Understanding the impact of root morphology on overturning mechanisms: a modelling approach

BACKGROUND AND AIMS: The Finite Element Method (FEM) has been used in recent years to simulate overturning processes in trees. This study aimed at using FEM to determine the role of individual roots in tree anchorage with regard to different rooting patterns, and to estimate stress distribution in the soil and roots during overturning. METHODS: The FEM was used to carry out 2-D simulations of tree uprooting in saturated soft clay and loamy sand-like soil. The anchorage model consisted of a root system embedded in a soil block. Two root patterns were used and individual roots removed to determine their contribution to anchorage. KEY RESULTS: In clay-like soil the size of the root-soil plate formed during overturning was defined by the longest roots. Consequently, all other roots localized within this plate had no influence on anchorage strength. In sand-like soil, removing individual root elements altered anchorage resistance. This result was due to a modification of the shape and size of the root-soil plate, as well as the location of the rotation axis. The tap root and deeper roots had more influence on overturning resistance in sand-like soil compared with clay-like soil. Mechanical stresses were higher in the most superficial roots and also in leeward roots in sand-like soil. The relative difference in stresses between the upper and lower sides of lateral roots was sensitive to root insertion angle. Assuming that root eccentricity is a response to mechanical stresses, these results explain why eccentricity differs depending on root architecture. CONCLUSIONS: A simple 2-D Finite Element model was developed to better understand the mechanisms involved during tree overturning. It has been shown how root system morphology and soil mechanical properties can modify the shape of the root plate slip surface as well as the position of the rotation axis, which are major components of tree anchorage.     

The anchorage mechanics of deep rooted larch, Larix europea L. japonica

The anchorage of deep rooted 16-year-old larch trees, Larixeuropea japonica, has been studied by combining winching testswith analyses of strain around the base of the trunk and rootsystem and mechanical tests on individual roots. These showedthat anchorage is provided by the laterals which emerge fromaround the stem base, sinker roots which emerge along theirlength, and tap roots positioned directly underneath the bole.During anchorage failure the leeward laterals are bent and eventuallybreak close to their base, whilst the windward laterals arepulled out of the ground, with their sinker roots intact. Afterinitially being confined by the soil and bending, the tap rootrotates in the soil. Anchorage failure is similar when the soilis dry as when it is wet, but failure occurs closer to the trunk.Strain measurements along the lateral roots revealed that thestresses were highest close to the trunk and that these regionsof the roots contribute most to tree stability. The two major components of anchorage were found to be the resistanceof leeward laterals to bending and the resistance of tap rootsand windward sinkers to uprooting. Bending tests on leewardlaterals revealed that they provide around 25% of tree anchorage.Almost 75% of the anchorage strength must, therefore, be providedby the windward sinkers and tap roots. Anchorage strength ofroots was positively correlated to their cross-sectional area.The vertical orientation of the sinkers makes the anchoragesystem of larch more efficient than the plate system formedby Sitka spruce on waterlogged soils and means that no root-soilplate is formed. Key words: Anchorage, root architecture, sinker roots, root bending strength, windthrow     

A generic 3D finite element model of tree anchorage integrating soil mechanics and real root system architecture

Understanding the mechanism of tree anchorage in a forest is a priority because of the increase in wind storms in recent years and their projected recurrence as a consequence of global warming. To characterize anchorage mechanisms during tree uprooting, we developed a generic finite element model where real three-dimensional (3D) root system architectures were represented in a 3D soil. The model was used to simulate tree overturning during wind loading, and results compared with real data from two poplar species (Populus trichocarpa and P. deltoides). These trees were winched sideways until failure, and uprooting force and root architecture measured. The uprooting force was higher for P. deltoides than P. trichocarpa, probably due to its higher root volume and thicker lateral roots. Results from the model showed that soil type influences failure modes. In frictional soils, e.g., sandy soils, plastic failure of the soil occurred mainly on the windward side of the tree. In cohesive soils, e.g., clay soils, a more symmetrical slip surface was formed. Root systems were more resistant to uprooting in cohesive soil than in frictional soil. Applications of this generic model include virtual uprooting experiments, where each component of anchorage can be tested individually.     

