相关论文: Noisy traveling waves: effect of selection on gene…
We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model, that we shall call the exponential model, the…
We consider an extension of the noisy $N$-Branching Random Walk that models the evolution of a population subject to natural selection. We show the existence of a critical value for the noise which separates the limiting genealogical…
In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the…
In a series of recent works it has been shown that a class of simple models of evolving populations under selection leads to genealogical trees whose statistics are given by the Bolthausen-Sznitman coalescent rather than by the well known…
We consider a stochastic model describing a constant size $N$ population that may be seen as a directed polymer in random medium with $N$ sites in the transverse direction. The population dynamics is governed by a noisy traveling wave…
We review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of…
We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies.…
We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) $A$ and $a$, and that…
We consider the range $R^{(n)}$, the tree made up of visited vertices by a diffusive null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree $\mathbb{T}$ up to the $n$-th return time to its root and we consider the…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
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…
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…
We analyze a variant of the Noisy $K$-Branching Random Walk, a population model that evolves according to the following procedure. At each time step, each individual produces a large number of offspring that inherit the fitness of their…
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,…
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…
The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to have more than one clearly different phenotypes. We present a model for…
Evolutionary models for populations of constant size are frequently studied using the Moran model, the Wright-Fisher model, or their diffusion limits. When evolution is neutral, a random genealogy given through Kingman's coalescent is used…
Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also…