Related papers: A Mathematical Model with Modified Logistic Approa…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
Feeding a larger and wealthier global population without transgressing ecological limits is increasingly challenging, as rising food demand (especially for animal products) intensifies pressure on ecosystems, accelerates deforestation, and…
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,…
A system of impulsive differential equations with state-dependent impulses is used to model the growth of a single population on two limiting essential resources in a self-cycling fermentor. Potential applications include water purification…
Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human's ecosystem engineering that has profoundly modified the world's landscape. Despite the age-old concern that unchecked population and economic…
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations based on the time-independent Schr\"{o}dinger equation for a quantum particle subjected to a uniform…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
The paper was suggested by a brief note of the second author about the application of the Hubbert curve to predict decay of resource exploitation. A further suggestion came from the interpretation of the Hubbert curve in terms of a specific…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
Understanding the relationship between a populations probability of extinction and its carrying capacity frames conservation status assessments and guides efforts to understand and mitigate the ongoing biodiversity crisis. Despite this, our…