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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Yule-generated trees constrained by node imbalance.

Filippo Disanto1, Anna Schlizio, Thomas Wiehe

  • 1Institut für Genetik, Universität zu Köln, Zülpicher Straße 47a, 50674 Köln, Germany.

Mathematical Biosciences
|September 3, 2013
PubMed
Summary

We introduce Ω-trees, a new class of evolutionary trees that capture imbalance. Even with imbalance, these trees retain key statistical properties, offering insights into selection pressures in population genetics.

Keywords:
Binary rooted treeGenerating functionSubtreeTree imbalanceYule model

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Area of Science:

  • Evolutionary Biology
  • Population Genetics
  • Computational Biology

Background:

  • The Yule process is fundamental to evolutionary biology models.
  • Unbalanced trees can signify selection pressure, unlike neutral evolution models.
  • Existing models often assume balanced tree structures.

Purpose of the Study:

  • Introduce Ω-trees, a family of ranked trees with tunable internal node imbalance (0 ≤ ω).
  • Investigate the combinatorial properties of Ω-trees.
  • Analyze the distribution of subtrees with two leaves within Ω-trees.

Main Methods:

  • Defined Ω-trees based on the degree of internal node imbalance (ω).
  • Employed generating functions to study combinatorial properties.
  • Focused on the distribution of two-leaf subtrees.

Main Results:

  • Ω-trees represent a mathematically tractable subspace of Yule trees.
  • The expectation and variance of two-leaf subtrees in Ω-trees match unconstrained trees even for small ω.
  • Small ω values are unlikely in neutral evolution but can indicate selection.

Conclusions:

  • Ω-trees provide a framework to study evolutionary processes under selection.
  • The statistical invariants observed in Ω-trees simplify analysis while capturing imbalance.
  • These findings have implications for understanding pathogen genealogies and evolutionary dynamics.