Simulation of direct shear tests on rooted and non-rooted soil using finite element analysis

The finite element (FE) method has been used in recent years to simulate overturning processes in trees and to better comprehend plant anchorage mechanics. We aimed at understanding the fundamental mechanisms of root-soil reinforcement by simulating direct shear of rooted and non-rooted soil. Two- (2D) and three-dimensional (3D) FE simulations of direct shear box tests were carried out using readily available software for routine strength assessment of the root-soil composite. Both rooted and non-rooted blocks of soil were modelled using a simplified model of root distribution and root material properties representative of real roots. Linear elastic behaviour was assumed for roots and the soil was modelled as an ideally plastic medium. FE analysis showed that direct shear tests were dependent on the material properties specified for both the soil and roots. 2D and 3D simulations of direct shear of non-rooted soil produced similar results and any differences between 2D and 3D simulations could be explained with regard to the spatial complexity of roots used in the root distribution model. The application of FE methods was verified through direct shear tests on soil with analogue roots and the results compared to in situ tests on rooted soil in field conditions.     

The Mechanics of Root Lodging in Winter Wheat, Triticum aestivum L.

The anchorage of winter wheat, Triticum aestivum L., is providedby a cone of rigid coronal roots which emerge from around thestem base. During root lodging this cone rotates at its windwardedge below the soil surface, the soil inside the cone movingas a block and compressing the soil beneath. A theoretical modelof anchorage suggested that lodging resistance should be dependenton the diameter of the root-soil cone, coronal root bendingstrength and soil shear strength. We tested the predictions of the anchorage model by carryingout two series of experiments. In the first, varieties of contrastinglodging resistances were artificially lodged. The moment requiredto rotate plants into the soil, the diameter of the root-soilcone, and the bending strength of the coronal roots were recorded.The lodging moment was correlated with the size of the soilcone, as predicted. Generally, differences in anchorage strengthbetween varieties were due to differences in root-soil conediameter, although coronal root strength was also important. A second series of tests was carried out using model plantsanchored by plastic discs. The behaviour of the models duringartificial lodging supported the anchorage model; the forceresisting lodging was similar to that of plants with root-soilcones of the same size and the resisting force was dependenton the soil strength. These results suggest that root lodging resistance might beimproved by increasing both the angle of spread and the bendingstrength of the coronal roots. Key words: Anchorage, root-soil cone, coronal roots, lodging, wheat     

The Anchorage Mechanics of Maize, Zea mays

The anchorage system of mature maize Zea mays was investigatedby combining morphological and anatomical study of the rootsystem with mechanical tests on roots and with studies in whichplants were pulled over. The root system is dominated by 20–30adventitious roots which emerge in rings from the stem basepointing radially downwards and outwards, approximately 30°from the vertical. Roots are strengthened near their base bya heavily lignified exodermis which makes them rigid in bending;distally, strength and rigidity both decrease because rootsbecome thinner and less lignified. When plants were pulled over,a maximum anchorage moment of 5–20 Nm was mobilized atangles of 8–10°, larger plants having stronger anchorage.Movement was initially centred on the leeward side of the stem,anchorage being due to the resistance of both windward and leewardroots to axial motion through the soil and to bending. At displacementsover 10°, however, leeward roots buckled under combinedbending and compression and the centre of rotation shifted tothe windward perimeter of the root system; subsequent movementof the cone of roots and soil was resisted only by the bearingstrength of the soil beneath it. The differences between anchorage failure in balsam and sunflowersand that in maize probably results from the lower angular spreadand the weakness in compression of the maize roots which preventsthe leeward side of the root system from bearing large downwardloads. The system behaves more like that of wheat; these resultssuggest that the lodging resistance of both plants may be improvedby increasing the bending strength and angle of spread of theadventitious roots. Key words: Zea mays, roots, anchorage     

The Anchorage of Leek Seedlings: The Effect of Root Length and Soil Strength

The mechanical behaviour of single roots being extracted fromsoil was modelled as a process in which tension is transferredfrom the upper regions of the root to the soil via shear. Quantitativepredictions were made about the extraction forces and the shapeof the uprooting curves, and these were tested using leek radiclesof different lengths in soil of two different strengths. Results of uprooting tests were qualitatively similar to thepredictions. The pullout resistance rose with root length, untilthe breaking strength of the root was reached, at around 30mm: longer roots all broke before the tip was stressed. In wholeroot systems, therefore, failure will occur proximally beforethe line distal roots are mechanically stressed, so these canhave no anchorage function. Resistance to an upward force will be most economically achievedby having many strengthened proximal root axes, as in the adventitiousroot systems of grasses, sedges and stoloniferous dicots. Allium porrum, root, anchorage, shear, tension, soil     

The mechanics of anchorage in seedlings of sunflower, Helianthus annuus L.

