相关论文: Predator-prey dynamics on infinite trees: a branch…
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic…
We consider families of discrete time birth and death chains on trees, and show that in presence of a drift towards the root of the tree, the chains exhibit cut-off behavior along the drift and escape behavior in the opposite direction.
We consider a mortal random walker evolving with discrete time on a network, where transitions follow a degree-biased Markovian navigation strategy. The walker starts with a random initial budget $T_1 \in \mathbb{N}$ and must maintain a…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…
We extend the $N$ branching Brownian motions model of population invasion to higher-order asexual reproduction. Increasing reproduction order leads to qualitative changes: invasion fronts generically cease to exist beyond binary…
We show that the transience or recurrence of a random walk in certain random environments on an arbitrary infinite locally finite tree is determined by the branching number of the tree, which is a measure of the average number of branches…
Predator-prey coevolution is commonly thought to result in reciprocal arms races that produce increasingly extreme and complex traits. However, such directional change is not inevitable. Here, we provide evidence for a previously…
Given a discrete spatial structure $X$, we define continuous-time branching processes that model a population breeding and dying on $X$. These processes are usually called branching random walks. They are characterized by breeding rates…
We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/\tau…
We consider a critical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We are interested in the event $\mathcal{A}_i(n)$ that all individuals alive at time $n$ are offspring of the…
We study the dynamics of a ring of patches with vegetation-prey-predator populations, coupled through interactions of the Lotka-Volterra type. We find that the system yields aperiodic, recurrent and rare explosive bursts of predator density…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
We consider a supercritical branching process and define a contact tracing mechanism on its genealogical tree. We calculate the growth rate of the post tracing process, and give conditions under which the tracing is strong enough to drive…
We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr. From the persistence results, we can deduce properties of critical branching processes with offspring…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
The pursuit-evasion game is studied for two adversarial active agents, modelled as a deterministic self-steering pursuer and a stochastic, cognitive evader. The pursuer chases the evader by reorienting its propulsion direction with limited…
In this paper we consider two continuous-mass population models as analogues of logistic branching random walks, one is supported on a finite trait space and the other one is supported on an infinite trait space. For the first model with…