Related papers: Persistence analysis of the age-structured populat…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
The current paper is concerned with pointwise persistence in full chemotaxis models with local as well as nonlocal time and space dependent logistic source in bounded domains. We first prove the global existence and boundedness of…
I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…
This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system…
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…
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
Persistency is the property, for differential equations in $\R^n$, that solutions starting in the positive orthant do not approach the boundary. For chemical reactions and population models, this translates into the non-extinction property:…
Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
We study the extinction risk of a fragmented population residing on a network of patches coupled by migration, where the local patch dynamics include the Allee effect. We show that mixing between patches dramatically influences the…
This chapter focuses on variable maturation delay or, more precisely, on the mathematical description of a size-structured population consuming an unstructured resource. When the resource concentration is a known function of time, we can…
Age-structured models capture the dynamic behavior of populations over time and result in nonlinear integro-partial differential equations (IPDEs). These processes arise in various fields such as biotechnology, economics, or demography.…
We consider ecological difference equations of the form $X_{t+1}^i =X_t^i A_i(X_t)$ where $X_t^i$ is a vector of densities corresponding to the subpopulations of species $i$ (e.g. subpopulations of different ages or living in different…
Although species longevity is subject to a diverse range of selective forces, the mortality curves of a wide variety of organisms are rather similar. We argue that aging and its universal characteristics may have evolved by means of a…
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,…
Understanding why we age is a long-lived open problem in evolutionary biology. Aging is prejudicial to the individual and evolutionary forces should prevent it, but many species show signs of senescence as individuals age. Here, I will…
We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment, focusing on whether a population already established in one patch either successfully invades an adjacent empty…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…