A food chain ecoepidemic model: infection at the bottom trophic level

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 together the various equilibria, as well as persistent limit cycles, which are shown to be absent in the classical case. Finally, bistability is discovered among some equilibria, leading to situations in which the computation of their basins of attraction is relevant for the system outcome in terms of its biological implications

Spreading of families in cyclic predator-prey models

We study the spreading of families in two-dimensional multispecies predator-prey systems, in which species cyclically dominate each other. In each time step randomly chosen individuals invade one of the nearest sites of the square lattice eliminating their prey. Initially all individuals get a family-name which will be carried on by their descendants. Monte Carlo simulations show that the systems with several species (N=3,4,5) are asymptotically approaching the behavior of the voter model, i.e., the survival probability of families, the mean-size of families and the mean-square distance of descendants from their ancestor exhibit the same scaling behavior. The scaling behavior of the survival probability of families has a logarithmic correction. In case of the voter model this correction depends on the number of species, while cyclic predator-prey models behave like the voter model with infinite species. It is found that changing the rates of invasions does not change this asymptotic behavior. As an application a three-species system with a fourth species intruder is also discussed.Comment: to be published in PR

Severe population collapses and species extinctions in multi-host epidemic dynamics

Most infectious diseases including more than half of known human pathogens are not restricted to just one host, yet much of the mathematical modeling of infections has been limited to a single species. We investigate consequences of a single epidemic propagating in multiple species and compare and contrast it with the endemic steady state of the disease. We use the two-species Susceptible-Infected-Recovered (SIR) model to calculate the severity of post-epidemic collapses in populations of two host species as a function of their initial population sizes, the times individuals remain infectious, and the matrix of infection rates. We derive the criteria for a very large, extinction-level, population collapse in one or both of the species. The main conclusion of our study is that a single epidemic could drive a species with high mortality rate to local or even global extinction provided that it is co-infected with an abundant species. Such collapse-driven extinctions depend on factors different than those in the endemic steady state of the disease

On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a square lattice is found to be c_0=0.1765005(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda_c = (1-c_0)/c_0 = 4.66571(3) and a net transmissibility of (1-c_0)/(1 + 3 c_0) = 0.538410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the 2-d percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.Comment: 9 pages, 5 figures. Accepted for publication, Physical Review

Persistence of complex food webs in metacommunities

Metacommunity theory is considered a promising approach for explaining species diversity and food web complexity. Recently Pillai et al. proposed a simple modeling framework for the dynamics of food webs at the metacommunity level. Here, we employ this framework to compute general conditions for the persistence of complex food webs in metacommunities. The persistence conditions found depend on the connectivity of the resource patches and the structure of the assembled food web, thus linking the underlying spatial patch-network and the species interaction network. We find that the persistence of omnivores is more likely when it is feeding on (a) prey on low trophic levels, and (b) prey on similar trophic levels