Convection in the outer core is dominated by rotation effects. Theory indicates that convection in a rapidly rotating sphere of conducting fluid produces transversely isotropic magnetohydrodynamic induction, with an axis of symmetry parallel to the rotation vector. We have examined the long-term behavior of azimuthally averaged core magnetic fields maintained by transversely isotropic induction, using numerical calculations of spherical mean-field dynamos. The inductive effect of core convection is represented parametrically by a nonlinear, anisotropic α effect with magnitude Rα concentrated near the inner core boundary to simulate convection driven by inner core crystallization. Large values of the magnetic Reynolds number Rα, representing vigorous convection, result in nonreversing and relatively strong dipolar fields. Small but supercritical values of Rα produce relatively weak and oscillatory dipolar fields. Intermediate values of Rα result in a modified square-wave behavior for the dipole field, consisting of constant polarity epochs with nearly uniform intensity lasting several hundred thousand years, separated by polarity transitions. Duration of polarity epochs is extremely sensitive to Rα. The change from a frequent reversal regime to an infrequent reversal regime (superchron) requires only a small increase in Rα. Transitions in transversely isotropic α2 dynamos are caused by growth of reversed flux zones at high latitudes in each hemisphere, which merge to form a reversed dipolar field. Addition of a large-scale toroidal shear flow causes reversals to be initiated by growth of reversed flux zones at low latitudes. Virtual geomagnetic pole paths from successive reversals are alternatingly near- and far-sited. Transition fields are predominantly octupolar. The model predicts a positive correlation between polarity epoch duration and dipole field intensity. ¿ American Geophysical Union 1990