Related papers: Duality, Ancestral and Diffusion Processes in Mode…
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's fitness by $s_N$. Each individual dies at…
We study the following model for a diploid population of constant size $N$: Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the two parents passes each element independently with probability…
The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
Identifiability of evolutionary tree models has been a recent topic of discussion and some models have been shown to be non-identifiable. A coalescent-based rooted population tree model, originally proposed by Nielsen et al. 1998 [2], has…
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…
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…
This paper gives a new flavor of what Peter Jagers and his co-authors call `the path to extinction'. In a neutral population with constant size $N$, we assume that each individual at time $0$ carries a distinct type, or allele. We consider…
We study coalescent processes conditional on the population pedigree under the exchangeable diploid bi-parental population model of \citet{BirknerEtAl2018}. While classical coalescent models average over all reproductive histories, thereby…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the…
Gene conversion is a mechanism by which a double-strand break in a DNA molecule is repaired using a homologous DNA molecule as a template. As a result, one gene is 'copied and pasted' onto the other gene. It was recently reported that the…
{\bf Abstract} The trajectory of the frequency of an allele which begins at $x$ at time $0$ and is known to have frequency $z$ at time $T$ can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when $x=z=0$ are…
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…
Known results on the moments of the distribution generated by the two-locus Wright-Fisher diffusion model and a duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical methods…
Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
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…
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?". We focus on the situation in which…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…