Forces applied to plants will subject many of the roots to tension, which must be transferred to the soil via shear if uprooting is to be prevented. The stress distribution will depend on the relative stiffnesses of the earth and root, and the mode of failure will depend on the relative strength of the soil and of the root soil bond. This study of the anchorage of sunflower radicles combined uprooting tests performed by a tensile testing machine with mechanical tests on the roots and soil.
The maximum extraction force increased with length to an asymptotic value and was reached at a very low displacement. Root hairs and soil particles covered the tapered top 20 mm of extracted root, but the lower cylindrical region was bare. The soil was stiffer than the root, so shear stress was initially concentrated at the top of the root, soil strength over the top 20 mm resisting uprooting. Lower regions of the root were stressed later, their sparser root hairs being sheared off, and resist uprooting only by friction. In a further lest upper and lower regions of radicles were uprooted separately. As predicted, the upper region generated much greater resistance to uprooting per unit length, and at much lower displacements than the lower region.
The top of the radicle is well adapted for anchorage, the profuse root hairs and mucigel it produces glueing the root to the soil. The lower regions are thus protected from damage.     

An Experimental Investigation of the Resistance of Model Root Systems to Uprooting

The architecture of a tree root system may influence its abilityto withstand uprooting by wind loading. To determine how theroot branching pattern may alter the anchorage efficiency ofa tree, artificial model root systems with different topologiesand branching angles were built. The root systems were embeddedat various depths in wet sand and the pull-out resistance measured.A model to predict the uprooting resistance from the data collectedwas designed, allowing predictions of anchorage strength withregards to architecture. The dominant factors influencing pull-outresistance were the depth and length of roots in the soil. Themost efficient type of branching pattern predicted by the programwas one with an increased number of roots deep in the soil.The optimum branching angle most likely to resist pull-out isa vertical angle of 90° between a lateral and the main axis.The predicted mechanically optimal radial angle between a lateralbranch and its daughter is between 0 and 20°. Values ofbranching angle are compared with those measured in real woodyroot systems of European larch and Sitka spruce. Root architecture; root anchorage; pull-out resistance; windthrow; Picea sitchensis ; Larix decidua     

The role of root system architecture and root hairs in promoting anchorage against uprooting forces in Allium cepa and root mutants of Arabidopsis thaliana.

The role played by lateral roots and root hairs in promoting plant anchorage, and specifically resistance to vertical uprooting forces has been determined experimentally. Two species were studied, Allium cepa (onion) which has a particularly simple root system and two mutants of Arabidopsis thaliana, one without root hairs (rhd 2-1) and another with reduced lateral root branching (axr 4-2). Maximum strength of individual onion roots within a plant increased with plant age. In uprooting tests on onion seedlings, resistance to uprooting could be resolved into a series of events associated with the breakage of individual roots. Peak pulling resistance was explained in a regression model by a combination of a measure of plant size and the extent to which the uprooting resistance of individual roots was additive. This additive effect is termed root co-operation. A simple model is presented to demonstrate the role played by root co-operation in uprooting resistance. In similar uprooting tests on Arabidopsis thaliana, the mutant axr 4-2, with very restricted lateral development, showed a 14% reduction in peak pulling resistance when compared with the wild-type plants of similar shoot dry weight. The uprooting force trace of axr 4-2 was different to that of the wild type, and the main axis was a more significant contributor to anchorage than in the wild type. By contrast, the root hair-deficient mutant rhd 2-1 showed no difference in peak pulling resistance compared with the wild type, suggesting that root hairs do not normally play a role in uprooting resistance. The results show that lateral roots play an important role in anchorage, and that co-operation between roots may be the most significant factor.     

