CRC/TRR 388/1: "Dormant populations in heterogeneous random environments" (SP A09)

We study random spatio-temporal population models in random heterogeneous environ- ments with dormancy, an evolutionary force describing the ability of individuals to enter and exit a protective state typically at the cost of halting reproduction. We consider pop- ulation models with view at population sizes (e.g., multi-type branching random walk models in random, time-dependent environment) and on genetic-types relations (e.g., stochastic F-KPP equations in random environment). Our main goal is to understand the characteristics of situations in which dormancy may be a valid survival strategy for which we study the large-time asymptotics of the total population size, the long-time survival of the population or the coexistence of genetic types, respectively.The key novelty of this project is the introduction of space-dependent heterogeneous randomness for modeling a fluctuating, possibly hostile environment.
We reduce the complexity of this problem by taking expectations over the branch- ing mechanism (leading to the parabolic Anderson model (PAM) with time-dependent random potential on the integer lattice) and/or by taking scaling limits according to Donsker’s invariance principle, leading for example to dormant variants of the rough super-Brownian motion, to a dormant PAM with Gaussian white noise potential, or to dormant Fisher–KPP-type equations in random environment. A central objective then will be the description of the large-time asymptotics of the continuum models, i.e. mass asymptotics and survival/co-existence properties, for the models involving dormancy in particular in comparison to their non-dormant counterparts. In the PAM we expect to see far from central-limit behaviour and a concentration effect called intermittency.