Related papers: A time-dependent Poisson random field model for po…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics…
We describe a new construction of a family of measures on a group with the same Poisson boundary. Our approach is based on applying Markov stopping times to an extension of the original random walk.
We introduce an analytical model for population dynamics with intra-specific competition, mutation and assortative mating as basic ingredients. The set of equations that describes the time evolution of population size in a mean-field…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Mutational signatures are powerful summaries of the mutational processes altering the DNA of cancer cells. The usual approach to mutational signature analysis consists of decomposing the matrix of mutation counts from a sample of patients…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
When setting up field experiments, to test and compare a range of genotypes (e.g. maize hybrids), it is important to account for any possible field effect that may otherwise bias performance estimates of genotypes. To do so, we propose a…
As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…
We propose a one mutation model for cancer with a mutation rate that increases with time. Under rather general hypotheses the number of mutations is necessarily a (non homogeneous) Poisson process with the prescribed mutation rate. We show…
We show the convergence of the characteristic polynomial for random permutation matrices sampled from the generalized Ewens distribution. Under this distribution, the measure of a given permutation depends only on its cycle structure,…
The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable replaced by a stable subordinator and its…
The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
The paper is concerned with approximating the distribution of a sum W of n integer valued random variables Y_i, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson…
Multi-dimensional data frequently occur in many different fields, including risk management, insurance, biology, environmental sciences, and many more. In analyzing multivariate data, it is imperative that the underlying modelling…
An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both…