Related papers: Conditions for growth and extinction in matrix mod…
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
Population dynamics is constrained by the environment, which needs to obey certain conditions to support population growth. We consider a standard model for the evolution of a single species population density, that includes reproduction,…
We consider stochastic growth models to represent population subject to catastrophes. We analyze the subject from different set ups considering or not spatial restrictions, whether dispersion is a good strategy to increase the population…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
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…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
Heterogeneities in environmental conditions often induce corresponding heterogeneities in the distribution of species. In the extreme case of a localized patch of increased growth rates, reproducing populations can become strongly…
Stochastic fluctuations are central to the understanding of extinction dynamics. In the context of population models they allow for the description of the transition from the vicinity of a non-trivial fixed point of the deterministic…
Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…
We propose a variation of the GMS model of evolution of species. In this version, as in the GMS model, at each birth, the new species in the system is labeled with a random fitness mark, but in our variation, to each extinction event is…
Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and…
Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover…
Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness…
Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by…
The extinction and persistence of infective individuals are closely related to the random change of the environment. In this paper, via the random/stochastic SIRS models, we analyze qualitatively and quantitatively the impact caused by the…