Related papers: Stochastic population oscillations in spatial pred…
Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random…
We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…
The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
We consider a probabilistic cellular automaton to analyze the stochastic dynamics of a predator-prey system. The local rules are Markovian and are based in the Lotka-Volterra model. The individuals of each species reside on the sites of a…
We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…
Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…
We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial…
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…
We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when…
Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems, and characterized in the laboratory as showing unusual phase relationships in…
The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For…
Transposable elements, or transposons, are DNA sequences that can jump from site to site in the genome during the life cycle of a cell, usually encoding the very enzymes which perform their excision. However, some transposons are parasitic,…
We look at the interaction of dispersal and environmental stochasticity in $n$-patch models. We are able to prove persistence and extinction results even in the setting when the dispersal rates are stochastic. As applications we look at…
Understanding the interaction between turbulence and zonal flows is critical for modeling turbulence transport in fusion plasmas, often described through predator-prey dynamics. However, traditional deterministic models like the…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…