Wind is a major ecological factor for plants (Ennos, 1997) and a major economical factor for forestry (de Langre, 2008). Mechanical analyses have revealed that the multimodal dynamic behavior of trees is central to wind - tree interactions. Moreover, the trunk and branches influence dynamic modes, both in frequency and location (James et al., 2006; Spatz et al., 2007). Because of the complexity of tree architecture, finite element models (FEMs) have been used to analyze such dynamics (e.g. Sellier et al., 2006). However, these models require detailed geometric and architectural data and are tree-specific - two major restraints for their use in most ecological or biological studies. In this work, closed-form scaling laws for modal characteristics were derived from the dimensional analysis of idealized fractal trees that sketched the major architectural and allometrical regularities of real trees (Rodriguez et al., 2008). These scaling laws were compared to three-dimensional FEM modal analyses of two completely digitized trees with maximal architectural contrast. Despite their simplifying hypotheses, the models explained most of the spatiotemporal characteristics of modes that involved the trunk and branches, especially for sympodial trees. These scaling laws reduce the tree to (1) a fundamental frequency and (2) one architectural and three biometrical parameters. They also give quantitative insights into the possible biological control of wind excitability of trees through architecture and allometries. It is shown that the mechanical design of tree depends on branching symmetries and allometries, and is likely to be controlled through thigmomorphogenesis (Moulia et al., 2006).

References
de Langre, E. 2008. Effects of wind on plants. Annual Review of Fluid Mechanics 40: 141-168.
Ennos, A. R. 1997.Wind as an ecological factor. Trends Ecol. Evol. 12:108-111.
James, K. R., N. Haritos, and P. K. Ades. 2006. Mechanical stability of trees under dynamic loads. American Journal of Botany 93: 1522-1530.
Moulia, B., C. Coutand, and C. Lenne. 2006. Posture control and skeletal mechanical acclimation in terrestrial plants: implications for mechanical modelling of plant architecture. American Journal of Botany 93: 1477-1489.
Rodriguez, M., E. de Langre, and B. Moulia. 2008. A scaling law for the effects of architecture and allometry on tree vibration modes suggests a biological tuning to modal compartmentalization. American Journal of Botany 95: 1523-1537.
Sellier, D., T. Fourcaud, and P. Lac. 2006. A finite element model for investigating effects of aerial architecture on tree oscillations. Tree Physiology 26: 799-806.
Spatz, H.-C., F. Br"uchert, and J. Pfisterer. 2007. Multiple resonance damping or how do trees escape dangerously large oscillations? American Journal of Botany 94: 1603-1611.