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We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
We study a model of a multi-species ecosystem described by Lotka-Volterra-like equations. Interactions among species form a network whose evolution is determined by the dynamics of the model. Numerical simulations show power-law…
We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding,…
Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra…
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…
Recent investigations have provided important insights into the complex structure and dynamics of collectively moving flocks of living organisms. Two intriguing observations are, scale-free correlations in the velocity fluctuations, in the…
We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for…
In the analysis of complex ecosystems it is common to use random interaction coefficients, often assumed to be such that all species are statistically equivalent. In this work we relax this assumption by choosing interactions according to…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
The Lotka-Volterra system is a set of ordinary differential equations describing growth of interacting ecological species. This model has gained renewed interest in the context of random interaction networks. One of the debated questions is…
The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
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…