  We investigate the interplay between two fundamental mechanisms of microbial
population dynamics and evolution called dormancy and horizontal gene transfer.
The corresponding traits come in many guises and are ubiquitous in microbial
communities, affecting their dynamics in important ways. Recently, they have
each moved (separately) into the focus of stochastic individual-based modelling
(Billiard et al. 2016, 2018; Champagnat, M\'el\'eard and Tran, 2021; Blath and
T\'obi\'as 2020). Here, we examine their combined effects in a unified model.
Indeed, we consider the (idealized) scenario of two sub-populations,
respectively carrying 'trait 1' and 'trait 2', where trait 1 individuals are
able to switch (under competitive pressure) into a dormant state, and trait 2
individuals are able to execute horizontal gene transfer, turning trait 1
individuals into trait 2 ones, at a rate depending on the frequency of
individuals. In the large-population limit, we examine the fate of a single
trait i individual (a 'mutant') arriving in a trait j resident population
living in equilibrium, for $i,j=1,2,i \neq j$. We provide a complete analysis
of the invasion dynamics in all cases where the resident population is
individually fit and the initial behaviour of the mutant population is
non-critical. We identify parameter regimes for the invasion and fixation of
the new trait, stable coexistence of the two traits, and 'founder control'
(where the initial resident always dominates, irrespective of its trait). The
most striking result is that stable coexistence occurs in certain scenarios
even if trait 2 (which benefits from transfer at the cost of trait 1) would be
unfit when being merely on its own. In the case of founder control, the
limiting dynamical system has an unstable coexistence equilibrium. In all
cases, we observe the classical (up to 3) phases of invasion dynamics \`a la
Champagnat (2006).
