The Stabilizing Role of Mutation; or, Towards understanding Network Topologies under Evolutionary Dynamics
The Stabilizing Role of Mutation; or, Towards understanding Network Topologies under Evolutionary Dynamics"
- Date: Jun 22, 2020
- Time: 11:00 - 12:00
- Speaker: Johann Bauer, City University London
- Please see https://www.bevnon.be//
- Location: virtual platform
- Host: Arne Traulsen
It is well-known that the (multi-population) replicator dynamics (RD) is sensitive to assumptions such as infinite populations or that the system evolves in continuous time, with qualitatively different results if these assumptions are violated.
I briefly recapitulate some previous work, where we have shown that RD is also highly sensitive to the assumption that mutation occurs on a different time scale from selection, complementing earlier results in the literature. We have proposed the concept of mutation limits as a way of relating the equilibria of RD to a class of replicator-mutator dynamics (RMD) where mutation can have arbitrary (non-uniform) directions.
Building on these results on mutation limits, I present some recent results showing that mutation stabilizes RD in two-player constant-sum games leading to asymptotic stability of the associated equilibria.
This stability allows a stochastic discrete-time system, in this case a simple "reinforcement" dynamics, to be approximated in probability by RMD such that we can infer the long-term dynamics of the stochastic system, which in general is not possible for RD.
Thus, mutation creates a bridge between the deterministic RMD and stochastic discrete-time systems, showing that the assumption of separate time-scales for selection and mutation, while being useful, induces qualitative changes possibly rendering the analysis less applicable to biological systems.
I close with some illustrations on the range of our results, sketching what they mean for networked populations and the evolution of network topologies in certain systems.
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