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The authors have declared that no competing interests exist.

Conceived and designed the experiments: FD AS HK. Performed the experiments: HK. Analyzed the data: FD HK. Wrote the paper: FD AS HK. Designed and wrote the R and AmapMod functions used for analysis: FD.

This study aims at assessing the influence of slope angle and multi-directional flexing and their interaction on the root architecture of

The way in which a coarse root system is established spatially in a tree determines both its anchorage and its capacity to absorb water and nutrients

Coarse root system architecture has often been assessed by measuring a limited number of characteristics using topological analysis

The structural root system of trees is laid down when trees are juvenile

There is an increasing interest in understanding how tree root systems develop on hillslopes, largely because the diverse mechanical loads present can have consequences for the mechanical integrity of a tree, as well as the substrate in which it is anchored

Previous studies of tree root development on steep slopes give contrary results ^{−1} parallel to the slope,

The disparity in results of different studies show that it is necessary to distinguish and separate the effect of substrate geometry, the effect of MP and their interaction, and determine which stress results in which plastic response. Such an experiment has not yet been performed.

We chose to study the interaction between dynamic mechanical loading (flexing) and soil geometry (slope) in seedlings of

We hypothesize that (1) in plants on a slope without flexing, changes only in the direction of root growth occur, with shallow roots growing parallel to the soil surface (2) flexing in plants growing on a 0° slope results in modifications in stump, taproot and lateral root size (3) flexing in plants growing on a 45° slope should induce additive effects, whereby upslope root volume, length and branching are increased. Results are discussed with regard to the use of deep phenotyping to unravel the differences in root trait plasticity and architectural model.

Seeds of ^{−2}.s^{−1}) from 06∶00 to 24∶00. Relative humidity was constant at 80%. Plants were watered daily using a fine spray to avoid damaging the soil surface. Three weeks after seedling germination, one plant from each container was removed through cutting the stem at the soil surface using scissors, seedlings were 15 cm height. The flexing treatment then began. Half the plants were randomly assigned to the flexing treatment and the remainder were used as controls. Using a bamboo rod, the top of seedlings were gently flexed by hand and by the same person in various directions. Stems were displaced to 30° from the vertical, in different directions, for 5 min a day and for 5 days a week, for 23 weeks. Shoots were then removed by cutting stems at the soil surface and stem length and basal diameter were measured. Whole shoot dry biomass was determined by drying at 65°C for one week.

An aluminium frame was built to fit over the pots

Roots with a basal diameter less than 0.7 mm were not measured in this way, but the number and mean length of these “additional fine roots” borne by each root segment were noted. The position of nodules was not recorded. The taproot (order 1) is the largest root which continues vertically from the stump or root bole. The whole root dry weight of each seedling was then determined after drying at 65°C for one week.

The characteristics of trees, axes and root segments were computed in the same way as that described in _{root}

_{root} is root segment volume and length_{root} is root segment length. The proximal root taper was computed as the % of diameter decrease per cm of root length on the first 3.5 cm root length. Root density was obtained by dividing root dry weight by total root volume. Apical unbranched length is the length between the last branch and the apex of the root.

Root segments were classified into eight compartments ^{st} order root was used to classify the lateral roots as a function of their length to the collar. The distance to the soil surface limits between “shallow”, “intermediate depth” and “deep” roots were set to −35 and −70 mm respectively. The limits between horizontal, oblique and vertical roots were 30° and 60° towards the soil surface respectively (

(a) control tree n° 24 (b) Slope at 45° tree n° 7 (c) flexed tree n°29 (d) Slope+flexed tree n°19. Segments were coloured as a function of their compartment: grey = (1) stump, black = (2) taproot, dark blue = (3) zone of rapid taper (ZRT), light blue = (4) horizontal shallow roots beyond ZRT, green = (6) deep roots, yellow = (7) intermediate depth roots and magenta = (8) oblique roots. Size is arbitrary but proportional. The black frame is the container wall (0.3×0.3 m width) and the soil surface. North/Upslope is on the left.

The following adaptations to the computation were made to cope with the small tree size, growth on a slope and the specificities of the measurement method:

Spatial analysis was made in the same way for all trees, using X and Y axes parallel to the upper border of the container (i.e. parallel to the soil surface) and a Z axis perpendicular to X and Y and passing through the collar of the tree. The slope containers were all inclined towards the south. Therefore, X is both the north for all trees and the upslope direction (0° azimuth) in tilted pots.

