Eur. Phys. J. B 48, 557-565 (2005)
https://doi.org/10.1140/epjb/e2006-00016-2

The random replicator model at nonzero temperature

Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil

Corresponding author: ^a fontanari@ifsc.usp.br

Received: 7 August 2005
Published online: 19 January 2006

Abstract

The random replicator model with interspecies coupling strengths prescribed by the competitive exclusion principle – the Hebb rule – is studied analytically in the presence of fast noise that describes the flow of migrants between the ecosystem and the outer world. The stochastic dynamics leads to stationary states distributed according to the Gibbs distribution permitting thus an equilibrium statistical mechanics analysis. We find that a discontinuous phase transition separates a regime of strong competition, and consequently of low diversity, from more cooperative regimes. The statistical analysis is carried out for the annealed scheme, for which the evolutionary and ecological timescales coincide, as well as for the quenched scheme, for which the features that identify the species are fixed.