Natural Selection as an Inhibitor of Genetic Diversity: Multiplicative Weights Updates Algorithm and a Conjecture of Haploid Genetics
Abstract
In a recent series of papers a surprisingly strong connection was discovered between standard evolutionary models of natural selection and Multiplicative Weights Updates Algorithm, a ubiquitous model of online learning and optimization. These papers establish that, under specific assumptions, mathematical models of biological evolution can be reduced to studying discrete replicator dynamics, a close variant of MWUA, in coordination games. This connection allows for introducing insights from game theoretic dynamics into the field of mathematical biology. Using these results as a stepping stone, we show that mathematical models of haploid evolution imply the extinction of genetic diversity in the long term limit, a widely believed conjecture in genetics. In game theoretic terms we show that in the case of coordination games, under minimal genericity assumptions, discrete replicator dynamics converge to pure Nash equilibria for all but a zero measure of initial conditions. This result holds despite the fact that mixed Nash equilibria can be exponentially (or even uncountably) many, completely dominating in number the set of pure Nash equilibria. Thus, in haploid organisms the long term preservation of genetic diversity needs to be safeguarded by other evolutionary mechanisms such as mutations and speciation.
Additional Information
© 2015 ACM, Inc. Copyright is held by the owner/author(s). Affiliated with College of Computing, Georgia Institute of Technology. Supported by NSF Grants CCF-0914732 and CCF-1216019. Affiliated with College of Computing, Georgia Institute of Technology. Supported by ARC fellowship, and NSF grants CCF-1415498 and DMS-1407657. Affiliated with Center for the Mathematics of Information, California Institute of Technology. Supported by CMI Wally Baer and Jeri Weiss postdoctoral fellowship and Linde-SISL postdoctoral fellowship.Attached Files
Submitted - 1408.6270v3.pdf
Files
Name | Size | Download all |
---|---|---|
md5:bbf726eb3de9be9eb6df945810fcc84a
|
478.3 kB | Preview Download |
Additional details
- Eprint ID
- 54947
- Resolver ID
- CaltechAUTHORS:20150218-113809896
- CCF-0914732
- NSF
- CCF-1216019
- NSF
- Australian Research Council
- CCF-1415498
- NSF
- DMS-1407657
- NSF
- CMI Wally Baer and Jeri Weiss postdoctoral fellowship
- Linde Institute of Economic and Management Science
- Caltech Social and Information Sciences Laboratory
- Created
-
2015-02-20Created from EPrint's datestamp field
- Updated
-
2021-11-10Created from EPrint's last_modified field