Most of the roots were straight, but those which had reached the wall or the bottom of the pot generally followed the wall. To remove this artefact, such roots were virtually extended in the direction the root was growing before it attained the edge, keeping the same segment lengths (see

The angle to the soil surface of the taproot was computed using the line running between the collar and the point where the taproot crosses the “deep root limit” i.e. 70 mm depth

The mean segment length was large compared to the root system size. Therefore, according to

The stump and taproot of seedlings grown on slopes were 25% more inclined than in the control trees. Therefore, the lower stump limit was computed by using a standard stump length of 45 mm for all trees, instead of a standard stump depth. Because the stump makes no active contribution to tree stability, it was not used in total root volume computations

When specified “additional fine roots” were included in the root length and root number analysis.

The root directional deviation (RDD) was computed for each root according to

The topological index q_{b} was computed according to _{b} quantifies the position of an arbitrary binary tree between a wholly dichotomous pattern (q_{b} = 0) and a wholly herringbone pattern (q_{b} = 1). q_{b} is based on the sum of all path lengths from the collar to the exterior links. To check for the circular heterogeneity of branching pattern, we could not use q_{b} because an arborescence can be shared between several sectors. Instead we used simply the mean branching order

We computed three fractal branching parameters

the scaling parameter p_{branch} characterizes the tapering by branching, i.e. it is the cross sectional area (CSA) of the root before the branching point divided by the sum of all root CSA after the branching point. p_{branch} is >1 when tapering occurs.

the tapering between branching points p_{within},

the allocation parameter q is the share of the largest root segment after branching in the sum of CSA after the branching point:

The root diameter on the main axis was measured just before the branching point, but not directly after, therefore, if the main root segment after the branch was longer than 2 cm, the CSA of the parent axis 2 cm after the branching point - obtained by linear interpolation - was used in the computations.

For each of the biomass and architectural parameters, a three way analysis of variance was used to test the Slope and Flexing effects on the Y character; with the Block effect also included (each factor has two levels):

Y_{ijkl} is the value for the the tree l in level of Slope i, level of Flexing j and Block k. μ is the general mean, e_{ijkl} is the residual error. In the case of non-normal residuals (tested with the Shapiro test), variables were transformed to obtain a normal distribution. The corresponding significance tests of factors were reported in the tables, but the % variation in the value of each combination of treatments with regard to the control was computed from the untransformed variable.

According to

The significance of differences between sectors was computed using their contrasts. An even distribution results in 25% root volume, root length and number in the upslope and in the downslope sector. The reinforcement in volume of upslope sector is for example expressed as: volumeReinforcementUpslope = (relativeVolumeUpslope – 25%)/25%.

A principal component analysis (PCA) of the 34 trees was made using 17 variables on the centred and scaled values to assess the overall grouping of individuals with regard to these variables. The variables were selected so as to represent the main features of the seedlings.

The total seedling biomass was doubled in both the slope (no flexing) and flexed trees when compared to the control (

Colour coding according to Fig. 1. North/Upslope is on the left. Above: top view, perpendicular to the soil surface. Below, side view, perpendicular to the slope. The black line below is the soil surface. The grey dashed frame is the container side and bottom wall (0.3×0.3×0.11 m).

Variable | Unit | Controlmean(n = 7) | Controlsd | Slopemean(n = 9) | Flexingmean(n = 8) | Slope×Flexingmean(n = 10) | Block | Correlationwith d0 |

Root+shoot dry weight | g | 17.5 | 4.99 | 36**** | 34.3**** | 46.9 | 0.96**** | |

Stem length | cm | 94.3 | 8.72 | 130**** | 124**** | 142** | 0.94**** | |

Collar diameter | cm | 1.01 | 0.152 | 1.4**** | 1.4**** | 1.7 | 1**** | |

stem length/collar diam | / | 94.4 | 5.2 | 93.7 | 88.7*** | 83.5 | −0.83**** | |

Shoot dry weight | g | 14 | 4.42 | 29**** | 25.6**** | 34.9 | 0.95**** | |

Root dry weight | g | 3.49 | 0.674 | 7.03**** | 8.71**** | 11.9 | 0.91**** | |

RPC (biomass) | % | 20.3 | 2.5 | 19.7 | 25.5**** | 25.5 | ** | 0.35* |

RPC without 1^{st} order root |
% | 8.27 | 3.59 | 9.59 | 6.67* | 6.82 | −0.26 | |

