Related papers: How fast extinction occurs in bisexual populations…
We consider a critical bisexual branching process in a random environment generated by independent and identically distributed random variables. Assuming that the process starts with a large number of pairs $N$, we prove that its extinction…
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…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
Sexually reproducing populations with small number of individuals may go extinct by stochastic fluctuations in sex determination, causing all their members to become male or female in a generation. In this work we calculate the time to…
We consider a cyclically competing species model on a ring with global mixing at finite rate, which corresponds to the well-known Lotka-Volterra equation in the limit of infinite mixing rate. Within a perturbation analysis of the model from…
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system…
Populations are often subject to catastrophes that cause mass removal of individuals. Many stochastic growth models have been considered to explain such dynamics. Among the results reported, it has been considered whether dispersion…
The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…
Our paper computationally explores the extinction dynamics of an animal species effected by a sudden spike in mortality due to an extreme event. In our study, the animal species has a 2-year life cycle and is endowed with a high survival…
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…
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 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…
When four species compete stochastically in a cyclic way, the formation of two teams of mutually neutral partners is observed. In this paper we study through numerical simulations the extinction processes that can take place in this system…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
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…
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…
We review recent work aimed at modeling species extinction over geological time. We discuss a number of models which, rather than dealing with the direct causes of particular extinction events, attempt to predict overall statistical trends,…
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 Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation…