  One of the most important predictions in magnetohydrodynamics (MHD) is that
in the presence of a uniform magnetic field $\textbf{b}_{0}$ a transition from
weak to strong wave turbulence should occur when going from large to small
perpendicular scales. This transition is believed to be a universal property of
several anisotropic turbulent systems. We present for the first time direct
evidence of such a transition thanks to a three-dimensional direct numerical
simulation of incompressible balanced MHD turbulence with a grid resolution of
$3072^2 \times 256$. From large to small-scales, the change of regime is
characterized by i) a change of slope in the energy spectrum going from
approximately $-2$ to $-3/2$; ii) an increase of the ratio between the wave and
nonlinear times, with a critical ratio of $\chi_{c}\sim0.35$; iii) an absence
followed by a dramatic increase of the communication between Alfv\'en modes;
and iv) a modification of the iso-contours of energy revealing a transition
from a purely perpendicular cascade to a cascade compatible with the critical
balance type phenomenology. All these changes happen at approximately the same
transition scale and therefore can be seen as manifest signatures of the
transition from weak to strong wave turbulence.