Tap root PC | % | 2.96 | 2.38 | 2.34 | 5.02**** | 6.54 | 0.52*** | |

Stump PC | % | 9.12 | 2.51 | 7.62* | 13.9**** | 12.1 | * | 0.23 |

Max. radial distance | cm | 21.8 | 4.95 | 25.2 | 24 | 27.3 | 0.28 | |

Max. depth | cm | −10.2 | 2.01 | −13.5 | −12.5 | −13 | −0.24 | |

Overall root length^{iafr} |
cm | 248 | 119 | 475** | 473** | 725 | 0.69**** | |

1^{st} order root length |
cm | 16.9 | 6.81 | 19.6** | 14 | 22.6 | 0.43** | |

SRL 1^{st} order root |
cm/cm^{3} |
4.11 | 1.5 | 2.48* | 1.66**** | 1.44 | −0.69**** | |

SRL lateral roots^{iafr} |
cm/cm^{3} |
88.4 | 41.3 | 56.2* | 147**** | 123 | 0.19 | |

Mean root tip diameter | cm | 0.065 | 0.011 | 0.07 | 0.049** | 0.056 | −0.07 | |

Root density | g/cm^{3} |
0.528 | 0.235 | 0.422** | 0.781** | 0.564 | −0.1 |

The root partitioning coefficient (RPC) increased by 25% in flexed plants compared to controls. However, when all 1^{st} order roots (stump+taproot) were excluded from the ratio, flexed plants had a 20% lower RPC. Conversely, if only the taproot was taken into account, RPC was 71% higher in flexed trees compared to controls. If only the stump was taken into account, slope trees had a 17% lower RPC whereas flexed trees possessed a 50% higher RPC (

The slope×flexed interaction was never significant in the above mentioned variables, except for those related to the size of the trees. The block effect was never significant in any variable studied, except for RPC, which could not be explained.

The mean total number of roots was significantly greater in both slope and flexed trees compared to control trees, but no differences were found in specific root number (^{rd} order roots. 1^{st} order roots in the slope trees were 20% less tapered than in control trees. The mean proximal taper of 2^{nd} order roots and deep root individual root dimensions were not significantly different from the control in any treatment.

Colour coding according to Fig. 1. Lateral roots growing perpendicular to the slope direction are shown as dots on the taproot. Root characteristics (e.g. root number, root size) are the average in each group.

(a) Loadings for the 16 original variables. Blue: General tree and root system characteristics and branching variables. RPC = root partitioning coefficient, DW1D = cubic root of seedling dry weight, RnAxes = number of root axes divided by root dry weight, muaxeVolZRT = mean axis volume in the ZRT, SRLaterals = specific root length of laterals, qbShallow = Qb in the shallow root compartment, ILLtapRoot = interlateral length on the taproot, SRLstumpTapv = specific root volume of the first order root. Orange: relative root volume (RV) by compartment; RVhzbeyond is shallow root beyond ZRT, RVtaproot is for the taproot, RVdeep is for deep roots, RVstump is for the stump, RVinterm is for intermediate depth roots and RVZRT is for the ZRT relative root volume. Red: circular distribution of root volume: RvolUpZRT is the volume of root in the ZRT upslope (or north) divided by the whole volume in the ZRT. RvolPerpShallow is the proportion of perpendicular to slope (or east and west) shallow roots out of the total shallow roots. (b) Loadings for the 34 trees of the sample. Black = control; blue = slope; red = flexed; orange = slope+flexing.

Variable | Unit | Controlmean | Controlsd | Slopemean | Flexingmean | Slope×flexingmean | Correlation with d0 | |

Root number | total iafr | n | 20.3 | 8.6 | 48** | 45.1** | 67.6 | 0.64**** |

SRN (Root number/rootDW) | total iafr | n/g | 5.64 | 1.86 | 7.25 | 5.07 | 5.68 | −0.08 |

Mean axis length | horizontal surface | degree | 13.9 | 4.54 | 15.9 | 18* | 17 | 0.46** |

Mean axis length | Intermediate depth | degree | 14.2 | 3.95 | 14.4 | 15.6 | 14.4 | −0.01 |

Mean axis length | deep roots | degree | 14.9 | 4.38 | 14.6 | 15.1 | 15.3 | 0.05 |

