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Variability on external conditions has important consequences for the dynamics and the organization of biological systems. In many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental…
We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness…
We consider stochastic growth models to represent population subject to catastrophes. We analyze the subject from different set ups considering or not spatial restrictions, whether dispersion is a good strategy to increase the population…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is…
The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to…
Anthropogenic activity threatens biodiversity through climate change, habitat fragmentation, and increasing frequency and scale of disturbance. Various theoretical studies have sought to shed light on how these factors could promote or…
Interfaces moving in a disordered medium exhibit stochastic velocity fluctuations obeying universal scaling relations related to the presence or absence of conservation laws. For fluid invasion of porous media, we show that the fluctuations…
Models are often employed to integrate knowledge about epidemics across scales and simulate disease dynamics. While these approaches have played a central role in studying the mechanics underlying epidemics, we lack ways to reliably predict…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
In large asexual populations, multiple beneficial mutations arise in the population, compete, interfere with each other, and accumulate on the same genome, before any of them fix. The resulting dynamics, although studied by many authors, is…
Response time-delay is an ubiquitous phenomenon in biological systems. Here we use a simple stochastic population model with time-delayed switching-rate conversion to quantitatively study the biological influence of the response time-delay…
Human flourishing is often severely limited by persistent violence. Quantitative conflict research has found common temporal and other statistical patterns in warfare, but very little is understood about its general spatial patterns. While…
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a…
We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in…
Building upon the eco-evolutionary game dynamics framework established by Tilman et al., we investigate stochastic fluctuations in a two-strategy system incorporating environmental feedback mechanisms, where the payoff matrix exhibits…
We examine the effect of a slowly-varying time-dependent parameter on invasion fronts for which an unstable homogeneous equilibrium is invaded by either another homogeneous state or a spatially periodic state. We first explain and motivate…
For most organisms with viscous population structure, spatially localized growth drives the invasive advance of a favorable mutation. We model a two-allele competition where recurrent mutation introduces a genotype with a rate of local…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…