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Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to…
Epidemic outbreaks of new pathogens, or known pathogens in new populations, cause a great deal of fear because they are hard to predict. For theoretical models of disease spreading, on the other hand, quantities characterizing the outbreak…
Many populations in nature are fragmented: they consist of local populations occupying separate patches. A local population is prone to extinction due to the shot noise of birth and death processes. A migrating population from another patch…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
When a small number of individuals of organism of single species is confined in a closed space with limited amount of indispensable resources, their breading may start initially under suitable conditions, and after peaking, the population…
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin…
The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…
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…
Let $N$ be a natural number. We consider a population which lives on $I_N=\{-N,-N+1,\dots,N-1,N\}$. Each individual gives birth at rate $\lambda$ on each of its neighboring sites and dies at rate 1. No births are allowed from the inside of…
The population size has far-reaching effects on the fitness of the population, that, in its turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate…
Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited…
We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…
The neutron population in a prototype model of nuclear reactor can be described in terms of a collection of particles confined in a box and undergoing three key random mechanisms: diffusion, reproduction due to fissions, and death due to…
We consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
Environmental noise can cause an exponential reduction in the mean time to extinction (MTE) of an isolated population. We study this effect on an example of a stochastic birth-death process with rates modulated by a colored Gaussian noise.…
The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in…
We study a spatially explicit harvesting model in periodic or bounded environments. The model is governed by a parabolic equation with a spatially dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative external…