Mean axis diameter | horizontal surface | cm | 0.124 | 0.03 | 0.17**** | 0.106**** | 0.128 | 0.15 |

Mean axis diameter | Intermediate depth | cm | 0.119 | 0.03 | 0.122 | 0.1* | 0.104 | −0.07 |

Mean axis diameter | deep roots | cm | 0.102 | 0.04 | 0.0932 | 0.09 | 0.0914 | 0.03 |

Mean axis volume | horizontal surface | cm^{3} |
0.2 | 0.13 | 0.405*** | 0.167** | 0.26 | 0.3* |

Mean axis volume | Intermediate depth | cm^{3} |
0.205 | 0.12 | 0.178 | 0.127* | 0.134 | −0.2 |

Mean axis volume | deep roots | cm^{3} |
0.137 | 0.13 | 0.106 | 0.0973 | 0.0931 | −0.04 |

Relative root volume | order 3 | % | 6.36 | 4.33 | 9.53 | 5.05* | 5.86 | −0.16 |

Mean axis taper at 3.5 cm | order 2 on stump | %diam/cm | 4.14 | 0.98 | 3.68 | 3.56 | 3.38 | −0.5** |

Mean axis taper at 3.5 cm | order 2 below stump | %diam/cm | 3.89 | 1.13 | 3.97 | 3.86 | 3.78 | −0.12 |

Mean axis taper | order 1 | %diam/cm | 6.16 | 2.55 | 5.04*** | 7.69 | 4.35 | −0.42** |

Mean axis taper | order >1 | %diam/cm | 4.75 | 0.71 | 4.99 | 4.67 | 5.07 | 0.12 |

q_{b} |
total iafr | 0.576 | 0.16 | 0.277**** | 0.382* | 0.246 | −0.46** | |

q_{b} |
shallow roots iafr | 0.674 | 0.25 | 0.232**** | 0.339** | 0.195** | −0.56*** | |

q_{b} |
intermediate depth iafr | 0.531 | 0.4 | 0.766 | 0.527 | 0.396 | −0.11 | |

q_{b} |
deep roots iafr | 0.613 | 0.39 | 1 | 0.829 | 0.778 | −0.02 | |

Mean p_{branch} |
stump | 1.2 | 0.2 | 1.05** | 1.23 | 1.09 | −0.2 | |

Mean p_{branch} |
taproot | 1.42 | 0.31 | 1.31 | 1.87** | 1.59 | 0.05 | |

Mean p_{branch} |
laterals | 0.985 | 0.24 | 0.981 | 0.658**** | 0.739 | −0.44** | |

Mean p_{within} |
stump | % cm/cm | 9.16 | 13 | 8.98 | 7 | 3.97 | −0.19 |

Mean p_{within} |
taproot | % cm/cm | 24.6 | 19.4 | 16.6* | 24.9 | 15.4 | −0.38* |

Mean p_{within} |
laterals | % cm/cm | 4.96 | 1.02 | 6.48 | 4.23 | 4.2 | −0.28 |

Mean q | stump | 0.781 | 0.17 | 0.841 | 0.926*** | 0.933 | 0.6**** | |

Mean q | taproot | 0.743 | 0.08 | 0.8** | 0.791** | 0.903 | 0.57*** | |

Mean q | laterals | 0.666 | 0.09 | 0.665 | 0.504**** | 0.551 | −0.34* | |

Mean inter-lateral length | stump iafr | cm | 0.568 | 0.36 | 0.364 | 0.394 | 0.328 | −0.5** |

Mean inter-lateral length | taproot iafr | cm | 3.93 | 2.95 | 1.73 | 1.1* | 1.65* | −0.45** |

Mean inter-lateral length | order II iafr | cm | 2.87 | 1.45 | 1.26 | 1.11* | 1.48** | −0.33* |

Mean apical unbranched length | cm | 12.7 | 3.37 | 13.5 | 14.5 | 13.7 | 0.25 | |

Mean branching angle | order 2 on stump | degree | 82.2 | 8.27 | 83.2 | 85.3 | 82.4 | 0.14 |

Mean branching angle | order 2 below stump | degree | 87.2 | 10.7 | 72.1*** | 85.7 | 73.2 | −0.47** |

Taproot angle toward soil surface | taproot | degree | −71 | 18 | −53.4**** | −83.6* | −59.3 | 0.13 |

