We give criteria on the existence of a so-called mark function in the context of marked metric
measure spaces (mmm-spaces). If an mmm-space admits a mark function, we call it …

We give a de Finetti type representation for exchangeable random coalescent trees (formally
described as semi-ultrametrics) in terms of sampling iid sequences from marked metric …

In a random complete and separable metric space that we call the lookdown space, we
encode the genealogical distances between all individuals ever alive in a lookdown model …

EURANDOM PREPRINT SERIES 2019-008 July 1, 2019 Probabilistic Structures in Evolution
Chapter 1 A. Greven, F. den Hollander ISSN Page 1 EURANDOM PREPRINT SERIES …

The paper has four goals. First, we want to generalize the classical concept of the branching
property so that it becomes applicable for historical and genealogical processes (using the …

The goal of this work is to decompose random populations with a genealogy in subfamilies
of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We …

We survey results on the description of stochastically evolving genealogies of populations
and marked genealogies of multitype populations or spatial populations via tree-valued …

Kingman's coalescent is a random tree that arises from classical population genetic models
such as the Moran model. Concerning the structure of the tree-top there are two well-known …

13.1 Background A classical model for a spatial population evolving through neutral
resampling and migration is a system of interacting Fleming–Viot diffusions [2, 7, 16, 20, 24 …

This thesis focuses on mathematical properties of two population models, namely the
generalised Fleming-Viot process and the branching process. In both cases, the population …