  This work examines the global dynamics of classical solutions of a two-stage
(juvenile-adult) reaction-diffusion population model in time-periodic and
spatially heterogeneous environments. It is shown that the sign of the
principal eigenvalue $\lambda_*$ of the time-periodic linearized system at the
trivial solution completely determines the persistence of the species.
Moreover, when $\lambda_*>0$, there is at least one time-periodic positive
entire solution. A fairly general sufficient condition ensuring the uniqueness
and global stability of the positive time-periodic solution is obtained. In
particular, classical solutions eventually stabilize at the unique
time-periodic positive solutions if either each subgroup's intra-stage growth
and inter-stage competition rates are proportional, or the environment is
temporally homogeneous and both subgroups diffuse slowly. In the later
scenario, the asymptotic profile of steady states with respect to small
diffusion rates is established.
