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 Bienayme-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. [...]
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