Nicolas Lanchier

The Axelrod model for the dissemination of culture revisited

This article is concerned with the Axelrod model, a stochastic process which similarly to the voter model includes social influence, but unlike the voter model also accounts for homophily. Each vertex of the network of interactions is characterized by a set of

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects.

F

A spatially explicit model for competition among specialists and generalists in a heterogeneous environment

cultural features, each of which can assume

Fixation in the one-dimensional Axelrod model

q

Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions

states. Pairs of adjacent vertices interact at a rate proportional to the number of features they share, which results in the interacting pair having one more cultural feature in common. The Axelrod model has been extensively studied during the past ten years, based on numerical simulations and simple mean-field treatments, while there is a total lack of analytical results for the spatial model itself. Simulation results for the one-dimensional system led physicists to formulate the following conjectures. When the number of features

Stochastic spatial models of host-pathogen and host-mutualist interactions

F

INDIVIDUAL VERSUS CLUSTER RECOVERIES WITHIN A SPATIALLY STRUCTURED POPULATION

and the number of states

The Role of Space in the Exploitation of Resources

q

Evolutionary games on the lattice: death-birth updating process *

both equal two, or when the number of features exceeds the number of states, the system converges to a monocultural equilibrium in the sense that the number of cultural domains rescaled by the population size converges to zero as the population goes to infinity. In contrast, when the number of states exceeds the number of features, the system freezes in a highly fragmented configuration in which the ultimate number of cultural domains scales like the population size. In this article, we prove analytically for the one-dimensional system convergence to a monocultural equilibrium in terms of clustering when

Stochastic spatial model of producer-consumer systems on the lattice

F=q=2