Minimum message length encoding, evolutionary trees and multiple-alignment

Minimum message length encoding is a technique of inductive inference with theoretical and practical advantages. It allows the posterior odds-ratio of two theories or hypotheses to be calculated. Here it is applied to problems of aligning or relating two strings, in particular two biological macromolecules. We compare the r-theory, that the strings are related, with the null-theory, that they are not related. If they are related, the probabilities of the various alignments can be calculated. This is done for one-, three-, and five-state models of relation or mutation. These correspond to linear and piecewise linear cost functions on runs of insertions and deletions. We describe how to estimate parameters of a model. The validity of a model is itself an hypothesis and can be objectively tested. This is done on real DNA strings and on artificial data. The tests on artificial data indicate limits on what can be inferred in various situations. The tests on real DNA support either the three- or five-state models over the one-state model. Finally, a fast, approximate minimum message length string comparison algorithm is described.

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“…#+# Sl ancestors of A and B for use in multiple string alignment or in the reconstruction of evolutionary trees (Allison et al 1992). …”

Section: The One-state Modelmentioning

confidence: 99%

Finite-state models in the alignment of macromolecules

1992

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“…A simple way to do this is to allow a pad symbol "-" as an extra character in the alphabet and to treat alignments containing pads with the methods of the previous section. This is similar to the approach taken by Allison et al (1992). However, when a gap occurs, it is typically nearly as likely to span several residues as just one residue, contrary to the linear cost implied by the simple pad character solution.…”

Section: Introducing Deletions and Insertionsmentioning

confidence: 75%

“…Several authors have tackled the problem of finding ML alignments of two sequences (Bishop and Thompson 1986;Bishop et al 1987; Thorne et al 1991Thorne et al , 1992, and Allison et al (1992) showed how to find alignments for trees of several sequences according to a criterion closely related to ML; their method is only computationally feasible, however, with rather simple rules for insertions and deletions. There is therefore room to develop a more general notion of an ML alignment of a tree of sequences.…”

Section: Introductionmentioning

confidence: 99%

Tree-based maximal likelihood substitution matrices and hidden Markov models

Mitchison

Durbin

1995

J Mol Evol

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There has been considerable interest in the problem of making maximum likelihood (ML) evolutionary trees which allow insertions and deletions. This problem is partly one of formulation: how does one define a probabilistic model for such trees which treats insertion and deletion in a biologically plausible manner? A possible answer to this question is proposed here by extending the concept of a hidden Markov model (HMM) to evolutionary trees. The model, called a tree-HMM, allows what may be loosely regarded as learnable affine-type gap penalties for alignments. These penalties are expressed in HMMs as probabilities of transitions between states. In the tree-HMM, this idea is given an evolutionary embodiment by defining trees of transitions. Just as the probability of a tree composed of ungapped sequences is computed, by Felsenstein's method, using matrices representing the probabilities of substitutions of residues along the edges of the tree, so the probabilities in a tree-HMM are computed by substitution matrices for both residues and transitions. How to define these matrices by a ML procedure using an algorithm that learns from a database of protein sequences is shown here. Given these matrices, one can define a tree-HMM likelihood for a set of sequences, assuming a particular tree topology and an alignment of the sequences to the model. If one could efficiently find the alignment which maximizes (or comes close to maximizing) this likelihood, then one could search for the optimal tree topology for the sequences. An alignment algorithm is defined here which, given a particular tree topology, is guaranteed to increase the likelihood of the model. Unfortunately, it fails to find global optima for realistic sequence sets. Thus further research is needed to turn the tree-HMM into a practical phylogenetic tool.

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“…The final alignment may not be optimal for the L + M strings, but this algorithm can be used as an iterative step to improve a multiple alignment to at least a local optimum. This kind of deterministic heuristic is quite common, and an example has been described by Allison et al (1992b): Given K > the strings into two disjoint sets, S of size L and T of size M = K -L. The K way alignment is projected onto these two sets of strings to give two subalignments, AS over S and AT over T, which are realigned with the DPA to give a new overall K-way alignment. The process is iterated and terminates when there is no further improvement in the full K-way alignment.…”

Section: K/> 2 Stringsmentioning

confidence: 99%

The posterior probability distribution of alignments and its application to parameter estimation of evolutionary trees and to optimization of multiple alignments

Allison

Wallace

1994

J Mol Evol

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How to sample alignments from their posterior probability distribution given two strings is shown. This is extended to sampling alignments of more than two strings. The result is first applied to the estimation of the edges of a given evolutionary tree over several strings. Second, when used in conjunction with simulated annealing, it gives a stochastic search method for an optimal multiple alignment.

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Minimum message length encoding, evolutionary trees and multiple-alignment

Cited by 12 publications

References 20 publications

Finite-state models in the alignment of macromolecules

Finite-state models in the alignment of macromolecules

Tree-based maximal likelihood substitution matrices and hidden Markov models

The posterior probability distribution of alignments and its application to parameter estimation of evolutionary trees and to optimization of multiple alignments

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