Statistical Science

Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today

David J. Aldous

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Abstract

In 1924 Yule observed that distributions of number of species per genus were typically long­tailed, and proposed a stochastic model to fit these data. Modern taxonomists often prefer to represent relationships between species via phylogenetic trees; the counterpart to Yule’s observation is that actual reconstructed trees look surprisingly unbalanced. The imbalance can readily be seen via a scatter diagram of the sizes of clades involved in the splits of published large phylogenetic trees. Attempting stochastic modeling leads to two puzzles. First, two somewhat opposite possible biological descriptions of what dominates the macroevolutionary process (adaptive radiation; “neutral” evolution) lead to exactly the same mathematical model (Markov or Yule or coalescent). Second, neither this nor any other simple stochastic model predicts the observed pattern of imbalance. This essay represents a probabilist’s musings on these puzzles, complementing the more detailed survey of biological literature by Mooers and Heard, Quart. Rev. Biol. 72 [(1997) 31–54].

Article information

Source
Statist. Sci. Volume 16, Number 1 (2001), 23-34.

Dates
First available in Project Euclid: 27 August 2001

Permanent link to this document
http://projecteuclid.org/euclid.ss/998929474

Digital Object Identifier
doi:10.1214/ss/998929474

Mathematical Reviews number (MathSciNet)
MR1838600

Zentralblatt MATH identifier
1127.60313

Keywords
Descriptive statistics phylogenetic tree stochastic model tree balance Yule process

Citation

Aldous, David J. Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Statist. Sci. 16 (2001), no. 1, 23--34. doi:10.1214/ss/998929474. http://projecteuclid.org/euclid.ss/998929474.


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