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Spatial population models with local self-interactions

Applicant Cerný Jirí
Number 193063
Funding scheme Project funding
Research institution Departement Mathematik und Informatik Universität Basel
Institution of higher education University of Basel - BS
Main discipline Mathematics
Start/End 01.06.2021 - 31.05.2024
Approved amount 117'960.00
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Keywords (4)

random walks with self-interaction; spatial population with regulation; dynamic random environments; branching random walks in random environment

Lay Summary (German)

Lead
Die theoretische Evolutionsbiologie arbeitet mit Populationsmodellen, um dieEntwicklung von Spezies in ihrem Habitat zu verdeutlichen. Unser Projektuntersucht mathematische Modelle, welche die räumliche Entwicklung solcherPopulationen erklären.
Lay summary
Klassische mathematische Modelle zur Entwicklung von Populationen lassen oft
die räumliche Struktur ausser Acht. Diese ist jedoch wichtig, weil sich
Populationen nicht losgelöst von ihrem Lebensraum entwickeln und ihre
Individuen mit diesem und lokal miteinander interagieren. Die mathematische
Analyse solcher Modelle ist jedoch deutlich komplexer.

Wir untersuchen drei Auswirkungen der Interaktion zwischen Individuen und ihrer
(räumlichen und/oder zeitlichen) Umgebung: (1) Überleben versus Aussterben, (2)
Clusterwachstum versus lokale Diversität und (3) Geschwindigkeit und
Fluktuation in expandierenden Populationen.
Direct link to Lay Summary Last update: 25.05.2021

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Abstract

We consider spatial population models with local (self-)interactions. The interaction can be either induced by a common random (spatial) environment in which the individuals live or it can be modelled explicitly by a local feed-back mechanism which regulates an individual's offspring law depending on the configuration in a certain neighbourhood around it. These models are more realistic than classical branching random walks, where particles move and branch completely independently; they are also harder to analyse because of this lack of independence and also because they typically are not ``monotone'' systems, since adding additional individuals can be actually harmful for the present population.We focus on (1) extinction versus survival regimes, (2) in an equilibrium, when including neutral types: growth of clusters versus local diversity, (3) front speed and fluctuations in expanding populations in a random environment. A common connecting tool is the study of the spatial embedding of ancestral lines, which are random walks in a dynamic random environment.
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