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Clade size distribution under neutral evolutionary models.

Antonio Di Nunzio1, Filippo Disanto1

  • 1Dipartimento di Matematica, Università di Pisa, Italy.

Theoretical Population Biology
|February 17, 2024
PubMed
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This study analyzes clade size in random tree topologies under Yule and uniform distributions. Clade size is generally smaller and more variable under the uniform model for larger populations.

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Clade sizeLabeled topologyUniform distributionYule distribution

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Area of Science:

  • Phylogenetics and Evolutionary Biology
  • Probability Theory and Statistics

Background:

  • Understanding clade size in phylogenetic trees is crucial for evolutionary inference.
  • Previous studies have focused on specific tree distributions like the Yule model.
  • The impact of different tree generation models on clade properties remains an active research area.

Purpose of the Study:

  • To derive closed-form formulas for the probability mass function, mean, and variance of clade size.
  • To compare clade size distributions under Yule and uniform models for labeled tree topologies.
  • To investigate set-theoretic relationships between clades of multiple populations within random trees.

Main Methods:

  • Mathematical derivation of probability distributions for clade size.
  • Analysis of the clade size random variable under Yule and uniform tree models.
  • Calculation of mean and variance for clade size under both models.

Main Results:

  • Closed-form formulas for clade size probability mass function, mean, and variance were determined.
  • For large tree sizes (n), the uniform model yields smaller clade sizes than the Yule model.
  • The uniform model exhibits greater variability in clade size for populations of 5 or more leaves (k≥5).

Conclusions:

  • The choice of tree generation model significantly impacts clade size properties.
  • The derived formulas provide a basis for analyzing clade relationships and monophyly probabilities.
  • This research extends existing knowledge on clade size probabilities in random phylogenetic trees.