相关论文: Mutation in Populations Governed by a Galton-Watso…
We consider a continuous-time Bienaym\'e-Galton-Watson process with logistic competition in a regime of weak competition, or equivalently of a large carrying capacity. Individuals reproduce at random times independently of each other but…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given…
In this paper we consider inhomogeneous Galton-Watson trees, and derive various moments for such processes: the number of vertices, the number of leaves, and the height of the tree. Also we make a simple condition of finiteness. We use…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
We study survival properties of inhomogeneous Galton-Watson processes. We determine the so-called branching number (which is the reciprocal of the critical value for percolation) for these random trees (conditioned on being infinite), which…
We consider a class of non-local reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. For a confining fitness function, we prove well-posedness and write the solution explicitly, via some…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
We aim to understand the evolution of the genetic composition of cancer cell populations. To achieve this, we consider an individual-based model representing a cell population where cells divide, die and mutate along the edges of a finite…
Consider a critical Galton--Watson branching process with immigration, where the offspring distribution belongs to the domain of attraction of a $(1 + \alpha)$-stable law with $\alpha \in (0,1)$, and the immigration distribution either (i)…
Here we treat the transmission of disease through a population as a standard Galton-Watson branching process, modified to take the presence of vaccination into account. Vaccination reduces the number of secondary infections produced per…
The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial,…
We prove a scaling limit theorem for two-type Galton-Waston branching processes with interaction. The limit theorem gives rise to a class of mixed state branching processes with interaction using to simulate the evolution for cell division…
In this paper, we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space. The convergence is proved in the sense of probability by introducing an intermediate particle…
In this paper, we study the asymptotic (large time) behavior of a selection-mutation-competition model for a population structured with respect to a phenotypic trait, when the rate of mutation is very small. We assume that the reproduction…
We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…
We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the…
In this paper, we study a Galton-Watson process $(Z_n)$ with infinitely many types in a random ergodic environment $\bar{\xi}=(\xi_n)_{n\geq 0}$. We focus on the supercritical regime of the process, where the quenched average of the size of…
In ecology and population dynamics, gene-flow refers to the transfer of a trait from one population to another. This phenomenon appears in studying the evolution of social features, such as languages. From the mathematical point of view,…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…