  We study the connection between spherical wedge and full spherical shell
geometries using simple mean-field $\alpha^2$ dynamos. We solve the equations
for a one-dimensional time-dependent mean-field dynamo to examine the effects
of varying the polar angle $\theta_0$ between the latitudinal boundaries and
the poles in spherical coordinates. We investigate the effects of turbulent
magnetic diffusivity and $\alpha$ effect profiles as well as different
latitudinal boundary conditions to isolate parameter regimes where oscillatory
solutions are found. Finally, we add shear along with a damping term mimicking
radial gradients to study the resulting dynamo regimes. We find that the
commonly used perfect conductor boundary condition leads to oscillatory
$\alpha^2$ dynamo solutions only if the wedge boundary is at least one degree
away from the poles. Other boundary conditions always produce stationary
solutions. By varying the profile of the turbulent magnetic diffusivity alone,
oscillatory solutions are achieved with models extending to the poles, but the
magnetic field is strongly concentrated near the poles and the oscillation
period is very long. By introducing radial shear and a damping term mimicking
radial gradients, we again see oscillatory dynamos, and the direction of drift
follows the Parker--Yoshimura rule. Oscillatory solutions in the weak shear
regime are found only in the wedge case with $\theta_0 = 1^\circ$ and perfect
conductor boundaries. A reduced $\alpha$ effect near the poles with a turbulent
diffusivity concentrated toward the equator yields oscillatory dynamos with
equatorward migration and reproduces best the solutions in spherical wedges.
