2016/03/18 by Alexander S. Bratus, Bratus, Alexander S., Vladimir P. Posvyanskii +3
Social Sciences · Biochemistry, Genetics and Molecular Biology · Mathematics · #Evolutionary Game Theory and Cooperation #Evolution and Genetic Dynamics #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1603.05957
The now classical replicator equation describes a wide variety of biological\nphenomena, including those in theoretical genetics, evolutionary game theory,\nor in the theories of the origin of life. Among other questions, the permanence\nof the replicator equation is well studied in the local, well-mixed case.\nInasmuch as the spatial heterogeneities are key to understanding the species\ncoexistence at least in some cases, it is important to supplement the classical\ntheory of the non-distributed replicator equation with a spatially explicit\nframework. One possible approach, motivated by the porous medium equation, is\nintroduced. It is shown that the solutions to the spatially heterogeneous\nreplicator equation may evolve to equilibrium states that have a bounded\nsupport, and, moreover, that these solutions are of paramount importance for\nthe overall system permanence, which is shown to be a more commonplace\nphenomenon for the spatially explicit equation if compared with the local\nmodel.\n