Spacecraft observations in the strongly compressed subsolar magnetosheath show an inverse correlation between the proton temperature anisotropy (T⊥p/T∥p>1 where ⊥ and ∥ denote directions perpendicular and parallel to the background magnetic field) and the parallel proton &bgr; (&bgr;∥p). This manuscript uses one-dimensional hybrid simulations of the proton cyclotron anisotropy instability in homogeneous electron-proton plasmas to study this correlation which may represent a limited closure relation for fluid theories of anisotropic space plasmas. The emphasis is on driven simulations which increase the temperature anisotropy by periodically reducing the magnetic-field-aligned velocities of the protons. The late-time states from ensembles of both initial value and driven simulations yield very similar expressions for the proton anisotropy/&bgr;∥p inverse correlation, and provide a basis for explaining differences between sheath observations from different spacecraft. The driven simulations also yield expressions for the maximum instability growth rate and the fluctuating field energy as functions of &bgr;∥p and a parameter characterizing the anisotropy driver. ¿ American Geophysical Union 1994