Related papers: Extinction risk and structure of a food web model

We study a mechanistic mathematical model of extinction and coexistence in a generic hunter-prey ecosystem. The model represents typical scenarios of human invasion and environmental change, characteristic of the late Pleistocene,…

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large…

We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly…

Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…

The food web is a directed graph in which nodes label species and directed links represent the predation between species. The cascade model generates random food webs. The continuum cascade model is a Poisson approximation of the cascade…

Forty years ago, Robert May questioned a central belief in ecology by proving that sufficiently large or complex ecological networks have probability of persisting close to zero. To prove this point, he analyzed large networks in which…

In this paper we consider a three level food web subject to a disease affecting the bottom prey. The resulting dynamics is much richer with respect to the purely demographic model, in that it contains more transcritical bifurcations, gluing…

Ecological networks such as plant-pollinator systems and food webs vary in space and time. This variability includes fluctuations in global network properties such as total number and intensity of interactions but also in the local…

We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this…

We present a new model for extinction in which species evolve in bursts or `avalanches', during which they become on average more susceptible to environmental stresses such as harsh climates and so are more easily rendered extinct. Results…

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms…

We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…

We study an individual-based predator-prey model of biological coevolution, using linear stability analysis and large-scale kinetic Monte Carlo simulations. The model exhibits approximate 1/f noise in diversity and population-size…

Consider a large ecosystem (foodweb) with n species, where the abundances follow a Lotka-Volterra system of coupled differential equations. We assume that each species interacts with d other species and that their interaction coefficients…

In this paper, we study extinction in dynamical systems generated by reaction networks. We introduce two notions: weak extinction and strong extinction, and relate them to the structure of the underlying network through Lyapunov functions…

Degree distributions have been widely used to characterize biological networks including food webs, and play a vital role in recent models of food web structure. While food webs degree distributions have been suggested to follow various…

Recently we have introduced a simplified model of ecosystem assembly (Capitan et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper…

Large-scale structural patterns commonly occur in network models of complex systems including a skewed node degree distribution and small-world topology. These patterns suggest common organizational constraints and similar functional…

We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in…

We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are…