title: From typical sequences to typical genotypes.
abstract: We demonstrate an application of a core notion of information theory, typical sequences and their related properties, to analysis of population genetic data. Based on the asymptotic equipartition property (AEP) for nonstationary discrete-time sources producing independent symbols, we introduce the concepts of typical genotypes and population entropy and cross entropy rate. We analyze three perspectives on typical genotypes: a set perspective on the interplay of typical sets of genotypes from two populations, a geometric perspective on their structure in high dimensional space, and a statistical learning perspective on the prospects of constructing typical-set based classifiers. In particular, we show that such classifiers have a surprising resilience to noise originating from small population samples, and highlight the potential for further links between inference and communication.
authors.affiliation: Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig, Germany. Electronic address: Omri.Tal@mis.mpg.de.
authors.forename: Omri
authors.initials: O
authors.lastname: Tal
authors.affiliation: Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig, Germany. Electronic address: trandat@mis.mpg.de.
authors.forename: Tat Dat
authors.initials: TD
authors.lastname: Tran
authors.affiliation: Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig, Germany. Electronic address: jacobus.portegies@mis.mpg.de.
authors.forename: Jacobus
authors.initials: J
authors.lastname: Portegies
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005787:Gene Frequency; D005828:Genetics, Population; D005838:Genotype; D007257:Information Theory; D008957:Models, Genetic; D020641:Polymorphism, Single Nucleotide
keywords: Classification; Population cross entropy rate; Population entropy rate; Typical genotypes; Typical sequences