Related papers: The allelic partition for coalescent point process…
We consider a branching population where individuals live and reproduce independently. Their lifetimes are i.i.d. and they give birth at a constant rate b. The genealogical tree spanned by this process is called a splitting tree, and the…
The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial,…
The problem of estimating the growth rate of a birth and death processes based on the coalescence times of a sample of $n$ individuals has been considered by several authors (\cite{stadler2009incomplete, williams2022life,…
We define a multi-type coalescent point process of a general branching process with finitely many types. This multi-type coalescent fully describes the genealogy of the (quasi-stationary) standing population, providing types along ancestral…
Consider a random real tree whose leaf set, or boundary, is endowed with a finite mass measure. Each element of the tree is further given a type, or allele, inherited from the most recent atom of a random point measure…
Consider a population where individuals give birth at constant rate during their lifetimes to i.i.d. copies of themselves. Individuals bear clonally inherited types, but (neutral) mutations may happen at the birth events. The smallest…
It is becoming routine to obtain datasets on DNA sequence variation across several thousands of chromosomes, providing unprecedented opportunity to infer the underlying biological and demographic forces. Such data make it vital to study…
We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeleton of the coalescent tree; for each…
Coalescent processes, including mutation, are derived from Moran type population models admitting large offspring numbers. Including mutation in the coalescent process allows for quantifying the turnover of alleles by computing the…
We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give…
Consider an arbitrary large population at the present time, originated at an unspecified arbitrary large time in the past, where individuals in the same generation reproduce independently, forward in time, with the same offspring…
We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant…
The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to have more than one clearly different phenotypes. We present a model for…
Let $K_n$ denote the number of types of a sample of size $n$ taken from an exchangeable coalescent process ($\Xi$-coalescent) with mutation. A distributional recursion for the sequence $(K_n)_{n\in{\mathbb N}}$ is derived. If the coalescent…
We define a doubly infinite, monotone labeling of Bienayme-Galton-Watson (BGW) genealogies. The genealogy of the current generation backwards in time is uniquely determined by the coalescent point process $(A_i; i\ge 1)$, where $A_i$ is the…
We consider a general branching population where the lifetimes of individuals are i.i.d.\ with arbitrary distribution and where each individual gives birth to new individuals at Poisson times independently from each other. In addition, we…
Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the…
Longitudinal molecular data of rapidly evolving viruses and pathogens provide information about disease spread and complement traditional surveillance approaches based on case count data. The coalescent is used to model the genealogy that…
This paper studies the spatial coalescent on $\Z^2$. In our setting, the partition elements are located at the sites of $\Z^2$ and undergo local delayed coalescence and migration. That is, pairs of partition elements located at the same…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…