Related papers: Rare extinction events in cyclic predator-prey gam…
Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and…
A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is…
We study two types of stochastic processes, a mean-field spatial system of interacting Fisher-Wright diffusions with an inferior and an advantageous type with rare mutation (inferior to advantageous) and a (mean-field) spatial system of…
This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations…
We develop a stochastic human-rodent compartment model for Mpox transmission that combines diffusion noise with Hawkes self-exciting jumps in the human infection dynamics. Including Hawkes processes allows, for instance, to model the short…
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time…
The cross-entropy method (CE) developed by R. Rubinstein is an elegant practical principle for simulating rare events. The method approximates the probability of the rare event by means of a family of probabilistic models. The method has…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are…
We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate…
We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or…
We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of $\mathbb {Z}^d$. In each of the four models studied, an individual in a local population can reproduce, die or…
We present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian $N$-particle system of pair interactions with unbounded and, in general, non-Lipschitz continuous interaction potential. We establish the infinite…
In this paper, I model and study the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. I derive and solve an equation that is a natural generalization of the Taylor-Jonker…
In the present study, we have modified the traditional May-Holling-Tanner predator-prey model used to represent the interaction between least weasel and field-vole population by adding an Allee effect (strong and weak) on the field-vole…
We consider stochastic population processes that are almost surely absorbed at the origin within finite time. Our interest is in the quasistationary distribution, $\boldsymbol{u}$, and the expected time, $\tau$, from quasistationarity to…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
A demographic Allee effect occurs when individual fitness, at low densities, increases with population density. Coupled with environmental fluctuations in demographic rates, Allee effects can have subtle effects on population persistence…
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 investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…