Related papers: Tractable diffusion and coalescent processes for w…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
Sweepstakes reproduction refers to a highly skewed individual recruitment success without involving natural selection and may apply to individuals in broadcast spawning populations characterised by Type III survivorship. We consider an…
We investigate a new model for populations evolving in a spatial continuum. This model can be thought of as a spatial version of the Lambda-Fleming-Viot process. It explicitly incorporates both small scale reproduction events and large…
Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the…
A density-dependent branching process is a particle system in which individuals reproduce independently, but in a way that depends on the current population size. This feature can model a wide range of ecological interactions at the cost of…
In this work we describe a new model for the evolution of a diploid structured population backwards in time that allows for large migrations and uneven offspring distributions. The model generalizes both the mean-field model of Birkner et…
We introduce a stochastic model of a population with overlapping generations and arbitrary levels of self-fertilization versus outcrossing. We study how the global graph of reproductive relationships, or population pedigree, influences the…
We study the multi-type Cannings population model. Each individual has a type belonging to a given at most countable type space $E$. The population is hence divided into $|E|$ subpopulations. The subpopulation sizes are assumed to be…
We review recent progress in the understanding of the role of multiple- and simultaneous multiple merger coalescents as models for the genealogy in idealised and real populations with exceptional reproductive behaviour. In particular, we…
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 present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman…
The goal of this paper is to develop a theory of graphon-valued stochastic processes, and to construct and analyse a natural class of such processes arising from population genetics. We consider finite populations where individuals change…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection.…
Effective population size characterizes the genetic variability in a population and is a parameter of paramount importance in population genetics. Kingman's coalescent process enables inference of past population dynamics directly from…
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…
Consider a population evolving as a discrete-time supercritical multi-type Galton--Watson process. Suppose we run the process for $T$ generations, then sample $k$ individuals uniformly at generation $T$ and trace their genealogy backwards…
We analyse sequential Markov coalescent algorithms for populations with demographic structure: for a bottleneck model, a population-divergence model, and for a two-island model with migration. The sequential Markov coalescent method is an…
We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices…
We consider the problem of learning two families of time-evolving random measures from indirect observations. In the first model, the signal is a Fleming--Viot diffusion, which is reversible with respect to the law of a Dirichlet process,…