Mean root angletoward soil surface | horizontal order2 on stump | degree | −10.8 | 10.7 | −12 | −5.79* | −7.98 | 0.24 |

Mean root angletoward soil surface | horizontal order2 below stump | degree | −4.09 | 3.47 | −9.88*** | −4.34* | −6* | −0.05 |

Mean absolute RDD | order 2 | degree | 11.8 | 8.71 | 7.95 | 5.91 | 6.3 | −0.3* |

Mean axis winding | order 2 on stump | degree | 105 | 5.09 | 104 | 104 | 114 | 0.31* |

Mean axis winding | order 2 below stump | degree | 105 | 9.5 | 102 | 101 | 101 | −0.29* |

The topological index for the entire root systems indicated that control trees were moderately herringbone (q_{b} was close to 60%) (_{b} differed only in shallow roots with a 66% increase in flexed and a 50% increase in slope trees, but the factors were only partially additive (

The mean distance between laterals along the stump was not significantly influenced by the treatments, but this distance was 60% smaller along the taproot and 2^{nd} order roots in flexed trees but it was not the case in the slope+flexed trees. There was no effect of treatments on the apical unbranched length (

In control seedlings, tapering through branching was average on the stump (p_{branch} = 1.2), high on the taproot (1.43) and negligible on lateral roots. Mean p_{branch} was 13% lower in the stump in slope trees and 30% higher in the taproot but 33% lower in lateral roots of flexed trees (

Tapering between branching points was high in the taproot of control trees. p_{within} differed from the control only in the taproots of slope trees (−33%) (

In control trees, q averaged 78% in stump, 75% in taproot and 66% in laterals, intermediate between a herringbone and a dichotomous pattern. Mean q was +7% in the taproots of slope trees. In flexed trees, mean q was 19% larger in the stump, 6% greater in the taproot and 25% smaller in laterals roots (

The mean branching angle of 2^{nd} order roots was smaller beneath the stump in slope trees only (

However, the mean angle towards the soil surface of 2^{nd} order roots was smaller in shallow roots of flexed (−5.8°) compared to control trees (−10.8°) and greater in roots below the stump in slope trees (−9.9°) and flexed trees (−4.34°) compared to control trees (−4.1°). A low RDD, or root winding, in all treatments indicated very slight root reorientations (

In the control trees, the stump represented 45% of the total root volume and all the 1^{st} order roots (i.e. stump+taproot) made up 60% of the total root volume (

Variable | unit | Controlmean | Control sd | Slope mean | Flexing mean | Slope×flexing mean |

Relative volume | ||||||

(1) Stump | % | 45 | 12.9 | 38.9* | 54.3** | 47.4 |

Relative volume, stump excluded | ||||||

(2 & 5) Taproot & Sinkers | % | 26.7 | 21.7 | 20.2 | 44**** | 49.8 |

(3) ZRT | % | 11.6 | 9.04 | 20.2** | 9.18* | 12.6 |

(4) Horizontal shallow beyond ZRT | % | 32.7 | 24.4 | 41.7 | 20.4** | 23.6 |

(8 & 9) Intermediate & Oblique | % | 26.5 | 25.1 | 15.9* | 21.7 | 12.4 |

(7) Deep roots | % | 2.54 | 3.55 | 1.31* | 4.68 | 1.5 |

Relative length^{iafr} |
||||||

(3 & 4) Horizontal shallow | % | 26.7 | 21.7 | 20.2 | 44**** | 49.8 |

(8 & 9) Intermediate & Oblique | % | 11.6 | 9.04 | 20.2** | 9.18* | 12.6 |

(7) Deep roots | % | 32.7 | 24.4 | 41.7 | 20.4** | 23.6 |

Relative number^{iafr} |
||||||

(3 & 4) Horizontal shallow | % | 47.9 | 27.5 | 63.9* | 44.2 | 58.4 |

(8 & 9) Intermediate & Oblique | % | 31.4 | 24.1 | 24.7 | 37.6 | 27.6 |

(7) Deep roots | % | 9.8 | 15.8 | 2.81 | 8.6 | 4.4 |

Mean stump volume was 14% smaller in slope trees and mean volume of intermediate depth roots and deep roots was 40% lower whereas the mean volume of the ZRT was 75% higher (

