Related papers: A probabilistic analysis of a continuous-time evol…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
We derive a Poisson random field model for population site polymorphisms differences within and between two species that share a relatively recent common ancestor. The model can be either equilibrium or time inhomogeneous. We first consider…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
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…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
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…
We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die,…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
We have analyzed the relations between the mutational pressure, recombination and selection pressure in the bit-string model with sexual reproduction. For specific sets of these parameters we have found three phase transitions with one…
Genetic fitness optimization using small populations or small population updates across generations generally suffers from randomly diverging evolutions. We propose a notion of highly probable fitness optimization through feasible…
We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Genetic recombination is one of the most important mechanisms that can generate and maintain diversity, and recombination information plays an important role in population genetic studies. However, the phenomenon of recombination is…
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle…
Clusters of genes that have evolved by repeated segmental duplication present difficult challenges throughout genomic analysis, from sequence assembly to functional analysis. Improved understanding of these clusters is of utmost importance,…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity of recombining segments, several studies examined whether this could lead to the…
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…
Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large…