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The Probabilities of Trees and Cladograms under Ford's α-Model
Tomás M Coronado1, Arnau Mir1, Francesc Rosselló1
1Balearic Islands Health Research Institute (IdISBa) and Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain.
Thescientificworldjournal
|June 1, 2018
Summary
Ford's α-model, a popular phylogenetic tree growth model, has issues with its probability formulas. This study provides corrected explicit formulas for unlabeled and phylogenetic trees, improving accuracy for evolutionary studies.
Area of Science:
- Evolutionary biology
- Computational phylogenetics
- Mathematical modeling
Background:
- Ford's α-model is a widely used parametric model for bifurcating phylogenetic tree growth.
- The model encompasses specific cases like the uniform and Yule models.
- Phylogenetic tree shape indices are often studied using the probability distribution defined by this model.
Purpose of the Study:
- To address inaccuracies in the existing explicit formulas for probabilities in Ford's α-model.
- To provide corrected explicit formulas for the probabilities of unlabeled and phylogenetic trees.
- To enhance the reliability of analyses using Ford's α-model.
Main Methods:
- Derivation of corrected explicit formulas for tree probabilities.
- Mathematical analysis of Ford's α-model.
Main Results:
- New explicit formulas for the probabilities of unlabeled trees under Ford's α-model.
- New explicit formulas for the probabilities of phylogenetic trees under Ford's α-model.
- Demonstration of the failure cases of the original Ford formulas.
Conclusions:
- The corrected formulas accurately represent probabilities for Ford's α-model.
- These findings resolve known issues and improve the model's applicability.
- Enhanced accuracy supports more reliable phylogenetic inference and analysis.
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