Before revision:  In the numerically tractable cases of N\leqslant 6, we find that the diffusive threshold generically decreases as N increases and that  these many-species instabilities generally require all species to be diffusing .
After revision:  In the numerically tractable cases of N\leqslant 6, we find that the diffusive threshold generically decreases as N increases and that these many-species instabilities cannot be described by reduced models with fewer species .