Related papers: Population extinction in a time-modulated environm…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods…
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…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
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…
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction.The…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate…
A simulation model of a population having internal (genetic) structure is presented. The population is subject to selection pressure coming from the environment which is the same in the whole system but changes in time. Reproduction has a…
The fitness of a biological strategy is typically measured by its expected reproductive rate, the first moment of its offspring distribution. However, strategies with high expected rates can also have high probabilities of extinction. A…
We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the…
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…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…
We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…
We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
Let $T$ be the extinction moment of a critical branching process $Z=(Z_{n},n\geq 0) $ in a random environment specified by iid probability generating functions. We study the asymptotic behavior of the probability of extinction of the…
In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the positive quadrant. For the latter, extinction means…