Related papers: Dynamics of an infinite age-structured particle sy…
We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…
We study the dynamics of an infinite system of point particles of two types. They perform random jumps in $\mathbf{R}^d$ in the course of which particles of different types repel each other whereas those of the same type do not interact.…
Experiments motivated by predictions of quantum mechanics indicate non-trivial correlations between spacelike-separated measurements. The phenomenon is referred to as a violation of strong-locality and, after Einstein, called ghostly action…
This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions…
Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics.…
We introduce a continuous-time Markov chain describing dynamic allelic partitions which extends the branching process construction of the Pitman sampling formula in Pitman (2006) and the birth-and-death process with immigration studied in…
In this paper, we study a finite population undergoing discrete, nonoverlapping generations, that is structured into $D$ demes, each containing $N$ individuals of two possible types, $A$ and $B$, whose viability coefficients, $s_A$ and…
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and…
In nature, most microbial populations have complex spatial structures that can affect their evolution. Evolutionary graph theory predicts that some spatial structures modelled by placing individuals on the nodes of a graph affect the…
Consider a sequence of Markov processes $X^1, X^2,...$ with state space $E$, where $X^N$ has a strong drift to $D \subseteq E$, such that $\Phi(X^N)$ is slow for some appropriate $\Phi: E\to D$. Using the method of martingale problems, we…
A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the…
Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent…
We report on a fundamental role of a non-normalized formal steady state, i.e., an infinite invariant density, in a semi-Markov process where the state is determined by the inter-event time of successive renewals. The state describes certain…
This paper investigates a nonlinear logistic model for age-structured population dynamics. The model incorporates interdependent fertility and mortality functions within a logistic framework, offering insights into stationary solutions and…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
To our knowledge, the populations are generally assumed to be homogeneous in the traditional approach to evolutionary game dynamics. Here, we focus on the inhomogeneous populations. A simple model which can describe the inhomogeneity of the…
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…