Substitution Matrices and Mutual Information Approaches to Modeling Evolution

Kitchovitch, Stephan; Song, Yuedong; Wath, R. van der; Lió, Píetro

doi:10.1007/978-3-642-11169-3_19

Cited by 2 publications

(4 citation statements)

References 35 publications

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“…Many concentrate on microsatellites [ 12 ], but they have also assessed AFLPs [ 29 ], and single-nucleotide polymorphisms [ 14 ]. Recent theoretical uses of Shannon entropy and mutual information in genetics also include: dynamics of populations of genetically variable individuals in landscapes [ 36 ]; dynamics of molecules in gene expression networks [ 37 , 38 , 39 ]; analysis of gene-environment interactions, including genome wide association studies [ 40 – 44 ]; phylogenetic reconstruction [ 45 , 46 , 47 ]; mapping genes [ 48 , 49 ]; and derivations of classical population genetic results regarding drift and selection [ 50 ]. Outside genetics, there is much parallel work in species, phylogenetic and functional diversity involving entropy [ 51 – 54 ], so there may be further opportunities for expansion.…”

Section: Introductionmentioning

confidence: 99%

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Chao

Jost²,

Hsieh

et al. 2015

PLoS ONE

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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.

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Section: Introductionmentioning

confidence: 99%

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Chao

Jost²,

Hsieh

et al. 2015

PLoS ONE

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“…As a result it is inappropriate to use a single substitution matrix for all problems, and in reality different bioinformatics applications tend to use matrices that are reliable for the problem that they are trying to solve. In fact, in [7] it was demonstrated that the use of novel substitution matrices, generated for a particular set of sequences, tend to perform better for that set of sequences than standard substitution matrices, such as mtREV24 [8]. This is important in the current work since using an appropriate substitution matrix largely improves the detection of patterns.…”

Section: Substitution Matricesmentioning

confidence: 85%

“…High MI values conversely express a correlation between the sites. As we have previously shown [7], incorporating substitution matrices in the above calculation causes the appearances of regions of high MI that are otherwise not visible.…”

Section: Mutual Informationmentioning

confidence: 89%

“…It does so by obtaining the evolution probabilities from a given substitution matrix. We have previously shown in [7] that scaling the probabilities in such a way allows us to exhibit patterns that are not visible without the use of the appropriate substitution matrix. In this paper we have significantly improved on the algorithm, and aim to describe its implementation in detail.…”

Section: Introductionmentioning

confidence: 98%

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Using Mutual Information and Models of Evolution for Improved Pattern Detection

Kitchovitch

Leung

Song

et al. 2009

2009 International Joint Conference on Bioinformatics, Systems Biology and Intelligent Computing

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Many uses of Information Theory have recently been discovered in the field of bioinformatics -clustering and classification of data, sequence alignment scoring, discovering dependencies between sites in amino acid alignments, etc. Mutual Information has proven itself to be a very convenient metric for determining the dependency between two sets of data, and has advantages over other common statistical methods such as correlation. Models of evolution, or substitution matrices, have always been at the very heart of bioinformatics, with a large variety of applications based on PAM, BLOSUM, JTT or other matrices. In this paper we describe a novel algorithm that incorporates substitution rates from a given matrix when calculating the mutual information between sites in an amino acid alignment. We formally describe this algorithm in detail as well as some experimental results. As a result of this work we demonstrate that the incorporation of substitution matrices in the calculation leads to an improved detection of patterns of similarity between sites within a multiple sequence alignment.

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Substitution Matrices and Mutual Information Approaches to Modeling Evolution

Cited by 2 publications

References 35 publications

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Using Mutual Information and Models of Evolution for Improved Pattern Detection

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