Spatial populations with seed-bank : renormalisation on the hierarchical group / Andreas Greven, Frank den Hollander, Margriet Oomen.

Format:

Book

Author/Creator:

Greven, Andreas, 1953- author.

Hollander, F. den (Frank), author.

Oomen, Margriet, 1990- author.

Series:

Memoirs of the American Mathematical Society ; v. 1553.

Memoirs of the American Mathematical Society ; v. 1553

Language:

English

Subjects (All):

Probabilities.

probability.

Physical Description:

ix, 207 pages : illustrations ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, 2025.

Summary:

We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals carry type one of two types, live in colonies, and are subject to resampling and migration as long as they are active. Each colony has a structured seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. As geographic space labelling the colonies we consider a countable Abelian group endowed with the discrete topology. In earlier work we showed that the system has a one-parameter family of equilibria controlled by the relative density of the two types. Moreover, these equilibria exhibit a dichotomy of coexistence (= locally multi-type equilibrium) versus clustering (= locally mono-type equilibrium). We identified the parameter regimes for which these two phases occur, and found that these regimes are different when the mean wake-up time of a dormant individual is finite or infinite. The goal of the present paper is to establish the finite-systems scheme, i.e., identify how a finite truncation of the system (both in the geographic space and in the seed-bank) behaves as both the time and the truncation level tend to infinity, properly tuned together. If the wake-up time has finite mean, then there is a single universality class for the scaling limit. On the other hand, if the wake-up time has infinite mean, then there are two universality classes depending on how fast the truncation level of the seed-bank grows compared to the truncation level of the geographic space.

Notes:

Includes bibliographical references (pages 205-207).

ISBN:

1470473151

9781470473150

OCLC:

1511787767