Related papers: Population Dynamics and Non-Hermitian Localization
We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction-diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments.…
Growth is a multi-layered phenomenon in human societies, composed of socioeconomic and demographic change at many different scales. Yet, standard macroeconomic indicators average over most of these processes, blurring the spatial and…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
We study the limit of many small mutations of a model of population dynamics. The population is structured by phonological traits and is spatially inhomogeneous. The various sub-populations compete for the same nutrient which diffuses…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among…
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…
While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven,…
Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity…
The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context…
Time-independent scattering methods are widely employed to analyze transport in non-Hermitian systems. Their application, however, rests on a critical yet often overlooked assumption: that an incident wave is a pure superposition of…
The simplest nonlinear Schrodinger equation that contains the time derivative of the probability density is investigated. This equation has the same stationary solutions as its linear counterpart, and these solutions are the eigenstates of…
Theoretical understanding of evolutionary dynamics in spatially structured populations often relies on non-spatial models. Biofilms are among such populations where a more accurate understanding is of theoretical interest and can reveal new…
We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…
In recent years non-demographic variability has been shown to greatly affect dynamics of stochastic populations. For example, non-demographic noise in the form of a bursty reproduction process with an a-priori unknown burst size, or…
We ask the question "when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population?". We focus on the situation in which…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…