Related papers: The genealogy of a sample from a binary branching …
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
Recruitment dynamics, or the distribution of the number of offspring among individuals, is central for understanding ecology and evolution. Sweepstakes reproduction (heavy right-tailed offspring number distribution) is central for…
We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…
Consider a birth and death process started from one individual in which each individual gives birth at rate $\lambda$ and dies at rate $\mu$, so that the population size grows at rate $r = \lambda - \mu$. Lambert and Harris, Johnston, and…
The Yule branching process is a classical model for the random generation of gene tree topologies in population genetics. It generates binary ranked trees -- also called "histories" -- with a finite number $n$ of leaves. We study the…
Gene gain-loss-duplication models are commonly based on continuous-time birth-death processes. Employed in a phylogenetic context, such models have been increasingly popular in studies of gene content evolution across multiple genomes.…
Consider a finite renewal process in the sense that interrenewal times are positive i.i.d. variables and the total number of renewals is a random variable, independent of interrenewal times. A finite point process can be obtained by…
We consider a branching population where individuals have i.i.d.\ life lengths (not necessarily exponential) and constant birth rate. We let $N_t$ denote the population size at time $t$. %(called homogeneous, binary Crump--Mode--Jagers…
We describe a new general connection between $\Lambda$-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
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…
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…
Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…
We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…
Phylogenetic analyses which include fossils or molecular sequences that are sampled through time require models that allow one sample to be a direct ancestor of another sample. As previously available phylogenetic inference tools assume…
We consider weighted particle systems in which new generations are re-sampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo methods, widely used in applied…
Pedigrees, or family trees, are graphs of family relationships that are used to study inheritance. A fundamental problem in computational biology is to find, for a pedigree with $n$ individuals genotyped at every site, a set of…
We introduce and study a model of plane random trees generalizing the famous Bienaym\'e--Galton--Watson model but where births and deaths are locally correlated. More precisely, given a random variable $(B,H)$ with values in $\{1,2,3,…
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual…
We consider a model of stationary population with random size given by a continuous state branching process with immigration with a quadratic branching mechanism. We give an exact elementary simulation procedure of the genealogical tree of…