No differences in the circular distribution of root volume, number or length were found in seedlings on 0° slopes, regardless of flexing treatment (data no shown). In whole root system and in the ZRT, shallow roots beyond ZRT, intermediate depth roots and deep roots, slope seedlings had 2/3 or more of their root volume, number and length situated in the sector perpendicular to the slope direction (^{nd} order roots branching from the stump showed the same circular pattern as that of shallow roots. Downslope shallow roots were more herringbone (+30% for MBO) because only two seedlings developed 3^{rd} order roots in this sector (

Slope | Slope+flexed | |||||||

us | pp/2 | ds | us | pp/2 | ds | |||

Total | 19.3b | 33.2a | 14.3b | 29.4 | 23.7 | 23.2 | ||

ZRT | 19.8b | 33.5a | 13.1b | 36.6a | 24b | 15.4b | ||

Horizontal beyond ZRT | 0.74 | 19.1b | 34.2a | 12.5b | 2.4 | 32.3a | 24.4ab | 19b |

Intermediate depth | 8.76b | 32.1a | 27.1a | 16 | 25 | 34 | ||

Deep roots | 0c | 43.1a | 13.8b | 4.55b | 29.3ab | 37a | ||

Total | 17.3b | 33.5a | 15.7b | 28.9 | 22.8 | 25.5 | ||

Shallow | 20.4b | 33.7a | 12.2b | 34.1a | 23.2b | 19.5b | ||

Intermediate depth | 8.36b | 32a | 27.6a | 17.4 | 25.1 | 32.4 | ||

Deep | 0c | 41.7a | 16.6b | 8.56 | 26.9 | 37.7 | ||

Total^{iafr} |
16.7b | 34.1a | 15b | 32.9a | 22b | 23.1b | ||

Shallow^{iafr} |
20.3b | 34.2a | 11.3b | 38.3a | 22.1b | 17.5b | ||

Intermediate depth^{iafr} |
6.74b | 32.5a | 28.2a | 20.7 | 24.8 | 29.6 | ||

Deep^{iafr} |
0b | 41.7a | 16.7b | 10.9 | 25.9 | 37.2 | ||

Order II on stump (1) | 18.9b | 32.6a | 15.8b | 24.9 | 26.5 | 22.1 | ||

Order II below Stump (1) | 0.855c | 34.9a | 29.4b | 14.2b | 26.9a | 32a | ||

Total | 1.43a | 1.3a | 1.14b | 1.39 | 1.3 | 1.3 | ||

Shallow | 1.43a | 1.35a | 1.11b | 1.41 | 1.34 | 1.36 | ||

Intermediate depth | NA | NA | NA | 1.24 | 1.22 | 1.21 | ||

^{3}) |
||||||||

Shallow | 40 | 36.8 | 50.1 | 53.2b | 79.3ab | 103a | ||

Intermediate depth | 82.8 | 89 | 122 | 106 | 119 | 132 | ||

Shallow | 0.17 | 0.173 | 0.162 | 0.157a | 0.121b | 0.122b | ||

Intermediate depth | 0.116 | 0.125 | 0.119 | 0.109 | 0.103 | 0.1 | ||

Shallow | 15.9 | 15.3 | 16.6 | 19 | 16.5 | 18.8 | ||

Intermediate depth | 13 | 14.8 | 12.7 | 12.9 | 15 | 14.5 | ||

^{3}) |
||||||||

Shallow | 0.385 | 0.406 | 0.351 | 0.411 | 0.214 | 0.328 | ||

Intermediate depth | 0.169 | 0.19 | 0.149 | 0.118 | 0.147 | 0.123 | ||

Order II on stump | 4.1 | 3.71 | 4.05 | 3.39 | 3.36 | 3.65 | ||

Order II on stump | 99.8a | 79.7b | 66.9b | 90.4a | 85.8b | 60.7c | ||

Order II below Stump | NA | NA | NA | 114a | 75b | 51c | ||

Shallow | −11.6 | −11.5 | −11.6 | −12.9a | −6.21b | −5.49b | ||

Intermediate depth | −6.28 | −9.43 | −10.3 | −6.83 | −6.12 | −6.79 |

In slope+flexed seedlings no significant differences were found with regard to the all roots distribution, except for root number which had a 32% increase in the upslope sector (^{nd} order root branching below stump, compared to those downslope (^{nd} order root branching angles in slope+flexed seedlings were smaller than in slope trees.

