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There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…
We propose a novel network growth model coupled with the competition interaction to simulate macroevolution. Our work shows that the competition plays an important role in macroevolution and it is more rational to describe the interaction…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
In this kind of model, the main characteristic that determines population viability in the long term is the stochastic growth rate (SGR) denoted $\lambda_S$. When $\lambda_S$ is larger than one, the population grows exponentially with…
This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is…
This paper further develops work from a previous article which introduced a new way of modelling evolutionary game models with an emphasis on ecological realism, concerned with how ecological factors determine payoffs in evolutionary games.…
Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly…
We analyze an interacting particle system with a Markov evolution of birth-and-death type. We have shown that a local competition mechanism (realized via a density dependent mortality) leads to a globally regular behavior of the population…
Evolutionary prisoner's dilemma games are studied with players located on square lattice and random regular graphs defining four neighbors for each one. The players follow one of the three strategies: tit-for-tat, unconditional cooperation,…
Dynamical mechanisms that can stabilize the coexistence or diversity in biology are generally of fundamental interest. In contrast to many two-strategy evolutionary games, games with three strategies and cyclic dominance like the…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
The logistic birth and death process is perhaps the simplest stochastic population model that has both density-dependent reproduction, and a phase transition, and a lot can be learned about the process by studying its extinction time,…
We consider a supercritical branching random walk in time-inhomogeneous random environment with a random absorption barrier, i.e.,in each generation, only the individuals born below the barrier can survive and reproduce. Assume that the…
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
The war of attrition in game theory is a model of a stand-off situation between two opponents where the winner is determined by its persistence. We model a stand-off between a predator and a prey when the prey is hiding and the predator is…
Maintenance of cooperation was studied for a two-strategy evolutionary Prisoner's Dilemma game where the players are located on a one-dimensional chain and their payoff comes from games with the nearest and next-nearest neighbor…
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…
In any reaction-diffusion system of predator-prey models, the population densities of species are determined by the interactions between them, together with the influences from the spatial environments surrounding them. Generally, the prey…