  The goal of this article is to contribute towards the conceptual and
quantitative understanding of the evolutionary benefits for (microbial)
populations to maintain a seed bank (consisting of dormant individuals) when
facing fluctuating environmental conditions. To this end, we compare the long
term behaviour of `1-type' Bienaym\'e-Galton-Watson branching processes
(describing populations consisting of `active' individuals only) with that of a
class of `2-type' branching processes, describing populations consisting of
`active' and `dormant' individuals. All processes are embedded in an
environment changing randomly between `harsh' and `healthy' conditions,
affecting the reproductive behaviour of the populations accordingly. For the
2-type branching processes, we consider several different switching regimes
between active and dormant states. We also impose overall resource limitations
which incorporate the potentially different `production costs' of active and
dormant offspring, leading to the notion of `fair comparison' between different
populations, and allow for a reproductive trade-off due to the maintenance of
the dormancy trait. Our switching regimes include the case where switches from
active to dormant states and vice versa happen randomly, irrespective of the
state of the environment (`spontaneous switching'), but also the case where
switches are triggered by the environment (`responsive switching'), as well as
combined strategies. It turns out that there are rather natural scenarios under
which either switching strategy can be super-critical, while the others, as
well as complete absence of a seed bank, are strictly sub-critical, even under
`fair comparison' wrt. available resources. In such a case, we see a clear
selective advantage of the super-critical strategy, which is retained even
under the presence of a (potentially small) reproductive trade-off. [...]
