AI Article Synopsis
- The study examines how transition cost parameters relate to the reconstruction of ancestral binary states (0 or 1) on a phylogenetic tree.
- Two key thresholds (λ¹n and λ⁰n) are defined for each node in the tree, determining when a state can be reconstructed based on the cost ratios of transitions between states.
- A dynamic programming algorithm is introduced to calculate these thresholds efficiently, with potential applications in analyzing biological data by quantifying support for reconstructed states and understanding necessary evolutionary cost assumptions.
Article 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 {0,1} over a phylogenetic tree. As a main result, we show there are two thresholds λ¹n and λ⁰n , generally confounded, associated to each node n of the phylogenetic tree and such that there exists a maximum parsimonious reconstruction associating state 1 to n (resp. state 0 to n) if the ratio "10-cost"/"01-cost" is smaller than λ¹n (resp. greater than λ⁰n). 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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| http://dx.doi.org/10.1007/s11538-010-9574-8 | DOI Listing |
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