Related papers: Cannings models, population size changes and multi…
We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate…
We consider the lambda-coalescent processes with positive frequency of singleton clusters. The class in focus covers, for instance, the beta$(a,b)$-coalescents with $a>1$. We show that some large-sample properties of these processes can be…
We examine the total number of collisions $C_n$ in the $\Lambda$-coalescent process which starts with $n$ particles. A linear growth and a stable limit law for $C_n$ are shown under the assumption of a power-like behaviour of the measure…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the…
We study a class of Cannings models with population size $N$ having a mixed multinomial offspring distribution with random success probabilities $W_1,\ldots,W_N$ induced by independent and identically distributed positive random variables…
We provide new connections between multitype $\Lambda$-coalescents and multitype continuous state branching processes via duality and a homeomorphism on their parameter space. The approach is based on a sequential sampling procedure for the…
Recovery of population size history from molecular sequence data is an important problem in population genetics. Inference commonly relies on a coalescent model linking the population size history to genealogies. The high computational cost…
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…
Kingman's House-of-Cards model is a simple and celebrated model to describe the evolution of population under the competition of selection and mutation. Letting mutation probabilities vary on generations makes the model more realistic and…
The Wright-Fisher model and the Moran model are both widely used in population genetics. They describe the time evolution of the frequency of an allele in a well-mixed population with fixed size. We propose a simple and tractable model…
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines of descent governed by a simple coalescent process, and…
Coalescent theory combined with statistical modeling allows us to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. When sequences are sampled serially through…
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we…
We propose a change in focus from the prevalent paradigm based on the branching property as a tool to analyze the structure of population models, to one based on the self-similarity property, which we also introduce for the first time in…
Let $\Lambda$ be a finite measure on the unit interval. A $\Lambda$-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions ($\Lambda$-coalescent) in analogy to the duality…
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…
Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only…
We study a class of evolution models, where the breeding process involves an arbitrary exchangeable process, allowing for mutations to appear. The population size $n$ is fixed, hence after breeding, selection is applied. Individuals are…
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…