Modeling genetic diversity needs an underlying genealogy model. To choose a fitting model
based on genetic data, one can perform model selection between classes of genealogical …

In this paper we provide a systematic exposition of basic properties of integrated distribution
and quantile functions. We define these transforms in such a way that they characterize any …

Representation of coalescent process using pruning of trees has been used by Goldschmidt
and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the …

Abstract The Beta (2− α, α) n-coalescent with 1< α< 2 is a Markov process taking values in
the set of partitions of {1,…, n}. It evolves from the initial value {1},…,{n} by merging …

We study the frequency process $ f_ {1} $ of the block of 1 for a Ξ-coalescent Π with dust. If Π
stays infinite, $ f_ {1} $ is a jump-hold process which can be expressed as a sum of broken …

Modelling genetic diversity needs an underlying genealogy model. To choose a fitting model
based on genetic data, one can perform model selection between classes of genealogical …

We consider some genealogical properties of nested samples. The complete sample is
assumed to have been drawn from a natural population characterised by high fecundity and …

For Λ-n-coalescents with mutation, we analyse the minimal observable clade size O n. For a
given individual i∈{1,…, n}, the minimal observable clade size O n (i) is 1 plus the number of …

Trees play a central role in various research areas: In evolutionary biology they depict the
relationships between different species, in theoretical computer science they are used as …

We study the largest block size of Beta n-coalescents at small times as n tends to infinity,
using the paintbox construction of Beta-coalescents and the link between continuous-state …