A branching process model for dormancy and seed banks in randomly fluctuating environments

TL;DR

This paper models the evolutionary advantages of seed banks in fluctuating environments using branching processes, revealing conditions where dormancy strategies outperform active-only populations.

Contribution

It introduces a novel branching process framework comparing active-only and dormant-inclusive populations under environmental fluctuations and resource constraints.

Findings

Dormancy can provide a selective advantage in fluctuating environments.

Certain switching regimes lead to super-critical populations with seed banks.

Resource limitations influence the reproductive success of dormancy strategies.

Abstract

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. [...]