  We use numerical simulations to probe the dynamics of concentrated
suspensions of spherical microswimmers interacting hydrodynamically. Previous
work in the dilute limit predicted orientational instabilities of aligned
suspensions for both pusher and puller swimmers, which we confirm
computationally. Unlike previous work, we show that isotropic suspensions of
spherical swimmers are also always unstable. Both types of initial conditions
develop long-time polar order, of a nature which depends on the hydrodynamic
signature of the swimmer but very weakly on the volume fraction up to very high
volume fractions.
