Related papers: Finite populations with frequency-dependent select…
Consider a population of fixed size that evolves over time. At each time, the genealogical structure of the population can be described by a coalescent tree whose branches are traced back to the most recent common ancestor of the…
For a genetic locus carrying a strongly beneficial allele which has just fixed in a large population, we study the ancestry at a linked neutral locus. During this ``selective sweep'' the linkage between the two loci is broken up by…
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…
Consider a population that is expanding in two-dimensional space. Suppose we collect data from a sample of individuals taken at random either from the entire population, or from near the outer boundary of the population. A quantity of…
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…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree…
Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the…
Evolutionary game dynamics in finite populations provides a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call {\sigma} law,…
The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the…
This is an introductory review of deterministic mutation-selection models for asexual populations (i.e., quasispecies theory) and related topics. First, the basic concepts of fitness, mutations, and sequence space are introduced. Different…
Discrete ancestral problems arising in population genetics are investigated. In the neutral case, the duality concept has proved of particular interest in the understanding of backward in time ancestral process from the forward in time…
We introduce a multi-allele Wright-Fisher model with non-recurrent, reversible mutation and directional selection. In this setting, the allele frequencies at a single locus track the path of a hybrid jump-diffusion process with state space…
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…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
Mendelian randomization uses genetic variants to make causal inferences about the effect of a risk factor on an outcome. With fine-mapped genetic data, there may be hundreds of genetic variants in a single gene region any of which could be…
The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of…
We study the effect of biological confounders on the model selection problem between Kingman coalescents with population growth, and Xi-coalescents involving simultaneous multiple mergers. We use a low dimensional, computationally tractable…
We investigate the $\Lambda$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this…
The genealogy at a single locus of a constant size $N$ population in equilibrium is given by the well-known Kingman's coalescent. When considering multiple loci under recombination, the ancestral recombination graph encodes the genealogies…