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Expected shannon entropy and shannon differentiation between subpopulations for neutral genes under the finite island model

Chao, Anne, Jost, Lou, Hsieh, T.C., Ma, K.H., Sherwin, William B. and Rollins, Lee Ann 2015, Expected shannon entropy and shannon differentiation between subpopulations for neutral genes under the finite island model, PLoS One, vol. 10, no. 6, Article Number : e0125471, pp. 1-24, doi: 10.1371/journal.pone.0125471.

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Title Expected shannon entropy and shannon differentiation between subpopulations for neutral genes under the finite island model
Author(s) Chao, Anne
Jost, Lou
Hsieh, T.C.
Ma, K.H.
Sherwin, William B.
Rollins, Lee AnnORCID iD for Rollins, Lee Ann orcid.org/0000-0002-3279-7005
Journal name PLoS One
Volume number 10
Issue number 6
Season Article Number : e0125471
Start page 1
End page 24
Total pages 24
Publisher Public Library of Science (PLOS)
Place of publication San Francisco, Calif.
Publication date 2015
ISSN 1932-6203
Keyword(s) Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
MUTUAL INFORMATION
PHYLOGENETIC DIVERSITY
PARTITIONING DIVERSITY
SPECIES-DIVERSITY
SUBDIVIDED POPULATION
FUNCTIONAL DIVERSITY
ALLELIC FREQUENCIES
MUTATION
EVOLUTION
NUMBER
Summary Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.
Language eng
DOI 10.1371/journal.pone.0125471
Field of Research 060411 Population, Ecological and Evolutionary Genetics
Socio Economic Objective 970106 Expanding Knowledge in the Biological Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, Public Library of Science (PLOS)
Persistent URL http://hdl.handle.net/10536/DRO/DU:30073905

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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.