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We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…

Predicting the evolution of expanding population is critical to control biological threats such as invasive species and virus explosion. In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with…

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…

This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are…

We present a new model for extinction in which species evolve in bursts or `avalanches', during which they become on average more susceptible to environmental stresses such as harsh climates and so are more easily rendered extinct. Results…

We study a lattice model of a multi-species prey-predator system. Numerical results show that for a small mutation rate the model develops irregular long-period oscillatory behavior with sizeable changes in a number of species. The…

We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…

Difficulties identifying appropriate biodiversity impact metrics remain a major barrier to inclusion of biodiversity considerations in environmentally responsible investment. We propose and analyse a simple science-based local metric: the…

This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…

We analyze the influence of long-range correlated (colored) external noise on extinction phase transitions in growth and spreading processes. Uncorrelated environmental noise (i.e., temporal disorder) was recently shown to give rise to an…

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…

Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to…

Cyclic dominance is frequently believed to be a mechanism that maintains diversity of competing species. But this delicate balance could also be fragile if some of the members is weakened because an extinction of a species will involve 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…

This paper deals with coexistence and extinction of time periodic Volterra-Lotka type competing systems with nonlocal dispersal. Such issues have already been studied for time independent systems with nonlocal dispersal and time periodic…

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…

Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…

We study a variant of the cyclic Lotka-Volterra model with three-agent interactions. Inspired by a multiplayer variation of the Rock-Paper-Scissors game, the model describes an ideal ecosystem in which cyclic competition among three species…

We study the fixation probability of a mutant type when introduced into a resident population. As opposed to the usual assumption of constant pop- ulation size, we allow for stochastically varying population sizes. This is implemented by a…

We analysed some qualitative properties of the limit configuration of the solutions of a reaction-diffusion system of four competing species as the competition rate tends to infinity. Large interaction induces the spatial segregation of the…