  Symmetry-based ideas, such as the quark-lepton complementarity (QLC)
principle and the tri-bimaximal mixing (TBM) scheme, have been proposed to
explain the observed mixing pattern of neutrinos. We argue that such symmetry
relations need to be imposed at a high scale $\Lambda \sim 10^{12}$ GeV
characterizing the large masses of right-handed neutrinos required to implement
the seesaw mechanism. For nonhierarchical neutrinos, renormalisation group
evolution down to a laboratory energy scale $\lambda \sim 10^3$ GeV tends to
radiatively break these symmetries at a significant level and spoil the mixing
pattern predicted by them. However, for Majorana neutrinos, suitable
constraints on the extra phases $\alpha_{2,3}$ enable the retention of those
high scale mixing patterns at laboratory energies. We examine this issue within
the Minimal Supersymmetric Standard Model (MSSM) and demonstrate the fact
posited above for two versions of QLC and two versions of TBM. The appropriate
constraints are worked out for all these four cases. Specifically, a preference
for $\alpha_2 \approx \pi$ (i.e. $m_1 \approx -m_2$) emerges in each case. We
also show how a future accurate measurement of $\theta_{13}$ may enable some
discrimination among these four cases in spite of renormalization group
evolution.