The effect of root architecture and root loss through trenching on the anchorage of tropical urban trees (Eugenia grandis Wight)

Eugenia grandis (Wight) is grown in urban environments throughout Malaysia and root systems are often damaged through trenching for the laying down of roads and utilities. We investigated the effect of root cutting through trenching on the biomechanics of mature E. grandis. The force necessary to winch trees 0.2 m from the vertical was measured. Trenches were then dug at different distances (1.5, 1.0 and 0.5 m) from the trunk on the tension side of groups of trees. Each tree was winched sideways again and the uprooting force recorded. No trenches were made in a control group of trees which were winched until failure occurred. Critical turning moment (TM_crit) and tree anchorage rotational stiffness (TARS) before and after trenching were calculated. Root systems were extracted for architectural analysis and relationships between architectural parameters and TM_crit and TARS were investigated. No differences were found between TM_crit and trenching distance. However, in control trees and trees with roots cut at 1.5 m, significant relationships did exist between both TM_crit and TARS with stem dimensions, rooting depth and root plate size. TARS was significantly decreased when roots were cut at 0.5 m only. Surprisingly, no relationships existed between TM_crit and TARS with any root system parameter when trenching was carried out at 0.5 or 1.0 m. Our study showed that in terms of TARS and TM_crit, mechanical stability was not greatly affected by trenching, probably because rooting depth close to the trunk was a major component of anchorage.     

A Comparative Study of the Anchorage Systems of Himalayan Balsam Impatiens glandulifera and Mature Sunflower Helianthus annuus

The anchorage systems of Himalayan balsam Impatiens glanduliferaand mature sunflowers Helianthus annuus were investigated bycombining morphological and anatomical study of the root systemswith mechanical tests on roots and with studies in which matureplants were pulled over. The root system of balsam is dominated by large numbers of fleshytapering adventitious roots which point downwards from theirorigin at the wide stem base. Sunflowers, in contrast, havea tapering tap-root from which 20–30 well-branched lateralsemerge, pointing radially outwards and downwards. Roots of eachspecies have contrasting anatomy: those of balsam resemble stems,having a central watery pith and being strengthened peripherallyby lignification of vascular tissue; roots of sunflowers arestrengthened by a solid woody stele. Roots of both species arerigid in tension and, towards the base, in bending. Both species exhibited similar behaviour to that known for treessuch as Sitka spruce; when pulled over they rotated about ahinge leeward of the stem base and a root-soil ball was pulledout of the surrounding soil. Anchorage was resolved into threecomponents which, in order of decreasing magnitude, were (i)the resistance to pulling of the roots on the windward sideof the plant (and, for sunflower, the tap-root); (ii) the resistanceof roots and soil at the leeward hinge to rotation; and (iii)the weight of the root-soil ball. Sunflower had stronger anchoragebut achieved it at a greater cost in terms of the dry mass ofits root system. In each species, the morphology, anatomy and mechanical propertiesof the root system can be related to those of the stem. Thewide stem base of balsam allows large numbers of mechanicallyefficient fleshy roots to be attached whereas in sunflowersa woody tap-root system is necessary to anchor the much narrowerstem. Key words: Impatiens, Helianthus, roots, anchorage     

Root anchorage of inner and edge trees in stands of Maritime pine (<Emphasis Type="Italic">Pinus pinaster</Emphasis> Ait.) growing in different podzolic soil conditions

Static winching tests were carried out in order to determine the mechanical resistance of Maritime pine to overturning. The tested stands were selected according to podzolic soil conditions: wet Lande, characterised by a shallow ground water table and a hard pan horizon, and dry Lande, with a deeper ground water table and a hard pan absent or broken up. As this soil horizon limits the vertical growth of tree roots, anchorage resistance was investigated with regards to the presence or absence of a hard pan underneath each tree. To determine if mechanical behaviour differed within a stand, trees from inside the stand and edge trees at the border exposed to prevailing winds were also tested. The critical turning moment (TM_crit,total) at the base of the stem was positively related to the variable (H × DBH²) (H, total tree height; DBH, tree diameter). Linear regression analyses between TM_crit,total and (H × DBH²) showed that the presence of a hard pan had no significant effect on anchorage resistance in uprooted trees. Stem failure occurred for 82% of trees on dry Lande when (H × DBH²) < 1 m³. Moreover, stem failure type on dry Lande indicated that trees were better anchored. On soil with a hard pan, edge trees were found to be 20% more resistant to overturning than inner trees. Edge trees differed from inner trees in that the soil-root plate was two times larger and also possessed a larger surface area on the windward side.     

