Related papers: Extinction of Populations and the Schr\"{o}dinger …
We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation 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…
We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This…
We establish an analogy between the Fokker-Planck equation describing evolutionary landscape dynamics and the Schr\"{o}dinger equation which characterizes quantum mechanical particles, showing how a population with multiple genetic traits…
An explicit proposal for experiments leading to abrupt transitions in spatially extended bacterial populations in a Petri dish is presented on the basis of an exact formula obtained through an analytic theory. The theory provides accurately…
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,…
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…
We demonstrate an exact equivalence between classical population dynamics and Lindbladian evolution admitting a dark state and obeying a set of certain local symmetries. We then introduce {\em quantum population dynamics} as models in which…
We study the non-equilibrium phase transition between survival and extinction of spatially extended biological populations using an agent-based model. We especially focus on the effects of global temporal fluctuations of the environmental…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
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…
The question of whether biological populations survive or are eventually driven to extinction has long been examined using mathematical models. In this work we study population survival or extinction using a stochastic, discrete…
The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent…
We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves…
Established populations often exhibit oscillations in their sizes. If a population is isolated, intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a…
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…
In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates…
The prediction of critical transitions, such as extinction events, is vitally important to preserving vulnerable populations in the face of a rapidly changing climate and continuously increasing human resource usage. Predicting such events…
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. In this work, we study a one-dimensional…