QCD lattice simulations with 2+1 flavours (when two quark flavours are mass degenerate) typically start at rather large up-down and strange quark masses and extrapolate first the strange quark mass and then the up-down quark mass to its respective physical value. In recent years we have been experimenting with an alternative method of tuning the quark masses. We keep the average quark mass  $(m_s + m_u + m_d)$ fixed, and extrapolate from a symmetric point (with all three quark masses equal) towards the physical point, where the strange is much heavier than the other two quarks. With this procedure group theory strongly constrains the terms allowed in a fit. It also allows us to relate the effects of isospin breaking ($m_u \ne m_d$) to the effects of SU(3) breaking ($m_s \ne m_l$). 
One consequence of having different masses for the $u$ and $d$ quark is that there will be mixing between the $\Lambda^0$ and $\Sigma^0$ baryons. We have investigated this on the lattice, and predicted the mixing due to  QCD effects.