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Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. (English) Zbl 1127.60313

Summary: In 1924 Yule observed that distributions of number of species per genus were typically longđtailed, 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 A. O. Mooers and S. B. Heard [Q. Rev. Biol. 72, No. 1, 31–54 (1997)].

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
62A09 Graphical methods in statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis
92B15 General biostatistics
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