correlation estimates between SV and BWD ranged from ?0.29 to ?0.10.     

Numerical modelling of shape regulation and growth stresses in trees

The main objective of this paper is to present the results of a study of the interactions between the growth and design of a tree with regards to biomechanical factors at the plant level. A numerical incremental model dedicated to the calculation of tree mechanical behaviour has been integrated in the plant architecture simulation software AMAPpara. At any stage of tree growth, a new equilibrium was calculated considering the weight increment applied on the structure, i.e. the mass of new wood layers and vegetative elements, as well as the biomechanical reaction caused by cell maturation strains in both normal and reaction wood. The resulting incremental displacements allowed the tree shape to be modified. The field of growth stresses was calculated within the stem, using a cumulative process taking into consideration the past history of each growth ring. The simulation results of trunk and branch shape, as well as internal stresses, were examined after consideration of different growth strategies. A block of trees was also simulated in order to show the influence of spatial competition on stem curvature and the variability in growth stress.     

Tree-ring growth of silver fir (Abies alba Mill.) in two stands under different silvicultural systems in central Italy

A preliminary analysis was made of growth trends in two silver fir forests in the Apennines in central Italy. The forests are closely located but were managed differently in the past. The aim was to verify the climatic variation over time, the influence of extreme events on radial growth and the role of silvicultural systems in defining growth response. The two forests have distinct structures due to differing past silvicultural management. The Camaldoli Forest, containing one-storeyed, evenaged, pure silver fir stands, was essentially managed in the past for wood production and featured high plantation density, low to moderate thinning, and clear cutting every 80–100 years. The La Verna Forest includes multi-layered, unevenaged stands that are mixed in with beech and other broadleaves. Increment cores were collected from aged dominant and healthy trees in the two forests. Climatic data were taken from the Camaldoli station and covers the period 1885–1994. All the analysed dendroecological parameters displayed similar patterns and indicated suitable site conditions for the silver fir. Silvicultural systems played an important role in defining growth pattern and rate. In the evenaged system there were higher growth rates and a greater number of pointer years, whereas there were lower growth rates and long, homogeneous development stages in the semi-natural conditions of La Verna. A rising growth trend recorded in the last three decades in both series could be explained by the consistent extension of the growing season due to a significant increase of mean spring and autumn temperatures. No correlation was found with precipitation while significant correlations were found between tree ring growth and February, April and August temperatures. Preliminary results indicated that the silvicultural system does not bias, but just enhances the ability of the species to record the effects of disturbing factors.