Résumé
Tree stems are slender structures and are never perfectly vertical and symmetric. As a consequence, the increase in tree mass that occurs during growth always causes bending movements disturbing stem orientation. In the absence of a compensatory mechanism, the accumulation of these downward bending movements over time would necessarily result in an ever-increasing curvature of the stems, preventing vertical growth and ultimately leading to a weeping habit. To control the orientation of growing aerial organs in the field of gravity, some gravitropic correction is needed. In trees, this correction is achieved by the asymmetric production of mechanical stress during the maturation of the newly formed wood, often associated to the presence of reaction wood. The change in orientation of a growing stem depends on the balance between the disturbance related to the increase in mass, and the correction, related to the increase in diameter and the associated gravitropic reaction. A biomechanical model was developed to compute the rates of disturbance and correction theoretically associated to a growth increment. They were analytically expressed as a function of parameters defining stem morphology, cross-section anatomy and wood properties. The efficiency of the gravitropic correction depends on the asymmetry of wood maturation strain, eccentric growth, and gradients in wood stiffness. For a tree to keep its stem at a constant orientation during growth, the correction must compensate the disturbance at any time. Analyzing the size effects in the formulae, we show that this necessity might constrain stem allometric growth to be such that H~D1/2. This allometric constraint was quantified using literature data and compared to the condition for elastic stability (H~D2/3). When a tilted stem grows, the gravitropic constraint quickly becomes more constraining than elastic stability, and this constraint is larger when the tilt angle is larger. We conclude that traits determining the gravitropic performance set constraints on the growth of tilted stems, and may be the main constraint limiting the horizontal extension of branches.