The PCA highlighted the intensity in grouping of the four tree types (

Both the slope and flexing treatments increased plant size significantly, augmenting also variables such as number of roots. The poor development of control trees was associated with a higher variability of size and root architecture parameters. These results were not due to differences in soil moisture content. No run-off was observed during watering because the substrate was highly absorbent. At a small scale, a higher water accumulation may have occurred at the deepest point in the rotated containers, downslope, which could partly explain the increased length of taproot in the slope treatment compared to the trees grown on flat ground. Nevertheless, some soil compaction downslope of inclined plants could be seen, which may be due to the consolidating effects of water infiltration downslope. In a similar experiment, when containers were inclined 22° and 45°, total dry biomass of inclined plants increased by 100%, compared to controls

The control trees were smaller and possessed only a thick taproot and only a few branches whereas larger trees from other treatments also possessed 3^{rd} order roots, especially near the soil surface. Hence, root systems from the slope and flexed treatments were more dichotomous, as were also compartments or circular sectors with a small number of roots. Similarly, because of their small size, control trees had a smaller q in the stump and taproot.

Tapering by branching or between branches took place mainly on the only vertical root, i.e. the taproot. Such a rapid decrease of root biomass as a function of soil depth is typical in most plants

Pot and soil geometry may explain several slope effects: taproots grew vertically downwards and each pot was inclined, thus 40% more soil volume was available in the vertical direction beneath the centre of each tree. Additionally the bottom of the container was inclined. Therefore, slope trees had a larger maximal rooting depth and relative stump volume and a smaller taproot SRL, taper and q. Lateral roots remained closely parallel to the soil surface even at 10 cm depth, as also found by ^{nd} order axes as a control tree in a 2.8 cm thick soil layer instead of 4 cm. Similarly, deep lateral roots could not develop upslope because as they emerged from the taproot, their growth would be impeded by the base of the pot (

The predominant overall development of lateral roots in the sectors perpendicular to the slope direction cannot be explained by geometric differences: in trees on slopes, the distance between the stump and pot wall was approximately the same in the four main directions, although the circular distribution of volume and length and number of shallow roots was highly heterogeneous. Stem and crown weight plays an important role in determining the distribution of internal stresses within a mature tree ^{nd} order roots in the perpendicular to slope sector in slope trees but a uniform circular distribution of 2^{nd} order roots on the stump in slope+flexed trees. This disparity may result from heterogeneous root mortality or late root emergence but was probably not from heterogeneous initial initiation of roots, as flexing took place 3 weeks after germination. Additionally, the circular sector of additional fine roots was not determined.

Although flexing intensity was low, the resulting changes in seedling structure were major. Stem base diameter and taper increased, as has often been reported for many species (see e.g.

Flexed plants possessed more numerous, thinner, longer and straighter lateral roots which had a more homogeneous vertical distribution along the taproot than in control plants. As these roots hold the taproot in position all along its length, deeper lateral roots will move the centre of rotation of the taproot further to the bottom, constraining overall rotation

Changes in the inclination and branching angles in 1^{st} order roots and lateral roots also improved plant anchorage because a vertical taproot with horizontal laterals provide the best mechanical design in the type of soil used

Slope and flexing factors were additive for most of the root characteristics. A large part of changes due to the factor slope originated from geometrical constraints, and were also found in slope+flexed seedlings. Elsewhere, as flexing had larger effects on root architecture than slope, slope+flexed trees were similar to the flexed only trees, as seen in the PCA, meaning that plants responded to flexing more than they did to slope treatment.

The largest interaction between the two factors could be seen with regard to the circular distribution. As a response to flexing, 2^{nd} order roots were distributed all around the stump to ‘pin’ it in place, but upslope shallow roots were more developed, particularly in the ZRT, likely at the expense of downslope shallow roots. Roots in the upslope sector will provide better anchorage for the stump because (

