Related papers: Two population models with constrained migrations
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
We study the extremes of branching random walks under the assumption that the underlying Galton-Watson tree has infinite progeny mean. It is assumed that the displacements are either regularly varying or they have lighter tails. In the…
Forest-fire and avalanche models support the notion that frequent catastrophes prevent the growth of very large populations and as such prevent rare large-scale catastrophes. We show that this notion is not universal. A new model class…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift $c$. At the point $x > 0$, we add an absorbing barrier, i.e.\ individuals touching the barrier are instantly killed without…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying…
We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes linear diffusion and logistic growth, and the boundary between…
In this paper, we consider a two-player two-strategy game with random payoffs in a population subdivided into $d$ demes, each containing $N$ individuals at the beginning of any given generation and experiencing local extinction and…
We discuss the conditions under which a population of anomalously diffusing individuals can be characterized by demographic fluctuations that are anomalously scaling themselves. Two examples are provided in the case of individuals migrating…
This paper presents a physical perspective on the human migration phenomenon claiming that human social behaviors are somehow but not completely inspired by nature. Human displacement or migration in the world is highly affected by…
We consider a critical branching process $Y_{n}$ in an i.i.d. random environment, in which one immigrant arrives at each generation. Let $% \mathcal{A}_{i}(n)$ be the event that all individuals alive at time $n$ are offspring of the…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. We are interested in the…
We study a dynamic model of ecosystems where immigration plays an essential role both in assembling the species community and in mantaining its biodiversity. This framework is particularly relevant for insular ecosystems. Population…
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated…
Understanding the relationship between a populations probability of extinction and its carrying capacity frames conservation status assessments and guides efforts to understand and mitigate the ongoing biodiversity crisis. Despite this, our…
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…