Related papers: Population Dynamics in Spatially Heterogeneous Sys…
We consider continuous space-time decay-surge population models which are semi- stochastic processes for which deterministically declining populations, bound to fade away, are rein- vigorated at random times by bursts or surges of random…
Numerous problems in development, regeneration, and disease involve simultaneous evolution of both spatial organization and the internal state of the constituents in addition to local interactions and crowding. This motivates us to study a…
A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements…
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,…
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…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
We study the absorbing-state phase transition in the one-dimensional contact process under the combined influence of spatial and temporal random disorders. We focus on situations in which the spatial and temporal disorders decouple. Couched…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
We model hypothetical bio-dispersal within a single Galactic region using the stochastic infection dynamics process, which is inspired by these local properties of life dispersal on Earth. We split the population of stellar systems into…
Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…
When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also…
In this paper we study some mathematical models describing evolution of population density and spread of epidemics in population systems in which spatial movement of individuals depends only on the departure and arrival locations and does…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an…
The growth of a population divided among spatial sites, with migration between the sites, is sometimes modelled by a product of random matrices, with each diagonal elements representing the growth rate in a given time period, and…
We study a stochastic model proposed recently in the genetic literature to explain the heterogeneity of cell populations or of gene products. Cells are located in two colonies, whose sizes fluctuate as birth and migration processes in…
We address the dynamics of interacting particles on a disordered lattice formed by a random comb. The dynamics comprises that of the asymmetric simple exclusion process, whereby motion to nearest-neighour sites that are empty is more likely…