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Abstract Details
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Activity Number:
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418
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Type:
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Contributed
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Date/Time:
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Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #301762 |
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Title:
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On Rogers's Proof of Identifiability for the GTR+Gamma+I Model
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Author(s):
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Juanjuan Chai*+ and Elizabeth Ann Housworth
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Companies:
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Indiana University and Indiana University
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Address:
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Department of Mathematics, Bloomington, IN, 47405,
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Keywords:
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Identifiability ;
Gamma distribution ;
invariable sites ;
general time reversible Markov model
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Abstract:
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Recently, Allman etc. pointed out an error in Rogers's proof of the identifiability of the popular general time reversible Markov model for DNA evolution with heterogeneous rates coming from a mixture of a Gamma distribution and invariable sites in phylogenetics. We provide a proof for the claim under dispute in Rogers's paper and thus complete the proof of generic identifiability for this model using only pairwise comparisons with calculus technique. Rate matrices with only one non-zero eigenvalue and phylogenies with only one or two distinct pairwise inter-species distances form the basis of the exceptional cases. However, we can identify when the collection of pairwise joint sequence distributions comes from these exceptional cases. It is not currently known whether using three-taxon or higher-order comparisons can yield identifiability for the GTR+Gamma+I model in these exceptional cases.
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