Related papers: Coalescences in Continuous-State Branching Process…
In this paper, we introduce a family of processes with values on the nonnegative integers that describes the dynamics of populations where individuals are allowed to have different types of interactions. The types of interactions that we…
We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations…
We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/\tau…
The Feller diffusion is studied as the limit of a coalescent point process in which the density of the node height distribution is skewed towards zero. Using a unified approach, a number of recent results pertaining to scaling limits of…
We construct a Markov process model to describe the evolution of labor division and its dynamical behavior is investigated by numerical simulations in detail. We have shown that under the mechanism of increasing returns, the division of…
We consider a continuous population whose dynamics is described by the standard stationary Fleming-Viot process, so that the genealogy of $n$ uniformly sampled individuals is distributed as the Kingman $n$-coalescent. In this note, we study…
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associated class of piecewise deterministic Markov processes,…
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…
We give a concise self-contained presentation of known and new limit theorems for the one-type Markov branching processes with continuous time. The new streamlined proofs are based on what we call, the tail generating function approach. Our…
Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent…
The Ancestral Selection Graph (ASG) is an important genealogical process which extends the well-known Kingman coalescent to incorporate natural selection. We show that the number of lineages of the ASG with and without mutation is…
We consider the genealogy of a sample of individuals taken from a spatially structured population when the variance of the offspring distribution is relatively large. The space is structured into discrete sites of a graph G. If the…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
We consider the discrete-time migration-recombination equation, a deterministic, nonlinear dynamical system that describes the evolution of the genetic type distribution of a population evolving under migration and recombination in a law of…
We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distribution we recover the Kingman,…
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…
Poissonian ensembles of Markov loops on a finite graph define a random graph process in which the addition of a loop can merge more than two connected components. We study Markov loops on the complete graph derived from a simple random walk…
We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the birth-and-death process with immigration studied in…
It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in…
We consider the critical Galton-Watson process with overlapping generations stemming from a single founder. Assuming that both the variance of the offspring number and the average generation length are finite, we establish the convergence…