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SUMMARY:A Lie algebraic classification of continuous-time Markov models - 
 Sumner\, J (Tasmania)
DTSTART:20110623T103000Z
DTEND:20110623T105000Z
UID:TALK31846@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:In recent work we have discussed the importance of multiplicat
 ive closure for the Markov models used in phylogenetics. For continuous-ti
 me Markov chains\, a sufficient condition for multiplicative closure of a 
 model class is ensured by demanding that the set of rate matrices belongin
 g to the model class form a Lie algebra. It is the case that some Markov m
 odels do form Lie algebras (eg. JC\, F81\, K3ST and GMM)\, and we refer to
  these models as ``Lie Markov models''. Importantly\, other Markov models 
 unequivocally do not form Lie algebras (the most conspicuous example being
  GTR). \nThe question then naturally arises: How do we generate a full lis
 t of Lie Markov models? To answer this question in full generality seems q
 uite difficult as the interaction between the operations of a Lie algebra 
 and the stochastic requirements of rate matrices are somewhat at odds\, an
 d it seems that this question has not been addressed in the algebraic or s
 tochastic mathematics literature. \nIn this talk\, we will discuss how we 
 have made signficant progress in generating Lie Markov models by demanding
  that the models have certain symmetrics under nucleotide permutations. >F
 rom a theoretical perspective\, we show that the Lie Markov models include
 \, and hence provide a unifying concept for\, ``group-based'' and "equivar
 iant" models\, whilst also generating many other interesting examples. We 
 also argue that our scheme is very pleasing in the context of applied phyl
 ogenetics\, as\, for a given symmetry of nucelotide substitution\, it prov
 ides a natural hierarchy of models with increasing number of parameters. \
 n\nThis is joint work with Jess Fernndez-Snchez and Peter Jarvis.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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