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A Practical Guide to Phylogenetics for Nonexperts

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Enumeration of binary trees compatible with a perfect phylogeny.

Julia A Palacios^1,2, Anand Bhaskar³, Filippo Disanto⁴

¹Department of Statistics, Stanford University, Stanford, CA, USA. juliapr@stanford.edu.

Journal of Mathematical Biology

|May 13, 2022

Summary

This study explores evolutionary models for molecular sequences, focusing on how mutation patterns constrain possible evolutionary tree shapes. We developed a recursive method to count these tree shapes, aiding in evolutionary parameter inference.

Keywords:

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Area of Science:

Computational evolutionary biology
Phylogenetics
Statistical genetics

Background:

Molecular sequence variation is often modeled using genealogies, which are rooted, timed trees representing shared ancestry.
The infinitely-many-sites mutation model assumes mutations occur at unique genomic locations, creating combinatorial constraints on possible genealogies.
Observed molecular variation can be summarized by a perfect phylogeny, a tree encoding mutational differences, but this may not uniquely define the evolutionary tree structure.

Purpose of the Study:

To investigate the enumerative properties of tree shapes compatible with perfect phylogenies under the infinitely-many-sites mutation model.
To determine the number of possible binary ranked and unranked tree shapes that can explain observed mutation patterns.
To explore implications for inferring evolutionary parameters from molecular sequence data.

Main Methods:

Developed a recursive enumeration method to count compatible tree shapes.
Considered both binary and multifurcating perfect phylogenies.
Analyzed the combinatorial constraints imposed by mutation patterns on tree structures.

Main Results:

Provided a recursive formula for enumerating binary ranked and unranked tree shapes consistent with perfect phylogenies.
Characterized the set of tree shapes conditioned on observed mutation patterns under the infinitely-many-sites model.
Demonstrated how mutation data restricts the space of possible evolutionary histories.

Conclusions:

The combinatorial structure of mutations significantly constrains the possible evolutionary tree shapes.
The recursive enumeration provides a computational framework for analyzing these constraints.
Results advance the statistical inference of evolutionary parameters from molecular sequence data.