喀斯特坡地2种地埂篱根-土复合体抗剪和抗冲性能综合评价

分析喀斯特地区不同地埂篱根系的形态和力学特性,量化其根-土复合体抗剪和抗冲性能的强弱,探寻该地区地埂篱根系固土抗蚀性能的评价因子,为喀斯特坡地水土流失治理中植被恢复措施的科学应用提供参考。选取重庆酉阳龙潭槽谷为研究区,分上、中、下坡分别布设拉巴豆和光叶苕子2种地埂篱,采用根系扫描仪和电子万能试验机测定其根系形态和力学参数,应变控制式直剪仪测定复合体抗剪强度,原状土冲刷水槽法测定复合体抗冲指数。结果表明：(1)抗剪复合体中,拉巴豆平均根长密度和根表面积密度分别高出光叶苕子59.32%和16.86%;抗冲复合体中,拉巴豆平均根长密度、根表面积密度和根体积密度较之光叶苕子高出30.48%、57.78%、92.98%;拉巴豆根系极限抗拉力和抗拉强度均显著高于光叶苕子。(2)2种地埂篱根系均能增强土壤的抗剪和抗冲性能,其中拉巴豆和光叶苕子复合体粘聚力较之对照土体分别增强了113.06%—124.37%和51.56%—87.12%,抗冲指数最高达到对照土体的2.81倍和2.45倍。(3)不同坡位,下坡2种植物的根长密度显著高于上、中坡;拉巴豆根系抗拉特性在下坡表现最优,光叶苕子在上坡表现更好;拉巴...     

Linking plant morphological traits to uprooting resistance in eroded marly lands (Southern Alps, France)

In marly catchments of the French Southern Alps, soils are subjected to harsh water erosion that can result in concentrated flows uprooting small plants. Evaluating and predicting plant resistance to uprooting from simple plant traits is therefore highly important so that the most efficient plant strategy for future restoration of eroded slopes can be defined. Twelve species growing on marly land were studied. For each species, in-situ lateral uprooting tests were conducted and morphological plant traits were measured on small plants at the early stages of their development. The results show that maximum uprooting force was most positively correlated with stem basal diameter. Resistance to uprooting depends on a combination of several traits. Tap root length, the proportion of fine lateral roots and root topology were the best predictors of anchorage strength.     

A new dimension to observations in minirhizotrons: A stereoscopic view on root photographs

Summary With a stereoscope, as used for the inspection of aerial photographs, sequential photographs of roots obtained by the endoscope method from minirhizotrons can yield much more information than hitherto. A series of photographs shows that most of the roots seen in a minirhizotron in grassland grew on the surface of the lexan tube, while there was a gap between the roots and the soil. Decay of the extensive root hair zones around the roots may make new root growth in the gap between rhizotron wall and soil invisible. Some consequences of these observations for the endoscope method are discussed.     

Shrinkage of Attached Roots of Opuntia ficus-indica in Response to Lowered Water Potentials--Predicted Consequences for Water Uptake or Loss to Soil

Attached 2-month-old roots of the succulent plant, Opuntia ficus-indica,shrank 0.4% radially during periods of maximal transpirationunder wet conditions. In contrast, reversible decreases in diameterof nearly 20% occurred for these roots as their ambient waterpotential () in the vapour phase decreased from –0.01to –10 MPa over 8 d, the changes being slightly more rapidat 40 °C than at 10 °C. Such substantial diameter changesbecame progressively less with root age, from a 43% decreasein diameter at 3 weeks to a 6% decrease at 12 months Root shrinkagewas slight when was decreased from –0.01 to –0.3MPa, the latter being similar to the root water potential.As was further decreased from –0.3 to –10 MPa,water movement out of cortical cells caused considerable rootshrinkage. The root hydraulic conductivity (L_p) decreased only30 to 60% for a change in from –0.01 to –10 MPacompared with a decrease of over 10⁶-fold for the soil hydraulicconductivity over this range. The overall conductivity of thesoil, the root-soil air gap, and the root was predicted to bedominated by L_p for _soil above –0.3 MPa. As simulated_soil decreased below –0.3 MPa, the root-soil air gap initiallybecame the primary limiter of water loss from the roots. Below–5 MPa for 1-month-old roots and below –2 MPa for12-month-old roots, the soil became the main limiter of waterloss. Thus, water uptake from wet soils apparently was mainlycontrolled by root properties Water loss to drying soils wascontrolled by the development of a root-soil air gap aroundshrinking roots during the initial phase of soil drying andby the reduction of the soil hydraulic conductivity at evenlower _soil. Root diameter, root hydraulic conductivity, root-soil air gap, soil hydraulic conductivity     

The function of buttress roots: a comparative study of the anchorage systems of buttressed (Aglaia and Nephelium ramboutan species) and non-buttressed (Mallotus wrayi) tropical trees

