This thesis introduces spatial models for populations with dormancy in random environments. The models are formulated as continuous-time two-type branching random walks, where individuals switch between active and dormant states. We consider two scenarios: one where the switching rates are influenced by the random environment, and another where they are independent of it. The random environment, which also governs the branching mechanism, is modelled in four specific configurations, each composed of particles: (1) a Bernoulli field of immobile particles, (2) a single moving particle, (3) a Poisson field of moving particles, and (4) a simple symmetric exclusion process. In each case, the environmental particles can act either as catalysts, which accelerate branching, or as traps, which kill individuals. The key distinction between the two types is that dormant individuals are protected from traps but do not participate in migration or reproduction. We quantify the impact of dormancy on population growth and survival by identifying the large-time asymptotics of the expected population size. Our mathematical approach is based on the parabolic Anderson model, analysed via the Feynman-Kac formula. Specifically, we extend the parabolic Anderson model to a two-type random walk to investigate the quantitative role of dormancy.
Helia Shafigh (Thu,) studied this question.