Trees are self-similar structures: their branch lengths and diameters vary allometrically within the tree architecture, with longer and thicker branches near the ground. These tree allometries are often attributed to optimisation of hydraulic sap transport and safety against elastic buckling. Here, we show that these allometries also emerge from a model that includes competition for light, wind biomechanics and no hydraulics. We have developed MECHATREE, a numerical model of trees growing and evolving on a virtual island. With this model, we identify the fittest growth strategy when trees compete for light and allocate their photosynthates to grow seeds, create new branches or reinforce existing ones in response to wind-induced loads. Strikingly, we find that selected trees species are self-similar and follow allometric scalings similar to those observed on dicots and conifers. This result suggests that resistance to wind and competition for light play an essential role in determining tree allometries.