Related papers: Exploring the Dynamics of Lotka-Volterra Systems: …
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…
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…
We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but…
Quantifying population dynamics is a fundamental challenge in ecology and evolutionary biology, particularly for species that are cryptic, microscopic, or extinct. Traditional approaches rely on continuous representations of population…
We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a…
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf…
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…
A principle of evolutionary adaptation is applied to the Lotka--Volterra models, in particular to the food webs. We present a relatively simple computational algorithm of optimization with respect to a given criterion. This algorithm boils…
The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a…
Does an ecological community allow stable coexistence? Identifying the general principles that determine the answer to this question is a central problem of theoretical ecology. Random matrix theory approaches have uncovered the general…
This paper is devoted to the analysis of a simple Lotka-Volterra food chain evolving in a stochastic environment. It can be seen as the companion paper of Hening and Nguyen (J. of Math. Biol. `18) where we have characterized the persistence…
A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in…
The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific…
Ecological networks describe the interactions between different species, informing us of how they rely on one another for food, pollination and survival. If a species in an ecosystem is under threat of extinction, it can affect other…
The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole. In order to understand the mechanism driving the…
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…
Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these…