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Parametric Maximum Parsimonious Reconstruction on Trees

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Abstract

We give a formal study of the relationships between the transition cost parameters and the generalized maximum parsimonious reconstructions of unknown (ancestral) binary character states \(\{\mathtt{0},\mathtt{1}\}\) over a phylogenetic tree. As a main result, we show there are two thresholds \(\lambda^{\mathtt{1}}_{n}\) and \(\lambda^{\mathtt{0}}_{n}\), generally confounded, associated to each node n of the phylogenetic tree and such that there exists a maximum parsimonious reconstruction associating state \(\mathtt{1}\) to n (resp. state \(\mathtt{0}\) to n) if the ratio “\(\mathtt{1}\mathtt{0}\)-cost”/“\(\mathtt{0}\mathtt{1}\)-cost” is smaller than \(\lambda^{\mathtt{1}}_{n}\) (resp. greater than \(\lambda^{\mathtt{0}}_{n}\)). We propose a dynamic programming algorithm computing these thresholds in a quadratic time with the size of tree.

We briefly illustrate some possible applications of this work over a biological dataset. In particular, the thresholds provide a natural way to quantify the degree of support for states reconstructed as well as to determine what kind of evolutionary assumptions in terms of costs are necessary to a given reconstruction.

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  1. Institut de Mathématiques de Luminy CNRS-UMR 6206, Campus de Luminy, Case 907, 13288, Marseille Cedex 9, France

    Gilles Didier

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  1. Gilles Didier
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Correspondence to Gilles Didier.

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Didier, G. Parametric Maximum Parsimonious Reconstruction on Trees. Bull Math Biol 73, 1477–1502 (2011). https://doi.org/10.1007/s11538-010-9574-8

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  • DOI: https://doi.org/10.1007/s11538-010-9574-8

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