Related papers: A master equation approach to the n-coalescent pro…
We establish convergence to the Kingman coalescent for the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may…
We define a Markov process in a forward population model with backward genealogy given by the $\Lambda$-coalescent. This Markov process, called the fixation line, is related to the block counting process through its hitting times. Two…
We show that genealogical trees arising from a broad class of non-neutral models of population evolution converge to the Kingman coalescent under a suitable rescaling of time. As well as non-neutral biological evolution, our results apply…
In this paper, we consider Galton-Watson processes with immigration. Pick $i(\ge2)$ individuals randomly without replacement from the $n$-th generation and trace their lines of descent back in time till they coalesce into $1$ individual in…
We study the common ancestor type distribution in a $2$-type Moran model with population size $N$, mutation and selection, and in the deterministic limit regime arising in the former when $N$ tends to infinity, without any rescaling of…
Kingman's coalescent is one of the most popular models in population genetics. It describes the genealogy of a population whose genetic composition evolves in time according to the Wright-Fisher model, or suitable approximations of it…
Moran or Wright-Fisher processes are probably the most well known model to study the evolution of a population under various effects. Our object of study will be the Simpson index which measures the level of diversity of the population, one…
We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting…
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age"…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…
We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied…
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,…
We consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312--316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at…
Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in…
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations of motion are time reversal invariant. One objection to irreversibility is based on Poincar\'e's recursion theorem: a…
In this paper we consider the two-type Moran model with $N$ individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution ${\mathbb P}$ on ${\mathbb R}_+$, and a type, either $1$ or $0$.…
Evolution in finite populations is often modelled using the classical Moran process. Over the last ten years this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such…
We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the…
We dedicate this paper to Sir John Kingman on his 70th Birthday. In modern mathematical population genetics the ancestral history of a population of genes back in time is described by John Kingman's coalescent tree. Classical and modern…
Mendelian randomization (MR) is an epidemiological method that can be used to strengthen causal inference regarding the relationship between a modifiable environmental exposure and a medically relevant trait and to estimate the magnitude of…