All flexed seedlings have a large rigid vertical stump (grey) and taproot (black) and finer lateral roots parallel to the soil surface (blue arrows), analogous to guy ropes around a vertical stake. The 1^{st} order root tapers and lateral roots (yellow and green arrows) become shorter and thinner with depth. The 1^{st} order root undergoes bending, whereas fine roots act in tension. The volume of soil in which the 1^{st} order roots can be potentially embedded is a truncated cone (black vertical hatched zone). The potential volume of soil which can be explored by the guying lateral roots is shown by the grey oblique hatched zones. Above: On 0° slope, most of the hatched zones are filled with soil (orange shading). Lateral roots are both horizontal and perpendicular to the 1^{st} order root. A design with fine and evenly distributed lateral roots is efficient for keeping the stem vertical when lateral forces are dominant. Below: On 45° slope: the above mentioned design is no longer efficient, the resulting root system pattern does not allow for the stump to be held in place, nor for lateral roots to firmly anchor the stump and taproot. As the 1^{st} order root is no longer perpendicular to the soil surface, there is no soil in a large part of the hatched zones downslope and lateral roots are oblique and not perpendicular to the stump and taproot. However, the hatched zone upslope is completely filled with soil (orange shading). Therefore, rotation of the stump is prevented by the thicker upslope shallow laterals which literally hold the stump in place. There is also a progressive shift in the circular distribution of deep laterals downslope as a function of soil depth (violet shading). These deeper roots will help the taproot to be strongly anchored in the soil.

In flexed×slope plants, taproots were oriented slightly more upslope and shallow lateral roots growing perpendicular to the slope and downslope had a smaller angle to the soil surface. Therefore, a larger soil volume will be encased by the downslope and perpendicular roots, resulting in a larger root-soil plate downslope, hence increasing root system anchorage. A negative interaction between slope and flexing for q_{b} of shallow roots and for taproot and 2^{nd} order roots inter-lateral length was obtained. It is possible that these interactions between flexing and slope angle were not greater, because certain root traits were confined within given plastic limits. Thus, the interaction of individual root trait reponses to several environmental processes does not equal the sum of trait responses.

Our results are comparable to those found by

During a winching test or a natural windstorm, the root-soil plate volume is largely composed of the side of the root system held in tension. Thus our results explain why, in winching tests performed up- down- and cross-slope on mature

We yielded clear-cut results, largely because in our experiment, all factors were simplified, i.e., we used a homogeneous substrate with direct seeding on a steep slope, as well as simple non directional flexing without airflow. We studied a pioneer species which is likely to possess highly plastic traits. All changes in root architecture could be tracked due to a complete 3D measurement and an in depth analysis. This paper therefore presents a framework for the study of 3D coarse root architecture in all its aspects, i.e., a “deep phenotyping”

It has previously been stressed that the architectural model determine the characteristic architecture of the root system in a given plant species and define the limits for plasticity of that species

Differences observed with regard to the inter-lateral length on the stump were related only to tree size (ρ = 0.5). Nevertheless, major plasticity was observed as plants allocated differently resources to various parts of the root system, in particular the diameter and length of laterals versus the taproot, and the circular distribution of overall lateral root development. Even though shallower roots have a significantly higher potential to contribute to plant productivity than deep roots

As for trees on flat ground

When planting trees on steep slopes in a windy climate, nursery and planting practices should allow for a symmetrical development of shallow roots, so that the optimal development of roots in the direction allowing the best mechanical support can occur.

In natural environments, many factors such as soil type and heterogeneity, slope angle, water supply, competition and complex wind patterns interact at various levels, therefore it is difficult to characterize the effect of each factor. As a tree grows, it will constantly perform trade-offs to improve performance with regard to e.g. light capture, resource acquisition and mechanical stability within the limits of its architectural model. Tree root systems on steep hillslopes will be highly variable and many types of architecture have been described in the literature, with no one conclusive study of slope effects on root system architecture. Even if it has not been described previously, in any case, woody plants on a steep slope likely have to avoid a downslope displacement of the stump. Therefore, development of larger shallow roots upslope, regardless of whole root system architecture would increase anchorage. An alternative would be the development of a well anchored thick shallow root downhill, acting like a chuck, like in

However, our study goes a long way in quantifying in one typical case, the previously unknown effects of substrate geometry on root architecture, and to differentiate the architectural consequences of inherent root architectural model and root trait plasticity.

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We thank E. Bertocchi, M. Chassagne and P. Taris for technical help. The glasshouse was managed by the Unité Expérimentale de l’Hermitage, UE 0570, INRA, 69 route d’Arcachon, 33612 CESTAS. We also thank the Linux, R and openALEA-AMAP open software community for software and support. AMAP (Botany and Computational Plant Architecture) is a joint research unit which associates CIRAD (UMR51), CNRS (UMR5120), INRA (UMR931), IRD (2M123), and Montpellier 2 University (UM27). We furthermore thank the anonymous reviewers for helpful comments on an earlier version of the manuscript.

^{th}plant biomechanics conference, Stockholm, August 28 to September 1 2006, 299–303.