The symbiotic branching model: duality and interfaces

Jochen Blath, Marcel Ortgiese

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Abstract

The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes various classic models in population dynamics, such as the stepping stone model and the mutually catalytic branching model. We are particularly interested in understanding the region of coexistence, i.e. the interface between the two types. In this chapter, we give an overview over our results that describe the dynamics of these interfaces at large scales. One of the reasons that this system is tractable is that it exhibits a rich duality theory. So at the same time, we
take the opportunity to provide an introduction to the strength of duality methods in the context of spatial population models.
Original languageEnglish
Title of host publicationProbabilistic Structures in Evolution
EditorsEllen Baake, Anton Wakolbinger
PublisherEMS Publishing House
Pages311–336
Number of pages26
ISBN (Electronic)978-3-98547-505-6
ISBN (Print)978-3-98547-005-1
DOIs
Publication statusPublished - 1 May 2021

Publication series

NameEMS Series of Congress Reports
PublisherEMS Publishing House
Volume17

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