The anchorage mechanics of mature buttressed trees of Aglaiaand Nephelium, and of non-buttressed Mallotus wrayi have beeninvestigated by combining a study of the morphology of theirroot systems with a series of anchorage tests. Both types possessed tap roots, but only buttressed trees possessedsinker roots, which branched from the ends of the buttresses.The anchorage strength of the buttressed trees was almost double(10.6 kNm) that of the unbuttressed ones (4.9 kNm), and themaximum moment was generated at lower angles. In but tressedtrees, the leeward buttresses were pushed into the soil beforebending and eventually breaking towards their tip, whilst thewindward buttresses pulled out of the soil or delaminated ifthey possessed sinker roots. The tap root rotated in the soilto windward. In contrast, during failure of unbuttressed treesthe tap root both moved and bent towards the leeward, the windwardroots were pulled out of the soil, and the leeward lateralssimply buckled. Strains along but tresses were much higher thanalong the laterals of unbuttressed trees. These results suggest that buttresses act in both tension andcompression and make a much larger contribution to anchoragethan the thin laterals of non-buttressed trees. The relativecontribution of the but tresses was determined by carrying outa further series of anchorage tests in which both buttressedand unbuttressed trees were pulled over after all their lateralshad been cut away. These trees were therefore only anchoredby their taproot. Failure of both types was similar to intactunbuttressed trees, and they had similar anchorage strengthstoeach other, 4 kNm, around 80% of the value for intact non-buttressedtrees, but only 40% of the strength of intact buttressed trees.Buttresses therefore contribute around 60% of the anchorageof buttressed trees, producing around six times more anchoragethan the thin laterals of unbuttressed trees. Key words: Anchorage, root architecture, sinker roots, tap roots, root bending strength, buttresses     

The effect of soil strength on the growth of pigeonpea radicles and seedlings

The effect of soil strength on the growth of pigeonpea radicles and seedlings was investigated in cores of three clay soils prepared at different water contents and bulk densities in the laboratory.Radicle elongation directly into soil cores was reduced from 50–70 mm d^-1 at strengths less than 0.5 MPa to 0 mm d^-1 at 3.5–3.7 MPa. The response to soil strength was affected by the water content of the soil, presumably as a result of reduced oxygen availability in wetter soil. This effect was apparent in soils wet to air-filled porosities less than 0.15 m³ m^-3.Radicles were more sensitive to high soil strength (>1.5 MPa) than were seedling roots which encountered the same conditions at 60 mm in the profile. Radicle growth ceased at 3.5 MPa which reduced seedling root growth by only 60%.Despite a 60% reduction in root length in the high strength zone, seedling roots compensated in zones of loose soil above and below the compacted layer, and total root length and shoot growth were unaffected. There was no evidence of a root signal response which results in reduced shoot growth in some species in response to high soil strength.The proliferation of roots in surface layers and the delayed penetration of the root system to depth in compacted soil are likely to expose seedlings to a greater risk of water-deficit in the field, particularly under dryland conditions where plants rely on stored subsoil water for growth.     

The Increase in Anchorage with Tree Size of the Tropical Tap Rooted TreeMallotus wrayi, King (Euphorbiaceae)

The mechanical development of the anchorage system of the taprooted tropical speciesMallotus wrayiKing (Euphorbiaceae) wasinvestigated by pulling over and examining trees with a diameterat breast height (d_bh) of 4.2 cm to 14.3 cm. The mode of mechanicalfailure depended upon the size of the tree: thicker trees (d_bhapprox.9 cm) failed in the ground with their tap roots pushing intothe soil on the winchward side; in smaller trees (d_bhapprox.7 cm) the trunk snapped before anchorage failure; and in verysmall trees (of d_bh<6 cm) neither type of failure occurredand the trees returned to their original upright position undamagedafter the test. The anchorage strength of the trees was correlatedwith the second power of trunk diameter rather than with thethird power that theory suggests is optimal because tap rootsdid not show an isometric increase in length or diameter. Thereforeas trees grow larger the ‘factor of safety’ againstanchorage failure falls, making them prone to fail in theirroots. These results suggest that only relatively small treespecies can rely solely on the tap root to prevent uprooting.It may be for this reason that most larger trees develop thicklateral roots.Copyright 1998 Annals of Botany Company Anchorage, tap roots, scaling,Mallotus wrayi, isometric growth, functional development, windthrow, root systems.