Related papers: Environmental vs demographic variability in stocha…
We propose a model for the dynamics of frequencies of a costly defense trait. More precisely, we consider Lotka-Volterra-type models involving a prey (or host) population consisting of two types and a predator (or parasite) population,…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
The composition of ecological communities varies not only between different locations but also in time. Understanding the fundamental processes that drive species towards rarity or abundance is crucial to assessing ecosystem resilience and…
Lotka Volterra model and its modified forms have long become a major area of interest for periodic motions in nonlinear systems with competitive species. The model given by Volterra shows that its periodicity is dependent on initial…
The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned…
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,…
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…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired…
We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one,…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
In this monograph, we introduce a new model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility. The interactions among these populations are described not in terms of…
We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a L\'{e}vy dust, which allows…
In this work, we explore the dynamics of species abundances within ecological communities using the Generalized Lotka-Volterra (GLV) model. At variance with previous approaches, we present an analysis of stochastic GLV dynamics with…
We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
Ecological communities are composed of species interactions that respond to environmental fluctuations. Despite increasing evidence of temporal variation in these interactions, most theoretical frameworks remain rooted in static…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
We study the dynamics of a ring of patches with vegetation-prey-predator populations, coupled through interactions of the Lotka-Volterra type. We find that the system yields aperiodic, recurrent and rare explosive bursts of predator density…