Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
arXiv:0803.2443 · doi:10.4064/bc80-0-1
Abstract
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in . Consequences and relations to some previous approaches are outlined.
Banach Center publications, in press
References in corpus (15)
- Evolutionary games on graphs
- Stochastic Dynamics of Invasion and Fixation
- Phase diagrams for Prisoner's Dilemma game on two-dimensional lattices
- Coevolutionary Dynamics: From Finite to Infinite Populations
- Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
- Co-evolutionary games on networks
- Evolutionary dynamics on degree-heterogeneous graphs
- Coevolutionary dynamics in large, but finite populations
- Rock-scissors-paper game on regular small-world networks
- Cyclic dominance and biodiversity in well-mixed populations
- Stochasticity and evolutionary stability
- Similarity based cooperation and spatial segregation
- Nongaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process
- Vertex dynamics during domain growth in three-state models
- Drift reversal in asymmetric coevolutionary conflicts: Influence of microscopic processes and population size