Related papers: The mutation process on the ancestral line under s…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r=0, this reduces to the study of a single…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
We establish connections between the absorption probabilities of a class of birth-death processes with killing, and the stationary tail of a related class of birth-death processes with catastrophes. The major ingredients of the proofs are a…
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…
Using graphical methods based on a `lookdown' and pruned version of the {\em ancestral selection graph}, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection,…
The Moran process is a foundational model of genetic drift and mutation in finite populations. In its standard two-allele form with population size $n$, allele counts, and hence allele frequencies, change through stochastic replacement and…
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
Observed differences in mean phenotypic values across human groups have attracted renewed interest with the rise of large-scale genomic studies and polygenic risk prediction. However, the genetic basis of these differences is far more…
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the…
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,…
Mutations are typically classified by their effects on the nucleotide sequence and by their size. Here, we argue that if our main aim is to understand the effect of mutations on evolutionary outcomes (such as adaptation or speciation), we…
We study the fixation probability for two versions of the Moran process on the random graph $G_{n,p}$ at the threshold for connectivity. The Moran process models the spread of a mutant population in a network. Throughtout the process there…
We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…
We consider a single genetic locus with two alleles $A_1$ and $A_2$ in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and…
Genetic association data from national biobanks and large-scale association studies have provided new prospects for understanding the genetic evolution of complex traits and diseases in humans. In turn, genomes from ancient human…
The evolution of complex molecular traits such as disulphide bridges often requires multiple mutations. The intermediate steps in such evolutionary trajectories are likely to be selectively neutral or deleterious. Therefore, large…
We analyse a model consisting of a population of individuals which is subdivided into a finite set of demes, each of which has a fixed but differing number of individuals. The individuals can reproduce, die and migrate between the demes…
Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…