Related papers: Splitting trees with neutral mutations at birth
Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random…
The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize…
We study the genetic behaviour of a population formed by haploid individuals which reproduce asexually. The genetic information for each individual is stored along a bit-string (or chromosome) with L bits, where 0-bits represent the…
A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the…
Mechanisms leading to speciation are a major focus in evolutionary biology. In this paper, we present and study a stochastic model of population where individuals, with type a or A, are equivalent from ecological, demographical and spatial…
Shannon information has, in the past, been applied to quantify the genetic diversity of many natural populations. Here, we apply the Shannon concept to consecutive generations of alleles as they evolve over time. We suppose a genetic system…
Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the…
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…
When an advantageous mutation occurs in a population, the favorable allele may spread to the entire population in a short time, an event known as a selective sweep. As a result, when we sample $n$ individuals from a population and trace…
We review and extend results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic…
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…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
To learn about the past from a sample of genomic sequences, one needs to understand how evolutionary processes shape genetic diversity. Most population genetic inference is based on frameworks assuming adaptive evolution is rare. But if…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as Xi-coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
If we follow an asexually reproducing population through time, then the amount of time that has passed since the most recent common ancestor (MRCA) of all current individuals lived will change as time progresses. The resulting "MRCA age"…
Under random mating, a progeny's alleles are independently sampled from the parental gene pools. Here is a new proof which avoids the usual algebraic complexity, based on a restated Mendel's First Law. Another simplified proof along the old…
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…