Related papers: Non-neutral theory of biodiversity
We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…
We study a four species ecological system with cyclic dominance whose individuals are distributed on a square lattice. Randomly chosen individuals migrate to one of the neighboring sites if it is empty or invade this site if occupied by…
This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here we consider species assembly models where the population dynamics is kept far from fixed points through the…
We introduce a new interacting particle system intended to model an example of ecological succession involving two species: the bracken and the european beech. The objective is to exhibit phase transitions by proving that there exist three…
In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
Studies of transient dynamics captures the time history of any dramatic changes in the dynamics of a system. The transient dynamics is investigated here in a classic ecological model of a bistable tri-trophic food chain. All the species in…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…
We continue the investigations of an ecosystem where a epidemic-affected population can move between two connected patches, by considering what happens to the system when the migration paths are interrupted in one direction, or when the…
This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance).…
Consider the following evolution model, proposed in \cite{BS} by Bak and Sneppen. Put $N$ vertices on a circle, spaced evenly. Each vertex represents a certain species. We associate with each vertex a random variable, representing the…
Recently, Lenski et al \cite{Elena,Lenski,Travisano} have carried out several experiments on bacterial evolution. Their findings support the theory of punctuated equilibrium in biological evolution. They have further quantified the relative…
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…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
Resource competition is a fundamental interaction in natural communities.However little is known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyze the competition of two…
Recently, Lenski et al [Elena,Lenski,Travisano] have carried out several experiments on bacterial evolution. Their findings support the theory of punctuated equilibrium in biological evolution. They have further quantified the relative…
Evolutionary and ecosystem dynamics are often treated as different processes --operating at separate timescales-- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field…
We identify a new universality class of phase transitions that arises in non-normal systems, challenging the classical view that transitions require eigenvalue instabilities. In traditional bifurcation theory, critical phenomena emerge when…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
We consider Schelling's bounded neighbourhood model (BNM) of unorganised segregation of two populations from the perspective of modern dynamical systems theory. We derive a Schelling dynamical system and carry out a complete quantitative…