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We investigate the compact interface property in a recently introduced variant of the stochastic heat equation that incorporates dormancy, or equivalently seed banks. There individuals can enter a dormant state during which they are no longer subject to spatial dispersal and genetic drift. This models a state of low metabolic activity as found in microbial species. Mathematically, one obtains a memory effect since mass accumulated by the active population will be retained for all times in the seed bank. This raises the question whether the introduction of a seed bank into the system leads to a qualitatively different behaviour of a possible interface. Here, we aim to show that nevertheless in the stochastic heat equation with seed bank compact interfaces are retained through all times in both the active and dormant population. We use duality and a comparison argument with partial functional differential equations to tackle technical difficulties that emerge due to the lack of the martingale property of our solutions which was crucial in the classical non seed bank case.
We introduce a new class of stochastic partial differential equations (SPDEs) with seed bank modeling the spread of a beneficial allele in a spatial population where individuals may switch between an active and a dormant state. Incorporating dormancy
We consider a family of nonlinear stochastic heat equations of the form $partial_t u=mathcal{L}u + sigma(u)dot{W}$, where $dot{W}$ denotes space-time white noise, $mathcal{L}$ the generator of a symmetric Levy process on $R$, and $sigma$ is Lipschitz
We consider the stochastic heat equation with a multiplicative white noise forcing term under standard intermitency conditions. The main finding of this paper is that, under mild regularity hypotheses, the a.s.-boundedness of the solution $xmapsto u(
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4textless{}Htextless{}1/2 in the space var
We investigate various aspects of the (biallelic) Wright-Fisher diffusion with seed bank in conjunction with and contrast to the two-island model analysed e.g. in Kermany, Zhou and Hickey, 2008, and Nath and Griffiths, 1993, including moments, statio