Related papers: Noise and Correlations in a Spatial Population Mod…
We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered,…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
Given an endogenous timescale set by invasion in a constant environment, we introduced periodic temporal variation in competitive superiority by alternating the species' propagation rates. By manipulating habitat size and introduction rate,…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to…
Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited…
How do competing populations convert a spatial advantage into macroscopic dominance? We introduce a stochastic model for resource competition that decouples the transient discovery phase from monopolization. Initial symmetry breaking is…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…
In contrast to the neutral population cycles of the deterministic mean-field Lotka--Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures…
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…
The far-reaching consequences of ecological interactions in the dynamics of biological communities remain an intriguing subject. For decades, competition has been a cornerstone in ecological processes, but mounting evidence shows that…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…
Artificial ecosystems provide an additional experimental tool to support laboratory work, field work, and theoretical development in competitive exclusion research. A novel application of a spatiotemporal agent based model is presented…