2007/11/01 by Tobias Galla, Galla, Tobias
Biochemistry, Genetics and Molecular Biology · Medicine · Social Sciences · #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #q-bio.PE
paper · pdf · doi:10.48550/arxiv.0711.0169
9 pages, 10 figures
arxiv created 2007/11/01 · openalex publication_date 2007/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation pressures. To this end we generalise existing path-integral approaches to replicator systems with random asymmetric couplings. This technique allows one to formulate an effective dynamical theory, which is exact in the thermodynamic limit and which can be solve for persistent order parameters in a fixed-point regime regardless of the symmetry of the interactions. The onset of instability can be determined self-consistently. We calculate quantities such as the diversity of the respective populations and their fitnesses in the stationary state, and compare results with data from a numerical integration of the replicator equations